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ENERGY INDEX DECOMPOSITION METHODOLOGY AT THE PLANT LEVEL By WISIT KUMPHAI Batchelor of Engineering Kasetsart University Bangkok, Thailand 1998 Master of Science Colorado State UniversityPueblo Pueblo, Colorado 2000 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY December, 2006 ii ENERGY INDEX DECOMPOSITION METHODOLOGY AT THE PLANT LEVEL Dissertation Approved: David B. Pratt Dissertation Adviser William J. Kolarik Wayne C. Turner Francis M. Epplin A. Gordon Emslie Dean of the Graduate College iii ACKNOWLEDGEMENTS I would like to express my deepest gratitude to my major advisor, Dr. David B. Pratt for his support, guidance, encouragement, and patience through this long journey. I would like to express my sincere appreciation to Dr. Wayne C. Turner for his continuous support, guidance, pragmatism, and friendship. He inspired me to be the best energy engineer I could be. I would like to recognize Dr. William J. Kolarik, a great boss who showed me that with hard work, we can accomplish anything. I would like to extend my appreciation to Dr. Francis M. Epplin who kept me grounded and shared valuable insights. I would like to thank the Oklahoma Industrial Assessment Center (IAC) for an exceptional educational experience like no other. IAC is only research program that challenges engineering students with REAL WORLD problems. The program encourages students to apply the knowledge learned in class to identify/solve problems, and improve process efficiency. At the same time, students learned how to professionally deal with clients, vendors, utility agents, etc. I would like to extend my gratitude to my fellow IAC colleagues who are currently on the same quest Robert Scott Frazier, Shankar Earni, and Haiyan Zhao. Thanks being such good friends. Thank you, Jean W. Ames for all her help from the first day I stepped foot in Stillwater. Thank you for Saturday evening dinners, and most of all, thank you for letting me be a part of your family. I would like to express my deepest gratitude to my parents, Dr. Siripong and Mrs. Wipapan Kumphai for your encouragements and support. My sister Ms. Pimpawan Kumphai, thanks for being a such a good friend, an excellent cook, the best travel companion anyone could ever wished for, and above all, a very good listener. Finally, I iv would like to thank my grandmothers, Mrs. Anong Akarasa who showed me the wisdom of how to be a good human being, Mrs. Panan Kumphai for your financial support. Hope you were here to witness YOUR accomplishments. v TABLE OF CONTENTS Chapter Page I. Introduction ...................................................................................................................1 Motivation of Study ......................................................................................................1 II. Literature Review.........................................................................................................4 2.1 Energy Intensity ...................................................................................................... 4 2.1.1 Measures of Energy Input................................................................................ 5 2.1.2 Measures of output........................................................................................... 6 2.2 Index Numbers......................................................................................................11 2.3 Aggregation Levels...............................................................................................15 2.4 Decomposition Methodology ............................................................................... 18 2.4.1 Multiplicative Decomposition ....................................................................... 18 2.4.2 Additive Decomposition ................................................................................19 2.5 Energy Index Decomposition methodology ......................................................... 20 2.5.1 Aggregate Energy Consumption Approach................................................... 21 2.5.2 Aggregate Energy Intensity Approach...........................................................22 2.5.3 Selection of approach (Energy intensity or consumption)............................. 23 2.5.4 Selection of method ....................................................................................... 24 2.5.5 Construction of Time Series Index Decomposition Method ......................... 29 2.6 Conclusion ............................................................................................................ 30 III. Statement of Research...............................................................................................31 3.1 Problem Statement ................................................................................................31 3.2 Research Goals...................................................................................................... 31 3.3 Major Research Tasks...........................................................................................32 3.4 Research Boundaries............................................................................................. 32 IV. Methodology.............................................................................................................33 4.1 Introduction...........................................................................................................33 4.2 Research Plan........................................................................................................ 33 V. Plant level energy consumption model development ................................................41 5.1 Introduction.....................................................................................................41 vi 5.2 Brick manufacturing process and building the model .......................................... 41 5.3 Brick Model construction and Evaluation ............................................................ 45 5.4 Calculation Example............................................................................................. 50 VI. Statistical validation process.....................................................................................52 6.1 Introduction...........................................................................................................52 6.2 Statistical Test Procedure......................................................................................52 VII. Experimental Results...............................................................................................58 VIII. Summary, Discussions, and REcommendations....................................................66 8.1 Introduction...........................................................................................................66 8.2 Major Contribution of This Research ................................................................... 66 8.3 Strengths and Limitations .....................................................................................67 8.4 Future Research .................................................................................................... 68 REFERENCES ............................................................................................................... 69 APPENDIXES................................................................................................................75 APPENDIX A: GRAPH OF SIMULATION RESULTS........................................... 76 APPENDIX B: TEST OF CORRELATION RESULTS.......................................... 104 VITA vii LIST OF TABLES Table Page I. INDUSTRIES OUTPUT DATA MEASURES ....................................................... 6 II. ENERGYINTENSITY INDICATORS FOR THE MANUFACTURING SECTOR .................................................................................................................. 9 III. BRICK ENERGY CONSUMPTION .................................................................... 46 IV. SIMULATION SCENARIOS FOR REFINED LASPEYRES ADDITIVE ENERGY INTENSITY INDEX ............................................................................ 49 V. SIMULATION SCENARIOS FOR LOG MEAN DIVISIA ADDITIVE ENERGY INTENSITY INDEX ............................................................................................. 49 VI. EXAMPLE CALCULATIONS OF REFINED LASPEYRES AND LOG MEAN DIVISIA INDEXES............................................................................................... 50 VII. EXAMPLE CALCULATIONS OF REFINED LASPEYRES AND LOG MEAN DIVISIA INDEXES............................................................................................... 51 VIII. CORRELATION TEST BETWEEN THE LASPEYRES INTENSITY INDEX AND PRODUCTION ............................................................................................ 60 IX. SUMMARY ARIMA MODEL FITTING RESULTS........................................... 64 viii LIST OF FIGURES Figure Page 1. The energy indicator pyramid (with sources of data).......................................16 2. General framework of the index decomposition methodologies......................21 3. Diagrammatic representation of brick manufacturing process.........................42 4. Decomposition of total energy intensity into structure and intensity effects ...51 5. Time series plot of Log Mean Divisia AIHHH (top) and differenced AIHHH (bottom) ............................................................................................................59 6. Refined Laspayres intensity index of series plot of LIHHH (above) and differenced LIHHH (below) .............................................................................59 7. Time series plot (above), ACF plot (middle), and PACF plot (below) of LIHHH..............................................................................................................61 8. Differenced Time series plots of LIHHH......................................................... 62 1 CHAPTER I INTRODUCTION Motivation of Study The motivation for this research is to develop a methodology for an economically based energy performance monitoring system that incorporates production information. This performance measure will closely monitor energy usage and reflect the production efficiency as a part of an ongoing process, a facility manager can keep track and in the future, predict on when to perform a recommissioning process. Recommissioning is a thorough and detailed process of reassuring that the facility mechanical and electrical systems (production and production support equipment) are operating optimally according to the building’s design intent. There is currently no definite schedule on when the recommissioning needs to be perform, Turner [2005] provided guidelines that the facility should consider recommissioning when one or more of the following occurs (“triggers”) 1. High energy consumption, 2. Occupant complaints, 3. Maintenance staff complaints (problems), 4. Economic interests (lessen operating costs including energy and maintenance), 5. New systems or significant expansion of existing system. Since most commercial building energy consumption is from environmental control systems (i.e., HVAC) and the function of the building is relatively constant compared to 2 manufacturing facilities, measuring these “triggers” is doable and relatively straightforward. For example, several studies by Liu and Claridge [2003] used energy system submetering as the main part of an ongoing commissioning process to continuously optimize a commercial building. A similar process of energy utilization monitoring as a tool to trigger recommissioning has not documented for an industrial facilities. This is likely due to the wide variations in product mix, product types, weather changes, production level, process changes, etc. One of the popular methods used in energy performance measurement is index numbers. There has been considerable research on energy performance indexes utilizing energy intensity indicators to monitor changes in production efficiency. The idea was originated by an economist in the early 1900s, Dr. Irving Fisher [Barber 1996]. However, most of the research work focuses on large scale indicators (national economy) as opposed to small scale indicators (individual company). Energy intensity indexes are used to compare and track changes in energy intensity at the national and enduse sector levels. There has been active research work on energy intensity indicators and energy intensity indexes on large scale economy i.e., country level, sector level, and industry level. Recent research direction focuses on the development of energy intensity indexes which incorporate environmental impacts [Ang 2000] and the national or sector levels. A small number of researchers have also been investigating the use of energy intensity indicators at the facility level (plant level). These researchers focus on comparisons of energy intensity between similar manufacturing plants in order to establish benchmarks in energy usage for general plants, best practice plants, and low efficiency manufacturing plants [Worrell 2003]. Recently, energy efficiency monitoring over time with the energy intensity index has also been used in the environmental conservation area and at the national level [Bernard 2005]. The lowest monitoring system in this area was at the sector level. Energy intensity indicators and energy intensity indexes are useful tools that paint a picture of the status of a country’s, industry’s, or sector’s energy efficiency. This enables 3 researchers, economists, and policy makers to establish benchmarks between countries, industries, or sectors and establish energy policy accordingly The goal of this research is to develop a practical energy performance monitoring index for use at the plant level to monitor the facility’s energy efficiency usage over time which will help the facility justify when to reevaluate the plant’s overall energy efficiency through recommissioning. A contribution of this research is to incorporate the potential savings to be generated by including the production into the indexes. It is an extension of two recent research topics, energy intensity studies and energy intensity index studies. 4 CHAPTER II LITERATURE REVIEW Introduction There has been considerable research on monitoring energy usage in industry. However, most research has focused on high level usage (i.e., continent, country, sector, or industry). Since the early 1990s, researchers directed their work to develop more sophisticated energy monitoring decomposition methodologies. Examples include Liu and Ang [1992], and Ang [1994] who monitor energy usage at lower levels but stopped at the industry level. Beginning in the late 1990s and continued through the early 2000s, research directions have changed to incorporate environmental factors into the index decomposition methods at the industry level [Bernard 2005]. This chapter introduces the fundamental components and types of energy monitoring index decomposition methodologies which include energy intensity, decomposition methodologies, and energy monitoring index and research work in these areas to date. 2.1 Energy Intensity Energy intensity (EI) is a measure of the efficiency with which energy resources are being used to produce goods [Freeman 1997]. EI is commonly expressed as ratio of energy input (e.g., Btu, kWh) to useful output (e.g., tons of products, dollars of revenue). 5 Energy intensity is also referred to in some publications as energy efficiency indicators (EEI) [Phylipsen et al.1998]. In this research, the term EI will be used to identify these measures. EIs are divided into two categories, physical EIs and economic EIs. Physical EI is based on the physical amount of energy used in the process. The energy input is expressed in thermodynamic units (e.g., Btu of delivered energy consumed in the production of aluminum) and useful output measured in volume of output e.g. tons of aluminum or market value of output e.g. dollars of aluminum. The economic EI is different from the physical counterpart because it expresses the energy input in terms of monetary value. There are several ways to measure energy input and production output. These are reviewed in the following two subsections. 2.1.1 Measures of Energy Input Freeman [1997] stated that three measures of energy consumption are site consumption of energy, total inputs of energy, and offsite produced energy. These are explained more completely below. 1. Site Consumption of Energy Site consumption of energy is the most comprehensive measure of energy consumption and represents the first use of energy sources regardless of whether they are consumed as a fuel or as a non fuel (raw material). This measure does not include byproduct fuels produced onsite from previously counted energy inputs. 2. Total Inputs of Energy Total input of energy includes all energy sources used to produce heat and power and to generate electricity whether produced offsite or onsite. This metric excludes energy generated from the facilities own raw materials (e.g., calcined carbon process). 3. Offsite Produced Energy Offsite produced energy includes all energy sources purchased or transferred from offsite to produce heat and power and to generate electricity. All non fuel uses of energy and all byproduct energy are excluded. 6 2.1.2 Measures of output Similar to the energy input, measures of output can be divided into two types, volume based output and value based output. Volume based output is the most straightforward measurement for each facility. However, it does not reflect the bottom line or profit of the company because it does not have a monetary value tagged to it. Table I shows an example of the Department of Energy’s measures of output by volume [Freeman 1997]. TABLE I INDUSTRIES OUTPUT DATA MEASURES1 Industry Volumebased Aluminum Aluminum production (tons) Cement Cement production (tons) Chloralkali Chlorine and sodium hydroxide production (tons) Copper Promary copper production (tons) Corn wet milling High fructose corn syrup (tons) Lime Lime production (tons) Lumber Lumber production (boardfeet) Nitrogen fertilizers Nitrogen fertilizer material production (tons) Paper Paper production (tons) Paper board Paper board production (tons) Plywood Plywood production (square feet 3/8" basis) Pulp Pulp production (tons) Steel Raw steel production (tons) Petroleum Petroleum products (barrels) Demand Indicators In order to better associate the economic values to the measures of output, alternative measures of output have been proposed. Some of these measures are reviewed below. 1. Gross output (Q) Gross output is a physical volume of output (e.g. tons of steel) and the most comprehensive measure of manufacturing production. It includes sales and inventory (I) change [Phylipsen 1998]. 1 Adapted from Table 1 in Freeman [1997] 7 2. Value of shipments (VS) Value of shipment is a measure of economic activity expressed in constant dollars. VS can be calculated from current dollar value of shipments (quantity produced multiplied by current sales price) adjusted for inflation by a price index. This measure reduces the impact of inflation when comparing shipments over time. VS = (VSc)/P (Eq. 1) Where VS = Value of shipment, VSc = Value of shipment in current dollars ($ at the time of sale), P = Price index. 3. Value of production (VP) Value of production is measured in constant dollars composed of value of shipments and net additions to inventories (I) then adjust for inflation with price index (P). VP = (VSc + Ic )/P = VS+I = (Q)(Pc)/P (Eq. 2) Where VS = Value of shipment, VSc = Value of shipment in current dollars ($ at the time of sale), Q = Gross output, Ic = Value of inventory in current dollars ($ at the time of sale), I = Value of inventory at time of addition, 8 P = Price index, Pc = Price in current dollars. If changes in the price index P correctly reflect the changes in current dollar prices, then VP and Q will move together over time [Freeman 1997]. 4. Value added (VA) Value added is measured in constant dollars. It is the value of shipments less the cost of materials (CM), and adjusted for inflation. VA = (VSc  CMc)/ P = VS – CM (Eq. 3) Where VS = Value of shipment VSc = Value of shipment in current dollars ($ at the time of sale) CM = Cost of materials CMc = Cost of materials in current dollars ($ at the time of sale) P = Price index Having considered measures of input and measures of output, we return now to our more general discussion of energy intensity As shown in Table II, the US Department of Energy lists the various potential indicators of energy intensity in the manufacturing sector. Choices of which indicator of energy intensity to use vary based on the researcher’s preference and situation. 9 TABLE II ENERGYINTENSITY INDICATORS FOR THE MANUFACTURING SECTOR Recent studies by Worrell [2003] and Boyd [1997] incorporate productivity effects into the energy intensity measures to justify the benefit of investing in energy efficiency improvement measures. Both papers conclude that implementing energy management best practices in the iron and steel industries increase overall productivity of the industry. Three major studies done the between 1982 and 1994 at the plant level are most closely related to this dissertation are Turner and Parker [1982], Boyd, et al. [1992], and Boyd, et al. [1994]. Turner and Parker [1982] introduced the concept of energy accounting used as energy productivity monitoring and control measurement systems. The study uses a “oneshot” energy efficiency measures composed of energy per unit of production (Btu/unit), energy per heating or cooling degrees (Btu/degreedays), and energy per facility area (Btu/square foot) as indicators. The research used the monthly indicators to compare two or more periods of the same months, for example, February energy indicators in the past 3 years. Turner and Parker [1982] also introduced the Carborundum Accounting System where product mix effect and degreeday based heating and cooling effect are used to adjust the indicators. (Thousand Btu/1987 Dollar) Energy / Gross Output Energy / Industrial Production Energy / Value Added Energy / Gross Product Originating Energy / Value of Shipments Energy / Value of Production Energy / AdjustedCapacity Value of Production 10 The first was completed by Boyd, et al. [1992] on modeling plantlevel industrial energy demand with the manufacturing energy consumption survey (MECS). The research is a survey and Phase I of a project to help the DOE determine the applicability of the Manufacturing Energy Consumption Survey (MECS) database and the Longitudinal Research Database (LRD) for industrial modeling and analysis. The paper focuses on six industries, paper mills, alkalies and chlorine, nitrogenous fertilizers, cement hydraulic, blast furnaces and steel mills, and primary aluminum. The report also describes several measures used at the plant level, namely energy intensity and technical efficiency. The results showed that the technical efficiency and distribution of energy intensities vary significantly at the plant level. Energy prices also vary significantly at the plant level where higher energy consumption plants pay less per unit energy (i.e., dollars/kilowatt hours). The second study by Boyd, et al. [1994] examined the vintagelevel energy and environmental performance of manufacturing establishments. The report examines relationships between an industrial plant’s vintage and its energy and environmental performance. It first examines new plants in the six major energy intensive industries. The report then focuses on the steel and cement industries. The purpose of the study was to; 1. define vintage and its metrics, 2. examine the energy intensities and pollutionabatement costs at plant level for different vintages, 3. determine the affect of manufacturing industry’s vintage distribution. The Vintage was assigned on the basis of external data, and a series of analyses which involve, energy intensity, utilization of each vintage, and the share of capacity or capital stock The study also defined energy and environmental performance which incorporated the Total Factor Productivity (TFP) approach and production model approach which used the following models; 11 1. smooth factor substitution models, 2. PuttyClay models, 3. FixedCoefficient models. The models above are mentioned as additional information but are not relevant to this research and therefore not presented in detail. The production efficiency used by Boyd, et. al. [1994] incorporated five input measures including capital, labor, electricity, fuels, materials, and output. The study also defined energy intensity as; 1. Input/output ratio, 2. Energy/capacity ratio, 3. Energy/ capital stock ratio, 4. Energy/output tonnage ratio. The results of the study show that newer plants (later vintage) exhibit lower fossil fuel intensities. The most significant declines were in the steel and cement industries. 2.2 Index Numbers Index numbers are statistical averages in time series that show how values compare by using ratios of items selected as representative of all items of a class of economic data. Index numbers are usually designed to equal 100 for a base period and changes in their components are computed at regular intervals in an attempt to indicate general changes in a specific class of economic data [Greaves and Coleman 1999]. Index numbers of price show the average percentage change of prices from one point in time to another. The percentage change in the price of a single commodity from one time to another can be calculated by dividing its price at the second time by its price at the first time. The ratio between these two prices is called the relative price of that particular commodity in relation to the two times. In the same manner, the index number can be 12 used to calculate percentage change in wages, quantity of goods imported or exported, or any subject matter involving divergent changes of a group of magnitudes. The index numbers are expressed in terms of time and can be applied to compare two magnitudes of a group of elements under any one set of circumstances and their magnitudes under another set of circumstances [Fisher 1927]. Energy index analysis is a study of changes in energy efficiency indicators through time. Early researchers chose to decompose industrial energy demand by using the Divisia approach. This includes the decomposition of the aggregate energy intensity index measured in terms of energy consumption per unit output of each energy intensive industry [Ang 1995]. Later research identified and discussed the issues and problems that commonly occur in constructing energy indicators; especially due to alternative measures of output in intensity indicators [Freeman 1997]. There are currently three energy intensity indexes commonly used, Laspeyres index, Divisia index, and Fisher Ideal index. Recent research focus is at the country level down to sector level (industry level). The direction of the energy intensity index analysis points toward environmental impacts, especially green house gas. The following is an overview of the development of each of these energy intensity indexes. Laspeyres index The Laspeyres index was proposed in 1871 by a German economist Étienne Laspeyres [Wikipedia 2006]. The index was proposed for measuring current prices or quantities in relation to those of a selected base period. It is a statistical price index which is calculated from a set ("basket") of fixed quantities of a finite list of goods by assuming that we know the prices at two different points in time. The analysis proceeds as follows. Let the price index be one in period 0 (reference period), which is then the base period. Then the value of the index in the first period (period 1) is equal to this ratio: the total price of the basket of goods in period two divided by the total price of exactly the same basket in period one. As for any price index, if all prices rise the index rises, and if all prices fall the index falls [Britannica 2005]. The index 13 shows the change in cost of buying in the current period, 1, the same basket of goods as in the base period, 0. The index measures the effect of price changes when the base period consumption levels are hypothetically maintained. This assumption expresses the weakness of the index [Selvanathan and Rao, 1997]. If the reference quantities (R) are selected as the base period quantity, i.e., qR1 = q01, qR2 = q02, qR3 = q03,…, q1n = q0n then Σ Σ = = =n i i i n i i i p q p q L 1 0 0 1 1 0 01 (Eq. 4 ) Where pi1 = The cost of buying the ith good in period 1 pi0 = The cost of buying the ith good in period 0 qi0 = The quantity of ith good bought in period 0 L01 = Laspeyres index of time 0 and t This index has been one of the most popular indexes used in energy decomposition methods studies, having been used by Alcantara and Roca [1995], Ang [19871999], Chen and Wu [1995], Boyd et al. [1987], and Howarth et al. [1993]. Divisia Index The Divisia index approach was introduced by Boyd [1987] by using the Tornqvist approximation stated as reference, detail of Tornqvist approximation is not relevant to this research. The Divisia index approach has been widely used in governmental statistics of energy intensity determination at the country, sector, and subsector levels. The Divisia index approach allows a decomposition of the percentage change in energy use into separate changes in total activity, economic structure, and energy intensity at the component level. When applied to annual data, the decomposition is performed for changes from one year to the next. The resulting changes are cumulated to a time series index that is normalized to one in 14 a selected base year. The chainweighted nature of the index makes the choice of base year arbitrary from the standpoint of the percentage changes over time. Divisia indexes assume that the data on the various factors vary in more or less a continuous fashion. Liu et al. [1998] indicate that the data are assumed to be available at every moment of time, instead of only at discrete (annual, quarterly, etc.) points in time [EIA 2005]. The index has many desirable properties that are useful for decomposition analysis including variable weighting over time and additive decomposition of relative growth rates [Liu et al. 1998]. The detail of Divisia index will be described in detail in Chapter 4. Paasche index In contrast to the Laspeyres index, the Paasche index measures the effect of price changes from period 0 to 1 if current period consumption had been used in the base period. The index was proposed by Paasche [1874]. If the reference quantity is selected as current period quantity vector, i.e., q01=qR1, q02= qR2, q03=qR3,…, q0n qRn =, then Σ Σ = = =n i i i n i i i p q p q P 1 0 1 1 1 1 01 (Eq. 5) Where pi1 = The cost of buying the ith good in period 1 pi0 = The cost of buying the ith good in period 0 qi1 = The quantity of ith good bought in period 1 I01 = The index of price change between period 0 and 1 P01 = Paasche index of time 0 and t Fisher Ideal Index The Fisher Ideal Index is the most recent introduction by Boyd [2004]. The index uses the chain weighted Fisher Ideal Index to resolve the residual problem in prior 15 indices. Residual problem is discussed in Chapter 4. This index is the geometric average of the Laspeyres and Paasche indices. F L P I = I ⋅ I (Eq. 6) Where IF = Fisher Ideal index IL = Laspeyres index IP = Paashe index Index numbers are statistical averages in time series that show how values compare by using ratios. The result is the percent changes between the period of interest and the reference period. This characteristic of index numbers can be applied to energy efficiency monitoring shown in later sections of this research. 2.3 Aggregation Levels Energy decomposition methodology is a process of breaking down an entity’s energy usage in order to study the sources of process energy consumption and its characteristics. Energy consumption can be determined on various levels as shown in Figure 1 1. The nation level is an aggregated level of several sectors. 2. The level of main sectors (e.g., manufacturing industry, residential, services, transportation) 3. The level of sectors (e.g., food and drugs industry, basic metal industry) 4. Level of individual firms 5. The level of processes within subsectors or of the individual firms 16 Figure 1 The energy indicator pyramid (with sources of data)2 Economic energy indicators can be developed on each level. They are generally developed in a way that depicts changes in overall energy consumption that are decomposed into changes in activity level. There have been significant studies of economic efficiency indicators at the country, industry, and sector level by using macro economic indicators and indexes since the early 1980’s [Ang1995]. Reitler et al. [1987] analyzed the factors influencing energy consumption in industry. Reitler et al. [1987] introduced a method to determine the role of changes in energy consumption in fuel and electricity in relation to the effects on production structure and specific consumption. They also used the Specific Energy Consumption (SEC) which is a ratio between energy consumption and an index of industrial production in that period. However, since the indicators were developed, there has been no evidence that these indicators were used to develop energy efficiency indexes at the plant level by either the decomposition method down to the process level 2 Adapted from International Energy Agency, “Indicators of Energy Use and Efficiency: Understanding the link between energy and human activity”, OECD Publications, Paris 1997 17 or aggregation method from the process up to the plant level (see Figure 1 on previous page). There are several energy indicators and each is used to measure different aspect of the energy usage. A recent study by Bernard [2005] showed that there have been efforts to compile these measurements and assess the information by using a principal component analysis to assess the information derived from several energy indicators. However, due to the large number of variations, it was difficult to establish meaningful benchmarks that could be used. A study by Brown et al. [1996] on the hierarchical structure of manufacturing systems provided a preliminary assessment of the quantity and quality of waste energy that may be economically practical to recover in the industrial sector. The report covered energy utilization data for 60 fourdigit SIC (standard industrial code) industries which represent 70% of the United States industrial manufacturing energy consumption. The report documented general flow diagrams and heat and mass balance for each operation. The energy and mass balances were on a per unit basis for a each unit operation for individual industrial processes. The report also presented process temperature, pressure, fuel requirements, thermal efficiency, and radiation and convection losses for each operation. By linking this research and utilizing the process levels presented and the plant level study by Boyd [1994], a plant level index could be created by incorporating relevant information tracked over time. By applying the index number methodology, a measure can be created to represent a short interval of time and represent the plant’s overall effectiveness from an energy and environmental standpoint (but in a financially driven nature). 18 According to Phylipsen [1998]’s methodology, energy efficiency indicators are developed by the following steps: 1. Create process routes and system boundaries, 2. Develop an energy efficiency indicator pyramid for the facility, 3. Determine the data required by looking at the disaggregated levels and find potential sources which may include, 3.1 Gross output, 3.2 Value of shipments, 3.3 Value of production, 3.4 Value added, 3.5 Production index. 4. Perform energy efficiency analysis by calculating the Specific Energy Consumption (SEC) and other components to obtain the Economic Energy Efficiency Indicator. 2.4 Decomposition Methodology In general, the decomposition methodology is a process of modeling time series that exhibit trend and seasonal effects. The basic idea behind these models is to decompose the time series into several factors i.e., trend, seasonal, cyclical, and error [Bowerman and O’Connell 1987]. Decomposition of industrial energy consumption is a process of decomposing the indexes in order to study the energy impacts of structural change and energy efficiency improvements. There are two major decomposition methods commonly used to study industrial energy consumption, multiplicative decomposition and additive decomposition. 2.4.1 Multiplicative Decomposition The multiplicative decomposition method models the time series by computing or calculating the factors in a multiplicative form. This model is useful when modeling time series that display increasing or decreasing seasonal variation. Equation 7 depicts the general multiplicative decomposition model defined by Bowerman and O’Connell [1987] 19 yt = TRt · SNt · CLt · IRt (Eq. 7) where yt = The observed value of the time series in time period t, TRt = The trend component (or factor) in time period t, SNt = The seasonal component (or factor) in time period t, CLt = The cyclical component (or factor) in time period t, IRt = The irregular component (or factor) in time period t. 2.4.2 Additive Decomposition The additive decomposition method models the time series by computing or calculating the factors in an additive form. This model is useful when modeling time series that display constant seasonal variation. Equation 8 depicts the general additive decomposition model defined by Bowerman and O’Connell [1987] yt = TRt +SNt + CLt + IRt (Eq. 8) where yt = The observed value of the time series in time period t, TRt = The trend component (or factor) in time period t, SNt = The seasonal component (or factor) in time period t, CLt = The cyclical component (or factor) in time period t, IRt = The irregular component (or factor) in time period t. 20 2.5 Energy Index Decomposition methodology The index decomposition methodology was introduced during the 1970s and was used to study the changes in product mix in industrial energy demand [Bossanyi 1979 and Nakamura 1978]. Ang and Zhang [2000] described the index decomposition methodology as a technique that provides a linkage between an aggregate and the original raw data gathered from industries where the information of interest (production quantities, energy consumption, emission, etc.) is captured in a concise and usable form. The notion is similar to the economic index numbers used to study the price and quantity level changes in aggregate commodity consumption. This methodology is also referred to as index number decomposition analysis by Rose and Casler [1996]. From the previous section we learned that there are many indexes used in the index decomposition methodology. In recent research (1992 to 1999) the indexes commonly used are Laspeyres (45%) and Divisia (28%) [Ang 2000]. This research considers these two commonly used indexes. Index decomposition methodology can be classified into two major approaches, the energy consumption approach and the energy intensity approach. A general framework from Ang [1994] is shown in Figure 2 on the next page. The energy consumption approach uses the decomposition technique to study changes in overall (total) industrial energy consumption over a period of time. The technique incorporates changes in aggregate production (production effect), production structure (structural effect) and sectoral energy intensities (intensity effect). The energy intensity approach methodology uses the decomposition method on the changes in the aggregate energy intensity (not the total consumption) and can be divided into several methods. 21 Figure 2 General framework of the index decomposition methodologies3 This research uses these common index decomposition methods and extends them to the plant level. Ang and Zhang [2000] concluded that in the last decade, the Laspeyres and the arithmetic mean Divisia index methods have been the two most often used decomposition methods. This research will use this argument to focus on these two index methods. 2.5.1 Aggregate Energy Consumption Approach The Aggregate Energy Consumption approach was used by Liu et al. [1992] who studied the Divisia index in detail. They also proposed a new method based on this index called the Adaptive Weighting Divisia method. The paper’s emphasis was on the methodological aspect of decomposition. However, the results of a study using the data of Singapore were shown to illustrate the application and the associated statistical problems of other existing methods. The use of the Divisia index in the decomposition of changes in industrial energy use was first introduced by Boyd et al. [1987 and 1988] but they did not discuss the integral path problem. The research by Liu et al. [1992] expanded the 1980's research where the decomposition is based on a finite number of industrial sectors. The study was mentioned by Ang and Lee [1994] who summarized the five main energy consumption approaches including Laspeyres/Paasche Method, MarshallEdgeworth Method, Simple Average Divisia Method, Parametric Divisia 3 Adapted from Ang [1994] 22 method, and Adaptive Weighting Divisia method. These methods are mentioned as an example, they do not pertain to this research. 2.5.2 Aggregate Energy Intensity Approach Aggregate energy intensity is the ratio of total industrial energy consumption to industrial output. The energy intensity approach is the decomposition of changes in the energy intensity into contributions from structural and intensity effects. The energy intensity approach has been used in a large number of empirical and country specific studies. Examples of such studies are Bossanyi [1979], Jenne and Cattell[1983], Ang [1987], Li et al. [1990], Gardner [1993] and Huang [1993]. While Liu et al. [1992] and Ang and Lee [1994] have studied the general methodological and application issues related to the energy consumption approach, similar studies for the energy intensity approach were not reported until Ang [1994]. Based on the energy intensity approach, two parametric Divisia methods were introduced by Ang [1994] as parallel methods to the energy consumption approach by Liu et al. [1992] with the formulations in both multiplicative and additive forms. Ang [1994] then consider the five specific methods that are equivalent to those considered in Ang and Lee [1994]. Comparisons were also made between the energy intensity approach and the energy consumption approach in actual application. Empirical results obtained using time series data for Singapore and Taiwan were presented to illustrate the issues raised. Ang [1994] introduced two general parametric Divisia methods based on the energy intensity approach, which are equivalent to those given in Liu et al. [1992] and describe their formulation in the multiplicative and additive forms. Ang [1994] then considered the five specific methods which are equivalent to those considered in Ang and Lee [1994]. The parametric Divisia index method allows a decomposition of the percentage change in energy use into separate changes in total activity, economic structure, and energy intensity at the component level. When applied to annual data, the decomposition is 23 performed for changes from one year to the next. The resulting changes are cumulated to a time series index that is normalized to one in a selected base year; this is referred to as the chainweighted nature of the index which makes the choice of base year subjective from the standpoint of the percentage changes over time. The Divisia indexes assume that the data on the various factors vary in more or less a continuous fashion. Liu et al. [1998] formally indicated that the data are assumed to be available at every moment of time, instead of only at discrete (annual, quarterly, etc.) points in time. Liu et al. [1998] indicated that the Divisia index has many desirable properties that are useful for decomposition analysis. These properties include variable weighting over time and additive decomposition of relative growth rates. However, decomposition based upon a general Divisia index approach does not yield a unique set of results because one can develop an infinite number of indexes, each corresponding to assumptions as to how the factors change between the observed discrete points in time. 2.5.3 Selection of approach (Energy intensity or consumption) Ang [1995] described the differences between intensity and consumption as the result of presentation and interpretation. In time series analysis, the energy intensity approach has the advantage of simplicity of results presentation because its estimated effects are typically expressed in indexes. Alternatively, particularly in periodwise decomposition, the results given by the additive energy consumption approach can be easily understood by nonspecialists because the results are expressed in energy units. The energy consumption approach is being not as appropriate as the energy intensity approach when studying the impact of structural change. In energy demand projection, an approach called energy elasticity approach is useful when elasticity estimates are needed to extrapolate future energy demand trends. When studying the energy consumption approach and the energy intensity approach, Ang [1995] suggested that the differences 24 between multiplicative and additive forms are minor. However, in the case of the energy elasticity approach, the multiplicative technique is superior to the additive forms. 2.5.4 Selection of method Similar to general index decomposition methodology described in the prior section, the index decomposition methodology in energy consumption can be divided into multiplicative and additive index decomposition methodologies (Figure 2 Page 20). The decomposed factors are structural effect and efficiency effect as shown in equations 9 and 10. Dtot = Dstr · Dint (Eq. 9) Itot = Istr + Iint (Eq. 10) where Dtot = Total change in overall energy usage (activity index) in time period t from multiplicative decomposition methodology, Dstr = Impact from structural change in time period t from multiplicative decomposition methodology, Dint = Impact from energy intensity change in time period t from multiplicative decomposition methodology, Itot = Total change in overall energy usage (activity index) in time period t from additive decomposition methodology, Istr = Impact from structural change in time period t from additive decomposition methodology, Iint = Impact from energy intensity change in time period t from additive decomposition methodology. The activity index (Itot) shows the changes in the level of activity for a sector of the economy. The units used to measure activity differ by sector (e.g., square footage of floor space, industrial production measured in dollars, passengermiles). Energy intensity indexes represent the effect of changing energy intensity for subsectors or detailed components of the economy. The structural index shows the effect of changing economic structure. This index is employed at higher levels of the indicators hierarchy and reflects 25 the impact on energy use of changes in the relative importance of sectors at lower levels of the hierarchy. It primarily shows the impact of shifts in the composition of sectors or subsectors with different absolute energy intensities. Since this research focuses on the plant level, the structural index refers to the percentage of product which is produced during a period i.e., changes in product mix. By following the procedures from Lermit and Jollands [2001] and Lui et al. [1998] via EIA [2005] we can demonstrate the index decomposition methodology. Consider the rate of change of total energy used for a particular sector of the economy where total energy (E) is expressed as the sum of the energy use for each of the components or subsectors within that sector. Typically, the component intensity is defined in terms of the available data as Ei/Ai. Thus, energy use for each component i can be represented as the product of activity (Ai) and the energy intensity in component i (Ii). Formally, we have =Σ =Σ i i i i i E E A I (Eq. 11) where Ai = Product of activity for component i, Ii = Energy intensity for component i, Ei = Energy use to produce component i, E = Total energy usage. Assume that the activities for each of the components are measured in similar units (e.g., dollars, passengermiles). Thus, total sector activity A is the sum of the activity levels for the components. If we express the share of the total sector’s activity for component i (Ai/A) as Si, Equation 11 can be rewritten as: =Σ i i i E AS I (Eq. 12) where A = Total sector activity, Ii = Energy intensity for component i, Si = Share of total sector’s activity for component i, E = Total energy usage. 26 The derivative of equation 12 with respect to time is ( ) dt AS dI dt AI dS dt S I dA dt dE i i i i i i i i i = Σ +Σ +Σ (Eq. 13) If we divide both sides of equation 13 by E, and perform the same manipulation to each of the terms on the right side, the entire expression can be recast in terms of logarithms or percentage growth rates of each of the variables ⎟⎠ ⎞ ⎜⎝ ⎛ = = Σ +Σ +Σ dt AS I d I dt AS I d S dt AS I d A dt E d E dt dE E i i i i i i i i i i i 1 ln 1 ln ln ln (Eq. 14) Because i i i i w E E E AS I = = (Eq. 15) Where wi = Share of energy consumed by component i . We can see that the growth rate of total energy is the energyweighted average of the growth rate of each of the factors: ⎥⎦ ⎤ ⎢⎣ =Σ ⎡ + + dt d I dt d S dt w d A dt d E i i i i ln ln ln ln (Eq. 16) While equation 16 holds instantaneously, it must be integrated over a discrete time period to yield a useable result. In general terms, this integration over the interval 0 to T generates ( ) dt dt E E w d A i T T =Σ∫ i 0 0 ln / ln [Activity effect (Dact)] (Eq. 17) + dt dt w d S i T i i Σ∫0 ln [Structural effect (Dstr)] + dt dt w d I i T i i Σ∫0 ln [Intensity effect (Dint)] 27 The logarithmic or percentage change in total energy consumption between any two points in time (Dtot) can therefore be decomposed into three effects. Dtot ~ Dact + Dstr + Dint (Eq. 18) An approximate solution to these integrals can be obtained by selecting an appropriate function of the end points at time 0 and T (Dtot) is an approximation because of the residual). This results in the following general expressions for each of the effects ) 0 D w* ln(A / A T i act i ⎟⎠ ⎞ ⎜⎝ ⎛ = Σ (Eq. 19) ln( / ) , ,0 * i i str i i T D =Σw S S (Eq. 20) ln( / ) , ,0 * int i i i i T D =Σw I I (Eq. 21) Depending upon the nature of the solution method, the three effects may not exactly sum to the total change, yielding a small residual term in equation 18. A solution yielding no residual term is defined as perfect decomposition where residuals are blended in the coefficients of the total change. The weights * i w in equations 19 – 21 are derived by an averaging of the initial and terminal shares of energy used in each of the components. How this averaging is performed reflects an assumption about the unobserved path of the variables A, S, and I between the initial and end periods. The most straightforward assumption is to assume that the path is linear between the end points; in this case the weights are defined ( ) / 2 ,0 , * i i i T w = w + w (Eq. 22) The choice of these weights results in what has been termed an Arithmetic mean Divisia approach. While easy to apply, this is an imperfect decomposition method and normally results in a small residual in equation 18; thus the sum of the three effects may not precisely equal the total change in energy use. 28 Ang and Choi [1997] proposed an advanced Divisia method that results in no residual, and thus yields a perfect decomposition of the effects. Their solution was to base the weights on what is termed a logarithmic mean function of the shares. The logarithmic mean of any two variables is defined as L(x,y) = (y – x)/ln(y/x) (Eq. 23) As applied to the energy consumption shares, the logarithmic mean function is defined L(wi,0, wi,T) = (wi,T  wi,0) / ln(wi,T / wi0) (Eq. 24) The final weights * i w are based upon a normalization that ensures that they exactly sum to one: * wi = L(wi,0,wi,T) / ( , ) ,0 i,T i i ΣL w w (Eq. 25) Lermit and Jollands [2001] provide a proof that this formulation of the weights yields no residual term, regardless of how the specific values of the variables vary over time. The use of the logarithmic mean Divisia method implies that all of the variables are growing at constant growth rates between the initial and terminal periods. Thus, the method assumes that unobserved values between the two periods lie on a path defined by an exponential growth curve. 29 2.5.5 Construction of Time Series Index Decomposition Method While the Divisia index decomposition method can be applied over any time period, it is applied to annual observations in this system of energy intensity indicators. The logarithmic change in energy use between each pair of successive years is decomposed using the log mean Divisia method, yielding the terms shown in equation 18. By implicitly setting the first of the two years equal to 1.0, an index number for the second year is obtained by taking the exponential of each of the terms as follows: Exp (Deng) = Exp (Dact + Dstr + Dint) = (Iact) ⋅ (Istr) ⋅ (Iint) (Eq. 26) where Iact = Exp(Dtot), Istr = Exp(Dstr), and Iint = Exp(Dint), Iact = Activity index, yearoveryear, Istr = Structure index, yearoveryear, Iint = Intensity index, yearoveryear. For each effect, the indexes are then chained to form a time series for the available data period. Ang [1998] introduces the method of factorizing changes in energy and environmental indicators through decomposition because of the following: 1. Perfect decomposition, 2. Factor changes in energy demand or gas emissions, 3. Handle zero values in data sets. Ang [1998] also indicates that the main objective of decomposition analysis is to quantify various underlying factors that contribute to changes in energy and environmental indicators over time. Two common approaches are decomposition of an aggregate index (energy intensity approach) where the aggregate index is given by dividing the aggregate intensity of one year, such as the ratio of industrial energy demand to industrial output. 30 This leads to estimates of factorized effects given in indexes. The other approach is the decomposition of differential quantity (consumption approach). This decomposition is a direct decomposition of a change in energy demand or gas emissions between two different years in physical terms. This change of quantity is given in the chosen measurement unit for energy demand or gas emissions, 2.6 Conclusion Index decomposition methods have been used to study energy usage for decades. The most widely used ones are derived from Divisia and Laspeyres index methodologies. This research seeks to extend the use of these methodologies into plant level studies to study the impacts of main energy consuming equipment to the total plant wide energy usage from a production and financial view. 31 CHAPTER III STATEMENT OF RESEARCH 3.1 Problem Statement There is a need for a standard methodology to develop a facilitylevel energy performance monitoring index that is independent of product mix that can be used to identify the energyside production efficiency as the product is being produced as well as the ability to monitor the changes of that measure over a period of time as part of a realtime commissioning and recommissioning effort. 3.2 Research Goals There is a need for more effective facilitylevel energy performance monitoring that is independent of product mix. The goal of this research is to address this problem by focusing on the following: 1. Develop an index number decomposition methodology to use as a facilitylevel energy performance monitoring index from existing higher level index number decomposition methodologies. 2. Use the developed index number to identify the energyside production efficiencies over time and that, with additional research, can be used to monitor the efficiency changes over a period of time as a part of a realtime commissioning and recommissioning effort. 32 3.3 Major Research Tasks To accomplish the goals, the major research tasks are identified as followed 1. Study the available index decomposition methodologies and select the potential ones to study in detail and use as a prototype to modify and use at the plant level. 2. From the selected existing energy intensity index methodologies, develop procedures to use the intensity index number as a facilitylevel energy performance monitoring. 3. Evaluate the methodology by using actual data by developing a simulation model which mimics a brick manufacturing plant. The simulation model uses equations from Jeschar and Bittner [1989] and evaluated by comparing the data output of the model with published journals on brick energy consumption by Prasertsan et al [1995], and Prasertsan and Theppaya [1995]. The energy intensity index is then used to monitor the energy usage. The model also reflects various weather, product mix, and efficiency deterioration scenarios. 3.4 Research Boundaries 1. The manufacturing plants presented in this research refer to manufacturing plants with flow shop or continuous flow production of one product type at a time or with the capability to submeter the individual product lines. Specifically, a brick manufacturing model is used in this research. 2. Index methodologies explored in this research are limited to Divisia and Laspeyres techniques due to their popularity in the past decade (see literature review). 3. The research will also recognize the weather impact. 33 CHAPTER IV METHODOLOGY 4.1 Introduction The goal of this research is to develop an energy index decomposition methodology used at the plant level to use as an energy performance monitoring tool. The research utilizes the existing sector time series index decomposition methods to generate an energy intensity index at the plant level. Traditional systems of energy intensity indicators are designed to track the changes in energy intensity for a total country’s economy, broad end use sectors, and subsectors. The proposed research will study the existing index number decomposition methodologies as plantlevel energy utilization monitoring tools. 4.2 Research Plan To accomplish the goal and objectives described above, the research was broken into phases. Phase I: Develop procedures to systematically identify input variables to be used as the facility’s energy monitoring input. Task 1 Develop a simple plant energy consumption model. The information needed is composed of historical data collected monthly over the past 3 years as follows: 1. Product type, 2. Quantity produced, 3. Cost of goods sold associated with each product type, 4. Monthly energy usage. 34 Task 2 Define product output as the number of production units and energy intensity as energy used per unit of production. Task 3 Identify sources of process energy input (electricity, natural gas, other fuel). Task 4 Develop a plant energy model to test the sensitivity of the indexes against 1. Trending (steepness) a. Mild b. Moderate c. Strong 2. Weather impact a. Mild (Houston, TX) b. Moderate (Oklahoma City, Oklahoma) c. High (Minneapolis, Minnesota) 3. Product mix and effects of product mix toward energy intensity index a. Equally produced b. High intensity c. Low intensity Phase II: Select the index decomposition methodologies Task 1 Define the potential existing index decomposition methodologies to be used in this research as Log Mean Divisia Additive method and Refined Laspeyres energy intensity approaches. Task 2 Use an S+ program4 to fit a time series ARIMA model to each index decomposition methodology and use AIC (Akaike Information Criterion), explained in Chapter 6 to justify the best model for each index. From the fitted model, plot the innovation (residual) by using S+. Acceptable time series models should have low AIC and random 4 S+ or SPLUS is a statistical software (language similar to MATLAB) developed by Insightful Inc. mainly used to analyze time series and predictive statistics 35 innovation plots. Tests of randomness will follow the LjungBox test at 95% confidence level explained in Chapter 6. Select 3 out of 7 methodologies that have the least complicated forms of ARIMA model and highest average absolute amplitude (most sensitive) when plotted on a time series graph. Phase III: Test the index methodologies on a model Test the proposed index decomposition methodology on the actual data obtained from a brick manufacturing model developed by Jeschar and Bittner [1989]. Phase IV: Formulate framework for future research In future research, this methodology is potentially useful as a time series production energy efficiency monitoring tool to detect irregularities in production energy usage or as a part of a realtime commissioning effort. Specific ideas with respect to these potential uses will be documented. Proposed usage of Index Decomposition Methods (ID) Since the concept presented in this research is similar to the application of index numbers to study the contributions of price and quantity levels to changes in aggregate commodity consumption, we present an index decomposition methodology (ID) framework using the index number concept. In general, ID can be performed as long as the aggregate indicator being studied, V, can be expressed in the form: =Σ m i i i in V X X ...X 1 2 where i= 1, 2, …, n (Eq. 27) where the first subscript of X denotes the ith sector among a total of m sectors and the second subscript denotes n different factors. The purpose of ID is to decompose a change in V into individual effects associated with the variation of each of the factors Xi1, Xi2, …, Xin [Ang and Zhang 2000]. This research will focus on two of the most popular indexes, Log Mean Divisia, and refined Laspeyres indexes proposed by Sun [1998]. 36 Log Mean Divisia Index (LMDI) The Log Mean Divisia index technique in additive form was proposed by Ang et al. [1998] and multiplicative form by Ang and Lui [2001]. These are commonly referred to as LMDI I. Ang and Choi [1997] and Ang et al. [2003] proposed LMDI II additive and multiplicative respectively. Both are perfect decomposition techniques which yield no residuals, the only difference is the weight function. Let =Σ i i i i ni V X X ...X 1 2 ; i= 1, 2, …, n (Eq. 28) Where Vi = Aggregate of interest i, which composed of n factors X = Attributes of interest (subscript i) denotes an attribute of the aggregate such as energy consuming sector, fuel type, etc. Therefore, from year 0 to year T; the aggregate changes from 0 0 2 0 1 0 ... i i i ni V =Σ x x x (Eq. 29) to T ni T i T i i V T x x ...x 1 2 =Σ (Eq. 30) We then have in perfect decomposition Multiplicative D = VT/V0 = Dx1 ⋅ Dx2…⋅ Dxn (Eq. 31) Additive ΔV = VT V0= ΔVx1 + ΔVx2+…+ ΔVxn (Eq. 32) where D = Multiplicative decomposition of changes via Divisia index, ΔV = Additive decomposition of changes via Divisia index. 37 Based on the proposed decomposition methodology by Ang et al. [1998] and Ang and Lui [2001] the LMDI I formula is as follows LMDI I (multiplicative) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = Σ 0 , , 0 0 ln ( , ) exp ( , ) k i T k i i T i T i xk x x L V V D L V V (Eq. 33) LMDI I (additive) Σ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Δ = i k i T k i i T xk i x x V L V V 0 , ( , 0 )ln , (Eq. 34) Based on the proposed decomposition methodology by Ang and Choi [1997] and Ang et al. [2003], the LMDI II formula is as follows: LMDI II (multiplicative) ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ΣΣ i k i T k i j j Tj i T i xk x x L w w D L w w 0 , , 0 0 ln ( , ) exp ( , ) (Eq. 35) LMDI II (additive) Σ Σ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Δ = i k i T T k i j j Tj i T i xk x x L V V L w w V L w w 0 , 0 , 0 0 ( , ) ln ( , ) ( , ) (Eq. 36) where T i w = T T i V /V , 0 i w = V 0 /V 0 i , L(a,b) = the logarithmic average of two positive numbers a and b given by a b L a b a b ln ln ( , ) − − = for a ≠ b = a for a=b (Eq. 37) 38 As mentioned earlier, the LMDI I and LMDI II are similar and the only difference is the weight function as followed: Multiplicative decomposition: ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = Σi k i T k i xk i x x D W 0 , exp * ln , (Eq. 38) Additive decomposition: Σ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Δ = i k i T T k i xk i x x V W L V V 0 , * ( , 0 )ln , (Eq. 39) where * i W = L(V ,V 0 )/ L(V T ,V 0 ) i T i in LMDI I, * i W = ( ) Σ ( ) j j Tj i T i L w ,w0 / L w ,w0 in LMDI II. 39 Refined Laspeyres Technique The refined Laspeyres technique is an improved Laspeyres technique and was improved by Sun [1998]. The Refined Laspeyres is only available in the additive decomposition method (no multiplicative technique research published to date). The total change in aggregate energy intensity can be written as Δ =Σ −Σ i i tot i T i T i i I S I S I , , ,0 ,0 ( ) ( ) ( )( ) , ,0 ,0 , ,0 ,0 , ,0 i,T i,0 i i i T i i i i T i i i T i =Σ S − S I +Σ I − I S +Σ S − S I − I (Eq. 40) where Et = Total industrial energy consumption, Ei,t = Energy consumption in industrial sector i, Yt = Total industrial production, Yi,t = Total industrial production sector i, Si,t = Production share of sector i (= Yi,t/Yt), It = Aggregate energy intensity (=Et/Yi,t), Ii,t = Energy intensity of sector i(=Ei,t/Yi,t). Note that ΔI is similar to ΔV of the Divisia additive decomposition method but is an aggregate intensity where as ΔV is an aggregate of the indicator being studied (intensity included). When the variations in variables Si and Ii are large, the residual/interaction is large. By splitting it equally between the two main effects, the formulae become: ( )( ) 2 ( ) 1 , ,0 ,0 , ,0 i,T i,0 i i i T i i str i T i ΔI =Σ S − S I + Σ S − S I − I (Eq. 41) ( )( ) 2 ( ) 1 int , ,0 ,0 , ,0 i,T i,0 i i i T i i i T i ΔI =Σ I − I S + Σ S − S I − I (Eq. 42) 40 where Et = Total industrial energy consumption, Ei,t = Energy consumption in industrial sector i, Yt = Total industrial production, Yi,t = Total industrial production sector i, Si,t = Production share of sector i (= Yi,t/Yt), It = Aggregate energy intensity (=Et/Yi,t), Ii,t = Energy intensity of sector i(=Ei,t/Yi,t). 41 CHAPTER V PLANT LEVEL ENERGY CONSUMPTION MODEL DEVELOPMENT 5.1 Introduction In order to study the energy intensity index according to Chapter 4, a plant level energy consumption model needs to be constructed. As defined in Chapter 4, one of the well known flowshop process is brick manufacturing process. The process is relatively straightforward. 5.2 Brick manufacturing process and building the model Process understanding [Kolarik 1999] helps a researcher gain insights of how energy is being used in the process and permits identification of critical variables (leverages) associated with energy usage. A Brick manufacturing process5 includes mixing ground clay with water, forming them into the desired shapes, then drying and firing them. There are six general phases in making bricks shown in Figure 3 on the next page 1. winning and storage of raw materials (shale clay), 2. preparing raw materials (crushing, grinding, screening and classifying), 3. forming units, 5 http://www.bia.org/BIA/technotes/t9.htm 42 4. drying, 5. kiln firing and cooling, 6. drawing and packing finished products. Figure 3 Diagrammatic representation of brick manufacturing process Winning and Storage Surface clays, shales and some fire clays are mined in open pits with power equipment. The clay or shale mixtures are then transported to plant storage areas. It is common practice to store enough raw materials for several days' operations. The materials then go through the blending process for more uniform raw materials, helps to control color and Crushing & Grinding Screening & Classifying Forming Dryer Kiln Cooler Packing Elec. Elec. Elec. Elec. Elec. Elec. Elec. Gas. Gas. Shale & Clay Bricks 43 permits some control over raw material suitability for manufacturing a given type of brick. Preparation The clay is crushed to break up large chunks and remove stones then ground prior to mixing other raw material. Most plants then screen the clay, passing it through inclined vibrating screens to control particle sizes. Forming The material goes to the Tempering process which produces a homogeneous, plastic mass ready for molding. It is most commonly achieved by adding water to the clay in a pug mill, a mixing chamber which contains one or more revolving shafts with blades. After pugging, the now plastic clay mass is ready to go to the forming step. At the present time, there are three principal processes for forming brick: the stiffmud, the softmud and the drypress processes. Extrusion process In the stiffmud process (extrusion process), clay is mixed with only sufficient water to produce plasticity, usually from 12 to 15 percent by weight. After thorough mixing, i.e., "pugging", the tempered clay goes through a deairing chamber in which a vacuum of 15 to 29 in. (375 to 725 mm) of mercury is maintained. Deairing removes air holes and bubbles, giving the clay increased workability and plasticity, thus resulting in greater strength. Next, the clay is extruded through a die to produce a column of clay in which two dimensions of the final unit are determined. The column then passes through an automatic cutter to make the final dimension of the brick unit. As the clay column leaves the die, textures or surface coatings may be applied. Drying process When wet clay units come from molding or cutting machines, they contain from 7 to 30 percent moisture, depending upon the forming method. Before the firing process begins, 44 most of this water is evaporated in dryer chambers at temperatures ranging from about 100°F to 400°F (38°C to 204°C). Drying time, which varies with different clays, is usually from 24 to 48 hr. Although heat may be generated specifically for dryer chambers, it is more commonly supplied as exhaust heat from firing kilns. In all cases, heat and humidity must be carefully regulated to avoid excessive cracking in the product. Firing and Cooling. Firing, one of the most specialized steps in the manufacture of brick, requires from 40 to 150 hr. depending upon kiln type and other variables. Several kilns are in use, the chief types being tunnel and periodic kilns. Fuel may be natural gas, coal, oil, sawdust, propane or combinations of these fuels. Dried units are set in periodic kilns according to a prescribed pattern that permits free circulation of hot kiln gases. A periodic kiln is one that is loaded, fired, allowed to cool and unloaded, after which the same processes are repeated. In a tunnel kiln, units are similarly loaded on special cars which pass through various temperature zones as they travel through the tunnel. The heat conditions in each zone are carefully controlled and the kiln operates continuously. Firing may be divided into six general stages: 1) watersmoking (evaporating free water), 2) dehydration, 3) oxidation, 4) vitrification, 5) flashing and 6) cooling. All except flashing and cooling are associated with rising temperatures in the kiln. Although the actual temperatures will differ with the clay or shale, watersmoking takes place at temperatures up to about 400°F (204°C), dehydration from about 300°F to 1,800°F (149°C to 982°C), oxidation from 1000°F to 1800°F (538°C to 982°C) and vitrification from 1,600°F to 2,400oF (871°C to 1,316°C). The rate of temperature change must be carefully controlled, depending on the raw materials, as well as the units being produced. Kilns are normally equipped with recording pyrometers or other temperature sensors to provide a constant check on the firing process. Near the end of the firing process, the units may be "flashed" to produce color variations. 45 After the temperature has reached the maximum and is maintained for a prescribed time, the cooling process begins. Fortyeight to 72 hr are required for proper cooling in periodic kilns; but in tunnel kilns, the cooling period seldom exceeds 48 hr. Because the rate of cooling has a direct effect on color and because excessively rapid cooling will cause cracking and checking of the ware, cooling is an important stage in the firing process. Drawing. Drawing is the process of unloading a kiln after cooling. It is at this stage that units are sorted, graded, packaged and taken to a storage yard or loaded onto rail cars or trucks for delivery. The majority of brick today are packaged in selfcontained, strapped cubes, which can be broken down into individual strapped packages for ease of handling on the jobsite. The packages and cubes are formed in such a manner as to provide openings for handling by fork lifts. Brick manufactured and selected to produce characteristic architectural effects resulting from nonuniformity in size, color and texture may not lend themselves to selfcontained packaging, and are usually shipped on wooden pallets. 5.3 Brick Model Construction and Evaluation When building a process model, there are two fundamental issues that need to be explored simultaneously, general principles and specific variables [Kolarik 1999]. Brick manufacturing uses various technologies but the major principle is a process of converting clay into brick via thermo reactions in the kiln (fusion process). Several major variables play a role in this process namely brick type, outside air condition, and processing time. Table III on the next page shows general brick energy intensity. The table shows that the kiln process uses approximately 90% of total energy usage. For simplification, the model can be reduced to the kiln process. 46 TABLE III BRICK ENERGY CONSUMPTION [BROWN 1996] No. Process Subprocess Elec. (Btu/lb) Gas(Btu/lb) Total (Btu/lb) % energy usage 1 Crushing 10 10 0.4% 2 Screening Separation 3 3 0.1% 3 Forming Extrusion 61 61 2.3% Soft plastic forming 61 61 2.3% Dry press forming 61 61 2.3% 4 Drying 2 29 31 1.2% 5 Kiln 64 2300 2364 89.9% 6 Cooling 36 36 1.4% 7 Packing 2 2 0.1% Total 2629 100.0% Kiln, dryer, and cooler mass and energy equation by Jeschar and Bittner [1989] of the process is ( ) ( ) ( ) ( )v G G U G U LE L E U LE U B u S S S U T T t U S R m C T T m C T T Q m h m C T T m C T T m h • − • − • • − • − • • + ⋅ − + ⋅ − + ⋅ = ⋅ ⋅ − + ⋅ ⋅ − + ⋅Δ 1 ,1 1 , ,3 1 3 ,3 1 3 (Eq. 43) Where B m • = Mass flow rate of natural gas in kg/second S m • = Mass flow rate of brick in kg/second T m • = Mass flow rate of transport in kg/second 1 G m • = Mass flow rate of gas in kg/second LE m • = Mass flow rate of air out of the kiln in kg/second u h = Lower calorific value (lower heating value) of natural gas in kJ/kg S,3−1 C = Specific heat of brick in kJ/kgsec T ,3−1 C = Specific heat of transport in kJ/kgsec G U C ,1− = Specific heat of gas in kJ/kgsec 47 L E U C , − = Specific heat of air in kJ/kgsec S 3 T = Temperature of brick at stage 3 in °C G1 T = Temperature of gas at stage 1 in °C U T = Ambient temperature in °C t3 T = Temperature of transport at state 3 in °C LE T = Temperature of air exiting in °C k T = Temperature of kiln in °C D T = Temperature of brick exiting the dryer in °C η = Overall kiln efficiency (includes but not limited to heat loss and combustion) R Δh = Specific reaction enthalpy during the drying process v Q • = Kiln energy consumption in kJ/second v Q • = Heat loss By only focus on the kiln, Equation 43 can be modified into Equations 44 and 45. ( ) ( ) [ (1,778 )] 1 − • • • − − ⋅ ⋅ ⎥⎦ ⎤ ⎢⎣ = ⎡ ⋅ ⋅ − + ⋅ ⋅ − mG mS CS Tk TD mT CT Tk TD CG Tk TLE (Eq. 44) ( ) ( ) η (25 ) ⋅ 1 ⎥⎦ ⎤ ⎢⎣ = ⎡ ⋅ − + ⋅ ⋅ − + ⋅ ⋅ − • • • • k G G U S S k D T T k D Q m C T m C T T m C T T (Eq. 45) The kiln model is constructed in SPlus, assuming bake time of 48 hours. In order to study the process leverages, the model composed of three variations, weather impact, product mix impact, and efficiency (trending) impact. Weather impact uses average daily outside temperature of three locations for mild, medium, and high at near sea levels. These locations are as followed Mild climate impact: Houston, TX Medium climate impact: Oklahoma City, OK High climate impact: Minneapolis, MN 48 Production mix impact studies the variation in energy consumption due to changes in product mix. In general, brick bake temperatures can vary from 800°C to 1200°C depending on the product requirements. In this model, temperatures of the kiln are set at Product type 1: 900°C Product type 2: 1,000°C Product type 3: 1,100°C The model is set to run at three product mixtures, high, medium, and low for 48 hours (2 days). A uniform distribution random number generator is used to generate production schedules composed of three product types. The product mix with high temperature requirements composed of 50% more chance of product type 3 then the other two. The product mix with medium temperature requirement has an equal chance of producing all three products, and product mix with low temperature requirement has 50% more chance of product type 1 than the other two. One of the objectives of this research is to study the efficiency deterioration over time. An artificial trend is created to test the response of the brick model. The trend increases overtime (efficiency decreases). Initial efficiency was set at 80%. Trend increases in a straight line manner over 3 years in 3 levels, mild, medium, and high. The model validation is done by compare the energy intensity of the output in kJ/kg to brick energy intensity studies by Jeschar and Bittner [1989], Prasertsan et al [1995], and Prasertsan and Theppaya [1995]. Name convention of the calculated energy intensity index is as follows: Index Intensity Ambient temp Trend Product mix L, A I H, M, L H, M, L H, M, L L: Laspeyres index (first digit only) A: Log Mean DivisiA index I: Intensity H: High M: Medium L: Low 49 For example, LIHML represents Laspeyres intensity index for high ambient temperature impact (Minneapolis, MN), medium efficiency deterioration, and composed mostly with product with low temperature kiln requirements. Full simulation scenarios are shown in Table IV and V. TABLE IV SIMULATION SCENARIOS FOR REFINED LASPEYRES ADDITIVE ENERGY INTENSITY INDEX Small Medium Large Small LILLL LILML LILHL Weather Medium LIMLL LIMML LIMHL Large LIHLL LIHML LIHHL Small Medium Large Small LILLM LILMM LILHM Weather Medium LIMLM LIMMM LIMHM Large LIHLM LIHMM LIHHM Small Medium Large Small LILLH LILMH LILHH Weather Medium LIMLH LIMMH LIMHH Large LIHLH LIHMH LIHHH Mix medium Mix Small Mix Large Trend Trend Trend TABLE V SIMULATION SCENARIOS FOR LOG MEAN DIVISIA ADDITIVE ENERGY INTENSITY INDEX Small Medium Large Small AILLL AILML AILHL Weather Medium AIMLL AIMML AIMHL Large AIHLL AIHML AIHHL Small Medium Large Small AILLM AILMM AILHM Weather Medium AIMLM AIMMM AIMHM Large AIHLM AIHMM AIHHM Small Medium Large Small AILLH AILMH AILHH Weather Medium AIMLH AIMMH AIMHH Large AIHLH AIHMH AIHHH Mix Small Mix medium Mix Large Trend Trend Trend 50 5.4 Calculation Example Table VI shows an example of a manufacturing plant which produces two product types in two years period. In year 0, Product type 1 used 8 MBtu (8,000 Btu) of energy to produce 10 pounds of product and Product type 2 used 20 MBtu of energy to produce 40 pounds of product. This resulted in energy intensity to produce product type 1 and types 2 are 0.8 and 0.5 respectively. We can observe that product type 1 is more energy intensive (energy used per pounds of product) than product type 2. In year 1, Product type 1 used 35 MBtu of energy to produce 50 pounds of product and Product type 2 used 16 MBtu of energy to produce 40 pounds of product. Both energy intensities of both products reduce from 0.8 to 0.7 for product type 1 and 0.5 to 0.4 for product type 2. However, the total facility energy intensity increases by from 0.56 to 0.57. TABLE VI EXAMPLE CALCULATIONS OF REFINED LASPEYRES AND LOG MEAN DIVISIA INDEXES E = Energy consumption (MBtu) Y = Production (Lb) S = Production share of product types I = Aggregate energy intensity Year 0 Year 1 E0 Y0 S0 I0 ET YT ST IT Product type 1 8 10 0.20 0.8 35 50 0.56 0.7 Product type 2 20 40 0.80 0.5 16 40 0.44 0.4 Plant wide 28 50 1 0.56 51 90 1 0.57 After applying plant level additive index decomposition methods shown in Table VII on the next page Figure 4 on the following page confirmed that there has been an increase in the plant level energy intensity as shown that the index (ΔItot) is positive. The structural energy intensity indexes (ΔIstr) for both are positive. This reflects the increase in energy intensity (0.11 and 0.10) of the product mix (product type 1 and product type 2). However, the energy intensity indexes ΔIint of both Refined Laspeyres and Log Mean Divisia are negative (0.1 and 0.096 respectively) which indicated that the overall plant has improved in production energy efficiency. 51 TABLE VII EXAMPLE CALCULATIONS OF REFINED LASPEYRES AND LOG MEAN DIVISIA INDEXES Index Decomposition (Additive) Refined Laspeyres Log Mean Divisia ΔI tot 0.007 0.007 ΔI str 0.11 0.10 ΔI int 0.100 0.096 Figure 4 Decomposition of total energy intensity into structure and intensity effects From the example we can conclude that due to the expansion of production share of product type 1, which is a more energy intensive than product type 2, the plant aggregate energy intensity increase by 0.7%. Despite improvements in energy efficiency (negative value) as reflected by the changes in overall production energy intensity (ΔI int). Since the impact of changes in production mix is more significant, it leads to an increase in aggregate energy intensity. Plant level energy intensity index (Itot) ΔItot = 0.007 Refined Laspeyres ΔItot = 0.007 Log Mean Divisia Structure effect (Istr) ΔIstr = 0.11 Refined Laspeyres ΔIstr = 0.10 Log Mean Divisia Intensity effect (Iint) ΔIint = 0.1 Refined Laspeyres ΔIint = 0.096 Log Mean Divisia 52 CHAPTER VI STATISTICAL VALIDATION PROCESS 6.1 Introduction This chapter introduces the statistical techniques to be used to validate the energy intensity indexes as mentioned in the Statement of Research. The objectives of using these techniques are to show that the index can be used to monitor the production efficiency without the influence of product mix. This can be achieved by performing correlation test between intensity index and the production mix. The chapter also proposes a standardize process of using energy intensity index to monitor the “bare” efficiency by fitting ARIMA models. 6.2 Statistical Test Procedure After the indexes are determined through the brick model, they are tested according to Phase II in Chapter 4. The tests include the following 1. Energy intensity index selection between Refined Laspeyres Additive method and Log Mead Divisia Additive method 2. Show that the intensity index does not have the influence of product mix. In other words, the changes in product type do not affect the energy intensity index. This can achieve by performing Pearson’s test of correlation. 3. Fit the intensity index to time series ARIMA (Auto Regressive Integrated Moving Average) model. 53 Test of Correlation Test the correlation between the Intensity index and the changes due to product type. Use the Pearson’s Test of Correlation with H0: There is no correlation between intensity index and product types ρ=0 Ha: There is a correlation between intensity index and product types ρ≠0 In this dissertation, Pearson’s test of correlation is being used to measure the relation between two variables, energy intensity index and product types produced. Correlation coefficients (ρ) range from 1.00 to +1.00 where negative correlation coefficients represent negative correlation (1.00 represents a perfect negative correlation) and positive correlation coefficients represent positive correlation (+1.00 represents a perfect positive correlation). A correlation coefficient of 0.00 represents a lack of correlation. Pearson correlation (Simple Linear Correlation ) was selected because it assumes that the two variables are measured on at least an interval scale. The correlation coefficient does not depend on the specific measurement units used; for example, the correlation between height and weight will be identical regardless of whether inches and pounds, or centimeters and kilograms are used as measurement units. The test statistic for correlation test is the Pvalue at 95% level of significance. If the Pvalue is less than or equal to 0.05, reject H0 which means that there is evidence of correlation between intensity index and changes in product type. If Pvalue is over 0.05, fail to reject the null hypothesis, which means that there is no correlation between the intensity index and changes in product type 54 Fitting ARIMA Model6 The goal of the research is to establish ground work for forecasting the need for recommissioning of an industrial facility. ARIMA (Auto Regressive Integrated Moving Average) models are one of the most general classes of models used for forecasting a time series. ARIMA Model ARIMA models are standardized statistical models used to fit time series data in forecasting applications. The model composed of three main parts, AR(autoregressive), MA (moving average), and I(integrated). AR term represents the prediction of the current value of the time series as a function of the past values, MA is a current value which is a combination of past white noise (forecast errors) values, and I is trending in the time series. The MA term also helps to smooth out shortterm fluctuations, thus highlighting longerterm trends or cycles [Chou 1970]. Several forms of ARIMA models are used in industrial engineering applications especially as Statistical Process Control tools. Most notably are Exponentially Weighted Moving Average (EWMA), Exponentially Weighted Moving Deviations (EWMD), and CuSum control charts. EWMA, EWMD, and CuSum charts are considered effective for detecting small sustained shifts in the process [Kolarik 1999]. These techniques are a subset of ARIMA models and contain only the moving average (MA) terms. In order for a time series to be analyze, some need to be differenced (detrend) to be made stationary is said to be an "integrated" version of a stationary series. A nonseasonal ARIMA model is classified as an "ARIMA(p,d,q)" model where p is the number of autoregressive terms, d is the number of nonseasonal differences, q is the number of lagged forecast errors in the prediction equation. 6 http://www.duke.edu/~rnau/411arim.htm 55 To fit the appropriate ARIMA model for a time series the series need to be stationary. This can be achieved by detrending or differencing the series (integrated term). Seasonal ARIMA models In some cases, the time series exhibit a repetitive pattern. In this research, average daily ambient temperatures in 3 years period exhibit a repetitive pattern. The seasonal part of an ARIMA model has the same structure as the nonseasonal part but the factors operate across multiples of lags (the number of periods in a season). A seasonal ARIMA model is classified as an ARIMA(p,d,q)x(P,D,Q) model where P=number of seasonal autoregressive (SAR) terms D=number of seasonal differences Q=number of seasonal moving average (SMA) terms In identifying a seasonal model, the first step is to determine whether or not a seasonal difference is needed, in addition to or perhaps instead of a nonseasonal difference. If the seasonal pattern is both strong and stable over time (e.g., high in the Summer and low in the Winter, or vice versa), then a seasonal difference should be used. Differencing Fitting an ARIMA model is the determination of the order of differencing needed to stationarize the series. Normally, the correct amount of differencing is the lowest order of differencing that yields a time series which fluctuates around a welldefined mean value and whose autocorrelation function (ACF) plot decays fairly rapidly to zero, either from above or below. If the series still exhibits a longterm trend, or otherwise lacks a tendency to return to its mean value, or if its autocorrelations are positive out to a high number of lags (e.g., 10 or more), then it needs a higher order of differencing. The seasonal difference of a time series is the series of changes from one season to the next. For monthly data, in which there are 12 periods in a season, the seasonal difference 56 of Y at period t is Y(t)Y(t12). In this research, the data are in weekly period. Should seasonal difference is required, the periods are 52 periods in a season. Model Fit Test To determine the fit of model, this research uses the Akaike information criterion (AIC) [Akaikein 1974]. AIC is a statistical model fit measure which quantifies the relative goodnessoffit of various previously derived statistical models given a sample of data. It uses a rigorous framework of information analysis based on the concept of entropy. It also examines the complexity of the model together with the goodness of its fit to the sample data to produce a measure which balances between the two in order to prevent over fitting [Wikipedia 2006]. AIC = 2k − 2ln(L) (Eq. 46) where k is the number of parameters, L is the likelihood function. When normally distributed errors are assumed then AIC becomes n AIC = 2k − 2ln RSS (Eq. 47) where n is the number of observations, RSS is the residual sum of squares. The preferred model is that with the lowest AIC value. The AIC methodology attempts to find the minimal model that correctly explains the data, which can be contrasted with more traditional approaches to modeling, such as starting from a null hypothesis. 57 Test of Randomness After fitting an ARIMA model, the residual needs to be tested for randomness to ensure proper fit. This research uses LjungBox statistic test [Shumway and Stoffer 2000] to test residual. The LjungBox test is based on the autocorrelation plot and tests the "overall" randomness based on a number of lags. It is often referred to as a "portmanteau" test. H0: The data are random. Ha: The data are not random. The test statistic is: Σ= − = + h j LB n j Q n n j 1 2 ( ) ( 2) ρ (Eq. 48) Where n is sample size ρ(j) is autocorrelation at lag j h is number of lags being tested Based on a Chisquare distribution, reject if 2 LB 1 ,h Q α χ − > 58 CHAPTER VII EXPERIMENTAL RESULTS Introduction This chapter shows the results from the model created in Chapter 5 and statistics tests proposed in Chapter 6. Index Selection After calculating the two main indexes, Refined Laspeyres and Log Mean Divisia on the results showed that both indexes respond differently to the changes of the model. The indexes were used to monitor weekly the energy intensity changes for three years with the energy intensity of the first week. From the model, from visually examining the response, Log Mean Divisia appears to respond better to trend input than Refined Laspeyres as shown in Figure 5 (top). After further analysis by differencing both index time series, the Log Mean Divisia response show significant increase in variations of energy intensity compare to Laspeyres shown in Figure 5 (bottom). This increase in variation of all Log Mean Divisia intensity indexes is due to the logarithmic term in the index’s formula. The results of the Log Mean Divisia intensity index are consistent through all 27 scenarios shown in Appendix A. 59 Time 0 50 100 150 0 2000 6000 10000 Time 0 50 100 150 4000 0 2000 Figure 5 Time series plot of Log Mean Divisia AIHHH (top) and differenced AIHHH (bottom) The Refined Laspeyres responses are more consistent in magnitude than Log Mean Divisia. Figure 6 shows the response of Refined Laspeyres intensity index of the same data. These results illustrate a pattern that was reflected widely throughout the data. Time 0 50 100 150 0.2 0.0 0.2 0.4 0.6 Time 0 50 100 150 0.6 0.2 0.2 0.6 Figure 6 Refined Laspayres intensity index of series plot of LIHHH (above) and differenced LIHHH (below) 60 Base on this evidence, the Refined Laspeyres is more suitable for plant level long term (three years) monitoring Correlation Test H0: There is no correlation between Laspeyres intensity index and production ρ=0 H1: There is a correlation between Laspeyres intensity index and production ρ≠0 The correlation test between the Laspeyres intensity index and production as shown in Table VIII reveal that there is no correlation between the index and the production. This means that the index can be used to monitor the “bare” energy intensity without the influence of the product mix. TABLE VIII CORRELATION TEST BETWEEN THE LASPEYRES INTENSITY INDEX AND PRODUCTION No. Name CORR PValue CORR PValue 1 LIHHH 0.059 0.463 0.040 0.618 2 LIMHH 0.054 0.505 0.045 0.584 3 LIHMH 0.052 0.535 0.049 0.542 4 LIHHM 0.051 0.523 0.057 0.486 5 LIMMH 0.044 0.583 0.053 0.514 6 LIHMM 0.052 0.519 0.059 0.468 7 LIMHM 0.055 0.498 0.054 0.491 8 LIMMM 0.056 0.487 0.056 0.491 9 LILHH 0.059 0.468 0.040 0.623 10 LIHLH 0.039 0.630 0.057 0.484 11 LIHHL 0.029 0.723 0.061 0.459 12 LILLH 0.039 0.635 0.056 0.487 13 LIHLL 0.007 0.927 0.061 0.459 14 LILHL 0.028 0.730 0.061 0.454 15 LILLL 0.007 0.933 0.071 0.379 16 LILMM 0.047 0.558 0.058 0.474 17 LIMLM 0.546 0.500 0.058 0.474 18 LIMML 0.015 0.850 0.068 0.400 19 LILLM 0.044 0.587 0.059 0.464 20 LIMLL 0.005 0.952 0.073 0.368 21 LILML 0.017 0.830 0.067 0.411 22 LIHML 0.018 0.824 0.066 0.416 23 LIMHL 0.026 0.078 0.062 0.441 24 LILMH 0.050 0.541 0.049 0.546 25 LIHLM 0.050 0.540 0.061 0.453 26 LIMLH 0.033 0.680 0.060 0.461 27 LILHM 0.048 0.553 0.056 0.494 Original Series Differenced Series 61 ARIMA Model Fit The LIHHH plot has a slight trend as seen in Figure 7 indicate the response to the deterioration of the system efficiency. ACF plot shows that the data are correlated which implies a nonstationary time series. Figure 7 Time series plot (above), ACF plot (middle), and PACF plot (below) of LIHHH After the nonseasonal differencing, the time series appear more stable as shown in Figure 8. As preliminary analysis, the ACF cuts off at lag =1 and the PACF tails off. According to Shumway and Stoffer [2000] suggest initial guess for ARIMA(0,1,1) model. 62 Figure 8 Differenced Time series plots of LIHHH Model fitting by SPlus yield coefficient MA = 0.9068 with lowest of AIC = 79.65. The residual diagnostics of ARIMA(0,1,1) reveal random residuals. The fitted LIHHH can be expressed as 1 1 0.968 − − = + + t t t t x x ω ω (Eq. 49) where xt = time series value at time t, xt1 = time series value at time t1, ωt = error value at time t, ωt1 = error value at time t1. 63 Plot of Standardized Residuals 20 40 60 80 100 120 140 160 3 2 1 0 1 2 3 ACF Plot of Residuals ACF 0 5 10 15 20 1.0 0.0 0.5 1.0 PACF Plot of Residuals PACF 5 10 15 20 0.2 0.0 0.2 Pvalues of LjungBox ChiSquared Statistics Lag pvalue 2 4 6 8 10 0.0 0.2 0.4 0.6 0.8 ARIMA Model Diagnostics: LIHHH ARIMA(0,1,1) Model with Mean 0 The seasonal fit of ARIMA(0,1,1)x(0,1,0)52 yield AIC = 27.16 which is greater than the ARIMA(0,1,1) and therefore not recommended. The remaining ARIMA model fitting graphs are shown in Appendix A. A summary of the ARIMA model fitting is shown in Table IX on the next page. 64 TABLE IX SUMMARY ARIMA MODEL FITTING RESULTS NO. Name ARIMA AR Diff MA AIC 1 LIHHH (0,1,1) 0 1 0.9 79.94 2 LIMHH (0,1,1) 0 1 0.907 79.66 3 LIHMH (0,1,1) 0 1 0.93 99.93 4 LIHHM (0,1,1) 0 1 0.884 182 5 LIMMH (0,1,1) 0 1 0.933 99.7 6 LIHMM (0,1,1) 0 1 0.916 207.6 7 LIMHM (0,1,1) 0 1 0.879 183.4 8 LIMMM (0,1,1) 0 1 0.911 208.4 9 LILHH (0,1,1) 0 1 0.905 79.36 10 LIHLH (0,1,1) 0 1 0.958 116.6 11 LIHHL (0,1,1) 0 1 0.915 32.78 12 LILLH (0,1,1) 0 1 0.958 116.3 13 LIHLL (0,1,1) 0 1 0.966 70.59 14 LILHL (0,1,1) 0 1 0.914 33.09 15 LILLL (0,1,1) 0 1 0.965 70.88 16 LILMM (0,1,1) 0 1 0.916 207.2 17 LIMLM (0,1,1) 0 1 0.942 230.1 18 LIMML (0,1,1) 0 1 0.938 58.22 19 LILLM (0,1,1) 0 1 0.946 229.4 20 LIMLL (0,1,1) 0 1 0.966 75.31 21 LILML (0,1,1) 0 1 0.936 53.61 22 LIHML (0,1,1) 0 1 0.938 53.33 23 LIMHL (0,1,1) 0 1 0.916 37.78 24 LILMH (0,1,1) 0 1 0.929 99.62 25 LIHLM (0,1,1) 0 1 0.946 229.8 26 LIMLH (0,1,1) 0 1 0.959 116.9 27 LILHM (0,1,1) 0 1 0.886 181.6 The ARIMA model fitting summarized in Table IX reveal that it is possible to fit the energy intensity index in a time series model. The results show that all the models are moving average (MA) models. Weather due to seasonal changes is not as significant when fitting the model as the trending from efficiency deterioration. In a more energy intensive process weather may play a more prominent role in the ARIMA model fitting and may require a seasonal model. 65 Discussion of Experimental Results The experiments conducted for time series of the Refined Laspeyres energy intensity index and the Log Mean Divisia indexes with from the brick model over a 3 year period with 3 scenarios of product mixes, 3 scenarios of weather patterns, and 3 scenarios of system efficiency deteriorations accounts for 27 total scenarios. Time series plots of the Refined Laspeyres energy intensity index of 27 scenarios show the effects of the three main effects. Trending effects are very strong in the Log Mean Divisia index. The indexes increase rapidly in all 27 scenarios with increasing rate of amplitudes. This may be due to the logarithmic nature of the index and therefore is not recommended for use in long term monitoring. The Refined Laspeyres energy intensity index is used to test for correlation with the influence of product mix. The results show that the intensity indexes are statistically correlated with the product mix and therefore can be used to monitor the “bare” energy intensity of the production process. The intensity index time series can be used to develop ARIMA models. All 27 scenarios resulted in the recommendation of an ARIMA (0,1,1) model which is an Integrated Moving Average model. None of the weather impacts were significant enough to include in the seasonal ARIMA model, ARIMA (p,d,q)x(P,D,Q)52. 66 CHAPTER VIII SUMMARY, DISCUSSIONS, AND RECOMMENDATIONS 8.1 Introduction From Chapter 7, statistical test results indicated that the Refined Laspeyres energy intensity index is the more suitable to use as a plantlevel energy monitoring index than Log Mean Divisia because of the consistency in responding to changes and not amplify the changes over time. The results also show that Refined Laspeyres energy intensity index has no correlation with the production mix. In other words, the energy intensity index is not influence by changes in product mix. This chapter presents the major contributions and the usefulness of this research. This chapter also includes the strength and limitations of the techniques and the use of energy intensity index. Finally, the chapter explores opportunities to improve the technique and future development of this research. 8.2 Major Contribution of This Research In industrial settings, one of the challenges energy managers encounter when performing monitoring on the facility’s energy usage is the influence of changes in product mix, production quantity, and weather impact. These factors influence the energy usage in the plant and mask the “bare” production energy efficiency. This research introduces a procedure to unmask the bare production energy efficiency by incorporating the use of 67 energy intensity index as a tool to monitor the changes in energy consumption. The intensity index uses energy intensity, kJ/kg, as a part of calculation which eliminates the production quantity mask. Further statistical tests showed that the Refined Laspeyres intensity index is not influenced by the changes in product mix. These benefits provide energy engineers with better knowledge of the facility’s production efficiency. The research results also indicate that the intensity index can be fitted into an ARIMA model which is one of the most used models in forecasting. Energy managers can use this model to monitor the current facility production efficiency changes. In addition, since ARIMA models are one of the most powerful models used to better understand the data or used for prediction, engineers can use these models to plan for future recommissioning effort by applying forecasting techniques. The increasing in energy intensity (trend) and erratic energy intensity behavior can help engineers understand the healthiness of the process and able to project on when improvements are needed. 8.3 Strengths and Limitations From the experimental results, the advantage of the use of energy intensity index as an alternative production energy efficiency monitoring technique is that the index is not influenced by the changes in product type. The model tested was on weekly data over a three years period. After fitting the ARIMA model, the weather impact was recognized as a part of general white noise (residual). Researchers wishing to continue this study need to recognize the weather impact and also test for seasonality of the model in the time series fitting. More complex models may be used should the weather plays an important role. An example of more complex model include but not limited to SRIMA or ARIMA(p,d,q)x(P,D,Q). The study was performed on a flow shop environment, the modeled facility was not air conditioned. In other production type environments for example, a facility with air conditioning and complex production lines, more complex data gathering processes may be required, for example submetering of multiple furnaces, motors, and the production 68 lines. For thermally heavy processes including air conditioning, the author speculates that additional air conditioning submetering may be required. The indexes used in this research are assumed to be intensity index (energy used per unit of production) not value based. Researchers can later convert to currencybased intensity indexes (dollars of energy per unit of production) to justify the future forecasting for a recommissioning project. 8.4 Future Research There are opportunities for expansion of this research 1. Index decomposition methodology mainly composed of Intensity index, Production Mix index, and Production Quantity index (please refer to Chapter 2). This research explores the energy intensity index. As an overall facility wellbeing, the product mix and production quantity (production index) can be further explored in similar way. 2. Use other types of trend signals. This research explored the linear decay of the overall efficiency over a long term period of 3 years. Further studies are needed to explore other types of decay signals. This may also include actual data gathering over a long term period from the time when major energy conservation efforts have been implemented. 3. The expanded universe of the plantlevel energy intensity index monitoring is to develop forecasting processes to plan for future recommissioning. Since this research uses ARIMA models as a standardized model of the indexes, it can be expanded into forecasting. 4. Short term (one year) monitoring with LMDI. 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Energy Efficiency Trends in Canada 1990 to 2002, Office of Energy Efficiency Natural Resources Canada. Chen, C. Y., Wu, R.H. (1995). Effects of restructuring of international trade on changing energy use patterns and CO2 emissions in Taiwan: 19811991. Proceedings of the 18th International Association of Energy Economics International Conference, Washington DC. Diewert, W. E. (1980). Capital and theory of productivity measurement. NinetySecond Annual Meeting of the American Economic Association, American Economic Association. EIA (2005). Energy Information Administration. Fisher, I. (1927). The making of index numbers A study of their varieties, tests, and reliability. Cambridge, Massachusetts, The Riverside Press. Freeman, S. L., Niefer, Mark J., and Roop, Joseph M. (1997). "Measuring industrial energy intensity: practical issues and problems." Energy Policy 25: 703714. 72 Fuller, W. A. (1996). Introduction to statistical time series. New York, NY, John Wiley & Sons, Inc. Gardner, D. (1993). "Industrial energy use in Ontario from 1962 to 1984." Energy Economics 15(1): 2532. Hicks, T. W., Dutrow, Elizabeth (2001). Energy performance benchmarking for manufacturing plants. ACEEE Summer Study on Energy Efficiency in Industry (5th 2001), Tarrytown, NY. Howarth, R. B., Schipper, L., Andersson, B. (1993). "The structure and intensity of energy use: trends in five OECD nations." Energy Journal 14(2): 27  45. Huang, J. P. (1993). "Industrial energy use and structural change: a case study of the People’s Republic of China." Energy Economics 15(2): 131 – 136. Hulten, C. R. (1973). "Divisia Index Numbers." Econometrica 41(6): 10171025. Jenne, C., Cattell, R. (1983). "Structural change and energy efficiency in industry." Energy Economics 5(2): 114  123. Jeschar, R., Bittner, HansGeorg. (1989). "Possibility for optimization of tunnel kiln processes in the brick and tile industry; Quality improvement and reduction in energy consumption." Ziegelindustrie International 42(10). Kolarik, W. J. (1999). Creating Quality Process Design for Results, McGrawHill. Lermit, J. a. J., Nigel (2001). Monitoring energy efficiency performance in New Zealand: a conceptual and methodological framework. W. Energy Efficiency and Conservation Authority, New Zealand. Liu, F. L., Ang, B.W. (2003). "Eight methods for decomposing the aggregate energyintensity of industry." Applied Energy 76: 1523. 73 Liu, M., Claridge, David E. (2003). "Continuous Commissioning(SM) of Building Energy Systems." Journal of Solar Engineering Engineering 125. Liu, X. Q., Ang, B.W (1992). "THE APPLICATION OF THE DIVISIA INDEX TO THE DECOMPOSITION OF CHANGES IN INDUSTRIAL ENERGY CONSUMPTION." Energy Journal 13(4): 161  178. Ortiz, D. (2002). Summary of the “DOE Workshop on Indicators of Energy Intensity in the U.S. Economy”. DOE Workshop on Indicators of Energy Intensity in the US Economy. Arlington, Virginia: 120. Paasche, H. (1874). "Ueber die Preisentwicklung der letzten Jahre nach den Hamburger Borsennotirungen." Jahrbucher fur Nationalokonomie und Statistik: 168  178. Phylipsen, G. J. M., Blok K., and Worrell, E. (1998). Handbook on International Comparisons of Energy Efficiency in the Manufacturing Industry. The Netherlands: Dept. of Science, Technology & Society, Utrecht University, Elsevier. Prasertsan, S., Theppaya, T. (1995). "A Study toward energy savings in brick making: Part 1 Key paramenters for energy savings." RERIC International Energy Journal 17(2). Prasertsan S., P. G., Teppaya, T., Kirirat, P. (1995). "A study toward energy saving in brick making Part 2  Simulation of processes in brick kiln." RERIC International Energy Journal 17(2). Price, L. (1997). Energy efficiency in the United States iron and steel industry: An international perspective. ACEEE summer study on energy efficiency in industry (1997), Washington, D.C., American Council for EnergyEfficient Economy. Reitler, W., Rudolph, M., Schaefer, H. (1987). "Analysis of the factors influencing energy consumption in industry a revised method." Energy Economics: 145  148. Rose, A., Casler, S. (1996). "Input–output structural decomposition analysis: a critical appraisal." Economic Systems Research 8: 33  62. 74 Selvanathan, E. A., Prasada Rao, D.S. (1997). Index Numbers A Stochastic Approach. Ann Arbor, The University of Michigan Press. Sun, J. W. (1998). "Changes in energy consumption and energy intensity: A complete decomposition model." Energy Economics 20: 85100. The Institute of Energy Economics, J. (2000). A STUDY OF ENERGY EFFICIENCY INDICATORS FOR INDUSTRY IN APEC ECONOMIES. A. P. E. R. CENTRE, Institute of Energy Economics, Tokyo Japan. Turner, W. C. (2005). Commissioning. AEE Skills Update IV. W. C. Turner, Association of Energy Engineers. Turner, W. C., Parker, S. A. (1984). "Energy Accounting: A New Field Develops." IIE Transactions. Vogt, A., Barta, Janos. (1997). The making of tests for index numbers: mathematical methods of descriptive statistics. Germany, PhysicaVerlag Heidelberg. Vollmann, T. E., Berry, William L., Whybark, Clay D. (1997). Manufacturing planning and control systems, McGrawHill Companies, Inc. Wei, W. W. (1990). Time series analysis univariate and multivariate methods, Addison Wesley Publishing Company. Wikipedia Price index. Worrell, E., Laitner, John A., Ruth, Michael, Finman, Hodayah (2003). "Productivity benefits of industrial energy efficiency measures." Energy 28: 1081  1098. 75 APPENDIXES 76 APPENDIX A: GRAPH OF SIMULATION RESULTS Refined Laspayres Energy Intensity Index 1. Time series of Refined Laspayres Energy Intensity Index (Top) 2. Auto Correlation of Refined Laspayres Energy Intensity Index (Middle) 3. Partial Refined Laspayres Energy Intensity Index (Bottom) 77 78 79 80 81 82 83 84 85 86 87 88 89 90 Log Mean Divisia Energy Intensity Index 4. Time series of Log Mean Energy Intensity Index (Top) 5. Auto Correlation of Log Mean Energy Intensity Index (Middle) 6. Partial Refined Log Mean Energy Intensity Index (Bottom) 91 92 93 94 95 96 97 98 99 100 101 102 103 104 APPENDIX B: TEST OF CORRELATION RESULTS Correlation test of detrended Refined Laspayres intensity index #***** Refined Laspayres Intensity Index ****** cor.test(LIHHH, prodHw) Pearson's productmoment correlation data: LIHHH and prodHw t = 0.7365, df = 153, pvalue = 0.4625 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05944053 > cor.test(LIMHH, prodHw) Pearson's productmoment correlation data: LIMHH and prodHw t = 0.6679, df = 153, pvalue = 0.5052 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05391762 > cor.test(LIHMH, prodHw) Pearson's productmoment correlation data: LIHMH and prodHw t = 0.6215, df = 153, pvalue = 0.5352 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05018343 > cor.test(LIHHM, prodMw) Pearson's productmoment correlation data: LIHHM and prodMw t = 0.6405, df = 153, pvalue = 0.5228 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05171571 105 > cor.test(LIMMH, prodHw) Pearson's productmoment correlation data: LIMMH and prodHw t = 0.5507, df = 153, pvalue = 0.5827 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.04447645 > cor.test(LIHMM, prodMw) Pearson's productmoment correlation data: LIHMM and prodMw t = 0.646, df = 153, pvalue = 0.5192 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05215641 > cor.test(LIMHM, prodMw) Pearson's productmoment correlation data: LIMHM and prodMw t = 0.6792, df = 153, pvalue = 0.4981 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05482426 > cor.test(LIMMM, prodMw) Pearson's productmoment correlation data: LIMMM and prodMw t = 0.6961, df = 153, pvalue = 0.4874 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.056184 > cor.test(LILHH, prodHw) Pearson's productmoment correlation data: LILHH and prodHw t = 0.7278, df = 153, pvalue = 0.4678 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05874133 > cor.test(LIHLH, prodHw) 106 Pearson's productmoment correlation data: LIHLH and prodHw t = 0.4825, df = 153, pvalue = 0.6302 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.03897485 > cor.test(LIHHL, prodLw) Pearson's productmoment correlation data: LIHHL and prodLw t = 0.355, df = 153, pvalue = 0.7231 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.02868749 > cor.test(LILLH, prodHw) Pearson's productmoment correlation data: LILLH and prodHw t = 0.4753, df = 153, pvalue = 0.6352 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.03839904 > cor.test(LIHLL, prodLw) Pearson's productmoment correlation data: LIHLL and prodLw t = 0.092, df = 153, pvalue = 0.9268 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.007435621 > cor.test(LILHL, prodLw) Pearson's productmoment correlation data: LILHL and prodLw t = 0.3461, df = 153, pvalue = 0.7297 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.02797184 > cor.test(LILLL, prodLw) Pearson's productmoment correlation 107 data: LILLL and prodLw t = 0.0838, df = 153, pvalue = 0.9334 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.006771146 > cor.test(LILMM, prodMw) Pearson's productmoment correlation data: LILMM and prodMw t = 0.587, df = 153, pvalue = 0.558 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.04740542 > cor.test(LIMLM, prodMw) Pearson's productmoment correlation data: LIMLM and prodMw t = 0.6759, df = 153, pvalue = 0.5001 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05456157 > cor.test(LIMML, prodLw) Pearson's productmoment correlation data: LIMML and prodLw t = 0.1901, df = 153, pvalue = 0.8495 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.01536753 > cor.test(LILLM, prodMw) Pearson's productmoment correlation data: LILLM and prodMw t = 0.5447, df = 153, pvalue = 0.5868 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.04399379 > cor.test(LIMLL, prodLw) Pearson's productmoment correlation data: LIMLL and prodLw t = 0.0603, df = 153, pvalue = 0.952 108 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.004878067 > cor.test(LILML, prodLw) Pearson's productmoment correlation data: LILML and prodLw t = 0.2148, df = 153, pvalue = 0.8302 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.01736321 > cor.test(LIHML, prodLw) Pearson's productmoment correlation data: LIHML and prodLw t = 0.2234, df = 153, pvalue = 0.8236 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.01805429 > cor.test(LIMHL, prodLw) Pearson's productmoment correlation data: LIMHL and prodLw t = 0.3216, df = 153, pvalue = 0.7482 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.0259903 > cor.test(LILMH, prodHw) Pearson's productmoment correlation data: LILMH and prodHw t = 0.6135, df = 153, pvalue = 0.5405 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.04953381 > cor.test(LIHLM, prodMw) Pearson's productmoment correlation data: LIHLM and prodMw t = 0.6149, df = 153, pvalue = 0.5395 alternative hypothesis: coef is not equal to 0 sample estimates: 109 cor 0.04965111 > cor.test(LIMLH, prodHw) Pearson's productmoment correlation data: LIMLH and prodHw t = 0.414, df = 153, pvalue = 0.6795 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.03344878 > cor.test(LILHM, prodMw) Pearson's productmoment correlation data: LILHM and prodMw t = 0.5947, df = 153, pvalue = 0.5529 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.04802122 110 Correlation test of detrended Refined Laspayres intensity index cor.test(LIHHH.mod, prodHw) Pearson's productmoment correlation data: LIHHH.mod and prodHw t = 0.4992, df = 152, pvalue = 0.6184 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.04045753 > cor.test(LIMHH.mod, prodHw) Pearson's productmoment correlation data: LIMHH.mod and prodHw t = 0.5491, df = 152, pvalue = 0.5837 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.04449444 > cor.test(LIHMH.mod, prodHw) Pearson's productmoment correlation data: LIHMH.mod and prodHw t = 0.6107, df = 152, pvalue = 0.5423 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.04947506 > cor.test(LIHHM.mod, prodMw) Pearson's productmoment correlation data: LIHHM.mod and prodMw t = 0.6988, df = 152, pvalue = 0.4858 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05658693 > cor.test(LIMMH.mod, prodHw) Pearson's productmoment correlation data: LIMMH.mod and prodHw t = 0.6539, df = 152, pvalue = 0.5142 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05296247 111 > cor.test(LIHMM.mod, prodMw) Pearson's productmoment correlation data: LIHMM.mod and prodMw t = 0.727, df = 152, pvalue = 0.4683 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05886591 > cor.test(LIMHM.mod, prodMw) Pearson's productmoment correlation data: LIMHM.mod and prodMw t = 0.6617, df = 152, pvalue = 0.5091 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05359633 > cor.test(LIMMM.mod, prodMw) Pearson's productmoment correlation data: LIMMM.mod and prodMw t = 0.6911, df = 152, pvalue = 0.4905 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05596997 > cor.test(LILHH.mod, prodHw) Pearson's productmoment correlation data: LILHH.mod and prodHw t = 0.4928, df = 152, pvalue = 0.6229 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.03993842 > cor.test(LIHLH.mod, prodHw) Pearson's productmoment correlation data: LIHLH.mod and prodHw t = 0.7022, df = 152, pvalue = 0.4836 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05686178 > cor.test(LIHHL.mod, prodLw) 112 Pearson's productmoment correlation data: LIHHL.mod and prodLw t = 0.7425, df = 152, pvalue = 0.4589 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.06011677 > cor.test(LILLH.mod, prodHw) Pearson's productmoment correlation data: LILLH.mod and prodHw t = 0.6965, df = 152, pvalue = 0.4872 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05640439 > cor.test(LIHLL.mod, prodLw) Pearson's productmoment correlation data: LIHLL.mod and prodLw t = 0.7425, df = 152, pvalue = 0.4589 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.06011677 > cor.test(LILHL.mod, prodLw) Pearson's productmoment correlation data: LILHL.mod and prodLw t = 0.75, df = 152, pvalue = 0.4544 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.06072259 > cor.test(LILLL.mod, prodLw) Pearson's productmoment correlation data: LILLL.mod and prodLw t = 0.8833, df = 152, pvalue = 0.3785 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.07146103 > cor.test(LILMM.mod, prodMw) Pearson's productmoment correlation 113 data: LILMM.mod and prodMw t = 0.7113, df = 152, pvalue = 0.478 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05760082 > cor.test(LIMLM.mod, prodMw) Pearson's productmoment correlation data: LIMLM.mod and prodMw t = 0.7175, df = 152, pvalue = 0.4742 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05809506 > cor.test(LIMML.mod, prodLw) Pearson's productmoment correlation data: LIMML.mod and prodLw t = 0.8446, df = 152, pvalue = 0.3996 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.06834972 > cor.test(LILLM.mod, prodMw) Pearson's productmoment correlation data: LILLM.mod and prodMw t = 0.7338, df = 152, pvalue = 0.4642 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.0594142 > cor.test(LIMLL.mod, prodLw) Pearson's productmoment correlation data: LIMLL.mod and prodLw t = 0.9024, df = 152, pvalue = 0.3683 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.07299632 > cor.test(LILML.mod, prodLw) Pearson's productmoment correlation data: LILML.mod and prodLw 114 t = 0.824, df = 152, pvalue = 0.4113 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.06668282 > cor.test(LIHML.mod, prodLw) Pearson's productmoment correlation data: LIHML.mod and prodLw t = 0.8162, df = 152, pvalue = 0.4157 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.06605504 > cor.test(LIMHL.mod, prodLw) Pearson's productmoment correlation data: LIMHL.mod and prodLw t = 0.7727, df = 152, pvalue = 0.4409 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.06255038 > cor.test(LILMH.mod, prodHw) Pearson's productmoment correlation data: LILMH.mod and prodHw t = 0.6047, df = 152, pvalue = 0.5463 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.04899197 > cor.test(LIHLM.mod, prodMw) Pearson's productmoment correlation data: LIHLM.mod and prodMw t = 0.7522, df = 152, pvalue = 0.4531 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.06089597 > cor.test(LIMLH.mod, prodHw) Pearson's productmoment correlation data: LIMLH.mod and prodHw t = 0.7396, df = 152, pvalue = 0.4607 alternative hypothesis: coef is not equal to 0 115 sample estimates: cor 0.05987879 > cor.test(LILHM.mod, prodMw) Pearson's productmoment correlation data: LILHM.mod and prodMw t = 0.6864, df = 152, pvalue = 0.4935 alternative hypo
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Title  Energy Index Decomposition Methodology at the Plant Level 
Date  20061201 
Author  Kumphai, Wisit 
Department  Industrial Engineering & Management 
Document Type  
Full Text Type  Open Access 
Abstract  The dissertation explores the use of a high level energy intensity index as a facilitylevel energy performance monitoring indicator with a goal of developing a methodology for an economically based energy performance monitoring system that incorporates production information. The performance measure closely monitors energy usage, production quantity, and product mix and determines the production efficiency as a part of an ongoing process that would enable facility managers to keep track of and, in the future, be able to predict when to perform a recommissioning process. The study focuses on the use of the index decomposition methodology and explored several high level (industry, sector, and country levels) energy utilization indexes, namely, Additive Log Mean Divisia, Multiplicative Log Mean Divisia, and Additive Refined Laspeyres. One level of index decomposition is performed. The indexes are decomposed into Intensity and Product mix effects. These indexes are tested on a flow shop brick manufacturing plant model in three different climates in the United States. The indexes obtained are analyzed by fitting an ARIMA model and testing for dependency between the two decomposed indexes. The results concluded that the Additive Refined Laspeyres index decomposition methodology is suitable to use on a flow shop, non air conditioned production environment as an energy performance monitoring indicator. It is likely that this research can be further expanded in to predicting when to perform a recommissioning process. 
Note  Dissertation 
Rights  © Oklahoma Agricultural and Mechanical Board of Regents 
Transcript  ENERGY INDEX DECOMPOSITION METHODOLOGY AT THE PLANT LEVEL By WISIT KUMPHAI Batchelor of Engineering Kasetsart University Bangkok, Thailand 1998 Master of Science Colorado State UniversityPueblo Pueblo, Colorado 2000 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY December, 2006 ii ENERGY INDEX DECOMPOSITION METHODOLOGY AT THE PLANT LEVEL Dissertation Approved: David B. Pratt Dissertation Adviser William J. Kolarik Wayne C. Turner Francis M. Epplin A. Gordon Emslie Dean of the Graduate College iii ACKNOWLEDGEMENTS I would like to express my deepest gratitude to my major advisor, Dr. David B. Pratt for his support, guidance, encouragement, and patience through this long journey. I would like to express my sincere appreciation to Dr. Wayne C. Turner for his continuous support, guidance, pragmatism, and friendship. He inspired me to be the best energy engineer I could be. I would like to recognize Dr. William J. Kolarik, a great boss who showed me that with hard work, we can accomplish anything. I would like to extend my appreciation to Dr. Francis M. Epplin who kept me grounded and shared valuable insights. I would like to thank the Oklahoma Industrial Assessment Center (IAC) for an exceptional educational experience like no other. IAC is only research program that challenges engineering students with REAL WORLD problems. The program encourages students to apply the knowledge learned in class to identify/solve problems, and improve process efficiency. At the same time, students learned how to professionally deal with clients, vendors, utility agents, etc. I would like to extend my gratitude to my fellow IAC colleagues who are currently on the same quest Robert Scott Frazier, Shankar Earni, and Haiyan Zhao. Thanks being such good friends. Thank you, Jean W. Ames for all her help from the first day I stepped foot in Stillwater. Thank you for Saturday evening dinners, and most of all, thank you for letting me be a part of your family. I would like to express my deepest gratitude to my parents, Dr. Siripong and Mrs. Wipapan Kumphai for your encouragements and support. My sister Ms. Pimpawan Kumphai, thanks for being a such a good friend, an excellent cook, the best travel companion anyone could ever wished for, and above all, a very good listener. Finally, I iv would like to thank my grandmothers, Mrs. Anong Akarasa who showed me the wisdom of how to be a good human being, Mrs. Panan Kumphai for your financial support. Hope you were here to witness YOUR accomplishments. v TABLE OF CONTENTS Chapter Page I. Introduction ...................................................................................................................1 Motivation of Study ......................................................................................................1 II. Literature Review.........................................................................................................4 2.1 Energy Intensity ...................................................................................................... 4 2.1.1 Measures of Energy Input................................................................................ 5 2.1.2 Measures of output........................................................................................... 6 2.2 Index Numbers......................................................................................................11 2.3 Aggregation Levels...............................................................................................15 2.4 Decomposition Methodology ............................................................................... 18 2.4.1 Multiplicative Decomposition ....................................................................... 18 2.4.2 Additive Decomposition ................................................................................19 2.5 Energy Index Decomposition methodology ......................................................... 20 2.5.1 Aggregate Energy Consumption Approach................................................... 21 2.5.2 Aggregate Energy Intensity Approach...........................................................22 2.5.3 Selection of approach (Energy intensity or consumption)............................. 23 2.5.4 Selection of method ....................................................................................... 24 2.5.5 Construction of Time Series Index Decomposition Method ......................... 29 2.6 Conclusion ............................................................................................................ 30 III. Statement of Research...............................................................................................31 3.1 Problem Statement ................................................................................................31 3.2 Research Goals...................................................................................................... 31 3.3 Major Research Tasks...........................................................................................32 3.4 Research Boundaries............................................................................................. 32 IV. Methodology.............................................................................................................33 4.1 Introduction...........................................................................................................33 4.2 Research Plan........................................................................................................ 33 V. Plant level energy consumption model development ................................................41 5.1 Introduction.....................................................................................................41 vi 5.2 Brick manufacturing process and building the model .......................................... 41 5.3 Brick Model construction and Evaluation ............................................................ 45 5.4 Calculation Example............................................................................................. 50 VI. Statistical validation process.....................................................................................52 6.1 Introduction...........................................................................................................52 6.2 Statistical Test Procedure......................................................................................52 VII. Experimental Results...............................................................................................58 VIII. Summary, Discussions, and REcommendations....................................................66 8.1 Introduction...........................................................................................................66 8.2 Major Contribution of This Research ................................................................... 66 8.3 Strengths and Limitations .....................................................................................67 8.4 Future Research .................................................................................................... 68 REFERENCES ............................................................................................................... 69 APPENDIXES................................................................................................................75 APPENDIX A: GRAPH OF SIMULATION RESULTS........................................... 76 APPENDIX B: TEST OF CORRELATION RESULTS.......................................... 104 VITA vii LIST OF TABLES Table Page I. INDUSTRIES OUTPUT DATA MEASURES ....................................................... 6 II. ENERGYINTENSITY INDICATORS FOR THE MANUFACTURING SECTOR .................................................................................................................. 9 III. BRICK ENERGY CONSUMPTION .................................................................... 46 IV. SIMULATION SCENARIOS FOR REFINED LASPEYRES ADDITIVE ENERGY INTENSITY INDEX ............................................................................ 49 V. SIMULATION SCENARIOS FOR LOG MEAN DIVISIA ADDITIVE ENERGY INTENSITY INDEX ............................................................................................. 49 VI. EXAMPLE CALCULATIONS OF REFINED LASPEYRES AND LOG MEAN DIVISIA INDEXES............................................................................................... 50 VII. EXAMPLE CALCULATIONS OF REFINED LASPEYRES AND LOG MEAN DIVISIA INDEXES............................................................................................... 51 VIII. CORRELATION TEST BETWEEN THE LASPEYRES INTENSITY INDEX AND PRODUCTION ............................................................................................ 60 IX. SUMMARY ARIMA MODEL FITTING RESULTS........................................... 64 viii LIST OF FIGURES Figure Page 1. The energy indicator pyramid (with sources of data).......................................16 2. General framework of the index decomposition methodologies......................21 3. Diagrammatic representation of brick manufacturing process.........................42 4. Decomposition of total energy intensity into structure and intensity effects ...51 5. Time series plot of Log Mean Divisia AIHHH (top) and differenced AIHHH (bottom) ............................................................................................................59 6. Refined Laspayres intensity index of series plot of LIHHH (above) and differenced LIHHH (below) .............................................................................59 7. Time series plot (above), ACF plot (middle), and PACF plot (below) of LIHHH..............................................................................................................61 8. Differenced Time series plots of LIHHH......................................................... 62 1 CHAPTER I INTRODUCTION Motivation of Study The motivation for this research is to develop a methodology for an economically based energy performance monitoring system that incorporates production information. This performance measure will closely monitor energy usage and reflect the production efficiency as a part of an ongoing process, a facility manager can keep track and in the future, predict on when to perform a recommissioning process. Recommissioning is a thorough and detailed process of reassuring that the facility mechanical and electrical systems (production and production support equipment) are operating optimally according to the building’s design intent. There is currently no definite schedule on when the recommissioning needs to be perform, Turner [2005] provided guidelines that the facility should consider recommissioning when one or more of the following occurs (“triggers”) 1. High energy consumption, 2. Occupant complaints, 3. Maintenance staff complaints (problems), 4. Economic interests (lessen operating costs including energy and maintenance), 5. New systems or significant expansion of existing system. Since most commercial building energy consumption is from environmental control systems (i.e., HVAC) and the function of the building is relatively constant compared to 2 manufacturing facilities, measuring these “triggers” is doable and relatively straightforward. For example, several studies by Liu and Claridge [2003] used energy system submetering as the main part of an ongoing commissioning process to continuously optimize a commercial building. A similar process of energy utilization monitoring as a tool to trigger recommissioning has not documented for an industrial facilities. This is likely due to the wide variations in product mix, product types, weather changes, production level, process changes, etc. One of the popular methods used in energy performance measurement is index numbers. There has been considerable research on energy performance indexes utilizing energy intensity indicators to monitor changes in production efficiency. The idea was originated by an economist in the early 1900s, Dr. Irving Fisher [Barber 1996]. However, most of the research work focuses on large scale indicators (national economy) as opposed to small scale indicators (individual company). Energy intensity indexes are used to compare and track changes in energy intensity at the national and enduse sector levels. There has been active research work on energy intensity indicators and energy intensity indexes on large scale economy i.e., country level, sector level, and industry level. Recent research direction focuses on the development of energy intensity indexes which incorporate environmental impacts [Ang 2000] and the national or sector levels. A small number of researchers have also been investigating the use of energy intensity indicators at the facility level (plant level). These researchers focus on comparisons of energy intensity between similar manufacturing plants in order to establish benchmarks in energy usage for general plants, best practice plants, and low efficiency manufacturing plants [Worrell 2003]. Recently, energy efficiency monitoring over time with the energy intensity index has also been used in the environmental conservation area and at the national level [Bernard 2005]. The lowest monitoring system in this area was at the sector level. Energy intensity indicators and energy intensity indexes are useful tools that paint a picture of the status of a country’s, industry’s, or sector’s energy efficiency. This enables 3 researchers, economists, and policy makers to establish benchmarks between countries, industries, or sectors and establish energy policy accordingly The goal of this research is to develop a practical energy performance monitoring index for use at the plant level to monitor the facility’s energy efficiency usage over time which will help the facility justify when to reevaluate the plant’s overall energy efficiency through recommissioning. A contribution of this research is to incorporate the potential savings to be generated by including the production into the indexes. It is an extension of two recent research topics, energy intensity studies and energy intensity index studies. 4 CHAPTER II LITERATURE REVIEW Introduction There has been considerable research on monitoring energy usage in industry. However, most research has focused on high level usage (i.e., continent, country, sector, or industry). Since the early 1990s, researchers directed their work to develop more sophisticated energy monitoring decomposition methodologies. Examples include Liu and Ang [1992], and Ang [1994] who monitor energy usage at lower levels but stopped at the industry level. Beginning in the late 1990s and continued through the early 2000s, research directions have changed to incorporate environmental factors into the index decomposition methods at the industry level [Bernard 2005]. This chapter introduces the fundamental components and types of energy monitoring index decomposition methodologies which include energy intensity, decomposition methodologies, and energy monitoring index and research work in these areas to date. 2.1 Energy Intensity Energy intensity (EI) is a measure of the efficiency with which energy resources are being used to produce goods [Freeman 1997]. EI is commonly expressed as ratio of energy input (e.g., Btu, kWh) to useful output (e.g., tons of products, dollars of revenue). 5 Energy intensity is also referred to in some publications as energy efficiency indicators (EEI) [Phylipsen et al.1998]. In this research, the term EI will be used to identify these measures. EIs are divided into two categories, physical EIs and economic EIs. Physical EI is based on the physical amount of energy used in the process. The energy input is expressed in thermodynamic units (e.g., Btu of delivered energy consumed in the production of aluminum) and useful output measured in volume of output e.g. tons of aluminum or market value of output e.g. dollars of aluminum. The economic EI is different from the physical counterpart because it expresses the energy input in terms of monetary value. There are several ways to measure energy input and production output. These are reviewed in the following two subsections. 2.1.1 Measures of Energy Input Freeman [1997] stated that three measures of energy consumption are site consumption of energy, total inputs of energy, and offsite produced energy. These are explained more completely below. 1. Site Consumption of Energy Site consumption of energy is the most comprehensive measure of energy consumption and represents the first use of energy sources regardless of whether they are consumed as a fuel or as a non fuel (raw material). This measure does not include byproduct fuels produced onsite from previously counted energy inputs. 2. Total Inputs of Energy Total input of energy includes all energy sources used to produce heat and power and to generate electricity whether produced offsite or onsite. This metric excludes energy generated from the facilities own raw materials (e.g., calcined carbon process). 3. Offsite Produced Energy Offsite produced energy includes all energy sources purchased or transferred from offsite to produce heat and power and to generate electricity. All non fuel uses of energy and all byproduct energy are excluded. 6 2.1.2 Measures of output Similar to the energy input, measures of output can be divided into two types, volume based output and value based output. Volume based output is the most straightforward measurement for each facility. However, it does not reflect the bottom line or profit of the company because it does not have a monetary value tagged to it. Table I shows an example of the Department of Energy’s measures of output by volume [Freeman 1997]. TABLE I INDUSTRIES OUTPUT DATA MEASURES1 Industry Volumebased Aluminum Aluminum production (tons) Cement Cement production (tons) Chloralkali Chlorine and sodium hydroxide production (tons) Copper Promary copper production (tons) Corn wet milling High fructose corn syrup (tons) Lime Lime production (tons) Lumber Lumber production (boardfeet) Nitrogen fertilizers Nitrogen fertilizer material production (tons) Paper Paper production (tons) Paper board Paper board production (tons) Plywood Plywood production (square feet 3/8" basis) Pulp Pulp production (tons) Steel Raw steel production (tons) Petroleum Petroleum products (barrels) Demand Indicators In order to better associate the economic values to the measures of output, alternative measures of output have been proposed. Some of these measures are reviewed below. 1. Gross output (Q) Gross output is a physical volume of output (e.g. tons of steel) and the most comprehensive measure of manufacturing production. It includes sales and inventory (I) change [Phylipsen 1998]. 1 Adapted from Table 1 in Freeman [1997] 7 2. Value of shipments (VS) Value of shipment is a measure of economic activity expressed in constant dollars. VS can be calculated from current dollar value of shipments (quantity produced multiplied by current sales price) adjusted for inflation by a price index. This measure reduces the impact of inflation when comparing shipments over time. VS = (VSc)/P (Eq. 1) Where VS = Value of shipment, VSc = Value of shipment in current dollars ($ at the time of sale), P = Price index. 3. Value of production (VP) Value of production is measured in constant dollars composed of value of shipments and net additions to inventories (I) then adjust for inflation with price index (P). VP = (VSc + Ic )/P = VS+I = (Q)(Pc)/P (Eq. 2) Where VS = Value of shipment, VSc = Value of shipment in current dollars ($ at the time of sale), Q = Gross output, Ic = Value of inventory in current dollars ($ at the time of sale), I = Value of inventory at time of addition, 8 P = Price index, Pc = Price in current dollars. If changes in the price index P correctly reflect the changes in current dollar prices, then VP and Q will move together over time [Freeman 1997]. 4. Value added (VA) Value added is measured in constant dollars. It is the value of shipments less the cost of materials (CM), and adjusted for inflation. VA = (VSc  CMc)/ P = VS – CM (Eq. 3) Where VS = Value of shipment VSc = Value of shipment in current dollars ($ at the time of sale) CM = Cost of materials CMc = Cost of materials in current dollars ($ at the time of sale) P = Price index Having considered measures of input and measures of output, we return now to our more general discussion of energy intensity As shown in Table II, the US Department of Energy lists the various potential indicators of energy intensity in the manufacturing sector. Choices of which indicator of energy intensity to use vary based on the researcher’s preference and situation. 9 TABLE II ENERGYINTENSITY INDICATORS FOR THE MANUFACTURING SECTOR Recent studies by Worrell [2003] and Boyd [1997] incorporate productivity effects into the energy intensity measures to justify the benefit of investing in energy efficiency improvement measures. Both papers conclude that implementing energy management best practices in the iron and steel industries increase overall productivity of the industry. Three major studies done the between 1982 and 1994 at the plant level are most closely related to this dissertation are Turner and Parker [1982], Boyd, et al. [1992], and Boyd, et al. [1994]. Turner and Parker [1982] introduced the concept of energy accounting used as energy productivity monitoring and control measurement systems. The study uses a “oneshot” energy efficiency measures composed of energy per unit of production (Btu/unit), energy per heating or cooling degrees (Btu/degreedays), and energy per facility area (Btu/square foot) as indicators. The research used the monthly indicators to compare two or more periods of the same months, for example, February energy indicators in the past 3 years. Turner and Parker [1982] also introduced the Carborundum Accounting System where product mix effect and degreeday based heating and cooling effect are used to adjust the indicators. (Thousand Btu/1987 Dollar) Energy / Gross Output Energy / Industrial Production Energy / Value Added Energy / Gross Product Originating Energy / Value of Shipments Energy / Value of Production Energy / AdjustedCapacity Value of Production 10 The first was completed by Boyd, et al. [1992] on modeling plantlevel industrial energy demand with the manufacturing energy consumption survey (MECS). The research is a survey and Phase I of a project to help the DOE determine the applicability of the Manufacturing Energy Consumption Survey (MECS) database and the Longitudinal Research Database (LRD) for industrial modeling and analysis. The paper focuses on six industries, paper mills, alkalies and chlorine, nitrogenous fertilizers, cement hydraulic, blast furnaces and steel mills, and primary aluminum. The report also describes several measures used at the plant level, namely energy intensity and technical efficiency. The results showed that the technical efficiency and distribution of energy intensities vary significantly at the plant level. Energy prices also vary significantly at the plant level where higher energy consumption plants pay less per unit energy (i.e., dollars/kilowatt hours). The second study by Boyd, et al. [1994] examined the vintagelevel energy and environmental performance of manufacturing establishments. The report examines relationships between an industrial plant’s vintage and its energy and environmental performance. It first examines new plants in the six major energy intensive industries. The report then focuses on the steel and cement industries. The purpose of the study was to; 1. define vintage and its metrics, 2. examine the energy intensities and pollutionabatement costs at plant level for different vintages, 3. determine the affect of manufacturing industry’s vintage distribution. The Vintage was assigned on the basis of external data, and a series of analyses which involve, energy intensity, utilization of each vintage, and the share of capacity or capital stock The study also defined energy and environmental performance which incorporated the Total Factor Productivity (TFP) approach and production model approach which used the following models; 11 1. smooth factor substitution models, 2. PuttyClay models, 3. FixedCoefficient models. The models above are mentioned as additional information but are not relevant to this research and therefore not presented in detail. The production efficiency used by Boyd, et. al. [1994] incorporated five input measures including capital, labor, electricity, fuels, materials, and output. The study also defined energy intensity as; 1. Input/output ratio, 2. Energy/capacity ratio, 3. Energy/ capital stock ratio, 4. Energy/output tonnage ratio. The results of the study show that newer plants (later vintage) exhibit lower fossil fuel intensities. The most significant declines were in the steel and cement industries. 2.2 Index Numbers Index numbers are statistical averages in time series that show how values compare by using ratios of items selected as representative of all items of a class of economic data. Index numbers are usually designed to equal 100 for a base period and changes in their components are computed at regular intervals in an attempt to indicate general changes in a specific class of economic data [Greaves and Coleman 1999]. Index numbers of price show the average percentage change of prices from one point in time to another. The percentage change in the price of a single commodity from one time to another can be calculated by dividing its price at the second time by its price at the first time. The ratio between these two prices is called the relative price of that particular commodity in relation to the two times. In the same manner, the index number can be 12 used to calculate percentage change in wages, quantity of goods imported or exported, or any subject matter involving divergent changes of a group of magnitudes. The index numbers are expressed in terms of time and can be applied to compare two magnitudes of a group of elements under any one set of circumstances and their magnitudes under another set of circumstances [Fisher 1927]. Energy index analysis is a study of changes in energy efficiency indicators through time. Early researchers chose to decompose industrial energy demand by using the Divisia approach. This includes the decomposition of the aggregate energy intensity index measured in terms of energy consumption per unit output of each energy intensive industry [Ang 1995]. Later research identified and discussed the issues and problems that commonly occur in constructing energy indicators; especially due to alternative measures of output in intensity indicators [Freeman 1997]. There are currently three energy intensity indexes commonly used, Laspeyres index, Divisia index, and Fisher Ideal index. Recent research focus is at the country level down to sector level (industry level). The direction of the energy intensity index analysis points toward environmental impacts, especially green house gas. The following is an overview of the development of each of these energy intensity indexes. Laspeyres index The Laspeyres index was proposed in 1871 by a German economist Étienne Laspeyres [Wikipedia 2006]. The index was proposed for measuring current prices or quantities in relation to those of a selected base period. It is a statistical price index which is calculated from a set ("basket") of fixed quantities of a finite list of goods by assuming that we know the prices at two different points in time. The analysis proceeds as follows. Let the price index be one in period 0 (reference period), which is then the base period. Then the value of the index in the first period (period 1) is equal to this ratio: the total price of the basket of goods in period two divided by the total price of exactly the same basket in period one. As for any price index, if all prices rise the index rises, and if all prices fall the index falls [Britannica 2005]. The index 13 shows the change in cost of buying in the current period, 1, the same basket of goods as in the base period, 0. The index measures the effect of price changes when the base period consumption levels are hypothetically maintained. This assumption expresses the weakness of the index [Selvanathan and Rao, 1997]. If the reference quantities (R) are selected as the base period quantity, i.e., qR1 = q01, qR2 = q02, qR3 = q03,…, q1n = q0n then Σ Σ = = =n i i i n i i i p q p q L 1 0 0 1 1 0 01 (Eq. 4 ) Where pi1 = The cost of buying the ith good in period 1 pi0 = The cost of buying the ith good in period 0 qi0 = The quantity of ith good bought in period 0 L01 = Laspeyres index of time 0 and t This index has been one of the most popular indexes used in energy decomposition methods studies, having been used by Alcantara and Roca [1995], Ang [19871999], Chen and Wu [1995], Boyd et al. [1987], and Howarth et al. [1993]. Divisia Index The Divisia index approach was introduced by Boyd [1987] by using the Tornqvist approximation stated as reference, detail of Tornqvist approximation is not relevant to this research. The Divisia index approach has been widely used in governmental statistics of energy intensity determination at the country, sector, and subsector levels. The Divisia index approach allows a decomposition of the percentage change in energy use into separate changes in total activity, economic structure, and energy intensity at the component level. When applied to annual data, the decomposition is performed for changes from one year to the next. The resulting changes are cumulated to a time series index that is normalized to one in 14 a selected base year. The chainweighted nature of the index makes the choice of base year arbitrary from the standpoint of the percentage changes over time. Divisia indexes assume that the data on the various factors vary in more or less a continuous fashion. Liu et al. [1998] indicate that the data are assumed to be available at every moment of time, instead of only at discrete (annual, quarterly, etc.) points in time [EIA 2005]. The index has many desirable properties that are useful for decomposition analysis including variable weighting over time and additive decomposition of relative growth rates [Liu et al. 1998]. The detail of Divisia index will be described in detail in Chapter 4. Paasche index In contrast to the Laspeyres index, the Paasche index measures the effect of price changes from period 0 to 1 if current period consumption had been used in the base period. The index was proposed by Paasche [1874]. If the reference quantity is selected as current period quantity vector, i.e., q01=qR1, q02= qR2, q03=qR3,…, q0n qRn =, then Σ Σ = = =n i i i n i i i p q p q P 1 0 1 1 1 1 01 (Eq. 5) Where pi1 = The cost of buying the ith good in period 1 pi0 = The cost of buying the ith good in period 0 qi1 = The quantity of ith good bought in period 1 I01 = The index of price change between period 0 and 1 P01 = Paasche index of time 0 and t Fisher Ideal Index The Fisher Ideal Index is the most recent introduction by Boyd [2004]. The index uses the chain weighted Fisher Ideal Index to resolve the residual problem in prior 15 indices. Residual problem is discussed in Chapter 4. This index is the geometric average of the Laspeyres and Paasche indices. F L P I = I ⋅ I (Eq. 6) Where IF = Fisher Ideal index IL = Laspeyres index IP = Paashe index Index numbers are statistical averages in time series that show how values compare by using ratios. The result is the percent changes between the period of interest and the reference period. This characteristic of index numbers can be applied to energy efficiency monitoring shown in later sections of this research. 2.3 Aggregation Levels Energy decomposition methodology is a process of breaking down an entity’s energy usage in order to study the sources of process energy consumption and its characteristics. Energy consumption can be determined on various levels as shown in Figure 1 1. The nation level is an aggregated level of several sectors. 2. The level of main sectors (e.g., manufacturing industry, residential, services, transportation) 3. The level of sectors (e.g., food and drugs industry, basic metal industry) 4. Level of individual firms 5. The level of processes within subsectors or of the individual firms 16 Figure 1 The energy indicator pyramid (with sources of data)2 Economic energy indicators can be developed on each level. They are generally developed in a way that depicts changes in overall energy consumption that are decomposed into changes in activity level. There have been significant studies of economic efficiency indicators at the country, industry, and sector level by using macro economic indicators and indexes since the early 1980’s [Ang1995]. Reitler et al. [1987] analyzed the factors influencing energy consumption in industry. Reitler et al. [1987] introduced a method to determine the role of changes in energy consumption in fuel and electricity in relation to the effects on production structure and specific consumption. They also used the Specific Energy Consumption (SEC) which is a ratio between energy consumption and an index of industrial production in that period. However, since the indicators were developed, there has been no evidence that these indicators were used to develop energy efficiency indexes at the plant level by either the decomposition method down to the process level 2 Adapted from International Energy Agency, “Indicators of Energy Use and Efficiency: Understanding the link between energy and human activity”, OECD Publications, Paris 1997 17 or aggregation method from the process up to the plant level (see Figure 1 on previous page). There are several energy indicators and each is used to measure different aspect of the energy usage. A recent study by Bernard [2005] showed that there have been efforts to compile these measurements and assess the information by using a principal component analysis to assess the information derived from several energy indicators. However, due to the large number of variations, it was difficult to establish meaningful benchmarks that could be used. A study by Brown et al. [1996] on the hierarchical structure of manufacturing systems provided a preliminary assessment of the quantity and quality of waste energy that may be economically practical to recover in the industrial sector. The report covered energy utilization data for 60 fourdigit SIC (standard industrial code) industries which represent 70% of the United States industrial manufacturing energy consumption. The report documented general flow diagrams and heat and mass balance for each operation. The energy and mass balances were on a per unit basis for a each unit operation for individual industrial processes. The report also presented process temperature, pressure, fuel requirements, thermal efficiency, and radiation and convection losses for each operation. By linking this research and utilizing the process levels presented and the plant level study by Boyd [1994], a plant level index could be created by incorporating relevant information tracked over time. By applying the index number methodology, a measure can be created to represent a short interval of time and represent the plant’s overall effectiveness from an energy and environmental standpoint (but in a financially driven nature). 18 According to Phylipsen [1998]’s methodology, energy efficiency indicators are developed by the following steps: 1. Create process routes and system boundaries, 2. Develop an energy efficiency indicator pyramid for the facility, 3. Determine the data required by looking at the disaggregated levels and find potential sources which may include, 3.1 Gross output, 3.2 Value of shipments, 3.3 Value of production, 3.4 Value added, 3.5 Production index. 4. Perform energy efficiency analysis by calculating the Specific Energy Consumption (SEC) and other components to obtain the Economic Energy Efficiency Indicator. 2.4 Decomposition Methodology In general, the decomposition methodology is a process of modeling time series that exhibit trend and seasonal effects. The basic idea behind these models is to decompose the time series into several factors i.e., trend, seasonal, cyclical, and error [Bowerman and O’Connell 1987]. Decomposition of industrial energy consumption is a process of decomposing the indexes in order to study the energy impacts of structural change and energy efficiency improvements. There are two major decomposition methods commonly used to study industrial energy consumption, multiplicative decomposition and additive decomposition. 2.4.1 Multiplicative Decomposition The multiplicative decomposition method models the time series by computing or calculating the factors in a multiplicative form. This model is useful when modeling time series that display increasing or decreasing seasonal variation. Equation 7 depicts the general multiplicative decomposition model defined by Bowerman and O’Connell [1987] 19 yt = TRt · SNt · CLt · IRt (Eq. 7) where yt = The observed value of the time series in time period t, TRt = The trend component (or factor) in time period t, SNt = The seasonal component (or factor) in time period t, CLt = The cyclical component (or factor) in time period t, IRt = The irregular component (or factor) in time period t. 2.4.2 Additive Decomposition The additive decomposition method models the time series by computing or calculating the factors in an additive form. This model is useful when modeling time series that display constant seasonal variation. Equation 8 depicts the general additive decomposition model defined by Bowerman and O’Connell [1987] yt = TRt +SNt + CLt + IRt (Eq. 8) where yt = The observed value of the time series in time period t, TRt = The trend component (or factor) in time period t, SNt = The seasonal component (or factor) in time period t, CLt = The cyclical component (or factor) in time period t, IRt = The irregular component (or factor) in time period t. 20 2.5 Energy Index Decomposition methodology The index decomposition methodology was introduced during the 1970s and was used to study the changes in product mix in industrial energy demand [Bossanyi 1979 and Nakamura 1978]. Ang and Zhang [2000] described the index decomposition methodology as a technique that provides a linkage between an aggregate and the original raw data gathered from industries where the information of interest (production quantities, energy consumption, emission, etc.) is captured in a concise and usable form. The notion is similar to the economic index numbers used to study the price and quantity level changes in aggregate commodity consumption. This methodology is also referred to as index number decomposition analysis by Rose and Casler [1996]. From the previous section we learned that there are many indexes used in the index decomposition methodology. In recent research (1992 to 1999) the indexes commonly used are Laspeyres (45%) and Divisia (28%) [Ang 2000]. This research considers these two commonly used indexes. Index decomposition methodology can be classified into two major approaches, the energy consumption approach and the energy intensity approach. A general framework from Ang [1994] is shown in Figure 2 on the next page. The energy consumption approach uses the decomposition technique to study changes in overall (total) industrial energy consumption over a period of time. The technique incorporates changes in aggregate production (production effect), production structure (structural effect) and sectoral energy intensities (intensity effect). The energy intensity approach methodology uses the decomposition method on the changes in the aggregate energy intensity (not the total consumption) and can be divided into several methods. 21 Figure 2 General framework of the index decomposition methodologies3 This research uses these common index decomposition methods and extends them to the plant level. Ang and Zhang [2000] concluded that in the last decade, the Laspeyres and the arithmetic mean Divisia index methods have been the two most often used decomposition methods. This research will use this argument to focus on these two index methods. 2.5.1 Aggregate Energy Consumption Approach The Aggregate Energy Consumption approach was used by Liu et al. [1992] who studied the Divisia index in detail. They also proposed a new method based on this index called the Adaptive Weighting Divisia method. The paper’s emphasis was on the methodological aspect of decomposition. However, the results of a study using the data of Singapore were shown to illustrate the application and the associated statistical problems of other existing methods. The use of the Divisia index in the decomposition of changes in industrial energy use was first introduced by Boyd et al. [1987 and 1988] but they did not discuss the integral path problem. The research by Liu et al. [1992] expanded the 1980's research where the decomposition is based on a finite number of industrial sectors. The study was mentioned by Ang and Lee [1994] who summarized the five main energy consumption approaches including Laspeyres/Paasche Method, MarshallEdgeworth Method, Simple Average Divisia Method, Parametric Divisia 3 Adapted from Ang [1994] 22 method, and Adaptive Weighting Divisia method. These methods are mentioned as an example, they do not pertain to this research. 2.5.2 Aggregate Energy Intensity Approach Aggregate energy intensity is the ratio of total industrial energy consumption to industrial output. The energy intensity approach is the decomposition of changes in the energy intensity into contributions from structural and intensity effects. The energy intensity approach has been used in a large number of empirical and country specific studies. Examples of such studies are Bossanyi [1979], Jenne and Cattell[1983], Ang [1987], Li et al. [1990], Gardner [1993] and Huang [1993]. While Liu et al. [1992] and Ang and Lee [1994] have studied the general methodological and application issues related to the energy consumption approach, similar studies for the energy intensity approach were not reported until Ang [1994]. Based on the energy intensity approach, two parametric Divisia methods were introduced by Ang [1994] as parallel methods to the energy consumption approach by Liu et al. [1992] with the formulations in both multiplicative and additive forms. Ang [1994] then consider the five specific methods that are equivalent to those considered in Ang and Lee [1994]. Comparisons were also made between the energy intensity approach and the energy consumption approach in actual application. Empirical results obtained using time series data for Singapore and Taiwan were presented to illustrate the issues raised. Ang [1994] introduced two general parametric Divisia methods based on the energy intensity approach, which are equivalent to those given in Liu et al. [1992] and describe their formulation in the multiplicative and additive forms. Ang [1994] then considered the five specific methods which are equivalent to those considered in Ang and Lee [1994]. The parametric Divisia index method allows a decomposition of the percentage change in energy use into separate changes in total activity, economic structure, and energy intensity at the component level. When applied to annual data, the decomposition is 23 performed for changes from one year to the next. The resulting changes are cumulated to a time series index that is normalized to one in a selected base year; this is referred to as the chainweighted nature of the index which makes the choice of base year subjective from the standpoint of the percentage changes over time. The Divisia indexes assume that the data on the various factors vary in more or less a continuous fashion. Liu et al. [1998] formally indicated that the data are assumed to be available at every moment of time, instead of only at discrete (annual, quarterly, etc.) points in time. Liu et al. [1998] indicated that the Divisia index has many desirable properties that are useful for decomposition analysis. These properties include variable weighting over time and additive decomposition of relative growth rates. However, decomposition based upon a general Divisia index approach does not yield a unique set of results because one can develop an infinite number of indexes, each corresponding to assumptions as to how the factors change between the observed discrete points in time. 2.5.3 Selection of approach (Energy intensity or consumption) Ang [1995] described the differences between intensity and consumption as the result of presentation and interpretation. In time series analysis, the energy intensity approach has the advantage of simplicity of results presentation because its estimated effects are typically expressed in indexes. Alternatively, particularly in periodwise decomposition, the results given by the additive energy consumption approach can be easily understood by nonspecialists because the results are expressed in energy units. The energy consumption approach is being not as appropriate as the energy intensity approach when studying the impact of structural change. In energy demand projection, an approach called energy elasticity approach is useful when elasticity estimates are needed to extrapolate future energy demand trends. When studying the energy consumption approach and the energy intensity approach, Ang [1995] suggested that the differences 24 between multiplicative and additive forms are minor. However, in the case of the energy elasticity approach, the multiplicative technique is superior to the additive forms. 2.5.4 Selection of method Similar to general index decomposition methodology described in the prior section, the index decomposition methodology in energy consumption can be divided into multiplicative and additive index decomposition methodologies (Figure 2 Page 20). The decomposed factors are structural effect and efficiency effect as shown in equations 9 and 10. Dtot = Dstr · Dint (Eq. 9) Itot = Istr + Iint (Eq. 10) where Dtot = Total change in overall energy usage (activity index) in time period t from multiplicative decomposition methodology, Dstr = Impact from structural change in time period t from multiplicative decomposition methodology, Dint = Impact from energy intensity change in time period t from multiplicative decomposition methodology, Itot = Total change in overall energy usage (activity index) in time period t from additive decomposition methodology, Istr = Impact from structural change in time period t from additive decomposition methodology, Iint = Impact from energy intensity change in time period t from additive decomposition methodology. The activity index (Itot) shows the changes in the level of activity for a sector of the economy. The units used to measure activity differ by sector (e.g., square footage of floor space, industrial production measured in dollars, passengermiles). Energy intensity indexes represent the effect of changing energy intensity for subsectors or detailed components of the economy. The structural index shows the effect of changing economic structure. This index is employed at higher levels of the indicators hierarchy and reflects 25 the impact on energy use of changes in the relative importance of sectors at lower levels of the hierarchy. It primarily shows the impact of shifts in the composition of sectors or subsectors with different absolute energy intensities. Since this research focuses on the plant level, the structural index refers to the percentage of product which is produced during a period i.e., changes in product mix. By following the procedures from Lermit and Jollands [2001] and Lui et al. [1998] via EIA [2005] we can demonstrate the index decomposition methodology. Consider the rate of change of total energy used for a particular sector of the economy where total energy (E) is expressed as the sum of the energy use for each of the components or subsectors within that sector. Typically, the component intensity is defined in terms of the available data as Ei/Ai. Thus, energy use for each component i can be represented as the product of activity (Ai) and the energy intensity in component i (Ii). Formally, we have =Σ =Σ i i i i i E E A I (Eq. 11) where Ai = Product of activity for component i, Ii = Energy intensity for component i, Ei = Energy use to produce component i, E = Total energy usage. Assume that the activities for each of the components are measured in similar units (e.g., dollars, passengermiles). Thus, total sector activity A is the sum of the activity levels for the components. If we express the share of the total sector’s activity for component i (Ai/A) as Si, Equation 11 can be rewritten as: =Σ i i i E AS I (Eq. 12) where A = Total sector activity, Ii = Energy intensity for component i, Si = Share of total sector’s activity for component i, E = Total energy usage. 26 The derivative of equation 12 with respect to time is ( ) dt AS dI dt AI dS dt S I dA dt dE i i i i i i i i i = Σ +Σ +Σ (Eq. 13) If we divide both sides of equation 13 by E, and perform the same manipulation to each of the terms on the right side, the entire expression can be recast in terms of logarithms or percentage growth rates of each of the variables ⎟⎠ ⎞ ⎜⎝ ⎛ = = Σ +Σ +Σ dt AS I d I dt AS I d S dt AS I d A dt E d E dt dE E i i i i i i i i i i i 1 ln 1 ln ln ln (Eq. 14) Because i i i i w E E E AS I = = (Eq. 15) Where wi = Share of energy consumed by component i . We can see that the growth rate of total energy is the energyweighted average of the growth rate of each of the factors: ⎥⎦ ⎤ ⎢⎣ =Σ ⎡ + + dt d I dt d S dt w d A dt d E i i i i ln ln ln ln (Eq. 16) While equation 16 holds instantaneously, it must be integrated over a discrete time period to yield a useable result. In general terms, this integration over the interval 0 to T generates ( ) dt dt E E w d A i T T =Σ∫ i 0 0 ln / ln [Activity effect (Dact)] (Eq. 17) + dt dt w d S i T i i Σ∫0 ln [Structural effect (Dstr)] + dt dt w d I i T i i Σ∫0 ln [Intensity effect (Dint)] 27 The logarithmic or percentage change in total energy consumption between any two points in time (Dtot) can therefore be decomposed into three effects. Dtot ~ Dact + Dstr + Dint (Eq. 18) An approximate solution to these integrals can be obtained by selecting an appropriate function of the end points at time 0 and T (Dtot) is an approximation because of the residual). This results in the following general expressions for each of the effects ) 0 D w* ln(A / A T i act i ⎟⎠ ⎞ ⎜⎝ ⎛ = Σ (Eq. 19) ln( / ) , ,0 * i i str i i T D =Σw S S (Eq. 20) ln( / ) , ,0 * int i i i i T D =Σw I I (Eq. 21) Depending upon the nature of the solution method, the three effects may not exactly sum to the total change, yielding a small residual term in equation 18. A solution yielding no residual term is defined as perfect decomposition where residuals are blended in the coefficients of the total change. The weights * i w in equations 19 – 21 are derived by an averaging of the initial and terminal shares of energy used in each of the components. How this averaging is performed reflects an assumption about the unobserved path of the variables A, S, and I between the initial and end periods. The most straightforward assumption is to assume that the path is linear between the end points; in this case the weights are defined ( ) / 2 ,0 , * i i i T w = w + w (Eq. 22) The choice of these weights results in what has been termed an Arithmetic mean Divisia approach. While easy to apply, this is an imperfect decomposition method and normally results in a small residual in equation 18; thus the sum of the three effects may not precisely equal the total change in energy use. 28 Ang and Choi [1997] proposed an advanced Divisia method that results in no residual, and thus yields a perfect decomposition of the effects. Their solution was to base the weights on what is termed a logarithmic mean function of the shares. The logarithmic mean of any two variables is defined as L(x,y) = (y – x)/ln(y/x) (Eq. 23) As applied to the energy consumption shares, the logarithmic mean function is defined L(wi,0, wi,T) = (wi,T  wi,0) / ln(wi,T / wi0) (Eq. 24) The final weights * i w are based upon a normalization that ensures that they exactly sum to one: * wi = L(wi,0,wi,T) / ( , ) ,0 i,T i i ΣL w w (Eq. 25) Lermit and Jollands [2001] provide a proof that this formulation of the weights yields no residual term, regardless of how the specific values of the variables vary over time. The use of the logarithmic mean Divisia method implies that all of the variables are growing at constant growth rates between the initial and terminal periods. Thus, the method assumes that unobserved values between the two periods lie on a path defined by an exponential growth curve. 29 2.5.5 Construction of Time Series Index Decomposition Method While the Divisia index decomposition method can be applied over any time period, it is applied to annual observations in this system of energy intensity indicators. The logarithmic change in energy use between each pair of successive years is decomposed using the log mean Divisia method, yielding the terms shown in equation 18. By implicitly setting the first of the two years equal to 1.0, an index number for the second year is obtained by taking the exponential of each of the terms as follows: Exp (Deng) = Exp (Dact + Dstr + Dint) = (Iact) ⋅ (Istr) ⋅ (Iint) (Eq. 26) where Iact = Exp(Dtot), Istr = Exp(Dstr), and Iint = Exp(Dint), Iact = Activity index, yearoveryear, Istr = Structure index, yearoveryear, Iint = Intensity index, yearoveryear. For each effect, the indexes are then chained to form a time series for the available data period. Ang [1998] introduces the method of factorizing changes in energy and environmental indicators through decomposition because of the following: 1. Perfect decomposition, 2. Factor changes in energy demand or gas emissions, 3. Handle zero values in data sets. Ang [1998] also indicates that the main objective of decomposition analysis is to quantify various underlying factors that contribute to changes in energy and environmental indicators over time. Two common approaches are decomposition of an aggregate index (energy intensity approach) where the aggregate index is given by dividing the aggregate intensity of one year, such as the ratio of industrial energy demand to industrial output. 30 This leads to estimates of factorized effects given in indexes. The other approach is the decomposition of differential quantity (consumption approach). This decomposition is a direct decomposition of a change in energy demand or gas emissions between two different years in physical terms. This change of quantity is given in the chosen measurement unit for energy demand or gas emissions, 2.6 Conclusion Index decomposition methods have been used to study energy usage for decades. The most widely used ones are derived from Divisia and Laspeyres index methodologies. This research seeks to extend the use of these methodologies into plant level studies to study the impacts of main energy consuming equipment to the total plant wide energy usage from a production and financial view. 31 CHAPTER III STATEMENT OF RESEARCH 3.1 Problem Statement There is a need for a standard methodology to develop a facilitylevel energy performance monitoring index that is independent of product mix that can be used to identify the energyside production efficiency as the product is being produced as well as the ability to monitor the changes of that measure over a period of time as part of a realtime commissioning and recommissioning effort. 3.2 Research Goals There is a need for more effective facilitylevel energy performance monitoring that is independent of product mix. The goal of this research is to address this problem by focusing on the following: 1. Develop an index number decomposition methodology to use as a facilitylevel energy performance monitoring index from existing higher level index number decomposition methodologies. 2. Use the developed index number to identify the energyside production efficiencies over time and that, with additional research, can be used to monitor the efficiency changes over a period of time as a part of a realtime commissioning and recommissioning effort. 32 3.3 Major Research Tasks To accomplish the goals, the major research tasks are identified as followed 1. Study the available index decomposition methodologies and select the potential ones to study in detail and use as a prototype to modify and use at the plant level. 2. From the selected existing energy intensity index methodologies, develop procedures to use the intensity index number as a facilitylevel energy performance monitoring. 3. Evaluate the methodology by using actual data by developing a simulation model which mimics a brick manufacturing plant. The simulation model uses equations from Jeschar and Bittner [1989] and evaluated by comparing the data output of the model with published journals on brick energy consumption by Prasertsan et al [1995], and Prasertsan and Theppaya [1995]. The energy intensity index is then used to monitor the energy usage. The model also reflects various weather, product mix, and efficiency deterioration scenarios. 3.4 Research Boundaries 1. The manufacturing plants presented in this research refer to manufacturing plants with flow shop or continuous flow production of one product type at a time or with the capability to submeter the individual product lines. Specifically, a brick manufacturing model is used in this research. 2. Index methodologies explored in this research are limited to Divisia and Laspeyres techniques due to their popularity in the past decade (see literature review). 3. The research will also recognize the weather impact. 33 CHAPTER IV METHODOLOGY 4.1 Introduction The goal of this research is to develop an energy index decomposition methodology used at the plant level to use as an energy performance monitoring tool. The research utilizes the existing sector time series index decomposition methods to generate an energy intensity index at the plant level. Traditional systems of energy intensity indicators are designed to track the changes in energy intensity for a total country’s economy, broad end use sectors, and subsectors. The proposed research will study the existing index number decomposition methodologies as plantlevel energy utilization monitoring tools. 4.2 Research Plan To accomplish the goal and objectives described above, the research was broken into phases. Phase I: Develop procedures to systematically identify input variables to be used as the facility’s energy monitoring input. Task 1 Develop a simple plant energy consumption model. The information needed is composed of historical data collected monthly over the past 3 years as follows: 1. Product type, 2. Quantity produced, 3. Cost of goods sold associated with each product type, 4. Monthly energy usage. 34 Task 2 Define product output as the number of production units and energy intensity as energy used per unit of production. Task 3 Identify sources of process energy input (electricity, natural gas, other fuel). Task 4 Develop a plant energy model to test the sensitivity of the indexes against 1. Trending (steepness) a. Mild b. Moderate c. Strong 2. Weather impact a. Mild (Houston, TX) b. Moderate (Oklahoma City, Oklahoma) c. High (Minneapolis, Minnesota) 3. Product mix and effects of product mix toward energy intensity index a. Equally produced b. High intensity c. Low intensity Phase II: Select the index decomposition methodologies Task 1 Define the potential existing index decomposition methodologies to be used in this research as Log Mean Divisia Additive method and Refined Laspeyres energy intensity approaches. Task 2 Use an S+ program4 to fit a time series ARIMA model to each index decomposition methodology and use AIC (Akaike Information Criterion), explained in Chapter 6 to justify the best model for each index. From the fitted model, plot the innovation (residual) by using S+. Acceptable time series models should have low AIC and random 4 S+ or SPLUS is a statistical software (language similar to MATLAB) developed by Insightful Inc. mainly used to analyze time series and predictive statistics 35 innovation plots. Tests of randomness will follow the LjungBox test at 95% confidence level explained in Chapter 6. Select 3 out of 7 methodologies that have the least complicated forms of ARIMA model and highest average absolute amplitude (most sensitive) when plotted on a time series graph. Phase III: Test the index methodologies on a model Test the proposed index decomposition methodology on the actual data obtained from a brick manufacturing model developed by Jeschar and Bittner [1989]. Phase IV: Formulate framework for future research In future research, this methodology is potentially useful as a time series production energy efficiency monitoring tool to detect irregularities in production energy usage or as a part of a realtime commissioning effort. Specific ideas with respect to these potential uses will be documented. Proposed usage of Index Decomposition Methods (ID) Since the concept presented in this research is similar to the application of index numbers to study the contributions of price and quantity levels to changes in aggregate commodity consumption, we present an index decomposition methodology (ID) framework using the index number concept. In general, ID can be performed as long as the aggregate indicator being studied, V, can be expressed in the form: =Σ m i i i in V X X ...X 1 2 where i= 1, 2, …, n (Eq. 27) where the first subscript of X denotes the ith sector among a total of m sectors and the second subscript denotes n different factors. The purpose of ID is to decompose a change in V into individual effects associated with the variation of each of the factors Xi1, Xi2, …, Xin [Ang and Zhang 2000]. This research will focus on two of the most popular indexes, Log Mean Divisia, and refined Laspeyres indexes proposed by Sun [1998]. 36 Log Mean Divisia Index (LMDI) The Log Mean Divisia index technique in additive form was proposed by Ang et al. [1998] and multiplicative form by Ang and Lui [2001]. These are commonly referred to as LMDI I. Ang and Choi [1997] and Ang et al. [2003] proposed LMDI II additive and multiplicative respectively. Both are perfect decomposition techniques which yield no residuals, the only difference is the weight function. Let =Σ i i i i ni V X X ...X 1 2 ; i= 1, 2, …, n (Eq. 28) Where Vi = Aggregate of interest i, which composed of n factors X = Attributes of interest (subscript i) denotes an attribute of the aggregate such as energy consuming sector, fuel type, etc. Therefore, from year 0 to year T; the aggregate changes from 0 0 2 0 1 0 ... i i i ni V =Σ x x x (Eq. 29) to T ni T i T i i V T x x ...x 1 2 =Σ (Eq. 30) We then have in perfect decomposition Multiplicative D = VT/V0 = Dx1 ⋅ Dx2…⋅ Dxn (Eq. 31) Additive ΔV = VT V0= ΔVx1 + ΔVx2+…+ ΔVxn (Eq. 32) where D = Multiplicative decomposition of changes via Divisia index, ΔV = Additive decomposition of changes via Divisia index. 37 Based on the proposed decomposition methodology by Ang et al. [1998] and Ang and Lui [2001] the LMDI I formula is as follows LMDI I (multiplicative) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = Σ 0 , , 0 0 ln ( , ) exp ( , ) k i T k i i T i T i xk x x L V V D L V V (Eq. 33) LMDI I (additive) Σ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Δ = i k i T k i i T xk i x x V L V V 0 , ( , 0 )ln , (Eq. 34) Based on the proposed decomposition methodology by Ang and Choi [1997] and Ang et al. [2003], the LMDI II formula is as follows: LMDI II (multiplicative) ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ΣΣ i k i T k i j j Tj i T i xk x x L w w D L w w 0 , , 0 0 ln ( , ) exp ( , ) (Eq. 35) LMDI II (additive) Σ Σ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Δ = i k i T T k i j j Tj i T i xk x x L V V L w w V L w w 0 , 0 , 0 0 ( , ) ln ( , ) ( , ) (Eq. 36) where T i w = T T i V /V , 0 i w = V 0 /V 0 i , L(a,b) = the logarithmic average of two positive numbers a and b given by a b L a b a b ln ln ( , ) − − = for a ≠ b = a for a=b (Eq. 37) 38 As mentioned earlier, the LMDI I and LMDI II are similar and the only difference is the weight function as followed: Multiplicative decomposition: ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = Σi k i T k i xk i x x D W 0 , exp * ln , (Eq. 38) Additive decomposition: Σ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Δ = i k i T T k i xk i x x V W L V V 0 , * ( , 0 )ln , (Eq. 39) where * i W = L(V ,V 0 )/ L(V T ,V 0 ) i T i in LMDI I, * i W = ( ) Σ ( ) j j Tj i T i L w ,w0 / L w ,w0 in LMDI II. 39 Refined Laspeyres Technique The refined Laspeyres technique is an improved Laspeyres technique and was improved by Sun [1998]. The Refined Laspeyres is only available in the additive decomposition method (no multiplicative technique research published to date). The total change in aggregate energy intensity can be written as Δ =Σ −Σ i i tot i T i T i i I S I S I , , ,0 ,0 ( ) ( ) ( )( ) , ,0 ,0 , ,0 ,0 , ,0 i,T i,0 i i i T i i i i T i i i T i =Σ S − S I +Σ I − I S +Σ S − S I − I (Eq. 40) where Et = Total industrial energy consumption, Ei,t = Energy consumption in industrial sector i, Yt = Total industrial production, Yi,t = Total industrial production sector i, Si,t = Production share of sector i (= Yi,t/Yt), It = Aggregate energy intensity (=Et/Yi,t), Ii,t = Energy intensity of sector i(=Ei,t/Yi,t). Note that ΔI is similar to ΔV of the Divisia additive decomposition method but is an aggregate intensity where as ΔV is an aggregate of the indicator being studied (intensity included). When the variations in variables Si and Ii are large, the residual/interaction is large. By splitting it equally between the two main effects, the formulae become: ( )( ) 2 ( ) 1 , ,0 ,0 , ,0 i,T i,0 i i i T i i str i T i ΔI =Σ S − S I + Σ S − S I − I (Eq. 41) ( )( ) 2 ( ) 1 int , ,0 ,0 , ,0 i,T i,0 i i i T i i i T i ΔI =Σ I − I S + Σ S − S I − I (Eq. 42) 40 where Et = Total industrial energy consumption, Ei,t = Energy consumption in industrial sector i, Yt = Total industrial production, Yi,t = Total industrial production sector i, Si,t = Production share of sector i (= Yi,t/Yt), It = Aggregate energy intensity (=Et/Yi,t), Ii,t = Energy intensity of sector i(=Ei,t/Yi,t). 41 CHAPTER V PLANT LEVEL ENERGY CONSUMPTION MODEL DEVELOPMENT 5.1 Introduction In order to study the energy intensity index according to Chapter 4, a plant level energy consumption model needs to be constructed. As defined in Chapter 4, one of the well known flowshop process is brick manufacturing process. The process is relatively straightforward. 5.2 Brick manufacturing process and building the model Process understanding [Kolarik 1999] helps a researcher gain insights of how energy is being used in the process and permits identification of critical variables (leverages) associated with energy usage. A Brick manufacturing process5 includes mixing ground clay with water, forming them into the desired shapes, then drying and firing them. There are six general phases in making bricks shown in Figure 3 on the next page 1. winning and storage of raw materials (shale clay), 2. preparing raw materials (crushing, grinding, screening and classifying), 3. forming units, 5 http://www.bia.org/BIA/technotes/t9.htm 42 4. drying, 5. kiln firing and cooling, 6. drawing and packing finished products. Figure 3 Diagrammatic representation of brick manufacturing process Winning and Storage Surface clays, shales and some fire clays are mined in open pits with power equipment. The clay or shale mixtures are then transported to plant storage areas. It is common practice to store enough raw materials for several days' operations. The materials then go through the blending process for more uniform raw materials, helps to control color and Crushing & Grinding Screening & Classifying Forming Dryer Kiln Cooler Packing Elec. Elec. Elec. Elec. Elec. Elec. Elec. Gas. Gas. Shale & Clay Bricks 43 permits some control over raw material suitability for manufacturing a given type of brick. Preparation The clay is crushed to break up large chunks and remove stones then ground prior to mixing other raw material. Most plants then screen the clay, passing it through inclined vibrating screens to control particle sizes. Forming The material goes to the Tempering process which produces a homogeneous, plastic mass ready for molding. It is most commonly achieved by adding water to the clay in a pug mill, a mixing chamber which contains one or more revolving shafts with blades. After pugging, the now plastic clay mass is ready to go to the forming step. At the present time, there are three principal processes for forming brick: the stiffmud, the softmud and the drypress processes. Extrusion process In the stiffmud process (extrusion process), clay is mixed with only sufficient water to produce plasticity, usually from 12 to 15 percent by weight. After thorough mixing, i.e., "pugging", the tempered clay goes through a deairing chamber in which a vacuum of 15 to 29 in. (375 to 725 mm) of mercury is maintained. Deairing removes air holes and bubbles, giving the clay increased workability and plasticity, thus resulting in greater strength. Next, the clay is extruded through a die to produce a column of clay in which two dimensions of the final unit are determined. The column then passes through an automatic cutter to make the final dimension of the brick unit. As the clay column leaves the die, textures or surface coatings may be applied. Drying process When wet clay units come from molding or cutting machines, they contain from 7 to 30 percent moisture, depending upon the forming method. Before the firing process begins, 44 most of this water is evaporated in dryer chambers at temperatures ranging from about 100°F to 400°F (38°C to 204°C). Drying time, which varies with different clays, is usually from 24 to 48 hr. Although heat may be generated specifically for dryer chambers, it is more commonly supplied as exhaust heat from firing kilns. In all cases, heat and humidity must be carefully regulated to avoid excessive cracking in the product. Firing and Cooling. Firing, one of the most specialized steps in the manufacture of brick, requires from 40 to 150 hr. depending upon kiln type and other variables. Several kilns are in use, the chief types being tunnel and periodic kilns. Fuel may be natural gas, coal, oil, sawdust, propane or combinations of these fuels. Dried units are set in periodic kilns according to a prescribed pattern that permits free circulation of hot kiln gases. A periodic kiln is one that is loaded, fired, allowed to cool and unloaded, after which the same processes are repeated. In a tunnel kiln, units are similarly loaded on special cars which pass through various temperature zones as they travel through the tunnel. The heat conditions in each zone are carefully controlled and the kiln operates continuously. Firing may be divided into six general stages: 1) watersmoking (evaporating free water), 2) dehydration, 3) oxidation, 4) vitrification, 5) flashing and 6) cooling. All except flashing and cooling are associated with rising temperatures in the kiln. Although the actual temperatures will differ with the clay or shale, watersmoking takes place at temperatures up to about 400°F (204°C), dehydration from about 300°F to 1,800°F (149°C to 982°C), oxidation from 1000°F to 1800°F (538°C to 982°C) and vitrification from 1,600°F to 2,400oF (871°C to 1,316°C). The rate of temperature change must be carefully controlled, depending on the raw materials, as well as the units being produced. Kilns are normally equipped with recording pyrometers or other temperature sensors to provide a constant check on the firing process. Near the end of the firing process, the units may be "flashed" to produce color variations. 45 After the temperature has reached the maximum and is maintained for a prescribed time, the cooling process begins. Fortyeight to 72 hr are required for proper cooling in periodic kilns; but in tunnel kilns, the cooling period seldom exceeds 48 hr. Because the rate of cooling has a direct effect on color and because excessively rapid cooling will cause cracking and checking of the ware, cooling is an important stage in the firing process. Drawing. Drawing is the process of unloading a kiln after cooling. It is at this stage that units are sorted, graded, packaged and taken to a storage yard or loaded onto rail cars or trucks for delivery. The majority of brick today are packaged in selfcontained, strapped cubes, which can be broken down into individual strapped packages for ease of handling on the jobsite. The packages and cubes are formed in such a manner as to provide openings for handling by fork lifts. Brick manufactured and selected to produce characteristic architectural effects resulting from nonuniformity in size, color and texture may not lend themselves to selfcontained packaging, and are usually shipped on wooden pallets. 5.3 Brick Model Construction and Evaluation When building a process model, there are two fundamental issues that need to be explored simultaneously, general principles and specific variables [Kolarik 1999]. Brick manufacturing uses various technologies but the major principle is a process of converting clay into brick via thermo reactions in the kiln (fusion process). Several major variables play a role in this process namely brick type, outside air condition, and processing time. Table III on the next page shows general brick energy intensity. The table shows that the kiln process uses approximately 90% of total energy usage. For simplification, the model can be reduced to the kiln process. 46 TABLE III BRICK ENERGY CONSUMPTION [BROWN 1996] No. Process Subprocess Elec. (Btu/lb) Gas(Btu/lb) Total (Btu/lb) % energy usage 1 Crushing 10 10 0.4% 2 Screening Separation 3 3 0.1% 3 Forming Extrusion 61 61 2.3% Soft plastic forming 61 61 2.3% Dry press forming 61 61 2.3% 4 Drying 2 29 31 1.2% 5 Kiln 64 2300 2364 89.9% 6 Cooling 36 36 1.4% 7 Packing 2 2 0.1% Total 2629 100.0% Kiln, dryer, and cooler mass and energy equation by Jeschar and Bittner [1989] of the process is ( ) ( ) ( ) ( )v G G U G U LE L E U LE U B u S S S U T T t U S R m C T T m C T T Q m h m C T T m C T T m h • − • − • • − • − • • + ⋅ − + ⋅ − + ⋅ = ⋅ ⋅ − + ⋅ ⋅ − + ⋅Δ 1 ,1 1 , ,3 1 3 ,3 1 3 (Eq. 43) Where B m • = Mass flow rate of natural gas in kg/second S m • = Mass flow rate of brick in kg/second T m • = Mass flow rate of transport in kg/second 1 G m • = Mass flow rate of gas in kg/second LE m • = Mass flow rate of air out of the kiln in kg/second u h = Lower calorific value (lower heating value) of natural gas in kJ/kg S,3−1 C = Specific heat of brick in kJ/kgsec T ,3−1 C = Specific heat of transport in kJ/kgsec G U C ,1− = Specific heat of gas in kJ/kgsec 47 L E U C , − = Specific heat of air in kJ/kgsec S 3 T = Temperature of brick at stage 3 in °C G1 T = Temperature of gas at stage 1 in °C U T = Ambient temperature in °C t3 T = Temperature of transport at state 3 in °C LE T = Temperature of air exiting in °C k T = Temperature of kiln in °C D T = Temperature of brick exiting the dryer in °C η = Overall kiln efficiency (includes but not limited to heat loss and combustion) R Δh = Specific reaction enthalpy during the drying process v Q • = Kiln energy consumption in kJ/second v Q • = Heat loss By only focus on the kiln, Equation 43 can be modified into Equations 44 and 45. ( ) ( ) [ (1,778 )] 1 − • • • − − ⋅ ⋅ ⎥⎦ ⎤ ⎢⎣ = ⎡ ⋅ ⋅ − + ⋅ ⋅ − mG mS CS Tk TD mT CT Tk TD CG Tk TLE (Eq. 44) ( ) ( ) η (25 ) ⋅ 1 ⎥⎦ ⎤ ⎢⎣ = ⎡ ⋅ − + ⋅ ⋅ − + ⋅ ⋅ − • • • • k G G U S S k D T T k D Q m C T m C T T m C T T (Eq. 45) The kiln model is constructed in SPlus, assuming bake time of 48 hours. In order to study the process leverages, the model composed of three variations, weather impact, product mix impact, and efficiency (trending) impact. Weather impact uses average daily outside temperature of three locations for mild, medium, and high at near sea levels. These locations are as followed Mild climate impact: Houston, TX Medium climate impact: Oklahoma City, OK High climate impact: Minneapolis, MN 48 Production mix impact studies the variation in energy consumption due to changes in product mix. In general, brick bake temperatures can vary from 800°C to 1200°C depending on the product requirements. In this model, temperatures of the kiln are set at Product type 1: 900°C Product type 2: 1,000°C Product type 3: 1,100°C The model is set to run at three product mixtures, high, medium, and low for 48 hours (2 days). A uniform distribution random number generator is used to generate production schedules composed of three product types. The product mix with high temperature requirements composed of 50% more chance of product type 3 then the other two. The product mix with medium temperature requirement has an equal chance of producing all three products, and product mix with low temperature requirement has 50% more chance of product type 1 than the other two. One of the objectives of this research is to study the efficiency deterioration over time. An artificial trend is created to test the response of the brick model. The trend increases overtime (efficiency decreases). Initial efficiency was set at 80%. Trend increases in a straight line manner over 3 years in 3 levels, mild, medium, and high. The model validation is done by compare the energy intensity of the output in kJ/kg to brick energy intensity studies by Jeschar and Bittner [1989], Prasertsan et al [1995], and Prasertsan and Theppaya [1995]. Name convention of the calculated energy intensity index is as follows: Index Intensity Ambient temp Trend Product mix L, A I H, M, L H, M, L H, M, L L: Laspeyres index (first digit only) A: Log Mean DivisiA index I: Intensity H: High M: Medium L: Low 49 For example, LIHML represents Laspeyres intensity index for high ambient temperature impact (Minneapolis, MN), medium efficiency deterioration, and composed mostly with product with low temperature kiln requirements. Full simulation scenarios are shown in Table IV and V. TABLE IV SIMULATION SCENARIOS FOR REFINED LASPEYRES ADDITIVE ENERGY INTENSITY INDEX Small Medium Large Small LILLL LILML LILHL Weather Medium LIMLL LIMML LIMHL Large LIHLL LIHML LIHHL Small Medium Large Small LILLM LILMM LILHM Weather Medium LIMLM LIMMM LIMHM Large LIHLM LIHMM LIHHM Small Medium Large Small LILLH LILMH LILHH Weather Medium LIMLH LIMMH LIMHH Large LIHLH LIHMH LIHHH Mix medium Mix Small Mix Large Trend Trend Trend TABLE V SIMULATION SCENARIOS FOR LOG MEAN DIVISIA ADDITIVE ENERGY INTENSITY INDEX Small Medium Large Small AILLL AILML AILHL Weather Medium AIMLL AIMML AIMHL Large AIHLL AIHML AIHHL Small Medium Large Small AILLM AILMM AILHM Weather Medium AIMLM AIMMM AIMHM Large AIHLM AIHMM AIHHM Small Medium Large Small AILLH AILMH AILHH Weather Medium AIMLH AIMMH AIMHH Large AIHLH AIHMH AIHHH Mix Small Mix medium Mix Large Trend Trend Trend 50 5.4 Calculation Example Table VI shows an example of a manufacturing plant which produces two product types in two years period. In year 0, Product type 1 used 8 MBtu (8,000 Btu) of energy to produce 10 pounds of product and Product type 2 used 20 MBtu of energy to produce 40 pounds of product. This resulted in energy intensity to produce product type 1 and types 2 are 0.8 and 0.5 respectively. We can observe that product type 1 is more energy intensive (energy used per pounds of product) than product type 2. In year 1, Product type 1 used 35 MBtu of energy to produce 50 pounds of product and Product type 2 used 16 MBtu of energy to produce 40 pounds of product. Both energy intensities of both products reduce from 0.8 to 0.7 for product type 1 and 0.5 to 0.4 for product type 2. However, the total facility energy intensity increases by from 0.56 to 0.57. TABLE VI EXAMPLE CALCULATIONS OF REFINED LASPEYRES AND LOG MEAN DIVISIA INDEXES E = Energy consumption (MBtu) Y = Production (Lb) S = Production share of product types I = Aggregate energy intensity Year 0 Year 1 E0 Y0 S0 I0 ET YT ST IT Product type 1 8 10 0.20 0.8 35 50 0.56 0.7 Product type 2 20 40 0.80 0.5 16 40 0.44 0.4 Plant wide 28 50 1 0.56 51 90 1 0.57 After applying plant level additive index decomposition methods shown in Table VII on the next page Figure 4 on the following page confirmed that there has been an increase in the plant level energy intensity as shown that the index (ΔItot) is positive. The structural energy intensity indexes (ΔIstr) for both are positive. This reflects the increase in energy intensity (0.11 and 0.10) of the product mix (product type 1 and product type 2). However, the energy intensity indexes ΔIint of both Refined Laspeyres and Log Mean Divisia are negative (0.1 and 0.096 respectively) which indicated that the overall plant has improved in production energy efficiency. 51 TABLE VII EXAMPLE CALCULATIONS OF REFINED LASPEYRES AND LOG MEAN DIVISIA INDEXES Index Decomposition (Additive) Refined Laspeyres Log Mean Divisia ΔI tot 0.007 0.007 ΔI str 0.11 0.10 ΔI int 0.100 0.096 Figure 4 Decomposition of total energy intensity into structure and intensity effects From the example we can conclude that due to the expansion of production share of product type 1, which is a more energy intensive than product type 2, the plant aggregate energy intensity increase by 0.7%. Despite improvements in energy efficiency (negative value) as reflected by the changes in overall production energy intensity (ΔI int). Since the impact of changes in production mix is more significant, it leads to an increase in aggregate energy intensity. Plant level energy intensity index (Itot) ΔItot = 0.007 Refined Laspeyres ΔItot = 0.007 Log Mean Divisia Structure effect (Istr) ΔIstr = 0.11 Refined Laspeyres ΔIstr = 0.10 Log Mean Divisia Intensity effect (Iint) ΔIint = 0.1 Refined Laspeyres ΔIint = 0.096 Log Mean Divisia 52 CHAPTER VI STATISTICAL VALIDATION PROCESS 6.1 Introduction This chapter introduces the statistical techniques to be used to validate the energy intensity indexes as mentioned in the Statement of Research. The objectives of using these techniques are to show that the index can be used to monitor the production efficiency without the influence of product mix. This can be achieved by performing correlation test between intensity index and the production mix. The chapter also proposes a standardize process of using energy intensity index to monitor the “bare” efficiency by fitting ARIMA models. 6.2 Statistical Test Procedure After the indexes are determined through the brick model, they are tested according to Phase II in Chapter 4. The tests include the following 1. Energy intensity index selection between Refined Laspeyres Additive method and Log Mead Divisia Additive method 2. Show that the intensity index does not have the influence of product mix. In other words, the changes in product type do not affect the energy intensity index. This can achieve by performing Pearson’s test of correlation. 3. Fit the intensity index to time series ARIMA (Auto Regressive Integrated Moving Average) model. 53 Test of Correlation Test the correlation between the Intensity index and the changes due to product type. Use the Pearson’s Test of Correlation with H0: There is no correlation between intensity index and product types ρ=0 Ha: There is a correlation between intensity index and product types ρ≠0 In this dissertation, Pearson’s test of correlation is being used to measure the relation between two variables, energy intensity index and product types produced. Correlation coefficients (ρ) range from 1.00 to +1.00 where negative correlation coefficients represent negative correlation (1.00 represents a perfect negative correlation) and positive correlation coefficients represent positive correlation (+1.00 represents a perfect positive correlation). A correlation coefficient of 0.00 represents a lack of correlation. Pearson correlation (Simple Linear Correlation ) was selected because it assumes that the two variables are measured on at least an interval scale. The correlation coefficient does not depend on the specific measurement units used; for example, the correlation between height and weight will be identical regardless of whether inches and pounds, or centimeters and kilograms are used as measurement units. The test statistic for correlation test is the Pvalue at 95% level of significance. If the Pvalue is less than or equal to 0.05, reject H0 which means that there is evidence of correlation between intensity index and changes in product type. If Pvalue is over 0.05, fail to reject the null hypothesis, which means that there is no correlation between the intensity index and changes in product type 54 Fitting ARIMA Model6 The goal of the research is to establish ground work for forecasting the need for recommissioning of an industrial facility. ARIMA (Auto Regressive Integrated Moving Average) models are one of the most general classes of models used for forecasting a time series. ARIMA Model ARIMA models are standardized statistical models used to fit time series data in forecasting applications. The model composed of three main parts, AR(autoregressive), MA (moving average), and I(integrated). AR term represents the prediction of the current value of the time series as a function of the past values, MA is a current value which is a combination of past white noise (forecast errors) values, and I is trending in the time series. The MA term also helps to smooth out shortterm fluctuations, thus highlighting longerterm trends or cycles [Chou 1970]. Several forms of ARIMA models are used in industrial engineering applications especially as Statistical Process Control tools. Most notably are Exponentially Weighted Moving Average (EWMA), Exponentially Weighted Moving Deviations (EWMD), and CuSum control charts. EWMA, EWMD, and CuSum charts are considered effective for detecting small sustained shifts in the process [Kolarik 1999]. These techniques are a subset of ARIMA models and contain only the moving average (MA) terms. In order for a time series to be analyze, some need to be differenced (detrend) to be made stationary is said to be an "integrated" version of a stationary series. A nonseasonal ARIMA model is classified as an "ARIMA(p,d,q)" model where p is the number of autoregressive terms, d is the number of nonseasonal differences, q is the number of lagged forecast errors in the prediction equation. 6 http://www.duke.edu/~rnau/411arim.htm 55 To fit the appropriate ARIMA model for a time series the series need to be stationary. This can be achieved by detrending or differencing the series (integrated term). Seasonal ARIMA models In some cases, the time series exhibit a repetitive pattern. In this research, average daily ambient temperatures in 3 years period exhibit a repetitive pattern. The seasonal part of an ARIMA model has the same structure as the nonseasonal part but the factors operate across multiples of lags (the number of periods in a season). A seasonal ARIMA model is classified as an ARIMA(p,d,q)x(P,D,Q) model where P=number of seasonal autoregressive (SAR) terms D=number of seasonal differences Q=number of seasonal moving average (SMA) terms In identifying a seasonal model, the first step is to determine whether or not a seasonal difference is needed, in addition to or perhaps instead of a nonseasonal difference. If the seasonal pattern is both strong and stable over time (e.g., high in the Summer and low in the Winter, or vice versa), then a seasonal difference should be used. Differencing Fitting an ARIMA model is the determination of the order of differencing needed to stationarize the series. Normally, the correct amount of differencing is the lowest order of differencing that yields a time series which fluctuates around a welldefined mean value and whose autocorrelation function (ACF) plot decays fairly rapidly to zero, either from above or below. If the series still exhibits a longterm trend, or otherwise lacks a tendency to return to its mean value, or if its autocorrelations are positive out to a high number of lags (e.g., 10 or more), then it needs a higher order of differencing. The seasonal difference of a time series is the series of changes from one season to the next. For monthly data, in which there are 12 periods in a season, the seasonal difference 56 of Y at period t is Y(t)Y(t12). In this research, the data are in weekly period. Should seasonal difference is required, the periods are 52 periods in a season. Model Fit Test To determine the fit of model, this research uses the Akaike information criterion (AIC) [Akaikein 1974]. AIC is a statistical model fit measure which quantifies the relative goodnessoffit of various previously derived statistical models given a sample of data. It uses a rigorous framework of information analysis based on the concept of entropy. It also examines the complexity of the model together with the goodness of its fit to the sample data to produce a measure which balances between the two in order to prevent over fitting [Wikipedia 2006]. AIC = 2k − 2ln(L) (Eq. 46) where k is the number of parameters, L is the likelihood function. When normally distributed errors are assumed then AIC becomes n AIC = 2k − 2ln RSS (Eq. 47) where n is the number of observations, RSS is the residual sum of squares. The preferred model is that with the lowest AIC value. The AIC methodology attempts to find the minimal model that correctly explains the data, which can be contrasted with more traditional approaches to modeling, such as starting from a null hypothesis. 57 Test of Randomness After fitting an ARIMA model, the residual needs to be tested for randomness to ensure proper fit. This research uses LjungBox statistic test [Shumway and Stoffer 2000] to test residual. The LjungBox test is based on the autocorrelation plot and tests the "overall" randomness based on a number of lags. It is often referred to as a "portmanteau" test. H0: The data are random. Ha: The data are not random. The test statistic is: Σ= − = + h j LB n j Q n n j 1 2 ( ) ( 2) ρ (Eq. 48) Where n is sample size ρ(j) is autocorrelation at lag j h is number of lags being tested Based on a Chisquare distribution, reject if 2 LB 1 ,h Q α χ − > 58 CHAPTER VII EXPERIMENTAL RESULTS Introduction This chapter shows the results from the model created in Chapter 5 and statistics tests proposed in Chapter 6. Index Selection After calculating the two main indexes, Refined Laspeyres and Log Mean Divisia on the results showed that both indexes respond differently to the changes of the model. The indexes were used to monitor weekly the energy intensity changes for three years with the energy intensity of the first week. From the model, from visually examining the response, Log Mean Divisia appears to respond better to trend input than Refined Laspeyres as shown in Figure 5 (top). After further analysis by differencing both index time series, the Log Mean Divisia response show significant increase in variations of energy intensity compare to Laspeyres shown in Figure 5 (bottom). This increase in variation of all Log Mean Divisia intensity indexes is due to the logarithmic term in the index’s formula. The results of the Log Mean Divisia intensity index are consistent through all 27 scenarios shown in Appendix A. 59 Time 0 50 100 150 0 2000 6000 10000 Time 0 50 100 150 4000 0 2000 Figure 5 Time series plot of Log Mean Divisia AIHHH (top) and differenced AIHHH (bottom) The Refined Laspeyres responses are more consistent in magnitude than Log Mean Divisia. Figure 6 shows the response of Refined Laspeyres intensity index of the same data. These results illustrate a pattern that was reflected widely throughout the data. Time 0 50 100 150 0.2 0.0 0.2 0.4 0.6 Time 0 50 100 150 0.6 0.2 0.2 0.6 Figure 6 Refined Laspayres intensity index of series plot of LIHHH (above) and differenced LIHHH (below) 60 Base on this evidence, the Refined Laspeyres is more suitable for plant level long term (three years) monitoring Correlation Test H0: There is no correlation between Laspeyres intensity index and production ρ=0 H1: There is a correlation between Laspeyres intensity index and production ρ≠0 The correlation test between the Laspeyres intensity index and production as shown in Table VIII reveal that there is no correlation between the index and the production. This means that the index can be used to monitor the “bare” energy intensity without the influence of the product mix. TABLE VIII CORRELATION TEST BETWEEN THE LASPEYRES INTENSITY INDEX AND PRODUCTION No. Name CORR PValue CORR PValue 1 LIHHH 0.059 0.463 0.040 0.618 2 LIMHH 0.054 0.505 0.045 0.584 3 LIHMH 0.052 0.535 0.049 0.542 4 LIHHM 0.051 0.523 0.057 0.486 5 LIMMH 0.044 0.583 0.053 0.514 6 LIHMM 0.052 0.519 0.059 0.468 7 LIMHM 0.055 0.498 0.054 0.491 8 LIMMM 0.056 0.487 0.056 0.491 9 LILHH 0.059 0.468 0.040 0.623 10 LIHLH 0.039 0.630 0.057 0.484 11 LIHHL 0.029 0.723 0.061 0.459 12 LILLH 0.039 0.635 0.056 0.487 13 LIHLL 0.007 0.927 0.061 0.459 14 LILHL 0.028 0.730 0.061 0.454 15 LILLL 0.007 0.933 0.071 0.379 16 LILMM 0.047 0.558 0.058 0.474 17 LIMLM 0.546 0.500 0.058 0.474 18 LIMML 0.015 0.850 0.068 0.400 19 LILLM 0.044 0.587 0.059 0.464 20 LIMLL 0.005 0.952 0.073 0.368 21 LILML 0.017 0.830 0.067 0.411 22 LIHML 0.018 0.824 0.066 0.416 23 LIMHL 0.026 0.078 0.062 0.441 24 LILMH 0.050 0.541 0.049 0.546 25 LIHLM 0.050 0.540 0.061 0.453 26 LIMLH 0.033 0.680 0.060 0.461 27 LILHM 0.048 0.553 0.056 0.494 Original Series Differenced Series 61 ARIMA Model Fit The LIHHH plot has a slight trend as seen in Figure 7 indicate the response to the deterioration of the system efficiency. ACF plot shows that the data are correlated which implies a nonstationary time series. Figure 7 Time series plot (above), ACF plot (middle), and PACF plot (below) of LIHHH After the nonseasonal differencing, the time series appear more stable as shown in Figure 8. As preliminary analysis, the ACF cuts off at lag =1 and the PACF tails off. According to Shumway and Stoffer [2000] suggest initial guess for ARIMA(0,1,1) model. 62 Figure 8 Differenced Time series plots of LIHHH Model fitting by SPlus yield coefficient MA = 0.9068 with lowest of AIC = 79.65. The residual diagnostics of ARIMA(0,1,1) reveal random residuals. The fitted LIHHH can be expressed as 1 1 0.968 − − = + + t t t t x x ω ω (Eq. 49) where xt = time series value at time t, xt1 = time series value at time t1, ωt = error value at time t, ωt1 = error value at time t1. 63 Plot of Standardized Residuals 20 40 60 80 100 120 140 160 3 2 1 0 1 2 3 ACF Plot of Residuals ACF 0 5 10 15 20 1.0 0.0 0.5 1.0 PACF Plot of Residuals PACF 5 10 15 20 0.2 0.0 0.2 Pvalues of LjungBox ChiSquared Statistics Lag pvalue 2 4 6 8 10 0.0 0.2 0.4 0.6 0.8 ARIMA Model Diagnostics: LIHHH ARIMA(0,1,1) Model with Mean 0 The seasonal fit of ARIMA(0,1,1)x(0,1,0)52 yield AIC = 27.16 which is greater than the ARIMA(0,1,1) and therefore not recommended. The remaining ARIMA model fitting graphs are shown in Appendix A. A summary of the ARIMA model fitting is shown in Table IX on the next page. 64 TABLE IX SUMMARY ARIMA MODEL FITTING RESULTS NO. Name ARIMA AR Diff MA AIC 1 LIHHH (0,1,1) 0 1 0.9 79.94 2 LIMHH (0,1,1) 0 1 0.907 79.66 3 LIHMH (0,1,1) 0 1 0.93 99.93 4 LIHHM (0,1,1) 0 1 0.884 182 5 LIMMH (0,1,1) 0 1 0.933 99.7 6 LIHMM (0,1,1) 0 1 0.916 207.6 7 LIMHM (0,1,1) 0 1 0.879 183.4 8 LIMMM (0,1,1) 0 1 0.911 208.4 9 LILHH (0,1,1) 0 1 0.905 79.36 10 LIHLH (0,1,1) 0 1 0.958 116.6 11 LIHHL (0,1,1) 0 1 0.915 32.78 12 LILLH (0,1,1) 0 1 0.958 116.3 13 LIHLL (0,1,1) 0 1 0.966 70.59 14 LILHL (0,1,1) 0 1 0.914 33.09 15 LILLL (0,1,1) 0 1 0.965 70.88 16 LILMM (0,1,1) 0 1 0.916 207.2 17 LIMLM (0,1,1) 0 1 0.942 230.1 18 LIMML (0,1,1) 0 1 0.938 58.22 19 LILLM (0,1,1) 0 1 0.946 229.4 20 LIMLL (0,1,1) 0 1 0.966 75.31 21 LILML (0,1,1) 0 1 0.936 53.61 22 LIHML (0,1,1) 0 1 0.938 53.33 23 LIMHL (0,1,1) 0 1 0.916 37.78 24 LILMH (0,1,1) 0 1 0.929 99.62 25 LIHLM (0,1,1) 0 1 0.946 229.8 26 LIMLH (0,1,1) 0 1 0.959 116.9 27 LILHM (0,1,1) 0 1 0.886 181.6 The ARIMA model fitting summarized in Table IX reveal that it is possible to fit the energy intensity index in a time series model. The results show that all the models are moving average (MA) models. Weather due to seasonal changes is not as significant when fitting the model as the trending from efficiency deterioration. In a more energy intensive process weather may play a more prominent role in the ARIMA model fitting and may require a seasonal model. 65 Discussion of Experimental Results The experiments conducted for time series of the Refined Laspeyres energy intensity index and the Log Mean Divisia indexes with from the brick model over a 3 year period with 3 scenarios of product mixes, 3 scenarios of weather patterns, and 3 scenarios of system efficiency deteriorations accounts for 27 total scenarios. Time series plots of the Refined Laspeyres energy intensity index of 27 scenarios show the effects of the three main effects. Trending effects are very strong in the Log Mean Divisia index. The indexes increase rapidly in all 27 scenarios with increasing rate of amplitudes. This may be due to the logarithmic nature of the index and therefore is not recommended for use in long term monitoring. The Refined Laspeyres energy intensity index is used to test for correlation with the influence of product mix. The results show that the intensity indexes are statistically correlated with the product mix and therefore can be used to monitor the “bare” energy intensity of the production process. The intensity index time series can be used to develop ARIMA models. All 27 scenarios resulted in the recommendation of an ARIMA (0,1,1) model which is an Integrated Moving Average model. None of the weather impacts were significant enough to include in the seasonal ARIMA model, ARIMA (p,d,q)x(P,D,Q)52. 66 CHAPTER VIII SUMMARY, DISCUSSIONS, AND RECOMMENDATIONS 8.1 Introduction From Chapter 7, statistical test results indicated that the Refined Laspeyres energy intensity index is the more suitable to use as a plantlevel energy monitoring index than Log Mean Divisia because of the consistency in responding to changes and not amplify the changes over time. The results also show that Refined Laspeyres energy intensity index has no correlation with the production mix. In other words, the energy intensity index is not influence by changes in product mix. This chapter presents the major contributions and the usefulness of this research. This chapter also includes the strength and limitations of the techniques and the use of energy intensity index. Finally, the chapter explores opportunities to improve the technique and future development of this research. 8.2 Major Contribution of This Research In industrial settings, one of the challenges energy managers encounter when performing monitoring on the facility’s energy usage is the influence of changes in product mix, production quantity, and weather impact. These factors influence the energy usage in the plant and mask the “bare” production energy efficiency. This research introduces a procedure to unmask the bare production energy efficiency by incorporating the use of 67 energy intensity index as a tool to monitor the changes in energy consumption. The intensity index uses energy intensity, kJ/kg, as a part of calculation which eliminates the production quantity mask. Further statistical tests showed that the Refined Laspeyres intensity index is not influenced by the changes in product mix. These benefits provide energy engineers with better knowledge of the facility’s production efficiency. The research results also indicate that the intensity index can be fitted into an ARIMA model which is one of the most used models in forecasting. Energy managers can use this model to monitor the current facility production efficiency changes. In addition, since ARIMA models are one of the most powerful models used to better understand the data or used for prediction, engineers can use these models to plan for future recommissioning effort by applying forecasting techniques. The increasing in energy intensity (trend) and erratic energy intensity behavior can help engineers understand the healthiness of the process and able to project on when improvements are needed. 8.3 Strengths and Limitations From the experimental results, the advantage of the use of energy intensity index as an alternative production energy efficiency monitoring technique is that the index is not influenced by the changes in product type. The model tested was on weekly data over a three years period. After fitting the ARIMA model, the weather impact was recognized as a part of general white noise (residual). Researchers wishing to continue this study need to recognize the weather impact and also test for seasonality of the model in the time series fitting. More complex models may be used should the weather plays an important role. An example of more complex model include but not limited to SRIMA or ARIMA(p,d,q)x(P,D,Q). The study was performed on a flow shop environment, the modeled facility was not air conditioned. In other production type environments for example, a facility with air conditioning and complex production lines, more complex data gathering processes may be required, for example submetering of multiple furnaces, motors, and the production 68 lines. For thermally heavy processes including air conditioning, the author speculates that additional air conditioning submetering may be required. The indexes used in this research are assumed to be intensity index (energy used per unit of production) not value based. Researchers can later convert to currencybased intensity indexes (dollars of energy per unit of production) to justify the future forecasting for a recommissioning project. 8.4 Future Research There are opportunities for expansion of this research 1. Index decomposition methodology mainly composed of Intensity index, Production Mix index, and Production Quantity index (please refer to Chapter 2). This research explores the energy intensity index. As an overall facility wellbeing, the product mix and production quantity (production index) can be further explored in similar way. 2. Use other types of trend signals. This research explored the linear decay of the overall efficiency over a long term period of 3 years. Further studies are needed to explore other types of decay signals. This may also include actual data gathering over a long term period from the time when major energy conservation efforts have been implemented. 3. The expanded universe of the plantlevel energy intensity index monitoring is to develop forecasting processes to plan for future recommissioning. Since this research uses ARIMA models as a standardized model of the indexes, it can be expanded into forecasting. 4. Short term (one year) monitoring with LMDI. 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Kolarik, W. J. (1999). Creating Quality Process Design for Results, McGrawHill. Lermit, J. a. J., Nigel (2001). Monitoring energy efficiency performance in New Zealand: a conceptual and methodological framework. W. Energy Efficiency and Conservation Authority, New Zealand. Liu, F. L., Ang, B.W. (2003). "Eight methods for decomposing the aggregate energyintensity of industry." Applied Energy 76: 1523. 73 Liu, M., Claridge, David E. (2003). "Continuous Commissioning(SM) of Building Energy Systems." Journal of Solar Engineering Engineering 125. Liu, X. Q., Ang, B.W (1992). "THE APPLICATION OF THE DIVISIA INDEX TO THE DECOMPOSITION OF CHANGES IN INDUSTRIAL ENERGY CONSUMPTION." Energy Journal 13(4): 161  178. Ortiz, D. (2002). Summary of the “DOE Workshop on Indicators of Energy Intensity in the U.S. Economy”. DOE Workshop on Indicators of Energy Intensity in the US Economy. Arlington, Virginia: 120. Paasche, H. (1874). "Ueber die Preisentwicklung der letzten Jahre nach den Hamburger Borsennotirungen." Jahrbucher fur Nationalokonomie und Statistik: 168  178. Phylipsen, G. J. M., Blok K., and Worrell, E. (1998). Handbook on International Comparisons of Energy Efficiency in the Manufacturing Industry. The Netherlands: Dept. of Science, Technology & Society, Utrecht University, Elsevier. Prasertsan, S., Theppaya, T. (1995). "A Study toward energy savings in brick making: Part 1 Key paramenters for energy savings." RERIC International Energy Journal 17(2). Prasertsan S., P. G., Teppaya, T., Kirirat, P. (1995). "A study toward energy saving in brick making Part 2  Simulation of processes in brick kiln." RERIC International Energy Journal 17(2). Price, L. (1997). Energy efficiency in the United States iron and steel industry: An international perspective. ACEEE summer study on energy efficiency in industry (1997), Washington, D.C., American Council for EnergyEfficient Economy. Reitler, W., Rudolph, M., Schaefer, H. (1987). "Analysis of the factors influencing energy consumption in industry a revised method." Energy Economics: 145  148. Rose, A., Casler, S. (1996). "Input–output structural decomposition analysis: a critical appraisal." Economic Systems Research 8: 33  62. 74 Selvanathan, E. A., Prasada Rao, D.S. (1997). Index Numbers A Stochastic Approach. Ann Arbor, The University of Michigan Press. Sun, J. W. (1998). "Changes in energy consumption and energy intensity: A complete decomposition model." Energy Economics 20: 85100. The Institute of Energy Economics, J. (2000). A STUDY OF ENERGY EFFICIENCY INDICATORS FOR INDUSTRY IN APEC ECONOMIES. A. P. E. R. CENTRE, Institute of Energy Economics, Tokyo Japan. Turner, W. C. (2005). Commissioning. AEE Skills Update IV. W. C. Turner, Association of Energy Engineers. Turner, W. C., Parker, S. A. (1984). "Energy Accounting: A New Field Develops." IIE Transactions. Vogt, A., Barta, Janos. (1997). The making of tests for index numbers: mathematical methods of descriptive statistics. Germany, PhysicaVerlag Heidelberg. Vollmann, T. E., Berry, William L., Whybark, Clay D. (1997). Manufacturing planning and control systems, McGrawHill Companies, Inc. Wei, W. W. (1990). Time series analysis univariate and multivariate methods, Addison Wesley Publishing Company. Wikipedia Price index. Worrell, E., Laitner, John A., Ruth, Michael, Finman, Hodayah (2003). "Productivity benefits of industrial energy efficiency measures." Energy 28: 1081  1098. 75 APPENDIXES 76 APPENDIX A: GRAPH OF SIMULATION RESULTS Refined Laspayres Energy Intensity Index 1. Time series of Refined Laspayres Energy Intensity Index (Top) 2. Auto Correlation of Refined Laspayres Energy Intensity Index (Middle) 3. Partial Refined Laspayres Energy Intensity Index (Bottom) 77 78 79 80 81 82 83 84 85 86 87 88 89 90 Log Mean Divisia Energy Intensity Index 4. Time series of Log Mean Energy Intensity Index (Top) 5. Auto Correlation of Log Mean Energy Intensity Index (Middle) 6. Partial Refined Log Mean Energy Intensity Index (Bottom) 91 92 93 94 95 96 97 98 99 100 101 102 103 104 APPENDIX B: TEST OF CORRELATION RESULTS Correlation test of detrended Refined Laspayres intensity index #***** Refined Laspayres Intensity Index ****** cor.test(LIHHH, prodHw) Pearson's productmoment correlation data: LIHHH and prodHw t = 0.7365, df = 153, pvalue = 0.4625 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05944053 > cor.test(LIMHH, prodHw) Pearson's productmoment correlation data: LIMHH and prodHw t = 0.6679, df = 153, pvalue = 0.5052 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05391762 > cor.test(LIHMH, prodHw) Pearson's productmoment correlation data: LIHMH and prodHw t = 0.6215, df = 153, pvalue = 0.5352 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05018343 > cor.test(LIHHM, prodMw) Pearson's productmoment correlation data: LIHHM and prodMw t = 0.6405, df = 153, pvalue = 0.5228 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05171571 105 > cor.test(LIMMH, prodHw) Pearson's productmoment correlation data: LIMMH and prodHw t = 0.5507, df = 153, pvalue = 0.5827 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.04447645 > cor.test(LIHMM, prodMw) Pearson's productmoment correlation data: LIHMM and prodMw t = 0.646, df = 153, pvalue = 0.5192 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05215641 > cor.test(LIMHM, prodMw) Pearson's productmoment correlation data: LIMHM and prodMw t = 0.6792, df = 153, pvalue = 0.4981 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05482426 > cor.test(LIMMM, prodMw) Pearson's productmoment correlation data: LIMMM and prodMw t = 0.6961, df = 153, pvalue = 0.4874 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.056184 > cor.test(LILHH, prodHw) Pearson's productmoment correlation data: LILHH and prodHw t = 0.7278, df = 153, pvalue = 0.4678 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05874133 > cor.test(LIHLH, prodHw) 106 Pearson's productmoment correlation data: LIHLH and prodHw t = 0.4825, df = 153, pvalue = 0.6302 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.03897485 > cor.test(LIHHL, prodLw) Pearson's productmoment correlation data: LIHHL and prodLw t = 0.355, df = 153, pvalue = 0.7231 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.02868749 > cor.test(LILLH, prodHw) Pearson's productmoment correlation data: LILLH and prodHw t = 0.4753, df = 153, pvalue = 0.6352 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.03839904 > cor.test(LIHLL, prodLw) Pearson's productmoment correlation data: LIHLL and prodLw t = 0.092, df = 153, pvalue = 0.9268 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.007435621 > cor.test(LILHL, prodLw) Pearson's productmoment correlation data: LILHL and prodLw t = 0.3461, df = 153, pvalue = 0.7297 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.02797184 > cor.test(LILLL, prodLw) Pearson's productmoment correlation 107 data: LILLL and prodLw t = 0.0838, df = 153, pvalue = 0.9334 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.006771146 > cor.test(LILMM, prodMw) Pearson's productmoment correlation data: LILMM and prodMw t = 0.587, df = 153, pvalue = 0.558 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.04740542 > cor.test(LIMLM, prodMw) Pearson's productmoment correlation data: LIMLM and prodMw t = 0.6759, df = 153, pvalue = 0.5001 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05456157 > cor.test(LIMML, prodLw) Pearson's productmoment correlation data: LIMML and prodLw t = 0.1901, df = 153, pvalue = 0.8495 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.01536753 > cor.test(LILLM, prodMw) Pearson's productmoment correlation data: LILLM and prodMw t = 0.5447, df = 153, pvalue = 0.5868 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.04399379 > cor.test(LIMLL, prodLw) Pearson's productmoment correlation data: LIMLL and prodLw t = 0.0603, df = 153, pvalue = 0.952 108 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.004878067 > cor.test(LILML, prodLw) Pearson's productmoment correlation data: LILML and prodLw t = 0.2148, df = 153, pvalue = 0.8302 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.01736321 > cor.test(LIHML, prodLw) Pearson's productmoment correlation data: LIHML and prodLw t = 0.2234, df = 153, pvalue = 0.8236 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.01805429 > cor.test(LIMHL, prodLw) Pearson's productmoment correlation data: LIMHL and prodLw t = 0.3216, df = 153, pvalue = 0.7482 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.0259903 > cor.test(LILMH, prodHw) Pearson's productmoment correlation data: LILMH and prodHw t = 0.6135, df = 153, pvalue = 0.5405 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.04953381 > cor.test(LIHLM, prodMw) Pearson's productmoment correlation data: LIHLM and prodMw t = 0.6149, df = 153, pvalue = 0.5395 alternative hypothesis: coef is not equal to 0 sample estimates: 109 cor 0.04965111 > cor.test(LIMLH, prodHw) Pearson's productmoment correlation data: LIMLH and prodHw t = 0.414, df = 153, pvalue = 0.6795 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.03344878 > cor.test(LILHM, prodMw) Pearson's productmoment correlation data: LILHM and prodMw t = 0.5947, df = 153, pvalue = 0.5529 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.04802122 110 Correlation test of detrended Refined Laspayres intensity index cor.test(LIHHH.mod, prodHw) Pearson's productmoment correlation data: LIHHH.mod and prodHw t = 0.4992, df = 152, pvalue = 0.6184 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.04045753 > cor.test(LIMHH.mod, prodHw) Pearson's productmoment correlation data: LIMHH.mod and prodHw t = 0.5491, df = 152, pvalue = 0.5837 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.04449444 > cor.test(LIHMH.mod, prodHw) Pearson's productmoment correlation data: LIHMH.mod and prodHw t = 0.6107, df = 152, pvalue = 0.5423 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.04947506 > cor.test(LIHHM.mod, prodMw) Pearson's productmoment correlation data: LIHHM.mod and prodMw t = 0.6988, df = 152, pvalue = 0.4858 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05658693 > cor.test(LIMMH.mod, prodHw) Pearson's productmoment correlation data: LIMMH.mod and prodHw t = 0.6539, df = 152, pvalue = 0.5142 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05296247 111 > cor.test(LIHMM.mod, prodMw) Pearson's productmoment correlation data: LIHMM.mod and prodMw t = 0.727, df = 152, pvalue = 0.4683 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05886591 > cor.test(LIMHM.mod, prodMw) Pearson's productmoment correlation data: LIMHM.mod and prodMw t = 0.6617, df = 152, pvalue = 0.5091 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05359633 > cor.test(LIMMM.mod, prodMw) Pearson's productmoment correlation data: LIMMM.mod and prodMw t = 0.6911, df = 152, pvalue = 0.4905 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05596997 > cor.test(LILHH.mod, prodHw) Pearson's productmoment correlation data: LILHH.mod and prodHw t = 0.4928, df = 152, pvalue = 0.6229 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.03993842 > cor.test(LIHLH.mod, prodHw) Pearson's productmoment correlation data: LIHLH.mod and prodHw t = 0.7022, df = 152, pvalue = 0.4836 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05686178 > cor.test(LIHHL.mod, prodLw) 112 Pearson's productmoment correlation data: LIHHL.mod and prodLw t = 0.7425, df = 152, pvalue = 0.4589 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.06011677 > cor.test(LILLH.mod, prodHw) Pearson's productmoment correlation data: LILLH.mod and prodHw t = 0.6965, df = 152, pvalue = 0.4872 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05640439 > cor.test(LIHLL.mod, prodLw) Pearson's productmoment correlation data: LIHLL.mod and prodLw t = 0.7425, df = 152, pvalue = 0.4589 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.06011677 > cor.test(LILHL.mod, prodLw) Pearson's productmoment correlation data: LILHL.mod and prodLw t = 0.75, df = 152, pvalue = 0.4544 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.06072259 > cor.test(LILLL.mod, prodLw) Pearson's productmoment correlation data: LILLL.mod and prodLw t = 0.8833, df = 152, pvalue = 0.3785 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.07146103 > cor.test(LILMM.mod, prodMw) Pearson's productmoment correlation 113 data: LILMM.mod and prodMw t = 0.7113, df = 152, pvalue = 0.478 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05760082 > cor.test(LIMLM.mod, prodMw) Pearson's productmoment correlation data: LIMLM.mod and prodMw t = 0.7175, df = 152, pvalue = 0.4742 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.05809506 > cor.test(LIMML.mod, prodLw) Pearson's productmoment correlation data: LIMML.mod and prodLw t = 0.8446, df = 152, pvalue = 0.3996 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.06834972 > cor.test(LILLM.mod, prodMw) Pearson's productmoment correlation data: LILLM.mod and prodMw t = 0.7338, df = 152, pvalue = 0.4642 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.0594142 > cor.test(LIMLL.mod, prodLw) Pearson's productmoment correlation data: LIMLL.mod and prodLw t = 0.9024, df = 152, pvalue = 0.3683 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.07299632 > cor.test(LILML.mod, prodLw) Pearson's productmoment correlation data: LILML.mod and prodLw 114 t = 0.824, df = 152, pvalue = 0.4113 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.06668282 > cor.test(LIHML.mod, prodLw) Pearson's productmoment correlation data: LIHML.mod and prodLw t = 0.8162, df = 152, pvalue = 0.4157 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.06605504 > cor.test(LIMHL.mod, prodLw) Pearson's productmoment correlation data: LIMHL.mod and prodLw t = 0.7727, df = 152, pvalue = 0.4409 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.06255038 > cor.test(LILMH.mod, prodHw) Pearson's productmoment correlation data: LILMH.mod and prodHw t = 0.6047, df = 152, pvalue = 0.5463 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.04899197 > cor.test(LIHLM.mod, prodMw) Pearson's productmoment correlation data: LIHLM.mod and prodMw t = 0.7522, df = 152, pvalue = 0.4531 alternative hypothesis: coef is not equal to 0 sample estimates: cor 0.06089597 > cor.test(LIMLH.mod, prodHw) Pearson's productmoment correlation data: LIMLH.mod and prodHw t = 0.7396, df = 152, pvalue = 0.4607 alternative hypothesis: coef is not equal to 0 115 sample estimates: cor 0.05987879 > cor.test(LILHM.mod, prodMw) Pearson's productmoment correlation data: LILHM.mod and prodMw t = 0.6864, df = 152, pvalue = 0.4935 alternative hypo 



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