Energy Department Paper No. 6 Energy Efficiency: Optimization of Electric Power Distribution System Losses July 1982 World Bank Energy Department ENERGY EFFICIENCY: OPTIMIZATION OF ELECTRIC POWER DISTRIBUTION SYSTEM LOSSES (Final Report of Research Project No. R633) Mohan Munasinghe and Walter Scott (Consultant) Energy Department July 1982 Copyright (c) 1982 The World Bank 1818 H Street, N.W. Washington, D.C. 20433 U.S.A. This paper is one of a series issued by the Energy Department for the information and guidance of Bank staff. The paper may not be published or quoted as representing the views of the Bank Group, and the Bank Group does not accept responsibility for its accuracy or completeness. ENERGY EFFICIENCY: OPTIMIZATION OF ELECTRIC POWER DISTRIBUTION SYSTEM LOSSES Abstract Given the rising costs of energy supply and the high level of loss in LDC power systems, the objectives of this study were to develop pratical methods for (1) isolating technical losses in distributon systems; (2) evaluating economically, methods of reducing loss levels; and (3) incorporat- ing the effects of loss analysis into engineering criteria for design and operations. The results indicate that within realistic limits, for many dis- tributon systems. Loss reduction is far a cheaper alternative than adding new generating and bulk transmission capacity. The analysis stresses that both kWh and kW (or peak) losses are important, and these should be valued at the long-run marginal cost of bulk supply - the range of values used in the study spans the spectrum for hydro as well as thermal systems. It is shown that economically optimal target loss levels for networks are much lower than those commonly used at present. The study also identifies methodologies to isoloate losses and optimize loss levels on an economic basis. The relevance of loss analysis in establishing engineering desing and operating criteria are discussed. The findings can be used to develop specific practical loss-reduction projects. Most power utilities already have loss-reduction and network rehabilitation programs which could usefully incorporate the economic planning criteria contained here. As noted in the study, most such programs still use pre-determined (and often rule-of-thumb) target loss levels, voltage drop, and similar criteria as a basis for design. Therefore the existence of these programs does not guarantee that appropriate economic criteria are being used. Utilities should also recognize the importance of separating technical and non-technical causes of losses, and developing appropriate strategies to deal with each component. Identifying the causes of losses is an essential, but not necessarily obvious, first step in putting together an effective package of loss reduction measures. TABLE OF CONTENTS Page CHAPTER 1: INTRODUCTION AND SUMMARY 1 1.1 Background and Objectives 1 1.2 Summary 5 1.2.1 Models and Methodology 5 1.2.2 Principal Results 7 1.3 Conclusions and Potential for Application 10 1.3.1 Principal Conclusions and Recommendations 10 1.3.2. Potential for Application 10 CHAPTER 2: ECONOMIC BASIS FOR OPTIMIZING LOSSES 17 2.1 Economic Optimization of Distribution Losses 2.2 The Economic Value of kW add kWh Losses 19 CHAPTER 3: CALCULATING DISTRIBUTION SYSTEM LOSSES 23 3.1 Primary and Secondary Systems 23 3.2 Substation and Distribution Transformers 23 3.3 Power Factor Correction 29 3.4 Simplified Procedure (First Approximation) 33 CHAPTER 4: OPTIMIZING DISTRIBUTION LOSSES 38 4.1 Isolating Technical Losses on Primary Systems 38 4.2 Isolating Technical Losses in Distribution Transformers 40 4.3 Isolating Technical Losses on Secondary Systems 42 4.4 Economic Reduction of Losses 43 4.5 Engineering Design Criteria 47 4.6 Specification Requirements and Bid Evaluation for Distribution Transformers 48 CHAPTER 5: SUMMARY OF CASE STUDY RESULTS 49 5.1 Primary Conductor Loading 51 5.2 Power Factor Control 52 5.3 Distribution Transformers 55 5,4 Secondary Systems 64 5.5 Connections 67 5.6 Literature Search 67 APPENDICES A Economic Loss Optimization Model 69 B Computerized Analytical Models 76 C Case Study Details 97 D Basic Loading and Loss Parameters 124 E Bibliography CHAPTER 1 INTRODUCTION AND SUMMARY 1.1. Background and Objectives The world-wide scarcity of energy resources and the increasing costs of energy supply have highlighted the importance of energy conservation and elimination of waste by both procedures and users of energy. Power system loss reduction is one of the principal ways for achieving this in the electricity power sector. In the process of delivering electricity to consumers, losses are incurred at the generation, transmission and distribution stages of a power system, as shown in Figure 1.1. Generation losses may be improved by improving the efficiency of plant and reducing station-use, e.g., using new technologies like combined-cycle thermal plant, replacing old boilers and generally uprating old thermal generations, using higher efficiency designs in new hydro installations or replacing older turbines, etc. Leaving generation aside (where acceptable norms for losses vary according to the mix of plant), recent work indicates that average energy losses in the power delivery system, i.e., transmission and distribution, should normally be below 10% of gross generation, while economically optimal loss levels may be as low as 5%. The corresponding losses in many LDC networks approach 20%, even after allowing for substantial amounts of theft. While recognizing the importance of continued improvements in the efficiency of generation and bulk transmission, this study focusses on the reduction of both energy and peak power losses in distribution networks where up to three fourths of total system losses occur. As a rough illustration, if we con3ider a country like India with an annual electricity production of about 10 gigawatt-hours (GWh) in 1978, and assume a value of US45 per kWh, then reducing losses from 20% to 10% (of generation) would yield an annual saving of US$0.5 billion. We show in this study that such savings can often be realized through a rather modest expenditure in additional hardware, to improve the system. Two principal reasons account for high existing levels of distribution losses in developing countries. First, the selling price of electricity has failed to keep pace with the rapid increase in the costs of supply in the decade or so following the oil crisis of 1973. The consequent decline in the financial position of many LDC power companies has led to reduced investment and system maintenance, while low electricity prices have tended to over-stimulate demand. In general, most utilities would prefer to cut back expenditures on distribution systems rather than reduce generation and bulk transmission investments because the results of shortages in the latter case lead to major power outages that are highly visible, whereas distribution system weaknesses manifest themselves less spectacularly in terms of low voltage, high losses, and so on. Investments in new generation projects are also more attractive as a visible sign of "progress", whereas loss reducing network improvements are considerably less glamorous. -2- FIGURE 1.1 LOSSES IN DIFFERENT PARTS OF POWER SYSTEM (1) T Generation Station use + (2) EHv and HV transmission losses + nontechnical losses EHv and Hv TRANSMISSION (4) ower and energy (3) (4) demands of HV consumers (5) J'v distributi n losses nontechnical losses JPower and energy (6) (7 demands of DISTRIBUTION Mv consumers Lv distribution losses LV and nontechnical losses . DISTRIBUTION Power and energy demands of LV consumers Note: --mpower and energy flows losses E generation transformation - 3 - The second reason for high distribution system Loss levels also stems from the rapid rise in energy costs, recently. In brief, additional expenditures on system hardware can bring down system losses. Rules of thumb for system design, still used by many LDC utilities to tradeoff increased system investment costs versus reduced losses, implicitly embody relative costs more appropriate to the mid 1960's than the early 1980's. As a very rough illustration, let us take the international prices of oil and aLuminum (or copper) as proxies for the values of energy losses and of system hardware (e.g., conductors), respectively. As shown in Figure 1.2, oil prices (in constant terms) have increased about five-fold between 1965 and 1981, whereas the corresponding prices of aluminum and copper have remained roughly constant or even declined. Clearly, an engineer in 1981 should be willing to use a lot more of conductor to reduce system losses, than he would have in 1965. As shown later in this study, this means that acceptable overall target loss levels for the entire distribution network (i.e., excluding bulk transmission but including the distribution substation) should be less than 5% of generation, whereas the conventional wisdom has allowed for losses of up to 10% or more. Accordingly, this study seeks to help the Bank and its borrowers identify and reduce network losses. It shows that reducing losses is often more cost effective than building more generation capacity, and will therefore free scarce domestic resources and foreign exchange. The specific.objectives of this study were to: (1) identify the areas within a power system where loss optimization would be most effective, in the context of the developing countries;. (2) determine methods for isolating technical losses on an existing system; 1/ (3) develop and test (on the basis of a desk study) a framework for economically evaluating alternative means of reducing losses on an existing system and determining the optimal Loss levels; (4) develop practical methods for including the effects of losses in establishing the engineering criteria used in design and operations. The remainder of this chapter contains a summary of the models and methodology used in the study and its results, followed by the conclusions 1/ We recognize that other types of loss such as theft or unmetered consumption may also be significant in some systems and should be reduced. However, these issues are not within the scope of the present study. Minimizing such unaccounted-for energy may involve steps such as replacing broken meters, disconnecting and prosecuting customers who steal electricity, establishing a system of prepayment of bills, using different individuals to do the meter reading and billing (as an anti-corruption measure), and so or. -4- Figure 1.2. INTERNATIONAL PRICES FOR CRUDE OIL, ALUMINUM AND COPPER IN CONSTANT (1980) US DOLARS 20 CRUDE OIL 10 6 2.500 2000 o H-4 ALUMINUM 1000 . G CO C COPPER 40cc 0 E-I I I 1 t I 1950 1960 1970 1980 and a discussion of the potential for application of these results in Bank operations and the work of LDC power utilities. The basic economic model for optimizing distribution losses is described in Chapter II. The method of calculating distribution system losses is given in Chapter III. The methodology for combining the various engineering and economic models to optimize distribution loss levels is given in Chapter IV, while Chapter V summarizes the results of the case studies used to successfully test the methodology. A number of technical annexes provide methodological details. 1.2 Summary 1.2.1 Models and Methodology Economic Model The economic model seeks to maximize the long-range net benefits of electricity consumption (i.e., the total benefits minus the total cost). Since alternative distribution system plans that serve the same load are compared, the total benefits of consumption are the same in each case. The difference in net benefits between two networks is therefore the difference in costs. Total costs in each case consist of the sum of long-run marginal costs of bulk supply (from the generation and transmission system) plus the investment and operating costs of the distribution network. Minimizing these total costs, which is equivalent to maximizing net benefits, is achieved by trading off the increased costs of the distribution network against the decreased distribution losses. kW and kWh losses are valued at the long-run marginal cost of bulk supply. The methodology permits the system planner to add one or more new components to the distribution system. A cost-benefit test is performed to check whether benefit of reduced losses exceeds the increased system costs. If the test is satisfied, the system improvements are accepted and new changes are attempted. The process continues until the planner feels that all technically feasible loss reducing options have been tried and accepted or rejected. This is considered to be the optimal system. All cost-benefit calculations are done in real, present discounted value terms over a 20 year period, to capture long-run effects. Appropriate shadow prices are used to represent the true economic value of scarce resources. Finally, some corrections may be made to total costs of alternative distribution systems, to account for small differences among them in terms of quality of supply and outage costs to consumers. -6- Engineering Analytical Models The following analytical models translate the physical and electrical characteristics of a system component into a digital computer model for calculating demand and energy losses:2! . Transformer (station and distribution) . Regulator . Primary System . Secondary System Loading Model The loading model carries out two major functions: (1) Creates an annual loading model (hourly demands for entire year) from hourly loads for selected weeks or from hourly loads for selected months. (2) Computes load factors, load durations, loss factors, and loss duration for any block of demands as defined by hours and dates. Methodology Isolating technical losses are accomplished as follows: (1) Determine load characteristics by seasons and daily time periods. (2) Impose those loads on system which is represented by analytical models (station, primary, distribution transformer, and secondary). (3) Compute technical losses. Determining the best course of action to economically minimize losses for an existing system would be done as follows: (1), (2) and (3) as above. 2/ Preliminary loss calculation may be performed manually with desk calculators using the same methodology, to identify areas in which loss reduction would be most effective. However, such calculations can be carried out only on a sampling basis due to the time required, and the detailed analysis of a full distribution network involving many feeders will require computerized methods. -7-- (4) Develop alternative plans to minimize losses over a selected time frame (say 20 years). Repeat steps (1), (2) and (3) for each plan and each year. (5) Use economic model to determine annual values of losses and system costs and present discounted value of annual losses and system costs for each plan. (6) Select most economical plan which minimizes sum of loss value and system costs. Alternatively, any system improvement for which the value of loss reduction exceeds the increase in system cost is considered desirable. The methodology for including losses in the decision making process relative to engineering criteria would be similar to the above process (Steps (1) through (6)). 1.2.2 Principal Results The major findings of this project are: (1) While generation and bulk power transmission losses can be further improved, distribution loss reduction should be given high priority because it is a relatively neglected topic. (2) Specific areas which economically warrant loss optimization include: . Sub-transmission systems (especially 35 kV and below) . Substations where transmission or sub-transmission voltage levels are reduced to distribution voltage levels . Primary distribution systems . Distribution transformers . Secondary systems (3) The data is generally available to determine the following parameters for each block of load, either directly through empirical relationships or from industry averages. . Peak Demand . Peak Equivalent Hours . Average Loading . Load Factor Load Duration . Loss Equivalent Hours . Loss Factor -8- (4) The physical and electrical characteristics of a system (such as resistance, reactance, etc.) which are required for voltage/loading/loss calculations are readily available from nameplates, maps, records, manufacturers or industrial averages. (5) The procedures and equations for calculating voltage/loading/losses can be sufficiently simplified to use desk top calculators to determine areas needing in-depth study. (6) In-depth calculations of system voltage/loading/ losses involve large masses of data (loading cycles and system), iterative processing, and economic evaluation of many alternatives over long time spans (20 to 30 years). All practical methods to carry out these studies require the use of computerized models (loading, system and economical) and analyti- cal computer programs, which can be implemented on modern minicomputer systems that are available and can be readily purchased by most engineering departments. (7) The allocation of substation peak demand on a primary system in proportion to the nameplate ratings of the distribution transformers or peak month energy deliveries provides a practical foundation for computing and monitoring technical losses. (8) The allocation of the peak demand of a distribution transformer on the secondary system in proportion to consumer energy requirements provides a practical approximation for computing technical losses. (9) Distribution Transformer Load Management (TLM) uses metered consumer energy requirements to monitor transformer loading. TLM is relatively easy to establish, eliminates most burn outs, reduces losses, and generally produces savings at a benefit to cost ratio of about 15 to 1 ($15 saved per $1 of cost). (10) A search of technical references indicates that most distribution systems are currently designed and operated mainly on the basis of thermal capabilities of components and reliability criteria. The value (usually implicit) assigned to losses is often rather low, when establishing engineering criteria. (11) This project indicates that losses should be the most important consideration in establishing design (and operating) criteria. -9- (12) Within practical limitations, it is much less costly to save kilowatts of capacity and kilowatt-hours of energy by reducing distribution losses than to make up these losses by building more generation and bulk transmission facilities (for the cases studied). (13) Loss evaluation and correction are far too complex for generalities. However, for the somewhat average conditions of 50% load factor, 30% loss factor, demand charges in the range of $130 to $250 per kilowatt per year, and energy charges from $0.011 to $0.034 per kilowatt hour (equivalent to long run marginal supply costs of US44 to 9 per kWh), and a discount rate of 12%, this project indicates that economic loadings at peak should be:3! . Transformers from 80% to 100% of nameplate rating (with appropriate adjustments for the specific manufacturing standard used). . Primary main conductors -- from 15% to 25% of rated thermal capacity, and power factor above 95%. . Secondary conductors -- from 10% to 15% of capacity (or eliminated entirely). The above loading limits are well below the criteria used by most LDC as well as developed country utili- ties. Given these new loading criteria, it is anticipated that voltage drop would be small and line voltage regulators and even substation regula- tors would not be necessary. (14) The study indicates that loss reduction on distribu- tion primary system should include power factor con- trol with capacitors, reconductoring and new feeders, switching loads between feeders, and elimi- nating line voltage regulators (and possibly station regulators). (15) Economic loss levels for distribution systems will vary with load factors, loss factors, and costs. This project indicates that the economic distribu- tion loss levels are in the general range of: 3/ The range of US#4 to 9 per average kWh (in 1981 prices), and the high discount rate of 12% (based on the opportunity cost of capital) are on the conservative side. If energy was valued more highly, or if the discount rate was lower, the conclusions regarding loss reduction given here would be further reinforced. - 10 - - 3 to 5% of annual energy 4) - 5 to 8% of power at peak Economic loss levels for transmission are likely to be in the 2-3% range (annual energy). 1.3 Conclusions and Potential for Application 1.3.1 Principal Conclusions and Recommendations: (1) Within practical limitations, loss reduction at distribution level provides capacity at less cost than obtaining capacity by the construction of generation and transmission facilities. (2) The economical loss level is lower than the level generally accepted by most utilities. Also, losses should probably be the dominant item in establishing design and operating criteria. (3) Methodologies have been developed in this project to isolate technical losses and determine economic loss levels. The implications of these results for design criteria and for specification of components are also discussed. (4) Since the results of the desk study indicate a very high ratio of benefits to costs for loss reduction, it is recommended that the general approach to detect and correct losses be applied in a more routine and widespread implementation program in the LDC's that will help to further refine the methodo- logy. 1.3.2 Potential for Application The purpose of this section is to provide overall guidance to engineers in assessing power system loss levels, locating major causes of losses, and determining the loss reduction measures that are likely to yield a high benefit to cost ratio. The first problem is to determine if the loss levels, in a particu- lar system are within acceptable limits. The demand loss at peak (kW or MW) is of most concern, because this loss requires investment at all levels of the system. However, most utilities do not have demand losses available so those losses must be computed from total energy generated, energy losses and the peak demand over selected time periods, load factor, and the estimated 4/ The distribution substation, primary system, and distribution transformer/secondary lines account for about 10%, 55% and 35% respectively, of this total. - 11 - relationship between load factor and loss factor (See Appendix D for details). As a first step the system load factor and energy loss (average and peak) must be estimated. For completeness, we summarize below, the well-known expressions that may be used: Energy Generated (kWh) X 100 Load Factor (%) = Peak Demand (kW) X Hours Energy Loss X 100 Average Energy Loss (%) Energy Generated Table 1.1 provides some typical (average) values of the demand loss multiplier (i.e., ratio of peak period to average loss) for various load factors. Actual values will depend on the specific network under study. Table 1.1 Demand Loss Multiplier Versus Load Factor Demand Loss Load Factor Loss Factorl/ Multiplier 30 20.6 1.46 35 24.6 1.42 40 28.8 1.39 45 33.3 1.35 50 38.1 1.31 55 43.1 1.28 60 48.4 1.24 a/ Average of Type A and Type B loading from Table D.3 (Appendix D) Thus, if a utility provides the following for a selected year: Peak Demand = 365 MW Energy Generated 1,278,960 MWh Energy Loss 217,423 MWh 1,278,960 x 100 = 40% Load Factor 365 x 8760 Hours 217,423 x 100 = 17% Average Energy Loss = 1T278.960 The approximate demand loss at peak may be computed from the multiplier of Table 1.1: 17% x 1.39 (multiplier) = 23.6% Table 1.2 provide a measure of guidance for desirable and acceptable maximum loss levels for various parts of the whole power system (except generation - 12 - station-use which varies from as low as 0.5% for hydro plants to over 5% for coal-fired steam units). A total system power (kW) loss at peak in the neighborhood of 12.0% is good, implying that overall loss reduction measures are not critical and will not produce dramatic gains. However, a reasonable total loss level does not mean that loss reduction in specific parts of the system or geographic areas should not be pursued. Power factor correction, elimination of high impedance power transformers, and distribution transformer load management, should be investigated for all utilities. Table 1.3 provides a preliminary checklist of the more important characteristics associated with losses. The checklist is supplemented with more detailed comments concerning each item. -13 - Table 1.2. Normal System Demand Losses EffV TRANSMISSION (500-765 kV) SUBTRANSMISSION SECONDARY RV TRANSMISSION (69-115 kV) (115-480 V) GENERATION (230-345 kV) (4-35 kV) STEP-UP STATION ERV EV DISTRIBUTION DISTRIBUTION STATION STATION STATION TRANSFORMER DEMAND LOSSES (% of kW GENERATED) TARGET LEVEL MAXIMUM TO BE TOLERATED SYSTEM COMPONENT WITHIN CUMULATIVE WITHIN CUMULATIVE Step-up Station 0.25% 0.25% 0.50% 0.50% EHV Transmission & Station 0.50 0.75 1.00 1.50 KV Transmission & Station 1.25 2.00 2.50 4.00 Sub Transmission 2.00 4.00 4.00 8.00 Distribution Station 0.25 4.25 0.50 8.50 Distribution Primary 3.00 7.25 5.00 13.50 Distribution Transformer & 1.00 8.25 2.00 15.50 Secondary SOURCE: Authors' estimates, and W.J. Ross, "New Focus on Distribution Losses," Transmission and Distribution, December 1981. - 14 - Table 1.3 Preliminary Checklist for Power System Loss Levels Item Good Fair Excessive I. Demand loss for the entire Less than 10 to Over system at peak 10% 15% 15% II. System power factor (%) 95 to 100 90-95 Below 90 III. Impedance of Power 6% or 6% to Over Transformers less 10% 10% IV. Monitoring the loading Annual Occasional No of distribution transformers Maximum loading on Nameplate Up to 125% Over distribution transformers Nameplate 125% V. Primary conductor loading or less or less 40% VI. Secondary System maximum length Urban areas 1/4 kM 1/2 kM Over 1/2 kM Rural areas 1/2 kM 3/4 kM Over 3/4 kM VII. Standards and (See comments for details) Specifications Comments on Table 1.3 I. Loss reduction should be implemented in the following sequence: (1) Power factor correction to at least 95% by installing capacitors on primary lines (2) Replacing high impedance power transformers (3) Distribution transformer load management (4) Reducing primary conductor loading (5) Reducing secondary conductor loading (6) Reducing transmission conductor loading - 15 - II. Power factor correction should be accomplished by installing capacitors on the distribution primary system as near to load centers as practical. (1) Install fixed banks to provide 100% power factor or slightly leading power factor during off-peak loading periods. (2) Install switched banks to correct power factor during peak loading periods. III. The following are comments regarding power transformers. (1) The older tap changing under load transformers were often manufactured with impedances in the general neighborhood of 15%. These transformers should be removed from service and either scrapped or held for emergency use only. (2) Medium impedance transformers should probably be replaced because of their no-load losses. IV. Monitoring the loading of distribution transformers is essential to reduce losses and burnouts. The following are three suggested methods: (1) The lowest cost and most efficient method is to correlate consumers with their transformers and compute loading from energy usage. (2) Install thermal maxi-meters (3) Use clamp-on ammeters at peak time V. Conductor loading may be reduced by: (1) Switching loads to other feeders (2) Replacing existing conductors (3) Adding new feeders and sharing the load (4) Raising primary system voltages, e.g., 11 kV to 33 kV VI. The values in the table are averages (for 240 Volt systems) and therefore rather rough. They must be used only as a first check or warning, because specific figures will depend on load densities which are highly variable. The accepted methods for correcting overloaded secondary systems are: (1) Break the secondary system into smaller segments by adding distribution transformers (2) Replace conductors (3) Add more secondary lines - 16 - VII. Standards and specifications should be examined to determine if they are directed towards minimizing losses. The more important areas to be examined are: (1) Power factor correction targets and locations where capacitors are to be installed. The most effective locations are on the primary lines near the load centers. (2) Specifications for power transformers and distribution transformers to determine if manufacturers are being informed as to how kW and kWh losses will be evaluated. (3) Initial and normal design electrical loading of transformers and conductors. If thermal capabilities are the basis for electrical loading, then losses are probably excessive. (4) Maximum electrical loading of transformers and conductors before replacement is required. - 17 - CHAPTER 2 ECONOMIC BASIS FOR OPTIMIZING LOSSES This chapter summarizes the basis for establishing an economically optimal level of losses in distribution networks. A more detailed model is presented in Appendix A. The essence of the optimization model is the trade off between increased distribution costs and the resultant decrease in the cost of losses. While system costs are relatively easy to measure in terms of the economic value of physical inputs like capital, labor and fuels, the value of losses is more difficult to establish. Therefore, after discussing loss optimization, we establish below how physical losses in a power system may be valued in economic terms. 2.1 Economic Optimization of Distribution Losses Consider the electric power distribution system shown in Figure 2.1. An amount QI of electrical energy is supplied by the bulk power system of which an amount L is dissipated as losses and the remainder Qo is delivered to consumers.5/ The net benefits (NB) of electricity consumption from the social viewpoint is given by: NB = TB - SC Where TB is the total benefit of consumption and SC is the supply cost. TB depends on the amount of electricity consumed, i.e., TB(Q.). We may break SC down into two principal components: SC = BSC + DSC Where BSC is the bulk supply cost and DSC is the distribution system cost (investment, O&M, etc.). We use VQI, the value of input electricity (QI) as a measure of BSC, so that: 5/ This static analysis is deliberately simplified for clarity of presentation. This the quantities Ql, Q0 and L would actually be disaggregate (e.g., peak kW; peak, shoulder and off-peak kWh, etc.) and with each component being valued separately. Similarity, the calculation would have to be performed in present value terms over a long period (e.g., 30 years) to allow for the full life cycle of components and dynamic load growth. We also ignore quality of supply and outage costs considerations. All these aspects are incorporated rigorously into the analysis in Appendix A. - 18 - Figure 2.1 SIMPLIFIED REPRESENTATION OF LOSSES IN A DISTRIBUTION SYSTEM Input Fran Bu2k Supply System I Distribution Netwrk Losses Net~rkL=Q1-Q0 Output to Customers - 19 - SC = VQi + DSC and NB = TB - VQI - DSC Suppose we continue to supply Qo to consumers but are able to incrementally reduce distribution losses (L) by improving the network. Therefore, dis- tribution losses will increase, and therefore VQI will decrease, because Qi = Qo + L and we have just assumed that Qo is constant white L has decreased incrementally. TB is unchanged since Q0 is the same: The change in net benefits is given by: NB = -,VQI -,&DSC = -tAVL -A6DSC Where AVL is the change in value of losses which is assumed to be nega- tive. (Note thatALVL =jnUQI, although VQI is much greater than VL). In other words: Increase in Net Benefit = (Decrease in Value of Losses) - (Increase in Distribution System Costs) Therefore, net benefits to society would have increased if the reduction in value of losses exceeds the increase in distribution costs. Thus, an operational criterion which distribution planners should use is that loss reduction measures should continue up to the point where a marginal increment in distribution cost will be exactly counterbalanced by the decrease in value of losses. Equivalently, we can argue that net supply cost: NSC = VL + DSC should be minimized, to maximize NB These relationships are summarized in Figure 2.2, which shows that VL increases and DSC falls, as L increases, while the economically optimal loss level L* occurs when NSC (the sum of VL and DSC), is a minimum. 2.2 The Economic Value of kW and kWh Losses In the engineering studies that have been done so far, emphasis has been placed on applying accounting principles to loss evaluations, rather than economic principles. Although concepts such as present worth of annual revenue requirements, levelized annual costs, annual costs, and equivalent investment costs are used, there is no application of economic theory in the above procedure.6! 6/ See for example: D. L. Nickel, "Distribution Transformer Loss Evaluation: Proposed Techniques", IEEE, PES Winter Meeting New York, February, 1980, and other references in the Bibliography (on the economic analysis of losses). - 20 - Figure 2.2 OPTIMAL ECONOMIC LOSS LEVEL .(L*) VALUE At NSC VL- slope 3)Sc Physical Losses (L) NOTE: L* occurs at minimim point of NSC curve where NSC - VL + DSC. Alternatively the negative slope (broken line) of DSC curve is equal to positive slope of VL curve at this point. - 21 - The principal point we make is that both kilowatt and kilowatt-hour distribution losses at various time periods should be valued at the long run marginal costs (LRMC) of supply from the bulk supply system.7/ The valuation of kWh of energy losses does not pose major problems. If distribution losses decrease at any given moment, then the bulk supply LRMC of energy at different times (e.g., peak, shoulder, off-peak or by season of the year) provide a measure of the value of kWh lost in the distribution system. However, when distribution system improvements are made, the greater change occurs with respect to kW losses during the peak period. Although the distribution feeder peaks and the bulk system peak may not overlap, any reduction in kW losses during the bulk system peak will lead to a savings in generation and transmission (G&T) capacity. Even if G&T investments are not actually deferred, the LRMC of bulk kW supply may be used as a proxy for the value of kW losses in the distribution system at the time of the bulk system peak as described below. Thus, losses and customer loads are indistinguishable as far as bulk supply system is concerned. If for example, losses do not impose burdens on bulk capacity, then the incremental costs of serving customers will also be negligible. Furthermore, in an optimally planned electricity supply system, there are two conditions that must be satisfied: a. Optimal price equals the LRMC of supply; and b. Optimal incremental cost of system improvements equals the cost of outages avoided due to improved reliability. When losses are reduced, it is equivalent to a reduction in demand. Thus bulk system capacity additions may be deferred yielding cost savings represented by bulk supply LRMC. Alternatively, if the generation and transmission expansion investments continue relatively unchanged (e.g., due to lumpiness), then the improved bulk supply reliability will provide cost savings (due to averted outage costs at 71 In contrast, various previous authors incorrectly suggest lower values for these losses (especially kW losses). For example, in the article "Evaluation of the Costs of Losses in Power Systems", by B. F. Johnson, it is stated that "a demand charge should not be applied to losses in economic evaluation". In a similar vein C. J. Baldwin et. al. in their article "A Further Look At Losses", argue that small incremental losses should not have a kilowatt or capacity charge, assuming that small loss reductions will not affect large bulk capacity investments. For details of how LRMC is estimated, see for example: M. Munasinghe, "Principles of Modern Electricity Pricing", Proc. IEEE, Vol. 69, March, 1981, pp.332-348; or M. Munasinghe and J. J. Warford, Electricity Pricing, Johns Hopkins University Press, Baltimore, Maryland, 1982. - 22 - the margin) that are equivalent to the marginal savings that could have been realized from deferred G&T investments.8/ 8/ We note that in the first case, the cost savings accrue to the power supplying company whereas in the second case, the customers gain. Thus from a social viewpoint both costs savings are equivalent, whereas from the power company's viewpoint the former is more desirable. - 23 - CHAPTER 3 CALCULATING DISTRIBUTION SYSTEM LOSSES This section provides the generally accepted procedures, assumptions and equations used to calculate voltage/loading/losses on distribution systems. The engineer who has a desk calculator and wants to determine which locations warrant in-depth study will find this presentation to be useful. However, as mentioned in Appendix D, detailed studies can be accomplished only with digital computer models from the practical standpoint of the availability of time and engineering manpower resources.9/ Figure 3.1 is a very simplified distribution system consisting of a distribution substation, primary system, distribution transformer and a secondary system. It will be used to illustrate voltage/loading/loss calculations for these components: (1) Primary and Secondary Systems (2) Substation and Distribution Transformer (3) Power Factor Correction With Capacitors 3.1 Primary and Secondary Systems A demand such as Load 1 of Figure 3.1 requires power (voltage and current) to carry out a task which is measured as: Power (Watts) = Voltage (Volts) X Current (Amps) X Cosine 0 10/ The electrical resistances of the system components between the source (substation) and the load cause voltage drop and losses: Voltage Drop is a function of Current (I) and Resistance (R). Demand Loss is a function of the square of the Current (I) and Resistance. 9/ We note, however, that the computers to accomplish these calculations are very low cost in comparison to the accounting computers used for billing. The following computer facilities can be purchased in the USA for about $10,000 and is adequate to carry out all of the modeling and analytical studies described in this report: Central Processing Unit (16 Bit), 64 kilo Bytes of Memory, dual double density floppy disk drives (500 kB each), CRT terminal (24 lines, 80 char.), Printer (180 cps), complete operating system, Fortran IV compiler. 10/ Cosin 0 power factor. Figure 3.1 TYPICAL DISTRIBUTION SYSTEM LAYOUT SUBSTATION KVS T ILD1 + ILD2 1 ILSI+ ILS2 1' LOAD 2 opR2 R3 ILD2 4 LD2 LD1 + + ILS2 ILS1 A RSEC LOAD 1 DTI ILDI - 25 - Energy Loss is the summation of the Demand Losses (12R) over time (Hours). Computing voltage/loading/losses on a distribution primary system is a classic "Chicken and Egg" situation (Which comes first?). The voltage at the substation (KVST) is known but the level erodes due to resistances as we get further away from the station. The voltage level at each load point is required to compute the amount of current (I) required by each load. However, the current (I) is dependent upon voltage level (which is not known) and the line losses are dependent upon the square of that also unknown current. All one really knows at the beginning is: . Voltage level at station . Electrical characteristics of lines and equipment . Approximate demands at load centers Computing voltage/loading/losses on a primary or secondary system is an iterative process. For the sake of completeness, we summarize this simple engineering procedure as follows: (1) A voltage level at the furthest load (say Load 1) is assumed. (2) A current (ILD1) for the load is computed based upon a fixed demand for non-voltage sensitive devices such as motors or a variable demand for such devices as incandescent lamps. (3) The current (1LD1) is used to compute losses (ILD1)2 x RSEC in the portion of the system serving Load 1. (4) The above is repeated for all loads and all sections on the feeder with load flow in each section cumulated and noted. (5) Now, one begins at the station with the known voltage (KVST) and computes voltage drops to the end of the feeder using the loads and losses computed in the above Steps (1) thru (4). (6) The voltage level at Load I assumed in Step (1) is compared to the computed voltage level from Step (5). If they do not match, a new voltage level is assumed and Steps (1) thru (5) are repeated. - 26 - The above iterative process becomes very tedious, time consuming and expensive for a complex feeder serving several hundred load centers. Manually, an engineer might require 40 hours to compute voltage, loading and losses for a complex feeder whereas a digital computer can do the calculations in seconds. Division of a distritution primary or secondary system into loads and line sections will depend upon the configuration of the loads. Figure 3.2 illustrates the three basic loading configurations: (A) A concentrated load is the simplest arrangement (B) Equal loads disbursed evenly on a line may be replaced by a single total load. (C) Non-equal loads unevenly disbursed require analysis by nodes and sections. In the real world, most feeders are type (C) and require many calculations. For the simplified system shown in Figure 3.3 (A): I = Current in amperes I = kW kVLL x V KVLL = Line to Line Voltage at the Load (kilovolts or 1000's of volts) KVLL = KSource - Volts Drop (1000's of volts) KW Three Phase Load (kilowatts or . 1000's of watts) Volts Drop - I (R Cos 0 + X Sin 0) I = Current (Amps) R = Resistance (ohms) X = Reactance (ohms) Cos 0 = Power Factor of Load the voltage drop is for one conductor (line to neutral). The three phase line-to-line drop is (3) 1/2 times this value, and the single phase drop is twice the above value. The vector diagram of Figure 3.3 (B) shows that the above equation is approximate, but is sufficiently accurate for all practical purposes. - 27 - Figure 3.2 LOADING CONFIGURATION Line Source Load (A) Concentrated Load Source D1 1D2 D1 = 1/2 Distance for voltage calculations PI = 1/3 Distance for loss calculations (B) Uniformally Distributed Load L3 e S, S2 Q S3 S5 (C) Distributed Loads - 28 - Figure 3.3 I VB-R X -TC 7SOURCE L L I O R X 3,0 LOAD R x (A) Simplified System Calculated DroM IR Ix Cos a a. Sin 9 Error Actual DrO - VL s Vr, I ix (B) Vector Diagram Note: The error is relatively small - 29 - Losses for the simplified system are computed from the following equation. Losses (Watts) = I2R The above losses are for one conductor, so the total would be 3 times the above value for 3 phases. 3.2 Substation and Distribution Transformers A basic transformer is illustrated in Figure 3.4. The total demand on the transformer consists of the core losses and the demands associated with the loads. The total load on the transformer cause: (1) Demand Losses = I2R (2) Energy Losses = I2R over time (3) Loss of life if loading exceeds capacity over an extended period of time. The no-load or core losses (sometimes referred to as iron losses) and the resistances of station transformers should be obtained from the manufacturer and the nameplate information. The characteristics of specific distribution transformers should also be obtained from manufacturers or their nameplate. For estimating purposes and to give readers an appropriate benchmark, Tables 3.1 and 3.2 provide typical values of no-load and total losses at nameplate rating for a group of the more common sizes of single phase transformers built to U.S. National Electric Manufacturer Standards (NEMA). - 30 - Figure 3.4 BASIC TRANSFORMER MODEL Core Losses Demand (1) (kW) (kW kVAR) I I MODEL I Resistance o Single Phase o Three Phase o Bank of Transfo=er Reactance II II Demand Losses (kW) Energy Losses (kWH) Probable Loss of Life (%) (1) Demand may be: Single Phase Three Phase Mixed Single and Three Phase TABLE 3. 1 DISTRIuIUI TRANSEORER IIOSSES TYPICAL SINGLE PHASE UNITS (60 Hertz) 14400/24949 34500 GRD.Y/ 2400/4160Y 4800/8320Y 7200/12470Y G4D.Y 19920* to to to to to 120/240 VOLTS 120/240 VOLTS 120/240 VOLTS 120/240 VOLTS 120/240 VOLTS WATPS IOBS WATTS IXSS WATTS IOSS WA'TS IDSS WATTS IMSS KVA No Load Tbtal No Load Total No Load lbtal No Load Total No Load Tbtal 5 36 125 36 133 36 138 36 142 - - 10 59 180 59 183 59 184 59 200 59 202 15 76 232 76 242 76 255 76 263 76 290 25 109 380 109 370 109 404 109 420 109 432 37.5 158 495 158 521 158 550 158 565 158 557 50 166 611 166 613 166 671 166 717 166 714 75 274 916 274 918 274 937 274 1024 274 981 100 319 1192 319 1146 319 1200 319 1300 319 1247 167 530 2085 530 2085 530 2085 530 2085 530 2035 240/480 240/480 240/480 240/480 240/480 250 625 2800 625 2800 625 2800 625 2800 625 2800 333 800 3400 800 3400 800 3400 800 3400 800 3400 500 1100 4850 1100 4850 1100 4850 1100 4850 1100 4850 1/ Values are similar for 50 Hertz Units. - 32 - TABLE 3.2 DISTRIBUTION TRANSFORMER LOSSES OTHER THAN RATED VOLTAGE (Typical U.S. Single Phase Units - 60 Hertz) Percent Percent Percent Percent Percent Percent Rated No-load Load Rated No-load Load Voltage Loss Loss Voltage Loss Loss 80 0.61 1.56 100 1.00 1.00 81 0.62 1.52 101 1.03 0.98 82 0.64 1.47 102 1.06 0.96 83 0.66 1.45 103 1.08 0.94 84 0.67 1.41 104 1.12 0.93 85 0.69 1.37 108 1.25 0.86 86 0.71 1.36 106 1.18 0.89 87 0.72 1.32 107 1.21 0.88 88 0.74 1.28 108 1.25 0.86 89 0.76 1.25 109 1.28 0.84 90 0.77 1.24 110 1.32 0.83 91 0.79 1.21 111 1.36 0.81 92 0.81 1.18 112 1.39 0.80 93 0.83 1.15 113 1.44 0.79 94 0.85 1.13 114 1.48 0.77 95 0.88 1.11 115 1.52 0.76 96 0.90 1.09 116 1.56 0.75 97 0.92 1.07 117 1.60 0.73 98 0.95 1.04 118 1.65 0.72 99 0.98 1.02 120 1.74 0.70 - 33 - The relationship between Load Factor and Loss Factor is given by a typical empirical relationship of the form (see Appendix D for explanation): Loss Factor = 0.15 Load Factor + 0.85 (Load Factor)2 3.3 Power Factor Correction Power Factor correction with capacitors is one of the principal lines of defense against demand and energy losses. The basics of capacitors used for power factor correction will be discussed using the system of Figure 3.5. First and very important --- primary capacitors have been used for power factor correction and voltage regulation for over 40 years. The economics, their durability and benefits have been proven time after time by thousands of utilities. There is no reasonable or logical reason for refusing to apply capacitors to reduce losses. Many loads, especially motors and new types of electronic devices (such as speed controllers and investers) have high reactive power demands. In this example, we have assumed that the load has lagging power factor character- istics: Kilowatt Demand (kW) = 1000 kW Kilovar Demand (kVAR) = 1000 kVAR Kilovolt Amperes (kVA) = (10002 + 10002)1/2 = 1414 kVA Power Factor = 1000 kW x 100 = 70.7% 1414 kVA Per unit current is proportioned to kVA and is 1.414 Without power factor correction, the 1414 kVA of load must be transported all through the system from the generator to the load. The voltage drop and losses associated with transporting the 1414 kVA of load will be proportional to the current and the square of the current respectively: Voltage drop proportional to the per unit value of current or 1.414 Losses proportional to the square of per unit current which is (1.414)2 or 2.0 The lagging 1000 kVAR's of the load can be supplied by a 1000 kVAR capacitor bank located right at the load center. The resultant load on the system is: Kilowatt Demand = 1000 kW Kilovar Demand = 0 kVAR Kilovolt Amperes - 1000 kVA - 34 - Figure 3.5 POWER FACTOR CORRECTION Net Load 1000 kW 1000 kVAR 1.414 Units of Current 1414 kVA I 0rro Transmission Sub- Distribution Generation Transission Load (A) No Power Factor Correction 1000 kVAR Capacitor 1.00 Units of Current Load Net Load 1000 kW 0 kVAR 1000 kVAR (B) With 100% Power Factor - 35 - Power Factor 1000 kV x 100 = 100.0% 1000 kVA Per unit current is proportional to kVA or 1.00 The voltage drop and losses associated with the corrected load is now: Corrected Load Voltage Drop 1.00 x 100 = 70.7% 1.414 Corrected Load Losses 1.002 x 100 = 50.0% 1.4142 The capacitors reduced voltage drop by 30% and losses 50%. The effect on voltage drop and losses of correcting power factor may be calculated with the above equations or estimated from Table 3.3. TABLE 3.3 EFFECT ON VOLTAGE DROP AND LOSS PARAMETERS OF CORRECTING POWER FACTOR TO 100% Per Unit Corrected Level Kilovolt Amperes (kVA) Previous Voltage Power Factor Previous New Drop Losses 50% 1.00 .50 50% 25% 55 1.00 .55 55 30 60 1.00 .60 60 36 65 1.00 .65 65 42 70 1.00 .70 70 49 75 1.00 .75 75 56 80 1.00 .80 80 64 85 1.00 .85 85 72 90 1.00 .90 90 81 95 1.00 .95 95 90 3.4 Simplified Procedure (First Approximation) It would be possible and highly desirable to develop some tables and graphs to obtain a rough idea of losses for station transformers, primary feeders, distribution transformers and secondary systems. These graphs could be developed using existing analysis programs to generate the basic data. The conductor graphs could be something like Figure 3.6 with different figures for the various voltages and phases. The graph would provide kilowatt peak losses and a second graph (Figure 3.7) could provide For One Kilometer of Line 36 - 11000 Volts 3 Phase Various Conductor Peak- Sizes Peak , Demand (kW) Peak Loss (kW) Figure 3.6. Peak Demand Versus Peak Loss Various Load Peak Factors Loss (kW) Annual Energy Loss (kWk) Figure 3.7. Peak Loss Versus Annual Energy Loss Various Peak Transformers Demand (k'W) Copper Loss or Peak Loss (kW) No Load or Iron Loss (kWh) Figure 3.8 Peak Demand Versus Transformer Losses - 37 - energy losses. A group of transformer graphs (Figure 3.8) could be developed to obtain copper losses at peak as well as annual no-load losses. Figure 3.7 can be used to determine annual energy losses due to copper loss. In addition, a group of benefit to cost tables or graphs could be developed and issued in the form of a manual. These benefit to cost guidelines woufld be somewhat rough because of the simplifying assumptions required to keep the number of parameters and cases analysed within practical limits. The options of most interested would be: (1) Correcting Power Factor (2) Conductor change out (3) Station Transformer Change out (4) Distribution Transformer Change out (5) Decentralizing Secondary Systems The variables to be parametrized are: (1) Costs to install, remove, replace, and purchase (2) Discount rates (3) Costs of demand and energy (4) 0 and M costs - 38 - CHAPTER 4 OPTIMIZING DISTRIBUTION LOSSES This chapter provides an overview of the proposed methodologies to carry out the prime objectives of this project. . Isolating technical losses . Reducing losses to an economic level . Incorporating losses into the decision making process relative to design and operating criteria 4.1 Isolating Technical Losses on Primary Systems In general, the isolation of technical losses at the generation and transmission levels is not a problem because these facilities are usually well metered and well monitored. Similarly, the isolation of technical losses for a distribution substation is rarely a problem because these are also well metered and monitored. The isolation of losses for the remainder of the distribution system is more complex and difficult. Figure 4.1 shows a simplified version of a distribution system. The station transformer could be metered and there may be meters for each feeder at the station bus. But that would be no more metering until the meters at each consumer. Some utilities compare the energy delivered to their substations over a specified time period such as one year with the total energy billed to their consumers over the same time period. The difference betwwen the two totals is considered to be "Annual Energy Losses". For example, a utility might have recorded the following for a year: Total Energy Delivered to Substations 645,000 MWH Total Sales 470,850 MWH Difference (Assumed Losses) 174,150 MWH It appears that this utility has losses of: Loss = 174,150 x 100 = 27% of Total Delivered to 645,000 Substation Loss = 174,150 x 100 = 37% of Sales 470,850 There are two major sources of error in this commonly used method for computing losses: - 39 - Figure 4.1 DISTRIBUTION SYSTEM SUB TRANSMISSION STATION TRANSFORMER STATION BUS kW kVAR LEGEND O Breakers Primary System A Distribution Transformer --- Secondary System Regulator Capacitor Consumer Meters (S Spot Load (kW demand is known) - 40 - (1) The difference in energy between stations and sales includes energy used by consumers but not measured such as theft, bad meters and mis-read meters. The difference is actually "unaccounted for" energy. (2) The station meters are probably all read on the same day and represent 12 months of actual purchased energy. However, the readings of consumer meters are scattered over a period of time so there is a lag which tends to distort the analysis. For example, if consumers are billed on a monthly basis, different meters may be read several weeks apart. Even if the above method produces reasonably accurate results, it does not provide any clues as to "where" the losses are occurring. The Allocation Method used in this study was developed to determine the "where" of power flows on distribution primary lines and secondary lines and to enable an engineer to separate technical losses from other "unaccounted for" energy. The methodology is described below and illustrated in Figure 4.2: (1) Obtain or prepare a map of the distribution system at electrical single line level. The map must include information on conductors, phasing, distribution transformers, capacitors, regulators, etc. (2) Obtain the demands (kW and kVAR) of each feeder at each substation at the time of system peak. (3) Allocate the feeder demands to the distribution transformers in proportion to their rated capacity. (4) Compute voltage drops and on-peak demand losses using the methodology described in Chapter 3. (5) Compare the allocated demands plus losses with the original substation demand. If they do not compare favorably (say within 1%), then modify the load to be allocated and repeat steps (3), (4) and (5). (6) The probable energy losses for each feeder may be obtained from the loss factors derived per the methodology of Appendix D. Note: The above methodology requires iterative processing which may be done manually but is best done on a digital computer. 4.2 Isolating Technical Losses in Distribution Transformers There are two generally acceptable ways to obtain the loads on existing distribution transformers: - 41 - Ligure 4.2 ALLOCATING DEMANDS (BY FEEDER) Feeder Demand at Substation kW & kVAR YES Any Spot Loads? IF NO Subtract Spot Loads from Station Demand Allocate Demand Among Distribution Transformers In Proportion to o Connected kVA or o kWH for Peak Month Compute Voltage, Losses and Loading Is Loading Sare as Allocated Demand? YES No Modify Demand to be Allocated * (e.g. within a few percent) 42 - (1) Measurement --- installation of clamp-on thermal demand ammeters on selected transformers during the peak demand season (say 1/3 of the transformers each year). Another measurement method is to have lineman use a ammeter to measure the load (lineman must be there at time of peak). (2) Energy Usage by Consumers --- this method, often called Transformer Load Management or TLM, is very effective and for most utilities, the benefit to cost ratio is approximately 15 to 1 ($15 saved per $1 of cost). TLM is initiated and operated in the following manner: (a) Each consumer is correlated with his serving distribution transformer. (b) The energy usage (kWh) for the peak month is obtained from customer records and totalled for each transformer. (c) The demand on the transformer is computed from the energy and number of customers by class of service based on equations derived by each utility. For example, an empirical relation- ship which was derived from a survey of several U.S. utilities was: kVA Demand = 7.3 + (3.523 x kWh) - (0.022 x (kWh)2) kWH = Energy usage for one month The above equation is a good approximation for kWH's within the range of 2000 to 15000 kWH/month. After a demand has been determined for a transformer, the no-load, load and energy losses may be computed from the methods detailed in Appendix D. 4.3 Isolating Technical Losses on Secondary Systems The European style distribution system is based upon large distribution transformers feeding extensive secondary systems. A system such as the one shown in Figure 4.3 might serve from 50 to 200 consumers. There are two generally acceptable methods for determining the loading on a secondary system: (1) Meter sufficient number of points to determine demands at the transformer, at the mains, and at branch points (This is tedious and expensive). - 43 - (2) Expand the TLM (Transformer Load Management) system to include the secondary system: (a) Determine demand on transformer as described in the previous portion of this section. (b) Allocate the transformer demand among the segments of the secondary system in a manner similar to the methodology described for the primary system and illustrated in Figure 4.2. (3) Develop the following and use them to compute secondary system loading: (a) Coincidence factors for various quantities and classes of consumers such as those shown in Figure 4.4 (A). (b) Relationship between demands and monthly energy requirements by class of consumer such as those shown in Figure 4.4 (B). Note: It is not expected that the data of Figure 4.4 (A) and (B) will be directly applicable to World Bank Borrowing nations because they are based on USA residential consumers. However, they do illustrate the type of data that is needed and may be useful as a yardstick of comparison. 4.4 Economic Reduction of Losses Figure 4.5 illustrates the basic procedures for determining the economic levels for all system components. Following is a brief description of this procedure: (1) Select portion of system to be studied: . Station Transformers . Primary . Distribution Transformers . Secondary (2) Obtain electrical and physical characteristics of components and form model of system (either manually or on computer). (3) Select a loading cycle (day, week, month, year, etc.) and determine the following major parameters using the methodology described in Appendix D. . Peak Demand . Load Duration . Load Factor . Loss Factor - 44 - Figure 4.3 SERVICES PRIMARY IMAI -A' I *DISTRIBUTION TRANSFORMER TYPICAL EUROPEAN STYLE SECONDARY SYSTEM Voltage is 240/416 Volts (10/30) NEUTRAL 20 230V 400V Service to residential consumers 10 230 Volts Service to commercial 10/3.0 230/400 Volts - 45 - Figure 4.4 1.00 1.00 __ _ _ ___ _ _ _ __ _ _ _ _ 0.90 0.80 0.70 0.60 C 0.50 0.40 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 0.30 L A 0.20 _ A. Domestic - Without electric range ---B. Domestic - with electric range 0.10 C. Domestic - With air conditioning 1 2 5 10 20 50 100 Number of Consumers (A) Typical Coincidence Factors - Residential Consumers (US) 20 -- - - - 18 Consqmer kW versus W- The slope of the line yields the- 16 Conversion Factor (Kf) used in TLM- - - -- - calculations 14 - The (Kf) decreases with the number 12 of deree days in the 10 8 6 4 2 1 A 200 400 600 800 1000 2000 3000 kW9H Peak Month Cnsption per Cvnseker (BConers nr DFand Versus Ener usage for STLMer Season, (US) - 46 - Fizure 4.5 DETEMINING SYSTEM COSTS AND COSTS OF LOSSES (TRANSFORMERS, PRIMARIES AND SECONDARIES) Select Component of System Select Model Loading the Characteristics Component Analyze Losses, Loading, Voltage YES System Changes Add or Replace NO Economic Analysis Annual Costs (Investment, O&1 and Losses) Present Worth - -47 - (4) Compute technical losses using methodology of Chapter 3. . Loss at Peak (Demand) . Energy Losses (5) Select a practical variety of system changes to reduce losses. . Transformers Replace Shift Load . Primaries Capacitors Reconductor New Lines Switch Change Voltage Levels . Secondaries Reconductor (Shift Loads) Reduce or Eliminate (6) Determine costs associated with each alternative Power (demand and energy) Investment Labor Materials Other Operation and Maintenance (7) Carry out an economic evaluation of the alternatives using the methodology of Chapter 2. 4.5 Engineering Design Criteria It is important that design criteria reflect the cost of losses. This is especially true for the sizing of conductors, normal and emergency loading of conductors, and transformers, application of regulators, and power factor control. The general procedures for establishing design criteria are as follows: (1) Determine probable magnitudes of demands and loading patterns for the various levels of the system. Use average values as suggested in Appendix D if exact 'conditions are not available. (2) Determine installation, operation and maintenance costs for the facilities being evaluated such as varied sizes of conductors. (3) Impose load patterns from (1) above on the alternative sizes over a time period such as 20 - 48 - years. Compute losses using the methodologies of Appendix B and evaluate these losses per the methodologies of Appendix A. (4) Derive the present worth of all costs (installation, operation, maintenance, and losses) for the alternative sizes and select the size or sizes which most economically meet long range requirements. The above process can be accomplished with desk calculators, simple computer programs or full scale computer models. 4.6 Specification Requirements and Bid Evaluation for Distribution Transformers It is also important for the utilities to develop specifications that include loss criteria, for evaluating distribution transformers. That is, every request to manufacturers for distribution transformer bids should contain: (1) The evaluation methodology to be used (2) The loading parameters which will be used in evaluation . Load Factors (by seasons) . Loss Factors (by seasons) . Growth Rates (by seasons) . Time Horizon (3) Installation and replacement costs (4) The capacity costs by seasons (5) The energy costs by seasons (6) The discount rate The manufacturers can then direct their design towards producing transformers with the lowest overall cost on a present discounted value basis over the transformer lifetime (purchase, installation and maintenance costs, and value of losses). Another alternative is for the utility to work directly with the manufacturer to determine the lowest cost design, considering both manufacturing and operating costs. Transformers bids can also be evaluated on the basis of lowest life cycle present value of costs (including losses). Most of the basics for establishing design specifications and evaluating bids are contained in Appendices A, B, and D. - 49 - CHAPTER 5 SUMMARY OF CASE STUDY RESULTS This chapter contains a summary of the case study results, with details provided in Appendix C. Although they are desk studies, the case studies of this project provide affirmative answers on a preliminary basis to the following pertinent questions: . Do the proposed methodologies for isolating technical losses provide reasonable results? . Are the proposed methodologies practical and relatively simple to apply in the developing country context? . Does loss reduction appear to provide a high level of benefits relative to costs? . Should losses be a major factor in establishing engineering criteria for planning, design and operations? Our most important conclusion is that within practical limitations --- loss reductions at distribution level provides capacity and energy at far less cost than obtaining capacity and energy through the construction of new generation and transmission facilities. The case studies indicate that utilities can obtain savings up to $15 for every $1 of cost associated with reducing distribution system losses (primary system, distribution transformers, secondary system). Therefore losses should be recognized as a dominant factor in the engineering criteria used in system planning, design and operation. As an example Table 5.1 provides an overview of existing common loading practices for distribution facilities versus the economic loading levels indicated by the case study results: - 50 - TABLE 5.1 ECONOMICALLY JUSTIFIED DISTRIBUTION SYSTEM LOADING LEVELS BASED ON LOSS OPTIMIZATION VERSUS EXISTING GUIDELINES FOR LOADING Economic Maximum Loading Based Existing Maximum Loading On Optimized Losses Practices (As a % of (As a % of nameplate rating of nameplate rating or Thermal Limit) Thermal Limit) Thermal Reliability* Item Criteria Criteria Primary Conductors 100% 50% 15 to 25% Distribution Transformerl 180% N.A.** 80 to 100% Secondary Conductors 100% N.A.** 10 to 15% * Reserve for emergencies ** Rarely loaded to provide reserve for emergencies Based on U.S. design, 650 rise transformers. Conventional IEC Standard units (500C rise) may be able to take only up to about 125% of thermal limit without drastic reduction in useful lifetime. - 51 - As the table shows, the case studies indicate the need to make some very major departures from existing practices, namely that the value of losses should be the single most important element in establishing engineering criteria for the planning, design and operation of distribution systems. It must be recognized that the results of a desk study based on data from technical sources and from a few developing countries cannot be considered conclusive enough to develop worldwide guidelines, However, the results of this study strongly indicates that there is significant and immediate potential for savings to be realized through loss reduction in LDC's. 5.1 Primary Conductor Loading A portion of the distribution system of Punjab State, India was used in evaluating losses on a primary system for a variety of conductor loading levels. The objectives of this case study were to determine: (1) The investment costs for various primary systems serving an area over a 20 year time frame. The major variation between systems was the maximum conductor loading permitted. (2) The cost of losses (demand and energy) associated with each system. (3) The ratio of savings through loss reduction to the cost of reducing those losses. (4) Probable economic conductor loading limits. Specifically, case studies were made for the following conditions: (1) Primary models were studied over a 20 year time frame with maximum conductor loadings at 100%, 75%, 50% and 25%. (2) Losses were evaluated for two cost levels:11/ $130/kW/Year and $0.011/kWh (about US4 4 per average kWh) $250/kW/Year and $0.037/kWh (about US 9 per average kWh) 11/ The range of values US44 to 9 per average kWh lost is representative of a wide variety of all hydro, hydro-thermal, and all thermal systems found in LDC's. Some systems may have higher values of LRMC per kWh but hardly any would be lower. - 52 - (3) The present worth of costs was derived with the economic model described in Chapter II, using a discount rate of 12%.12/ The results of this case study is tabulated in Table 5.2 and shown graphically in Figure 5.1 Table 5.2 shows that for a system with maximum conductor loading of 100% and the higher value of losses, the present worth of losses will be $881,600 and the present worth of future investments is $4,900. If maximum conductor loading is reduced to 75%, the P.W. of investment rises to $15,500 and P.W. of losses reduces to $717,300. The incremental investment of $10,600 produces a reduction in losses of $164,300 for a benefit to cost ratio (BCR) of 15.5 to 1 ($15.5 saved per $1 of cost). Figure 5.1 indicates that the breakeven point (BCR-1) for maximum conductor loading is probably in the general neighborhood of 15 to 25% --- a substantially lower level than loading limits based on existing criteria. 5.2 Power Factor Control Power factor is controlled by most utilities with the aid of capacitors on the primary system. The basics of using capacitors to control power factor have been presented in Chapter 3 and the following is a brief review: (1) Many devices, especially motors, require "Lagging kVAR's to operate (2) The Lagging kVAR's may be supplied from the generators which requires the kVAR's to be transported through the entire system (transmission, sub-transmission, stations and primaries) or The lagging kVAR's may be supplied from capacitors located near the load centers. Basically, power factor control reduces demand which may be evaluated in a number of ways: (1) Reduced losses (2) Better voltage regulation (3) Released generation, transmission and distribution capacity to serve other existing loads. 12/ This long run average discount rate (or opportunity cost of capital) is on the conservative side, since it is at the upper end of the scale appropriate to most LDC's. A lower value would further enhance the arguments for and urgency of distribution loss reduction. -53 - TABLE 5.2 VALUE OF LOSS SAVINGS BY REDUCING MAXIMUM CONDUCTOR LOADING (NO POWER FACTOR CORRECTION) Maximum Investment ($x1OOO) Cost of Losses ($xlOOO) Benefit Conductor to Loading(%) Total Incremental 1/ Total Incremental 1/ Cost Ratio 2/ Losses Priced at $250/kW/year and $0.037/kWh 100% $ 4.9 $ - $881.6 $ - - 75% 15.5 10.6 717.3 164.3 15.5 50% 30.8 15.3 554.0 163.3 10.7 25% 104.0 73.2 332.9 221.1 3.0 Losses Priced at $130/kW/year and $0.0114/kWh 100% $ 4.9 $ - $445.4 $ - - 75% 15.5 10.6 362.6 82.8 7.8 50% 30.8 15.3 280.0 82.6 5.4 25% 104.0 73.2 168.2 111.8 1.5 1/ Incremental with respect to next higher level of maximum conductor loading. 2/ Dollars saved for each dollar of investment (Savings divided by Incremental Investment) 15.0- Figure 5.1 $250/kW/yr. INCREMENTAL BENEFIT-COST RATIO FOR SUCCESSIVE REDUCTIONS $0.037/kWill IN CONDUCTOR LOADING 25% * 10.0 Kd Practical Goal (n C$13olkw lyr. 50 $0.0114/kWiH O 0 1.0 - - .. - - - 9e&ey, ~_ 100% (4.6%) 75% (3^5%) 50% (2.9%) 25% 1.8%) 0% MAXIMUM CONDUCTOR LOADING (LOSS GIVEN IN PARENTRISIS) - 55 - (4) Savings in investment by delaying the need to add facilities to serve load growth In this case study, benefits have been evaluated for reducing losses only. This was accomplished by correcting the power factor from 80% to 95% for the Primary Conductor Loading systems. The system additions (without capacitors) to maintain conductor loading at 100%, 75%, 50% and 25% were left unchanged. Capacitors were added to those systems over the 20 years as required to maintain a 95% power factor. Consequently, capacitor additions are the same for each conductor loading condition. The benefits between systems vary because the load levels and losses vary with conductor loading. The maximum benefits from power factor control are related to the system with 100% maximum loading because there are more losses to eliminate by reducing kVAR flow. A summary of the study is tabulated in Table 5.3 and graphed in Figure 5.2. For the higher cost of losses and 100% conductor loading, the P.W. of annual costs of $19,700 in capacitors results in a P.W. savings of losses of $294 ,400. This situation provides $14.9 of savings for every $1 of cost --- an excellent benefit to cost ratio. Even the lowest benefit condition (lowest loss costs and 25% conductor loading) provides $2.9 in savings for every $1 of annual cost. It is clear that power factor control via capacitors reduces losses with a high benefit to cost ratio. It is highly probable that field studies will confirm that the installation of primary capacitors should be the first step in a loss reduction program, in most cases. 5.3 Distribution Transformers A computer program capable of modeling and analyzing distribution transformers was used to study the effects of various loading patterns on typical distribution transformers. The transformers used in the study are standard single phase transformers. The transformer portion of the study comprised of: . Transformer sizes 5, 10, 25, 50, 100 and 250 kVA . Load levels (% of nameplate) 50, 100, 150, 175, 200, 225, 250, 275 . Load Factors (%) 25, 50, 75, 100 . Cost of Losses (2 levels) a) $130/kW/yr. and $0.0114/kWH - 56 - Table 5.3 VALUE OF LOSS SAVINGS BY CORRECTING POWER FACTOR FROM 80% TO 95% AT VARIOUS AXIMUM CONDUCTOR LOADING LEVELS Various Maximum Conductor Loading P.W. of P.W. Cost of Losses($x1000) Capacitor * Annual Benefit Costs No With to ($x1000) Capacitor Capacitor Savings Cost Ratio Losses Priced at $250/kW/year and $0.037/kWH 100% $ 19.7 $ 881.6 $ 587.2 S 294.4 14.9 75% 19.7 717.3 477.7 239.6 12.2 50% 19.7 554.0 369.0 185.0 9.4 25% 19.7 332.9 221.7 111.2 5.6 Losses Priced at $130/kW/year and $0.0114/kWR 100% $ 19.7 $ 445.4 $ 296.7 $ 148.7 7.5 75% 19.7 362.6 241.5 121.1 6.1 50% 19.7 279.8 186.4 93.1 4.7 25% 19.7 168.2 112.0 56.2 2.9 * Dollars saved per dollar invested (Savings divided by investment) Figure 5.2 15.0 'U BENEFIT TO COST RATIOS ta 4) CORRECTION OF POWER FACTOR FROM 80% TO 95% FOR $250/kW 0 $0.037/kWl VARIOUS MAXIMUM CONDUCTOR LOADINGS LEVELS P-5 10.0O *0 0 S5.0$130/kW E-i $0.0114/kWiI r%4H 0% (3.1%)(2.5%) 50% (1.9% 25% (2.1%) 0% MAXIMM CONDUCTOR LOADING (Loss Given in Parenthesis) - 58 - b) S250/kW/yr. and $0.037/kWh (Approx. US49 per average kWh) The computer model was used to derive the no load losses (often referred to as Iron losses) and load losses (often referred to as Copper losses) for the above circumstances. The results of these analysis are tabulated in Table 5.4 and shown graphically in Figure 5.3. Anual costs with and without the cost of losses were then derived for each transformer at the various load levels. The results of these derivations are shown graphically in Figures 5.4 and 5.5 for the two levels of loss costs. Next, the existing practice of sizing transformers to meet demands based on thermal capabilities was compared with sizing transformers based on economics (cost of losses included). The two sizing techniques are shown on Figure 5.4 and 5.5 (X's and O's) and tabulated in Table 5.5. The study clearly indicates that losses must be considered in the sizing of transformers to meet specific load levels. In this example, proper sizing at the higher cost level produces annual savings of up to 48%. We must recognize that detailed engineering and economic analysis of transformer loading can be pursued at a more complex level. This study provides indicative results that could be confirmed by an indepth study, including such variables as: Loading cycles (before and during peak) Ambient temperatures Completely self protected (CSP) transformer Self protected (SP) transformer Growth rates Ratio of iron to copper losses Purchase costs Installation costs Replacement costs Maintenance Connections and voltages Taps A more definitive study would provide the methodology and guidelines related to: - 59 - TABLE 5.4 DISTRIBUTION TRANSFORMER NO LOAD (IRON) AND LOAD (COPPER) LOSSES VERSUS VARIOUS LOAD LEVELS (For typical U.S. Single Phase Units) Transformer No Load Load Losses (kW) at Various Load Levels Size Loss (kVA) (kW) 50% 100% 150% 200% 250% 5 0.045 0.037 0.144 0.323 0.572 0.893 10 0.070 0.060 0.237 0.532 0.944 1.473 25 0.130 0.118 0.467 1.048 1.860 2.903 50 0.225 0.204 0.808 1.814 3.222 5.030 100 0.400 0.375 1.491 3.348 5.945 9.283 250 0.925 0.781 3.105 6.972 12.383 19.336 Figure 5.3 DISTRIBUTION TRANSPORMER LOAD LOSS (WATTS) PER kW OF DEMAND 60 DEMAND AS % OF RATING OR SIZE 50 O 40 H '4 30 to YC E-4 E-4 H 20 10 0% 50% 100% 150% 200% DEMAND AS % OF NAMEPLATE RATING - 61 - TABLE 5.5 ANNUAL COSTS AND SAVINGS PRESENT TRANSFORMER LOADING PRACTICES VERSUS LOWEST COST LOADING PRACTICES Present Lowest Cost Peak Practice (1) Practice (2) Annual Demand Savings (50% L.F.) Size Cost Size Cost (kVA) (kVA) ($) (2) (kVA) ($) $ % Losses at $130/kW/yr. and $0.0114/kWH 5 5 $85 10 $ 75 $ 10 12% 10 5 150 10 110 40 27 15 10 160 25 140 20 13 20 10 220 25 160 60 27 25 25 182 25 182 - - 30 25 210 25 210 - - 35 25 250 50 243 7 3 40 25 300 50 261 39 13 45 25 350 50 280 70 20 50 25 402 50 300 102 25 Losses at $250/kW/yr. and $0.037/kWH 5 5 128 10 111 17 13% 10 5 263 25 163 100 38 15 10 271 25 200 71 26 20 10 460 25 240 220 48 25 25 295 25 295 - - 30 25 358 50 325 33 9 35 25 437 50 357 80 18 40 25 543 50 392 151 28 45 25 646 50 435 211 33 50 25 769 50 497 272 35 (1) Transformers loaded to thermal capabilities - Losses Ignored (2) Includes cost of losses Figure 5.4 - - - - - - - ANNUAL COST NO LOSS $600 ANNUAL COSTS INCLUDING LOSSES PRICED AT $130/kW/yr. and $0.037/kWH X SIZE BASED ON THERMAL CAPACITY $500 - SIZE BASED ON ECONOMICS $400 $300 0-5 0 10 20 30 40 kVA DEMAND (50% LOAD PACTOR) 6(00 - ANNUAL COSTS NO LOSSES ANNUAL COSTS INCLUDING LOSSES $500 PRICED AT $250/kW/yr. and $0.037/kWh X - SIZE BASED ON THERMAL CAPACITY $400 0 - SIZE BASED ON ECONOMICS $300 ^v $200 $100 / / 25 kVA 5 kVA 10 kVA 0 1 I I 0 10 20 30 40 kVA DEMAND (50% LOAD FACTOR) Figure 5.5 - TRANSFORMER COSTS VERFUS kVA DEMAND - 64 - . Purchasing . Initial installation for specific loads with an expected growth rate . Economic replacement levels Best combination of transformers to meet mixed single and three phase loads. This study provides positive evidence that the practices of the past have little validity under the circumstances of today. Further more specific field studies of distribution systems and loading conditions are required. Note on Substation Transformers Substation transformers may be a significant source of losses and should also be analysed in depth. Some of the older transformers, especially Tap Changing Under Load (TCUL), have impedances in the general range of 15%. It is highly probable that these older transformers can be replaced based upon only loss savings, and therefore changing out such units should be second in priority only to power factor correction. 5.4 Secondary Systems There are two basic types of secondary systems used by utilities: Centralized (originated in Europe) which is based upon large centrally located distribution transformers and extensive secondary systems serving anywhere from 10 to 200 consumers. Decentralized (originated in North America) which is based upon small transformers installed at or near the load centers with short secondary systems. Each transforemr serves from 1 to 15 consuemrs depending upon load density. Sixty (60) centralized secondary systems in the Bhikhiwind area of Punjab State, India were studied in this phase of the project. Each of these systems consisted of a single large transformer and an extensive secondary system serving an entire village. A computer model was developed for each of the centralized systems and the systems were analyzed as to voltage, loading and losses. Decentralized systems were then developed to serve the 60 villages. These decentralized systems displaced the single transformers and extensive secondaries with 11 kV piimary lines, small transformers located at load centers and short lengths of secondary lines. The results of this study are detailed in Appendix C and summarized in Table 5.6. - 65 - The major differences between the two concepts may be summarized as follows: The centralized systems transport power to the consumer over low voltage (240/416 volts) secondary lines. The decentralized systems transport the power directly to the consumer or a load center at high voltage (11,000 volts). A decentralized system generally requires more investment due to the greater length of primary lines and the use of many small transformers, In this study, the decentralized system requires $49,940 or 6.1% more investment than the centralized plan. If losses are ignored, the centralized approach would be chosen. Note: In more general applications other constraints may limit the technical-economic choice of options, e.g., urban areas where underground systems are mandated for non-economic reasons. But when losses are considered, the conclusions change significantly: Item Centralized Decentralized Losses On Peak (kW) 300.8 kW 62.6 kW Reduction - 79.2% Energy (kWH) 802,800 kWH 178,000 kWH Reduction - 77.2% Annual Costs Investment + 0 & M $110,130 $116,827 Losses at Highest Cost* 104,904 22,236 TOTAL $215,034 $139,063 Sangjs Dollars -$ 75,971 % -35.3% Benefit/Cost Ratio** 11.3 to I * $250/kW/yr. and $0.037/kWH ** Annual carrying charges (13.41%) on $49,940 or $6,697 compared to savings of $75,971 - 66 - TABLE 5.6 60 CENTRALIZED SECONDARY SYSTEMS VERSUS 60 DECENTRALIZED SECONDARY SYSTEMS Difference (Decentralize Minus I tem Centralized Decentralized Centralized) Transformer Statistics Quantity 60 172 112 Total Capacity kVA 4575 3695 (880) Average Size kVA 76 22 (54) Investment $94,550 $159,635 $65,085 Total Demand kW 2445 2187 (258) Average Demand kW 41 13 (28) % Loaded % 54 59 9 No Load Loss (Iron) kW 2.0 2.2 0.2 Peak Load Loss (Copper) kW 14.8 34.4 19.6 Energy Losses mWH 56.4 109.7 53.3 Primary Lines Total Length kM - $47.2 47.2 Investment - $212,400 $212,400 Secondary System Total Length kM 128.7 89.6 (4.0) Average per Transformer kM 2.1 0.5 (1.6) Investment $726,705 $499,158 ($227,547) Demand kW 2161 2161 - Peak Loss kW 284 26 (258) Percent Demand Loss t 13.1% 1.2% (11.9) Energy Loss mWH 746.4 68.3 (678.1) Total Investment $821,255 $871,193 $ 49,938 Annual Costs Investment of o&m: $110,130 $116,827 $ 6,697 Cost of Losses at: $130/kW, $0.0114/kWE $48,256 $10,167 ($38,089) $250/kW, $0.037/kWH $104,904 $22,236 ($82,668) Total Annual Costs Lower Cost of Losses $158,386 $126,994 ($31,392) Higher Cost of Losses $215,034 $139,063 ($75,971) - 67 - The 6.1% additional cost for the decentralized system provides savings at a benefit to cost ratio of 11.3 to 1 or $11.3 saved for every $1 of cost. We note that decentralization will be more difficult in congested areas--each area will have a least-cost mix of primaries and secondaries. Thus utility distribution engineers should have the tools and training to carry out detailed studies that will help them make the right decision. A study based on a group of systems in one country is not conclusive. However, the results are clear cut enough to justify further investigation. 5.5 Connections Connections were not investigated in this study but poor or high resistance connections cause significant losses at peak. These bad connections invariably lead to burnouts of lines and equipment resulting in unnecessary outages. Poor connections may be found anywhere but the more common reasons are: (1) Wrong sized connectors -- if too small, they do not provide sufficient area, or pressure -- if too large they do not grip tight enough. (2) Loose blades and pressure plates on blade disconnects, gang operated switches and cutouts. (3) Use of bronze connectors on aluminum conductors resulting in conductor creep and corrosion. (4) Use of all-aluminum connectors on copper conductors which results in corrosion and eventual failure of the connection. (5) Connecting aluminum conductors by simply wrapping the strands of one conductor around the other. This method works for hard drawn copper conductors but aluminum strands do not have sufficient tensile strength. Invariably, the connection becomes loose, causes losses, begins arcing, and burns down. Preventing poor connections requires using the right connectors at all times, the use of compression connectors for aluminum whenever possible, and monitoring existing connections. The most effective monitoring devices are infra-red detectors which can be used to pin point any hot spots on the system. 5.6 Literature Search One of the initial steps of the project involved a technical literature search (see Bibliography in Appendix) which yielded the following major results: (1) Equations for calculating losses are readily available - 68 - (2) Losses are being considered a significant factor only in the most recent articles dealing with the planning, design and operation of distribution facilities (i.e., within last few years). (3) Most distribution facilities are being loaded on the basis of: . Thermal capability (melt or damage limit) . Loss of life (such as transformers and regulators) . Reliability (capacity for emergencies) These criteria result in loading levels such as those in Table 5.1. APPENDIX A -69 - Page 1 of 7 APPENDIX A ECONOMIC LOSS OPTIMIZATION MODEL The main focus of this Appendix is to analyze the economic outcome of reducing losses in the distribution system, by applying the principles of cost benefit analysis. First, before separating out the distribution network from the system, the net benefit of consumption supplied by the entire eletric power system is considered. The electric power system is planned with a time horizon of T periods, each of duration 1 year. The various terms that enter into an expression for net benefit is next con- sidered. The total benefit (TB) of consumption of electricity in any time period 't' is a function of the total quantity of electricity consumed or demanded Qt in the absence of outages i.e. it is assumed that the quality of supply is perfect. then TBt TBt t ) In practice, the consumer's electricity supply would not be of perfect quality. Therefore, the quality of supply or the outage costs (OC) to con- sumers due to voltage and frequency fluctuations, outages, and so on, occurr- ing in period t must be taken into consideration. Two types of costs occur due to poor quality of supply - direct cost due to interruption of productive and leisure activity, equipment and motor burnouts etc.; indirect costs due to the cost incurred in installing stand-by generators to overcome poor supply quality of electricity. Thus, these costs primarily depend on the quality of supply or reliability (R ) in the period t. In addition, the greater the demand for electricity (k ), the larger will be the outage costs (OC) in the event of poor quality of supply. i.e. OCt= OCt (Rt,Qt) Finally, the total supply costs SCt are considered. It consists of invest- ment costs and operation and maintenance (O&M) costs. The present discounted value of net benefit to society (NB) for the planning period can be written as T NB < [TBt (Qt) - SCt (Rt,Qt) - Ot (Rt,Qt)] /(l+r)t where r appropriate discount rate APPENDIX A - 70- Page 2 of 7 Before attempting to maximise net benefit, the variables in the above expression must be examined. The term Q refers to the quantity of electricity demanded in period t which is a function of other variables Qt Qt t t, Rt t where Pt = price of electricity in period t Yt = income of period t Rt = quality of supply or level of reliability Zt = vector of other variables (for e.g. price of substitute energy) in period t. considering the other terms in the expression: Rt is the actual quality of supply which is dependent on the investments that are made, and the O&M spent on the systems. 1/ Previous work has been done to maximize net benefit by optimizing relia- bility through the trade-off between supply costs (SC ) and outage costs (OCt d Here we attempt to maximize net benefits by optimizing the supply cost term SC , i.e., by minimizing the technical losses in the distribution system. For this purpose the SC term is broken down into its components. t Total system costs consists of generation costs (GSC), transmission cost (TSC) and distribution system costs (DSC). SC = GSC + TSC + DSC (1) Since we are focusing on the distribution network, the generation d trans- mission systems costs can be represented by the LRMC of capacity. LRMC is defined as the ratio of change of system capacity costs associated with an incremental demand in the long run peak demand function. 1/ See, M. Munasinghe, J. J. Warford, "Electricity Pricing: Theory and Developing Country Case Studies", World Bank Research Publications. APPENDIX A -71 - Page 3 of 7 The expression LRMC = A(capacity costs)/ &(demand) Is used to calculate the LRMC of bulk supply, i.e. generation as well as transmission. This gives the costs/unit of power and energy supplied by the bulk system, and entering the distribution network. For example, if a units of energy are entering the distribution network then the costs of supply are: a .MC. then equation (1) can be written as: SC = a .MC + DSC DSC is composed of investment costs and O&M costs. The technical losses in the distribution network will be reflected in the a term, since more units of electricity will enter the distribution system it losses are higher. The next step involves giving an economic value to the distribution losses. For this purpose it is necessary to compare the net benefits arising from two alternative distribution systems. This approach can be extended to the com- parison of many alternative network configurations. Consider two distribution networks (1) and (2) in Figure A.1, each supplying differing amounts of electricity. Let ai be the units of electricity entering the distribution system 1, and b1 the corresponding units of electricity avail- able to the consumers. Let 11 be the losses in the system 1. In the distribution network, since a units are entering, with b units being demanded and 1 units being lost al 1 + b The net benefit from the power system can be written as: T NB = ;.(TBt - SCt - OCt ) /(l+r)t t=o For each system, the SC term is expanded into its component parts and the net benefit can be written as: T For System 1: NB1 = ( [(TB1t - (alt.MC1t+ DSC1 t) - OC1t)] /(l+r)t t=o () T For System 2: NB2 = [(TB - (a2MC + DSC2t) - OC2t)] /(l+r)t [ 2t 2 2t t tMO - 72 - APPENDIX A Page 4 of 7 Figure A.1 DISTRIBUTION LOSS REPRESENTATION Gl G2 a, a2 DSC1 DSC2 losses losses li 12 ( b1 b2 (1) (2) APPENDIX A -73 - Page5 3of7 Now let us make the simplifying assumption that Systems 1 and 2 are two alternative ways of meeting the same customer load, i.e., blt= b2t' We might imagine that System 1 is an upgraded version of System 2, where distribution costs have been increased to achieve reduced losses. Since TB = TB (bt), it can be assumed that the total benefits in the two systems are the same. i.e. TB1t= TB2t then T NB1- NB2 It 2t - (alt . It +DSCit - a2t .MC - DSC2t)- t-o (OCIt- OC2t)] / (l+r)t (3) In addition it is assumed that the MC s are the same for the two systems. Since the distribution network is only a small part of a much larger bulk electric supply system, the difference in marginal costs for the two networks at this level will be negligible. then the above equation (3) can be written as: NB 1- NB [(a2 - a ).MC + (DSC - DSC ) + t=o (OC2t - OC 1t) / (1+r)t (4) Since the amount of electrical units finally available to the consumers in the two systems is the same: b it b 2t As mentioned earlier, since: al t b + 1 and Iit it a2t b b2t + 12t' we can write: alt 2t it 2t - 74 - APPENDIX A Page 6 of 7 Thus the difference in amount of bulk power supplied to the two systems can be replaced by the difference in losses in the two systems. This expression is substituted in equation (4): T NB - NB '(2t - 1lt) .MC + (DSC2t - DSC It + 1 2 2t lt2t Iti t=o (6) t (OC2t - OCI )]/(I+r) This can be written as: T NB1 - NB 2 (1 2t.MC + MSC 2) - (1lt.MC + DSC I) + t=O (OC2t - OC1t)/(l+r)t (7) Let us group and redefine the loss terms together as follows: NSClt =DSC + VL 8) where NSC = Net Supply Cost and VLit =1 it.MC = Value of Losses Rewriting equation (7) in the difference form: ANB NSc - Aoc (9) where ANB NB1 2 ANSC =. NSC1 - NSC2 AOC'= 0c1 - 0C2' T T NSC, = E NSCit/(1+r)t; and 0C = Ci(rt t-o t=o 75 - APPENDIX A Page 7 of 7 Suppose we assume for the time being that the outage cost term AOC is negligible relative to .ANSC. 1/ In general AOC would be a small correc- tional term in the analysis. Neglecting OC we can rewrite (8): ANB - ANSC In other words NB >NB2 and system 1 provides better net benefits than system 2, if the former ias a lower value of net supply costs, i.e., NSC (OHMS) (AMPS) hus- - --------- -- 8127----- - 7260------ -- 450 48M 0.076 0.65 0.88 0.59 1.14 360 5505 5057 5812 451 48HI 0.078 0.66 0.88 0,60 1.16 360 5461 5032 5783 452 480M 0.324 1.23 1.35 1.36 3.32 346 2676 3034 3480 453 48M- 0326 -1.23 -1.35 1.37 3.34 345 - 2665 3025 3477-r 454 48HH 0.402 1.41 1.49 1.60 4.00 341 2305 2694 3097 455 13NN 0.515 2.40 1.72 2,68 5.01 322 1689 1874 2154 456 48H1 0.439 1,49 1.56 1.72 4.33 339 2159 2554 2936 457 13K 0.591- 2i81 - 1.87 --3.16 5,68 315 -1480 1637 1881- - 458 30M1* 0,515 1.76 1.71 2.04 5.00 333 1888 2254 2591 459 13MM 0.667 3.07 2.01 3.48 6.35 310 1346 1503 1728 460 30M 0.534 1,82 1.75 2.12 5.17 332 1831 2189 2516 461 30HK - 0536 -- 1.83 1.75 2.13 -5.19 332 1825 2183 - -2509- - 462 30MI4 0.555 1.89 1.79 2.21 5.36 330 1771 2122 2439 463 30MM 0.557 1.90 1,79 2.22 5.37 330 1766 2116 2432 464 30HK 0.652 2.23 1.98 2.62 6,21 323 1539 1856 2134 465 13KM 0.784 - 3,38 2,24 3.88 - 7.39 -304 1195 1362--- 1566 466 30MS 0.689 2.36 2.05 2.78 6.54 320 1464 1769 2033 1003 134 0.917 4.34 2.50 4.93 8.56 289 991 1104 1269 474 30M 0.765 2.62 2.20 3.10 7.21 315 1333 1617 1858 475 13HM 0.860 3.44 2.39 4.00 - 8.05 301 1133 1319 1516 * INCLUDES 17.0 DUNS FAULT RESISTANCE * ASSUMES 0 0HM$ FAULT RESISTANCE I0 - 102 - APPENDIX C Page 6 of 27 TABLE C.3 PRESENT WORTH OF SYSTEM IMPROVEMENTS CONDUCTOR LOADING STUDY Present Worth Description of Costs ($) Conductor Limited to 100% $ 4,900 Conductor Limited to 75% $ 15,500 Conductor Limited to 50% $ 30,800 Conductor Limited to 25% $104,000 The loss at peak for the various maximum conductor loading levels are shown in Table C.4 for selected years. These losses at peak (kW) for each year were converted to peak, should and off-peak demands plus peak, shoulder and off- peak energy losses. This was accomplished with a computer program which pro- vided the data in the form of Printout C.3. The demand and energy losses were then priced out and present worthed by one of the economic analysis models described in Appendix A (see Printout C.4). The results of the conductor loading study are summarized in Table C.5. TABLE C.4 DEMAND LOSS (kWl AT PEAK FOR VARIOUS CONDUCTOR LOADINGS LOSS AT PEAK PADRI FEEDER AREA AND % OF LOAD LOAD 100% 75% 50% 25% YEAR Vw- kW loss % kW loss % kW loss % kW loss % 1978 711 22 3.1 22 3.1 22 3.1 15 2.1 1980 858 32 3.7 32 3.7 32 3.7 12 1.4 1982 1033 48 4.6 48 4.6 35 3.4 17 1.6 1984 1231 69 5.6 69 5.6 46 3.7 24 1.9 1986 1478 101 6.8 73 4.9 37 2.15 34 2.3 1988 1725 141 8.2 92 5.3 49 2.8 38 2.2 1990 2011 132 6.6 73 3.6 68 3.4 48 2.4 1992 2314 191 8.3 93 4.0 90 3.9 66 2.9 1994 2854 158 5.5 126 4.4 126 4.4 70 2.5 1996 3375 179 5.3 175 5.2 151 4.5 75 2.2 1998 3930 246 6.3 241 6.1 160 4.1 104 2.6 AVERAGES 5.8% 4.6% 3.6% 2.2% 0 V -4 PK SH O.P. PK SH 0.P. LOSS FACTORS FOR YEAR 1 OF STUDY MINTER 0.62 0.40 0.33 SUMMER 0.50 0 32 0.26 HOURS 905. 1810. 1629. 920. 1840. 1656 PROPORTION (F FIRST ANNUAL PEAK 0.83 0.79 0.74 1.00 0.95 0.89 RG n^iLl SSES! AIMt qW gSIt! 969 I 1194 Ah2 DEMAND LOSSES (KU) 14.9 13.4 11.8 21.8 19.6 17.1 LOSS FACTORS FOR YEAR 2 OF STUDY MINTER 0,62 0.40 0.33 SUMMER 0.50 0632 0.26 HOURS 905. 1810. 1629. 920. 1840. 1656, PROPORTION OF FIRST ANNUAL PEAK - --88 084 0.79 1i.06 1,01 0.94 [0l JAEJ S10384-91 1260e- 71349t 12141 8lt 2 50) DEMAND LOSSES (KU) 18.5 16.6 14.6 27.0 24.3 21.2 LOSS FACTORS FOR YEAR 3 OF STUDY MINTER 0.62 0.40 0.33 SUMMER 0.50 0.32 0.26 HOURS 905, 1810. 1629. 920. 1840, 1656. PROPORTION Of FIRST ANNUAL PEAK .--- 0.94 -.89 160.83 _ 12 1.07 1.00 LOAD FACTORS 77,98 65.65 63.09 69.15 58.21 55.94 ENERGY LOSSES 12307.2 14291.2 9184.0 14624.0 16960.0 10912.0 DENAND LOSSES (KU) 21.9 19.7 17.3 32.0 28.8 25.2 LOSS FACTORS FOR YEAR 4 OF STUDY WINTER 0.62 0.40 0.33 SUNNER 0.50 0.32 0.26 HOURS 905. 1810. 1629. 920. 1840. 1656. PROPORTION OF FIRST ANNUAL PEAK - 0.99 .0.94 0.89 1113 - 1.06. LOAD FACTORS 77.98 65.65 63.09 69.15 58.21 55.94 ENERGY LOSSES 15384.0 170864.0 11480.0 18280.0 21200.0 13640.0 DEMAND LOSSES (KY) 27.4 24.6 21.6 40,0 36.0 31.4 LOSS FACTORS FOR YEAR 5 OF STUDY WINTER 0.62 0.40 0.33 SUMMER 0.50 0.32 0.26 HOURS 905. 1810# 1629. 920. 1840. 1656. PROPORTION OF FIRST ANNUAL PEAK - . 1,05 1,00 0,94 1#26 1.20 1t12 LOAD FACTORS 77.98 65.65 63.09 69.15 58.21 55.94 ENERGY LOSSES 18268.5 21213.5 13632.5 21707.5 25175.0 16197,5 DEADLSE K)32,6 29.3 25.7 47.5 42.8 37.3 LOSS FACTORS FOR YEAR 6 OF STUDY WINTER 0.62 0,40 0.33 SUMMIER 0650 0.32 0.26 HOURS 905. 1810. 142v. 920. 1840. 1656. PROPORTION OF fIRST-ANNUAL PEAK----- 1,12-.- 1,06 -0,99------ -----1.s34 - 1.Is27 --1.19. LOAD FACTORS 77 98 65.65 163,09 69.15 58.21 55.94 ENERGY LOSSES 212 5562 5, 26049.0 30210.0 19437.0 39.1 35.1 30.8 57.0 51.3 44.8 LOSS FACTORS FOR YEAR 7 OF STUDY MINTER 0.62 0.40 0.33 SUMMER 0.50 0.32 0.26 HOURS 905. 1810. 1629. 920. 1940. 1656. PROPORTION OF FIRST ANNUAL-PEAK...11 -11 .13- 64,39 A,lj S1:21 LOAD FACTORS 77.98 6 , 63.09 69 82 594 ENERGY LOSSES 26422.0 30681.4 19716.9 31395.9 36411.0 23426,7 94 DEMAND LOSSES (KV) 47.1 42.3 37.1 68.7 61.8 54.0 0V 0 PRINTOUT C.3 PRINTOUT C.4 SEASON I ENC = 0.050 0.034 0.034 SEASON 2 ENC = 0.050 0.034 0.034 SEASON I KNC a 125.00 SEASON 2 KC 125.00 R = 0.12 NYR = 20 ENERGY LOSSES BY PRICING PERIOD KILOUATT LOSSES VALUE OF VALUE OF DISCOUNTED OFF PEAK SHOULDER PEAK ENERGY LOSS KM LOSS KU LOSS TOTAL YEAR I SEASON 1 8384.3 97J5.9 6256,6 63.0 1 1868.0 YEAR 1 SEASON 2 9962.6 115 4.0 7433.8 1143.7 2 2725.0 669.7 6699,7 YEAR 2 SEASON 1 10384.2 12058.2 7749.0 1192.7 18.5 4181,6 YEAR 2 SEASON 2 12339.0 -270 600- 11509.6 18209o2 YEAR 3 SEASON 1 12307.2 9184.0 4 21.9 6923,6 YEAR 3 SEASON 124.0 10912,0 88 3 :0 100.0 YEAR 4 SEASON 1 15384.0 17064.0 11480.0 1766.9 27,4 10351.1 YEAR 4 SEASON 2 18280.0 . 21200,0 2098.6. 40.0 ..1_100.0 20866.9 55112.4 YEAR 5 SEASON 1 18268.5 21213.5 13632.5 2098.2 32.6 14421.2 YEAR 5 SEASON 2 21707.5 25175.0 16197.5 2492.0 47.5 21037.5 25451.8 80564.3 YEAR 6 SEASON 1 21922.2 25456.2 16359,0 2517,8 39.1 19305.4 TEAR 6 SEASON 2 26049.0.. 30210.0- 19437.0 2990.4 -.57#0 .2816215 . 30060.1 110624.4 YEAR 7 SEASON 1 26422.0 30681.4 176.9 3034.6 47.1 25192.1 YEAR 7 SEASON 2 31395.9 36411.0 23426,7 3604.3 68.7 36750.0 34745.3 145369.7 YEAR 8 SEASON 1 32306.4 37514*4 24108.0 3710.5 5706 32389.9 YEAR 8 SEASON 2 .38388.0 44520.0 28644,0 4407.0 84.0 --47250.0- 39697.0 185066,6 YEAR 9 SEASON 1 38844.6 45106.6 28987.0 4461,4 69.2 41044.3 YEAR 9 SEASON 2 46157.0 53530.0 34441.0 5298.9 101.0 59875.0 44701.6 229768.3 YEAR 10 SEASON 1 46152.0 53592.0 34440.0 5300.7 82.3 51326.8 YEAR 10 SEASON-2 54840.0 63600,0. 40920.0 .6295.7 49691.4 279459,7 YEAR I SEASON I 54229,6 62970.6 48467.0 4229.3 96.7 3 08 YEAR I SEASON 2 64437.0 74730. 480810 9.4 141,0 02400:8 54585.6 334045.2 YEAR 12 SEASON 1 64997.4 75475.4 48503.0 7465.1 11548 77889.9 YEAR 12 SEASON 2 77233,0 --89570.0. 57629.0 896A.4 169.0 -113625.0 59750.9 393796.1 YEAR 13 SEASON 1 50882.6 59085.2 37970,1 5844.0 90.7 89224.4 YEAR 13 SEASON 2 60461.1 70119.0 45114.3 6941.0 132,3 130162.5 59593.3 453389.4 YEAR 14 SEASON 1 61536.0 71456.0 45920.0 7067.6 109,7 102934 YEAR 14 SEASON 2 73120,0 94000,0 54560.0 0394,2 160.0 .150162.5 61547.2 514936.6 YEAR 15 SEASON 1 73343.2 05166.6 54730.9 8423.7 130.7 119277.0 YEAR 15 SEASON 2 87149,9 101071.0 65028.7 10004.9 190,7 14000.0 63781.1 578717.7 YEAR 16 SEASON 1 76920.0 09320.0 57400.0 0834.5 137.1 13404.5 YEAR 16 SEASON 2. 91400.0 .106000.0 48200.0 10492.8. 200.0 199000.0 64810,0 643527*7 YEAR 17 SEASON 1 49767.2 57790.0 37137.8 5715.9 81,7 147502,5 YEAR 17 SEASON 2 59135.8 68582.0 44125.4 6788.8 129.4 215175.0 61200.3 704728.1 YEAR I SEASON 1 57690.0 64990.0 43050.0 6625.9 102.8 160355o6 YEAR 18 SEASON 2 68550.0 79500.0 51150.0 7869.6 150.0 233925.0 59535-9 764244.0 YEAR 19 SEASON 1 68728.0 79807.4 M286.9 7893,6 122.5 175668.0 YEAR 19 SEASON 2 81665.9 94711.0 60936.7 9375.3 178.7 256262.5 58413.7 822677.7 YEAR 20 SEASON 1 945347 1097743 70544,6 10857.6 168,5 196729.9 YEAR 20 SEASON 2 112330-. 130274.0 83817.8 -12895.6 245.8 286987,5 58920.8 801598.5 ISCOUNTE2 TOTAL LOSS 881598.50041 141 0 9070 14291 9184 APPENDIX C Page 10 of 27 - 106 - TABLE C.5 VALUE OF LOSS SAVINGS BY REDUCING MAXIMUM O75DUCTOR LOADING (NO POWER FACTOR CORRECTION) Maximum Investment ($x1OOO) Cost of Losses ($xlOOO Conductor Incre- Benefit to Loading (%) Total Incremental 1/ Total mental 1/ Cost Ratio 2/ Losses Priced at $250/kW and $0.03 kWH 100% $ 4.9 $ - $ 881.6 $ - - 75% 15.5 10.6 717.3 164.3 15.5 50% 30.8 15.3 554.0 163.3 10.7 25% 104.0 73.2 332.9 221.1 3.0 Losses Priced at $130 kW and $0.01/kWH 100% $ 4.9 $ - 445.4 $ - - 75% 15.5 10.6 362.6 82.8 7.8 50% 30.8 15.3 280.0 82.6 5.4 25% 104.0 73.2 168.2 111.8 1.5 1/ Incremental with respect to next higher level of maximum conductor loading. 2/ Dollars saved for each dollar of investment (Savings divided by Incremental Investment) - 107 - APPENDIX C Page 11 of 27 Power Factor Control Capacitors were used to control power factor to 95% by adding them to the conductor study cases. The locations for the capacitors on the feeders were determined with the aid of the capacitor placement program described in Appendix B (see Printout B.7). The cost for installing the capacitors are detailed in Table C.6. TABLE C.6 CAPACITOR BANK COSTS (INSTALLED) Size Cost ($) 150 kVAR 3 Phase Bank $1,500 300 kVAR 3 Phase Bank $2,700 450 kVAR 3 Phase Bank $3,000 600 kVAR 3 Phase Bank $3,300 Switches and Controls for Switched Banks $ 900 Losses, the costs of losses, and investments were determined in a similar manner to the method used for the conductor loading study. The study indicates that the correction of the power factor from about 80% to approximately 95% will provide a one third reduction in losses. Correction of the power factor to approximately 95% will require the instal- lation of capacitors as shown in Table C.7. APPENDIX C Page 12 of 27 - 108 - TABLE C.7 CAPACITOR INSTALLATIONS REACTIVE CAPACITORS CAPACITOR LOAD IN SERVICES NET INSTALLATIONS Year kVAR (-kVAR) kVAR Number Size 1978 540 0 540 3 150 1980 661 -450 111 - 1982 796 -450 346 2 150 1984 967 -750 217 1 150 1986 1174 -900 274 1 150 1988 1378 -1050 328 2 150 1990 1628 -1350 278 1 150 1992 1925 -1500 425 2 150 1994 2260 -1800 460 3 150 1996 2636 -2250 386 2 150 1998 3125 -2550 575 3 150 The 21 banks of capacitors requires an investment of $31,500. It has been conservatively assumed that 50% of the banks will require switching to avoid excessive leading power factor during off-peak conditions which requires an additional $9,000 of investment. The present worth of the investments and the residual value of banks at the end of 20 years is $19,700. This amount was derived with the aid of the economic models described in Appendix A. The results of the study are summarized in Table C.8 and shown graphically in Figure C.2 of Chapter V. APPENDIX C - 109 - Page 13 of 27 TABLE C.8 VALUE OF LOSS SAVINGS BY CORRECTING POWER FACTOR TO 95% AT VARIOUS MAXIMUM CONDUCTOR LOADING P.W. of Maximum Capacitor P.W. Cost of Losses ($xlOOO) * Conductor Annual Benefit Loading Costs No With to (%) ($x1OOO) Capacitor Capacitor Savings Cost Ratio Losses Priced at $250/kW/yr. and $0.034 kWH 100% $ 19.7 $ 881.6 $ 587.2 $ 294.4 14.9 75% 19.7 717.3 477.7 239.6 12.2 50% 19.7 554.0 369.0 185.0 9.4 25% 19.7 332.9 221.7 111.2 5.6 Losses Priced at $130 kW/yr. and $0.01/kWH 100% $ 19.7 $ 445.4 $ 296.7 $ 148.7 7.5 75% 19.7 362.6 241.5 121.1 6.1 50% 19.7 279.8 186.4 93.1 4.7 25% 19.7 168.2 112.0 56.2 2.9 * Dollars saved per dollar invested (Savings divided by Investment) APPENDIX C - 110 - Page 14 of 27 Distribution Transformers Distribution transformers are available in many sizes, phasing, voltages, styles and electrical/mechanical characteristics. Some of the variations include: . Single phase or three phase . Pole mount, pad mount, vault mount . With taps and without taps . No protection . Self protected (Primary Fuse) . Completely Self protected (Fuse plus secondary breakers) . Dual Primary winding A group of single phase, pole mounted transformers with the following characteristics were selected for testing the methodology. TABLE C.9 TRANSFORMER CHARACTERISTICS (12.47/7.2 kV PRIMARY) No Load Total kVA Loss Loss Price Annual Rated % R % Z (kW) (kW) $ Cost* 5 2.3 2.7 0.045 0.162 $ 400 $ 57 10 1.9 2.1 0.068 0.26 470 68 25 1.5 1.9 0.13 0.51 680 98 50 1.3 2.3 0.225 0.89 1040 150 100 1.2 2.2 0.4 1.55 1760 253 250 1.0 5.0 0.925 3.7 4125 593 * Annual costs based on 20 years life, capital recovery at 12% plus 1% O&M. The transformer loading and analysis model described in Appendix B was used to impose loadings from 50% to 250% on the transformers. Table C.10 is a summary of the losses for the transformers being studied at various load levels. APPENDIX C - 111 - Page 15 of 27 TABLE C.10 DISTRIBUTION TRANSFORMER NO LOAD (IRON AND LOAD (COPPER) LOSSES VERSUS VARIOUS LOAD LEVELS Transformer No Load Load Losses (kW) at Various Load Levels Size Loss (kVA) (kW) 50% 100% 150% 100% 250% 5 0.045 0.037 0.144 0.323 0.572 0.893 10 0.070 0.060 0.237 0.532 0.944 1.473 25 0.130 0.118 0.467 1.048 1.860 2.903 50 0.225 0.204 0.808 1.814 3.222 5.030 100 0.400 0.375 1.491 3.348 5.945 9.283 250 0.925 0.781 3.105 6.972 12.383 19.336 The load losses are also shown graphically in Figure C.1 (Two Pages). These graphs do show the major differences in load losses between various sizes. Table C.11 is a comparison of losses for a 10 kW demand. Figure C.1 (1 of 2) 3.0- SINGLE PHASE DISTRIBUTION TRANSFORMER LOAD LOSSES FOR VARIOUS DEMANDS 2.0 (n 0 1. 1.0~ - 5 kVA 10 kVA 5 kVA OQ 00 0 10 20 30 40 Demand (kW) 12.0- Figure C.1 (2 of 2) 10.0 SINGLE PHASE DISTRIBUTION TRANSFORMERS LOAD LOSSES FOR VARIOUS DEKANDS 8.0 wq 6.0- n 6250 kVA I 100 kVA 4.0 50 kVA 2.0 00 0 100 200 300 400 Demand (kW) APPENDIX C - 114 - Page 18 of 27 TABLE C.11 TRANSFORMER LOSSES FOR A 10 kW DEMAND SIZE LOSSES (kW) % (kVA) No Load Load Total Difference 5 kVA 0.045 0.572 0.617 100% 10 kVA 0.068 0.237 0.305 49% 25 kVA 0.130 0.080 0.210 34% The energy losses are derived from the following equations on the assumption that the Annual Loss Factor is 30%. Energy Loss = kW No Load x 8760 hours + kW Load Loss x 8760 hours x .30 The energy loss for the 5 kVA transformer of Table C.9 would be Energy Loss = (0.045 x 8760) + (0.572 x 8760 x .3) = 394 + 1503 - 1897 kWH The losses for the 10 and 25 kVA transformers were derived in a similar manner and shown in Table C.12. - 115 - APPENDIX C Page 19 of 27 TABLE C.12 DEMAND AND ENERGY LOSSES FOR VARIOUS TRANSFORMERS SERVING 10 KW DEMAND WITH A 30% ANNUAL LOSS FACTOR ENERGY LOSSES SIZE DEMAND NO LOAD LOAD TOTAL (kVA) (kW) (kWH) (kWH) (kWH) 5 kVA 0.617 394 1503 1897 10 kVA 0.305 596 623 1219 25 kVA 0.210 1139 210 1349 For a demand charge of $250/kW/year and an energy change of $0.034/kWH, the cost of losses for the 5 kVA transformer will be = (0.617 x $250) + (1897 x $0.034) Annual Cost of Losses = $154 + $65 = $219 The above procedure was used to derive the costs of Table C.13. - 116 - APPENDIX C Page 20 of 27 TABLE C.13 ANNUAL COSTS FOR VARIOUS TRANSFORMERS SERVING A 10 kW DEMAND WITH A 30% ANNUAL LOSS FACTOR Cost of Losses Investment Total Difference Size Demand Energy Total Charges Annual In (kVA) ($) ($) ($) ($) Cost ($) Percent 5 $154 $ 65 $219 $ 57 $276 100.0 10 76 41 127 68 195 70.6 25 53 46 99 98 197 71.4 The 5 kVA has the thermal capability to serve a 10 kW load under average loading conditions and many utilities are electing to do so. However, at the assumed level of costs for losses, a 10 kVA transformer can serve the 10 kW load at 70% of the annual costs of the 5 kVA transformer and a 25 kVA is certainly a feasible selection if growth is expected. The above process was used to derive the data in Table C.5 and the graphs of Figures C.4 and C.5. The results have been based on a small segment of the many variables associated with distribution transformers. They are not conclusive but they certainly point out the need to explore further. APPENDIX C - 117 - Page 21 of 27 Secondary Systems There are two basic types of secondary systems used by utilities: centralized (originated in Europe) which is based upon large centrally located distribution transformers and extensive secondary systems serving anywhere from 10 to 200 consumers. Decentralized (originated in North America) which is based upon small transformers installed at or near the load centers with abbreviated or no secondary systems. Each transformer serves from 1 to 15 consumers depending upon load density. The major differences between the two concepts are: the centralized systems transport power to the consumer over low voltage (240/416 volts) secondary lines whereas, the Decentralized system transports the power directly to the consumer or central load centers at high voltage (11,000 volts). A Decentralized system generally requires more investment due to the greater length of primary lines and the use of many small transformers. If losses are ignored, and load densities properly accounted for, the centralized System with its higher secondary voltage appears to be the best choice. However, losses have become too valuable to ignore and their cost is rapidly offsetting the economics of scale of the centralized system. Sixty (60) centralized secondary systems in the Bhikhiwind areas of Punjab State, India were studied in this phase of the project. Each of these systems consisted of a single large transformer and an extensive secondary system serving an entire village. A computer model was developed for each of the centralized systems and the systems were analyzed as to voltage, loading and losses. Decentralized systems were then developed to serve the 60 villages. Each of these Decentralized systems displaced the single distribution transformer and its extensive secondaries with 11 kV primary lines, small transformers located at the load centers and short runs of secondary lines. One of the 60 centralized system is shown in Figure C-2 a decentralized system to serve. Those same loads are shown in Figure C-3. The character- istics of the two systems are summarized in Table C-14. The decentralized system required more investment but the losses are 83.7% less than the centralized system. Figure C.2 O DISTIRBUTION TRANSFORMER CONSUMER LOADS (KVA) 3 SECONDARY SYSTEM (240/416 VOLTS) PRIMARY SYSTEM (II KV) 3 5 3H 5 oC Figure C. 3 SMALL DISTIRBUTION TRANSFORMERS (KVA) CONSUMER LOADS (KVA) 3 SECONDARY SYSTEM(240/416 VOLTS) PRIVARY SYSTEM (II KV) 5 5H 5I I I o-i \ 54 APPENDIX C - 120 - Page 24 of 27 TABLE C.14 CENTRALIZED VERSUS DECENTRALIZED SECONDARY SYSTEMS Item Centralized DeCentralized Transformer Capacity 100 kVA 80 kVA 11 kV Lines - 1.29 kM Secondary Lines 2.53 kM 1.48 kM Investment $15,795 $17,169 Demand 44.5 kW 44.5 kW Loss at Peak 4.3 kW 0.7 kW Loss Reduction - 83.7% The basic costs used in study consist of the primary costs detailed in Table C.2, the installed transformer costs of Table C.15 and the secondary costs of Table C.16. APPENDIX C - 121 - Page 25 of 27 TABLE C.15 INSTALLED COSTS IN INDIA FOR THREE PHASE DISTRIBUTION TRANSFORMERS (INCLUDES POLES AND PLATFORMS) Costs (1980 US$) Transformer Size (kVA) Labor Materials Other Total Three Phase Transformers Mounted on Two Pole Structures (Cost of Structure is Included) 15 kVA $ 85 $ 725 $ 65 $ 875 25 kVA 85 810 65 960 50 kVA 85 1,015 80 1,180 63 kVA 85 1,435 80 1,600 75 kVA 95 1,635 85 1,815 100 kVA 95 1,740 85 1,920 200 kVA 95 2,960 125 3,180 300 kVA 95 3,705 145 3,945 APPENDIX C - 122 - Page 26 of 27 TABLE C.16 1/ Low Tension (LT) Line Costs in India- (US$/Kilometer) US$/kM Items Labor Materials Other Total Three Phase LT Lines Three One Phase Wires Neutral Wire 13 MM2 13 MM2 $ 810 $3,855 $ 225 $4,890 20 MM2 13 MM2 810 4,815 240 5,865 25 MM2 13 MM2 810 5,445 255 6,510 30 MM2 13 MM2 810 6,135 285 7,230 48 MM2 20 MM2 1,020 8,595 345 9,960 Table C.17 provides a summary of the results of Decentralzing the 60 systems. The study indicates that Decentralizing requires additional investment ($49,938) which results in an additional annual carrying charge of $6,697. However, the Decentralized system saves from $31,392 to $75,971 in losses for benefit to cost ratio of between 4.7 to 1 and 11.3 to 1. 1/ Prices supplied by the Rural Electrification Corporation (REC) of India. APPENDIX C - 123 - Page 27 of 27 TABLE C.17 60 CENTRALIZED SECONDARY SYSTEMS VERSUS 60 DECENTRALIZED SECONDARY SYSTEMS Difference DeCentralized Minus Item Centralized Decentralized Centralized Transformer Statistics Quantity 60 172 112 Total Capacity kVA 4575 3695 (880) Average Size kVA 76 22 (54) Investment $94,550 $159,635 $65,085 Total Demand kW 2445 2187 (258) Average Demand kW 41 13 (28) % Loaded % 54 59 9 No Load Loss (Iron) kW 2.0 2.2 0.2 Peak Load Loss (Copper) kW 14.8 34.4 19.6 Energy Losses mWE 56.4 109.7 53.3 PriaU Lines Total Length kM - $47.2 47.2 Investment - $212,400 $212,400 Secondary System Total Length kM 128.7 89.6 (4.0) Average per Transformer kM 2.1 0.5 (1.6) Investment $726,705 $499,158 ($227,547) Demand kW 2161 2161 - Peak Loss kW 284 26 (258) Percent Demand Loss % 13.1% 1.2% (11.9) Energy Loss mWE 746.4 68.3 (678.1) Total Investment $821,255 $871,193 $ 49,938 Annual Costs Investment plus O&M $110,130 $116,827 $ 6,697 Cost of Losses at: $130/kW, $0.01/kWH $48,256 $10,167 ($38,089) $250/kW, $0.034/kWH $104,904 $22,236 ($82,668) Total Annual Costs Lower Cost of Losses $158,386 $126,994 ($31,392) Higher Cost of Losses $215,034 $139,063 ($75,971) APPENDIX D Page 1 of 19 - 124 - APPENDIX D BASIC LOADING AND LOSS PARAMETERS The accuracy and usefulness of loss studies is directly dependent upon the quality of the parameters derived from basic loading data such as hourly loads over a specified time period. This section provides the basic definitions and equations to derive the following loading/loss parameters: . Peak Demand . Loading Equivalent Hours . Average Demand . Load Factor . Load Duration . Loss Equivalent Hours . Loss Factor Table D.1 and Figure D.1 show the hourly loads for a selected peak day where the Peak Demand occurred during the hour from 7 p.m. to 8 p.m. Equivalent Hours equals the number of hours of peak demand which requires the same quantity of energy as required by the actual demands over the specified time period. Equivalent Hours - Total Energy (kWH) Peak Demand (kW) For the example day: Equivalent Hours - 371 kWH 12.37 Hours 30 kW - 125 - APPENDIX D Page 2 of 19 TABLE D.1 AVERAGE HOURLY LOADS (KILOWATTS) PEAK DAY MORNING AFTERNOON/EVENING HOUR HOUR DEMAND DEMAND FROM TO KILOWATTS FROM TO KILOWATTS 12 AM 1 AM 10 12 PM 1 PM 13 1 AM 2 AM 8 1 PM 2 PM 15 2 AM 3 AM 6 2 PM 3 PM 16 3 AM 4 AM 7 3 PM 4 PM 19 4 AM 5 AM 8 4 PM 5 PM 21 5 AM 6 AM 9 5 PM 6 PM 24 6 AM 7 AM 10 6 PM 7 PM 27 7 AM 8 AM 12 7 PM 8 PM 30 8 AM 9 AM 15 8 PM 9 PM 28 9 AM 10 AM 14 9 PM 10 PM 23 10 AM 11 AM 13 10 PM 11 PM 19 11 AM 12 PM 11 11 PM 12 AM 13 TOTAL (KILOWATT HOURS) - 371 30 F PEAK AVERAGE HOURLY LOADS PEAK DAYS 25 - LOSSES 25 - 20 - AVERAGE LOAD (51.5% of PEAK) 15 -- 15.45 kW 10 - MID 2 4 6 8 10 NOON 2 4 6 8 10 MU) N IGiT A. M. A. M. NIGIF HOURS OF DAY APPENDIX D - 127 - Page 4 of 19 Average Demand is a constant demand over the specified time period which requires the same energy as required by the actual load over the specified time period. Average Demand = Total Energy (kWH) Total Hours For the example day: Average Demand = 371 kWH = 15.46 kW 24 Hours Load Factor (generally expressed in percentage) is the ratio of Average Demand to Peak Demand over a specified time period. Load Factor is also the ratio of actual energy to the energy required if the Peak Demand is on 100% of the time. Load Factor may be determined from the following relationships: (1) Average Demand and Peak Demand Load Factor (%) = Average Demand (kW) x 100 Peak Demand (KW) (2) Actual Energy and Energy if Peak is on 100% of the time Load Factor (%) = Actual Energy (kWH) x 100 Peak Demand (kW) x Total Hours For the example day: (1) Load Factor 15.46 kW x 100 - 51.5% 30.00 kW (2) Load Factor = 371 kWH x 100 = 51.5% 30 kW x 24 HR APPENDIX D --128 - Page 5 of 19 Load Duration is the relationship of demands and the duration of the demands over a specified time period. In Table D.2, the hourly demands have been sorted in descending order and the following computed: Frequency = Number of hours of occurrence for each demand Equal/Exceed = Summation of Frequencies Percent of Peak - Demand (kW) x 100 Peak (kW) Percent Duration Equal/Exceed x 100 Specified Time Square of Demands (Demand) 2 x Frequency The Load Duration parameters for the example have been plotted in Figure D.2 (Percent of Peak Versus Percent Duration). Losses are a function of the squares of the load current (amps) which is directly related to the squares of the demands. The squares of the demands for the example day are shown in Table D.2 and graphed in Figure D.3. Loss Equivalent Hours are the number of hours of peak load which will produce the same total losses as is produced by the actual loads over a specified time period. Loss Equivalent Hours - (Hourly Demand)2 (Peak demand)2 For the example day: Loss Equivalent Hours = 6849 kW2 HR 7.61 Hours 900 kwh2 APPENDIX D Page 6 of 19 - 129- TABLE D.2 LOAD DURATION AND LOSS TABLE PEAK DAY DEMAND EQUAL/ PERCENT OF PERCENT SQUARES KILOWATTS FREQUENCY EXCEED PEAK DURATION OF DEMAND 30 1 1 100.0% 4.2% 900 28 1 2 93.3 8.3 784 27 1 3 90.0 12.5 729 24 1 4 80.0 16.7 576 23 1 5 76.6 20.8 529 21 1 6 70.0 25.0 441 19 2 8 63.3 33.3 722 16 1 9 53.3 37.5 256 15 2 11 50.0 45.8 450 14 1 12 46.7 50.0 196 13 3 15 43.3 62.5 507 12 1 16 40.0 66.7 144 11 1 17 36.7 70.8 121 10 2 19 33.3 79.2 200 9 1 20 30.0 83.3 81 8 2 22 26.7 91.7 128 7 1 23 23.3 95.8 49 6 1 24 20.0 100.0 36 6849 100 90 - 80 - LOAD DURATION GRAPR PEAK DAY 70 - 60 14 50 So 0- 40 30 20 10 - 0 ID t4~ o 10 20 30 40 50 60 70 80 90 100 PERCENT OF TIME Figure D.3 900- 800- SQUARES OF HOURLY DEMANDS 700- PEAK DAY 600- 500- 400- 300- AVERAGE (31.7% of PEAK) -- ----------------------------------------------------- ------------------ 285 kW2 200- 100- 2 4 6 8 10 NOON 2 4 6 8 10 APPENDIX D - 132 - Page 9 of 19 Loss Factor is the percentage of time required by the peak load to produce the same losses as produced by the actual loads over a specified time period. Loss Factor may be computed from the following relationships: (1) Squares of Average Demand and Peak Demand Loss Factor (%) - Average Demand (kW)2 x 100 Peak Demand (kW)2 (2) Squares of all Actual Demands and Squares of Peak Demand on 100% of the time Loss Factor (%) - (Hourly Demand)2 x 100 (Peak Demand)2 x Hours For the example day: (1) Loss Factor = (15.46 kW)2 x 100 = 31.7% (30 kW)2 (2) Loss Factor - 6849 kW2 HR x 100 - 31.7% (30 kW)2 x 24 HR Energy and Demand Losses It is important to analyze not only kWh or energy losses but also kW or power losses during peak periods. An examination of the loading for the Example Day will provide some basics about the relationship between energy and demand losses. In the developing countries, technical energy losses of 15% are common so we will assume that 15% of the energy is lost enroute to delivery: Energy Loss - .15 x 371 - 55.7 kWH Energy losses represent fuel which must be imported by most of the develop- ing countries and/or it represents energy which could be used by the country for further development. APPENDIX D - 133 - Page 10 of 19 This energy loss may be divided among the 24 hourly loads in proportion to the squares of the demands (6th column of Table D.2). The peak hour would become responsible for: Peak Hour Loss - (900/6849) x 55.7 - 7.3 kW The losses associated with the other hours have been calculated in a similar manner and posted to Figure D.1. At peak, the demand loss is 7.3 kW or Peak Demand Loss (%) = (7.3/30) x 100 - 24.3% Almost 25% of the system's capacity (generation, transmission, and distribu- tion) is required to supply the demand loss at peak. For each percent of energy loss, this example loading pattern has 1.62% of peak demand loss. The Loss Factor is always less than or 'equal to the Load Factor because losses are proportional to the square of the loads. In the Example, the Load Factor is 51.5% and the Loss Factor is 31.7%. The load factor may be calculated from energy requirements (kWH) over a specified time and the peak load (kW). Load Factor (%) - Energy (kWH) x 100 (Peak KW x Hours If hourly loads are known, the loss factor may be calculated as follows: Loss Factor (%) - (Hourly Loads (kW)2 x 100 (Peak kW)2 x HRS However, hourly loads are rarely available so one must depend upon the probable relationship between Load Factors and Loss Factors as determined from studies. Figure D.4 illustrates two extreme loading conditions. APPENDIX D Page 11 of 19 - 134 - For Load Type A, the demand at any time is either at 100% or 0% full load. The Load Factor for Load Type A can vary from 0.0% to 100.0%. The Loss Factor for Load type A is always equal to the Load Factor. For Load Type B, the load is constant for 23 hours (from 0% to 100% of Full Load) and 100% of full load for the 24th hour. The Load Factor will vary from a low of 4.17% (when the constant portion is 0.0%) to a high of 100%. The Loss Factor equals the Load Factor at the low end (4.17%) and at the high end (100.0%). Between these values, the Loss Factors and Load Factors have the relationships shwon in Figure D.5 and Table D.3. - 135 - APPENDIX D Page 12 of 19 Fi&ure D.4 LOADING EXTREMES 100 75 V LOAD TYPE A DEMAND IS 100% 5 . OR 0.% K 25 5 10 15 20 24 HOURS PEAK DEBAND FOR ONE HOUR 100 F 75 - LOAD TYPE B 50 ~z.j 25 - CONSTANT DEMAND FOR 23 HOURS (MAY VARY FROM 0% TO 100.0% II 1I 5 10 15 20 24 HOURS - 136 - APPENDIX D Page 13 of 19 Figure D.5 RELATIONSHIP BETWEEN LOAD FACTORS AND LOSS FACTORS 100 80 0n 0 60 TYPE A LOADING 40 e ~.TYPE B LOADING 20 0 20 40 60 80 100 S LOAD FACTOR APPENDIX D Page 14 of 19 - 137 - TABLE D.3 LOAD FACTOR AND LOSS FACTOR RELATIONSHIP LOSS FACTORS (%) LOAD FACTOR TYPE B DISTRIBUTION (%) LOADING TRANSFORMER FEEDER 0.0% 4.2% 4.2 4.2% 5.0 4.2 4.2 4.2 10.0 4.5 4.7 6.0 20.0 6.8 8.1 10.1 25.0 8.7 10.1 13.0 30.0 11.1 13.0 16.0 35.0 14.1 16.0 19.6 40.0 17.6 19.4 23.2 45.0 21.6 23.8 27.8 50.0 26.1 28.0 32.0 55.0 31.1 33.1 37.0 60.0 36.7 38.2 42.8 65.0 42.8 44.7 48.8 70.0 49.4 51.5 55.0 75.0 56.5 59.1 62.6 80.0 64.2 66.5 70.0 85.0 72.3 75.0 77.0 90.0 81.0 83.9 85.5 95.0 90.3 90.4 90.5 100.0 100.0 100.0 100.0 APPENDIX D - 138 - Page 15 of 19 For all practical purposes, Type A Loading and Type B Loading represent the two extremes in the relationship between Load Factors and Loss Factors. For distribution transformers, the relationship between Loss Factors and Load Factors is expressed with the following empirical relationship Loss Factor - 0.15 Load Factor + 0.85 (Load Factor)2 This relationship is tabulated in Table D.3 and shown graphically in Figure D.6. Distribution feeders, the general relationship between Loss Factors and Load Factors is tabulated in Table D.3 and shown graphically in Figure D.6 (these relationships are based upon average values for many systems). Capacity is a valuable commodity so we will explore the relationship between "Energy Loss over a Specified Time Period" and "Demand Loss at Peak". The Minimum demand loss at peak is associated with Type A Loading (demand is either 100% or 0% for any given hour). For this type of loading, the peak demand loss is equal to the energy loss. If energy loss is 15%, then the demand loss is also 15%. For all practical purposes, the Maximum demand loss at peak is associated with Type B Loading (constant demand for all hours but one which is the peak demand). A computer model was developed for Loading Type B based on the following: Cload Constant Loading (0.0 to 100.0) Peak - 100.0 Load Factor (%) = (Cload x (Hours -1)/(Peak x Hours) x 100 Total Energy - (Clcad x (Hours-1)) + Peak PCT - Percent Energy Loss Energy List - (PCT/100.0) * total Energy DSQ - Demands Squared - ((Hours-1) x Cload ) + Peak 2 PSR - Peak Share of Losses - Peak 2/DSQ Demand Loss at Peak - PSH x Energy Lost - 139 - APPENDIX D Page 16 of 19 Figure D.6 100 I 80 DISTRIBUTION 60 FEEDER LOAD TYPE A 40 - DISTRIBUTION TRANSFORMER 20 LOAD TYPE B 0 0 20 40 60 80 100 % LOAD FACIOR - 140 - APPENDIX D Page 17 of 19 The Type B Loading model was used to derive the data detailed in Table D.4 and the graphs of Figure D.7 for a 25 hour loading cycle and an 8760 hour loading cycle. Table D.4 or the graphs of Figure D.7 may be used to approximate the per- cent demand loss at peak when the load factor and energy loss are known. For the Example Load (Exhibit D.1), the Load Factor is 51.5% and the energy loss is 15%. The 15% loss curve of Figure D.7 indicates that the the maximum peak loss would be 28% and we know that the minimum is 15%. An average value of (15 + 28)/2 = 21.5% could be used for studies (The calculated value was 24.3%). APPENDIX D Page 18 of 19 -141 - TABLE D.4 PERCENT DEMAND LOSS AT PEAK VERSUS VARIOUS ENERGY LOSS LEVELS TYPE B LOADING % DEMAND LOSS AT PEAK FOR VARIOUS ENERGY LOSS LEVELS LOAD FACTOR 5% 10% 15% 20% 25% 30 (%) (5) (%) (%) (%) (%) (%) 24 HOUR LOADING CYCLE 10 11.1 22.1 33.2 44.2 55.3 66.4 20 14.7 29.5 44.2 59.0 73.7 88.5 30 13.5 27.0 40.0 53.9 67.4 80.9 40 11.4 22.8 34.2 45.5 56.9 68.3 50 9.6 19.2 28.8 38.3 47.9 57.5 60 8.2 16.4 24.5 32.7 40.9 49.1 70 7.1 14.2 21.3 28.4 35.4 42.5 80 6.2 12.5 18.7 24.9 31.2 37.4 90 5.6 11.1 16.7 22.2 27.8 33.3 100 5.0 10.0 15.0 20.0 25.0 30.0 8760 HOUR LOADING CYCLE 20 24.9 49.8 74.7 99.6 - - 30 16.6 33.2 49.8 66.5 83.1 99.7 40 12.5 24.9 37.4 49.9 62.3 74.8 50, 60, 70, 80, 90, 100 Same as 24 hour cycle - 142 - APPENDIX D Page 19 of 19 Figure D.7 % DEMAND LOSS AT PEAK VERSUS LOAD LEVELS AND VARIOUS ENERGY LOSS LEmVE TYPE B LOADING 100 24 HOUR 8760 HOURS 80 60 0 40 2% 1 15% 20 -'10% 5% 0 20 40 60 80 100 % LOAD FACTOR APPENDIX E Page 1 of 3 - 143- BIBLIOGRAPHY Economic Analysis of Losses 1. C.J. Baldwin, C.J. Hoffman, P.J. Jeynes; "A Further Look at Cost of Losses", AIEE Transactions, Part III, Vol. 80, 1961. 2. N.E. Chang; "Generalized Equations on Loss Reductions with Shunt Capacitors", IEEE, Mid Winter Meeting Jan-Feb, 1972. 3. M. Chen, Y. Ohba, L. Reynolds, W.D. Dickerson; "Losses in Electrical Power Systems", Electric Power Systems Research, (1977/78). 4. J.H. Cronin, C.R. Murray, B.G. Selling; "Transformer Losses and Effect on Design", Proceedings of the American Power Conference, Vol. 40, Cal., 1978. 5. P.F. Johnson; "Evaluation of the Cost of Electrical Losses in Power Systems". 6. G.K. Nass; "Economics of Power System Reliability and Planning" Johns Hopkins Press, 1979. 7. M. Munasinghe; Economics of Power System Reliability and Planning, Johns Hopkins University Press, Baltimore, 1979. 8. M . Munasinghe, "Principles of Modern Electricity Pricing", Proc. IEEE, March 1981, pp, 332-48. 9. M. Munasinghe and J.J. Warford, Electricity Pricing, Johns Hopkins University Press, Baltimore, 1982. 10. D.L. Nickel; "Distribution Transformer Loss Evaluation: Load Characteristics and System Cost Parameters", IEEE, PES Winter Meeting, New York, Feb, 1980. 11. F.W. Symonds, M.C. Anderson; "The Application of Distribution Capacitors for Minimized Power and Energy Losses", IEEE, 1979. 12. D.I.H. Sun, W. Abe, R.R. Shoults, P. Eichenberger, D. Farris; "Calculation of energy Losses in a Distribution System", IEEE, July/Aug, 1980. 13. D.J. Ward, R.W. Smith; "Economic Transformer Loading - What Makes Sense with Todays Costs", Pacific Coast Electric Association Engineering and Operation Conference, March, 1980. APPENDIX E Page 2 of 3 - 144 - Technical Analysis 1. H.F. Hoebel; "Cost of Electric Distribution Losses", Electric Light and Power, March 15, 1959. 2. Kenneth W. Klein; "Another Look at Distribution Transformer Loss Ratios", Cleveland Electric Illuminating Company, October 14, 1959. 3. "Distribution System Energy Losses", REA Bulletin 45-4, August 28, 1975. 4. Edward L. Boyd; "Modified Standard Transformers Best Hedge Against Losses?", Electric Light and Power, May 1980. 5. Harold B. Margolis; "Evaluating Power System Losses", Transmission and Distribution, June, 1980. 6. D.L. Nickel, H.R. Braunstein; "Evaluating Transformer Loss Evalua- tion: I & II", Westinghouse Electric Corporation, February, 1980. 7. "General Requirements for Distribution Power and Regulating Trans- formers", American National Standards Institute Appendix C57.91 (1974). 8. Daniel J. Ward; "Economic Transformer Loading - What Makes Sense with Today's Cost?", General Electric Company, March 13, 1980. 9. John T. Shincovich; "Distribution System Transformer Loss Evaluation", Presented at the 31st Annual Power Distribution Conference, October 25, 1978. 10. M.W. Gangel, R.F. Propst; "Distribution Transformer Load Characteristics", General Electric Company, March 2, 1964. 11. J.H. Cronin, C.R. Murray, B.G. Seiling; "Transformer Losses and their Effect on Design", Proceedings of the American Power Conference, 1978. 12. Mo-Shing Chen, Yasuo Ohba, Lindian Reynolds, W. Donald Dickson; "Losses in Electrical Power System", Electric Power Systems Research 1 (1977/78) 9-19. 13. P.F. Johnson; "Evaluation of the Cost of Electrical Losses in Power Systems", Consumers Power Company, April, 1976. 14. C.J. Baldwin, C.H. Hoffman, P.H. Jeynes; "A Further Look at Cost of Losses", Presented AIEE Fall General Meeting, October 15-20, 1961. 15. D.I.H. Sun, S. Abe, R.R. Shoults, M.S. Chen, P. Eichenberger, D. Farris; "Calculation of Energy Losses in a Distribution System", Presented at the IEEE PES Summer Meeting, July 15-20, 1979. APPENDIX E Page 3 of 3 - 145- 16. N.E. Chang; "System Data Plus Computer Cuts Power Losses", Electric Light and Power, August, 1970. 17. F.W. Symonds, M.C. Anderson; "The Application of Distribution Capacitors for Minimized Power and Energy Losses", University of Tennessee (FWS), Tennessee Valley Authority (MCA), 1979. 18. Distribution System Losses, Electrical Engineering Handbook, Tenth Edition, McGraw-Hill Book Company, 1969. 19. Eugene F. Gorzelnik: "Motor Efficiency Can Mean Big Savings!", Electrical World, November, 1980. 20. "Energy Efficient Electric Motors", U.S. Department of Energy, DOE/CS0163 (May 1980). 21. "Voltage Levels on Rural Distribution Systems", REA Bulletin 169-4, Revised November, 1970. 22. Nelson E. Chang; "Determination of Primary Feeder Loses", Presented at the IEEE Summer Power Meeting, July 9-14, 1967. 23. Donald Sebesta, C.L. Wagner, D.L. Nickel; "Choose Correct Transformer-Loss Values", Electrical World, May 15, 1978. 24. Leon K. Kirchmayer; Economic Operation of Power Systems, John Wiley & Sons, Inc. and Chapman & Hall LTD. 1958. 25. J.F. Calvert, T.W. Sze; "A New Approach to Loss Minimization in Electric Power Systems", Presented at AIEE Fall General Meeting, October 7-11, 1957. 26. T.W. Sze, J.R. Garnett, J.F. Calvert; "Some Applications of a New Approach to Loss Minimization in Electrical Utility Systems", Presented at the AIEE Fall General Meeting, October 26-31, 1958.