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Efficiency of electric power generation in the United States-- Analysis and forecast based on data e

Efficiency of electric power generation in the

United States:Analysis and forecast based

on data envelopment analysis

Alexander Vaninsky ?

Mathematics Department,Hostos Community College of The City University of New York,

500Grand Concourse,Room B 409,Bronx,NY 10451,USA

Received 27May 2005;received in revised form 5February 2006;accepted 24February 2006

Available online 19April 2006

Abstract

This paper estimates the efficiency of electric power generation in the United States for the period of 1991through 2004using Data Envelopment Analysis (DEA).Operating expenses and energy loss are used as inputs,utilization of net capacity,as an output.Obtained results point to a relative stability in efficiency from 1994through 2000at levels of 99–100%with a sharp decline to 94–95%levels in the years following.Efficiency is also forecasted for year 2010,and calculated to equal 96.80%,which means it remains below the values of previous https://www.wendangku.net/doc/f02992553.html,stly,a model of efficiency management is introduced and discussed.

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Keywords:Electric;Power;Generation;Efficiency;DEA

1.Introduction

Electric power plays a critical role in the nation's economy.In 2004,total assets of the electric power industry in the United States constituted $911.6billion (company-level assets of shareholder-owned electric companies only),market capitalization,$331.0billion,and

total Energy Economics 28(2006)326–

338

?Corresponding author.Tel.:+17183197930,+17185186615;fax:+17185186706.

E-mail address:avaninsky@https://www.wendangku.net/doc/f02992553.html, .

doi:10.1016/j.eneco.2006.02.007

operating revenue,$353.3billion.Reliability of electric power supply is one of the main mo-tivating factors for technical innovation and change in market organization.Electric power production is a comprehensive process that includes generation,transmission,distribution,and retailing,involving large amounts of capital,labor,and financial resources,see Dugan et al.(2002),Morey (2001),and https://www.wendangku.net/doc/f02992553.html, for detail.

Generation of electric power is at the core of the production process,and efficiency here is of crucial importance,as it is closely related to security and adequacy of the electric power system.Security is the system's ability to withstand contingencies,such as changes in generator avail-ability,while system adequacy means having a sufficient supply of generation capacity on hand to maintain system security under all but the most extreme circumstances (Morey,2001).In-terestingly,the first efficiency contradiction surfaces here.System security and adequacy require more installed capacity,while higher efficiency necessitates its decrease.Aspirations for higher numbers of ultimate customers,usually far removed from one another geographically,lead to the creation of widespread electric power networks with multiple changes in voltage (high voltage for transmission to decrease energy loss,and low voltage for distribution,for safety provisions.)Ramified networks with varying voltages cause additional energy losses in transmission,coupled with an increase in labor and material expenses.At this point,the second efficiency contradiction comes into play.Variety and the large number of customers lead to greater energy losses and operating expenses.

Efficiency of electric power generation determines to what extent the electric power industry is able to balance these contradictory requirements.Roughly speaking,in this paper,we call the industry efficient if it succeeds at keeping the proper level of capacity utilization required for system security and adequacy with minimal operating expenses and energy loss.It is important to stress that we do not set up a benchmark of efficiency per se;our objective is to compare relative efficiencies in a series of consecutive years to find tendencies and to suggest a model for efficiency forecasting and management.

Examining the electric power industry,we consider every year as a separate object,and use Data Envelopment Analysis,a mathematical tool based on Linear Programming,to measure its efficiency,see Cooper et al.(2005)for detail.More precisely,it is a version of Dynamic DEA invented in F?re and Grosskopf (1997)that is used in this paper.In computations,we use statistical data of the Energy Information Administration (EIA),the independent statistical and analytical agency within the U.S.Department of Energy,posted on the web site https://www.wendangku.net/doc/f02992553.html, .

The rest of the paper is organized as follows:Section 2provides an overview of DEA,its applications within the electric power industry,and a brief description of the specific DEA model used for our purposes.In Section 3,statistical data and efficiency scores for 1991through 2004are presented and discussed.Finally,in Section 4we discuss models of efficiency forecasting and management,and apply them to data for 2010.

2.Data envelopment analysis and its applications in the electric power industry

Data Envelopment Analysis (DEA)was developed in Charnes et al.(1978),and Banker et al.(1984).A comprehensive description is provided in Cooper et al.(2005),with a list of literature sources available at https://www.wendangku.net/doc/f02992553.html, .DEA estimates relative efficiencies of objects in a group,referred to as Decision-Making Units (DMUs)that use inputs X =(X j ,j =1,...,s )to produce outputs Y =(Y i ,i =1,...,r ).In this paper,efficiency is defined as the ability of an object to produce given output with a minimal amount of inputs.

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A.Vaninsky /Energy Economics 28(2006)326–338

DEA allows all indicators to be combined into a single efficiency score scaled between0and1. Efficient objects receive a score equal to1,inefficient objects,less than1.To measure efficiency, DEA uses the efficiency ratio suggested in Farrell(1957):

E?P r

k?1

u k Y ktu

P s

l?1

m l X l

e1T

where u=(u1,...,u r)andν=(ν1,...,νs)are non-negative weights assigned to outputs and inputs, respectively,and u is an arbitrary-valued scalar,called intercept.

The main advantage of DEA is its ability to assign values to u,ν,and u objectively.To calculate an efficiency score,DEA allows each DMU to assign its own weight coefficients to each input, output,and the intercept favorably.However,the ability of a given DMU to achieve maximal possible efficiency score of1is restricted by the following requirement:with the weight coefficients assigned by any given DMU to itself,no other DMU in the group may receive an efficiency score greater than1.This means that a poorly performing DMU cannot achieve a high efficiency score for itself by playing with the weight coefficients,since an object that performs really well would have received the efficiency score greater than1.

The basic efficiency ratio(1)therefore,generates the following series of optimization problems: For each DMU i,i=1,...,n,find non-negative vectors u i=(u i1,...u ir)andνi=(νi1,...νis),and an arbitrary-valued scalar u i such that:

E i?P r

k?1

u ik Y iktu i

P s

p?1

m ip X ip

Y maxe2T

subject to

E j V1with all u i?eu il;N;u irT;v i?em il;N;m isT;and u i;i;j?1;N;n:e3T

DEA changes the series of optimization problems given by formulas(2)and(3)to a series of equivalent Linear Programming(LP)procedures of the following structure: LP-procedure:For each DMU i,i=1,...,n,find non-negative vectorλi=(λi1,λi2,…,λin)and scalarωi such that

x i Y min

subject to

X n

j?1

k ij X jk V x i X ik;k?1;N;s;

X n j?1k ij Y jp z Y ip;p?1;N;r;

328 A.Vaninsky/Energy Economics28(2006)326–338

n j ?1k ij ?1;

k ij z 0;j ?1;N ;n ;

0b x i V 1e4Twhere X jk and Y jp stand for the k -th input and p -th output of a DMU j ,respectively.

The LP-problem stated in formulas (4)has the following interpretation:for each DMU i ,the computer program designs a virtual object that produces at least the same outputs as DMU i while using at most ωi -share of its inputs.This virtual DMU is constructed of λi -fractions of all DMUs serving as building blocks,including DMU i itself.This LP-problem has at least one feasible solution:

x i ?1;k ii ?1;k ij ?0for i p j e5Twhich means that a virtual DMU is the same as the DMU i itself.For some DMUs this is the only solution,meaning that their performance cannot be improved by simulating structure and activities of peer DMUs.For other DMUs in the group,better solutions exist with a smaller value of ωi b 1.Such DMUs may perform better by acquiring the properties of their peers.The minimal value of ωi given by LP-problem (4)and efficiency score E i corresponding to problem (2),(3)are reciprocal to each other:

max E i ?1min x i :e6T

DMUs with E i =1are called efficient,and otherwise,inefficient.

The version of DEA used in this paper is referred to as input-minimization DEA with variable returns to scale (IM VRS).We use the input-minimization (IM)DEA model because operating expenses and energy loss indicators used as DEA inputs are more manageable than capacity utilization,a DEA output.With technological,organizational and managerial factors strongly dependent on the size of electric power systems,in designing the virtual DMU above,it was sensible to use only fractions of DMUs and not their multiples.This requirement leads to the restrictions imposed on λi in optimization problem (4):sum of λij by j should be equal to 1for all i .The corresponding DEA model is referred to as variable returns to scale (VRS)one.More details and other DEA models may be found in Cooper et al.(2005).

Application of DEA in the electric power industry may be traced back to the publications of Cote (1989),Hjalmarsson and Veiderpass (1992),and Bagdadioglu et al.(1996),who applied it to the analysis of impact of ownership on efficiency,and Miliotis (1992)who used DEA for comparative analysis of the efficiency of electricity distribution.Yunos and Hawdon (1997)consider organizational efficiency comparisons at the international level.A series of publications appeared in early 2000s:Sueyoshi and Goto (2001)investigated the performance of electric power generation in Japan,Chen (2002)presented an assessment of technical efficiency and cross-efficiency in Taiwan's electricity distribution sector,Pacudan and de Guzman (2002)researched productive efficiency of electricity distribution in the Philippines,Korhonen and Syrjanen (2003),cost efficiency in Finnish electricity distribution,Nemoto and Goto (2003),329A.Vaninsky /Energy Economics 28(2006)326–338

dynamic efficiency of electric power production in Japan,Pahwa et al.(2003)and Sanhueza and Rudnick(2003),evaluation of efficiency of electric distribution utilities.

Applications of DEA within the electric power industry are also presented in a series of publications posted on the Internet.Meimodi(1998)applied DEA to the analysis of efficiency of electricity production and price policy in Iran,Ajodhia et al.(2001)presented a DEA-based benchmark model aimed at simultaneous analysis of costs and quality levels,and applied the model to a sample of British,Dutch,Hungarian and Malaysian distribution firms;and Tahvanainen et al. (2004)evaluated the measures taken by several European countries implementing quality regulation in the electricity distribution business.

In contrast to the publications mentioned above,the goals of this paper are not bound by analysis of efficiency only.Among its other objectives,is to forecast efficiency and determine the main factors responsible for its increase.

3.Efficiency modeling and analysis

This paper aims to capture a general view on efficiency in electric power generation,and we have bounded our considerations with aggregated,measurable,and manageable technical–economic indicators only.For instance,we did not include in our research pure technical indicators,such as voltage dips or interruption time.Also,we did not include environmental and societal indicators that are out of the industry's control,such as“amount of energy supplied”or“number of customers”.Our research does not include factors that are important for efficiency estimation but could not be obtained from publicly available information sources,such as“economic losses from electric energy supply interruption”.The following three indicators were chosen as fitting factors of efficiency of electric power generation:utilization of net capacity,energy losses,and operating expenses.They are both measurable based on publicly available data,and are under control of the electric power industry.Taken together,they provide a general picture of efficiency of electric power generation.An ability to measure each of these indicators in relative units allows extensibility of the suggested approach for interregional and international comparisons.

The following information was collected from the EIA web site https://www.wendangku.net/doc/f02992553.html, for the years1991through2004:electric net summer capacity,net generation of electric power,retail sales of electricity in kW h,operating expenses,and revenue.Two last indicators are presented in nominal dollars.Based on this data,the following DEA inputs and outputs were formed as shown below:utilization of net capacity,operating expenses,and energy loss,see Table1.

Utilization of net capacity(DEA output)shows to what extent the electric power industry utilizes its production possibilities.We measured it as a ratio of net generation to electric net summer capacity multiplied by8760h per year.Note that the net generation indicator does not include the Table1

DEA inputs/outputs

Indicator Utilization of net

capacity,%a Operating expenses,

share of revenue,%

Energy loss,share of net

generation,%b

Role in DEA Output Input Input

max53.6787.9210.64

min46.7481.339.64

a Utilization of net capacity is percentage of net generation with respect to the net summer capacity times8760h per year.

b Difference between net generation and retail sales of electricity,%of net generation.

330 A.Vaninsky/Energy Economics28(2006)326–338

electric energy consumed by electric stations'auxiliaries and the losses in the transformers that were considered integral parts of the stations themselves.The formula for calculating the utilization of net capacity (CU)is this:

CU ?Net generation Summer capacity ?8760:e7TFor technical reasons and reasons related to reliability,generation capacity cannot be utilized in full,yet it is the responsibility of electric power industry to keep this indicator as high as possible to use capital investments in a rational measure.As follows from Table 1,observed values of net capacity utilization fluctuated between 46.74%and 53.67%during the research period.

Operating expenses (DEA input)is another indicator included in the research.It combines expenses of labor,fuel,materials,depreciation,production process management and administration,and several other components.To avoid the necessity of dealing with inflation rates and to pave the way of international comparisons,we measured this indicator as percentage of revenue from retail sales of electricity.As follows from Table 1,its observed values varied from 81.33%to 87.92%,corresponding to operating profit margin of 18.67%through 12.08%,respectively.

The last indicator included in the research is energy loss (DEA input).The nature of electric power supply dictates that its generation is at one geographical point and consumption is at another,the two often great distances apart.While transmission is conducted at high voltage to reduce network losses,generation and consumption are performed at low voltage for technical and safety reasons.The necessity to transmit electric energy to customers through ramified networks with multiple changes in voltage is a source of notable energy loss.In our research,energy loss includes both transmission and distribution losses,i.e.all electricity losses that occur between the points of generation and the ultimate customer.As follows from Table 1,observed values of the energy loss indicator varied between 9.64%and 10.64%of the net

generation.

Capacity Utilization

19911992199319941995199619971998199920002001200220032004

Year

%Fig.1.Capacity utilization.DEA output.

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A.Vaninsky /Energy Economics 28(2006)326–338

Graphs in Figs.1through 3represent the dynamics of the DEA inputs and outputs.As follows from the graph of utilization of net capacity in Fig.1,it had been on the rise from 1991through 1999,and on a decline thereafter.The drop in 2003to the sample's lowest value in 2003is a negative factor of efficiency dynamics.The decrease in capacity utilization is,among other factors,due to

positive

Operating Expenses, % of Revenue

19911992199319941995199619971998199920002001200220032004

Year

Fig.2.Operating expenses as percentage of revenue.DEA

input.

Energy Loss, % of Net generation

9.60

9.70

9.80

9.90

10.00

10.10

10.20

10.30

10.40

10.50

10.60

10.70

Year

Fig.3.Energy loss.DEA input.

332 A.Vaninsky /Energy Economics 28(2006)326–338

economic growth perspectives,natural disasters and blackouts throughout the United States in recent years,and a rising threat of terrorist activity in 2000s.All of these factors required additional energy reserves and as a result extra capacity at instant disposal (see note 1,Appendix).

The graph in Fig.2shows operating expenses measured as percentage of revenue.Its tendency reveals an increase up to the year 2000and a decrease afterwards.The maximal value of relative operating expenses,equal to 87.92%of operating revenue,was reached in 2000.The main factor for the increase in operating expenses and thus,decrease in operating profit margin,is the rise in fuel prices with prices for electric energy remaining relatively stable,since in the United States about 70%of electric power (70.9%in 2004)is generated by power stations employing petroleum,natural gas,or coal.The rebound of operating expenses after 2000is the electric power industry's adjustment to the new conditions of operation (see note 2,Appendix).

Lastly,changes in relative energy loss in time are shown in Fig.3.They are varied,being affected by two main factors.The first factor is the increase in demand for electric power,which leads to an increase in net generation (positive factor).The second factor is increase in the number,variety,and average remoteness of customers.It requires an increase in the frequency of changes in voltage (negative factor)to accommodate electric power transmission at longer distances.Interference of these two factors in time results in non-monotonous character of the energy loss trend.An index numbers model used for the extrapolation of energy loss,addressed in the next section,reveals that its rise is expected to continue at least up to 2010.

DEA allows all factors of the efficiency of electric power generation to be broken down into an efficiency score.In our study,efficiency scores were calculated using DEA given by formulas (2),

(3),and (4).The obtained results are presented in Fig.4and Table 2.The graph in Fig.4is V-shaped for the period of 1991through 1994,remaining relatively stable from 1994through 2000at high efficiency levels of 99–100%,and then falling sharply in 2001through 2004to levels of 94–96%(a rebound to 97.67%in 2003is not typical for this period).The reason for the negative efficiency dynamics in the later years is due to negative factors of efficiency prevailing over positive ones:the sharp decline in capacity utilization and the mixed dynamics of energy loss were not fully offset by only a moderate decrease in operating expenses.

Negative tendencies in efficiency of electric power generation of the later years deserve a thorough technical and economic analysis of the reasons and consequences,and implementation of measures for improvement in the near future.Factorial forecast of efficiency scores considered in the next section is an analytical tool of the assessment of these measures.

4.Efficiency forecast and management

In this section,we forecast the efficiency of electric power generation for 2010and discuss the results from the efficiency management perspective.The forecast is based on prospective data,posted on the web site https://www.wendangku.net/doc/f02992553.html, .Recall that in this paper,efficiency calculations use three DEA inputs/outputs:net capacity utilization (output),energy loss (input),and operating expenses (input).Capacity utilization may be estimated directly from the posted data,whereas energy loss requires index number modeling,because expected values of the required indicators are posted in Btus,the units of energy,rather than in dollars,as required for our purposes (Btu stands for British thermal unit;1kW h =3413Btu).As there are no published data on expected revenue and operating expenses,we used an autoregressive model to forecast their ratio.

Utilization of net capacity (CU)in 2010was calculated by formula (7)as a ratio of prospective values of net generation to electric net summer capacity multiplied by 8760h per year.Doing so,we obtained the value of CU 2010=51.08%,that falls within the range of historical data shown in Table 1.

333

A.Vaninsky /Energy Economics 28(2006)326–338

To forecast energy loss,the following index numbers model was used.Denote indicators of energy consumption,energy loss,and net generation,and as EC,EL,and NG,respectively,and apply the following series of algebraic transformations:

EL 2010NG 2010?NG 2010?EC 2010NG 2010?1?EC 2010NG 2010?1?EC 2010NG 2010?EC 2004EC 2004?NG 2004NG 2004?1?EC 20102004 ?NG 20042010 ?EC 20042004

:e8TThe last expression allows for a representation of energy loss in terms of index numbers,rather than quantitative indicators,and enables us to gauge them in arbitrary units.Denote indexes of energy Table 2

Efficiency scores

Year

19911992199319941995199619971998Efficiency,%

100.0099.1398.61100.00100.0099.6399.44100.00

Year

19992000200120022003200042010Efficiency,%100.00100.0098.9296.0697.6794.62(94.10)Notes :Efficiency of 2010is an expected

value.

Efficiency of the Electric Power Generation, 1991 - 2004

9899

100

101

19911992199319941995199619971998199920002001200220032004

Year

%Fig.4.Efficiency dynamics.

334 A.Vaninsky /Energy Economics 28(2006)326–338

consumption and net generation,as I EC,2010,2004=EC 2010/EC 2004and I NG,2010,2004=NG 2010/NG 2004,respectively,and energy consumption ratio,as M EC,2004=EC 2004/NG 2004.Then,using the EIA's current and prospective data,we get

EL 2010NG 2010?1?I EC ;2010;2004M EC ;2004I NG ;2010;2004?1?1:07708?0:893631:11159?0:1341?13:41%:e9T

Such a high value of energy loss is well above the historically high value of 10.64%shown in Table 1.Statistically,the reason for the increase in expected energy loss is positive difference between expected rates of increase in net generation (11.159%)and energy consumption (7.708%),formula (9)(see note 3,Appendix).The following may be suggested among some possible reasons for the forecasted increase in energy loss:expansion of areas covered by the electric power stations,and a rise in the number and variety of customers.Taken together,these factors lead to an increase in the distance of electric energy transmission and in the frequency of change in voltage.

As noted previously,the Energy Information Administration of the United States does not publish data on expected revenues and operating expenses.We,therefore,had to model the relative operating expenses indicator needed to forecast the efficiency score for 2010.We used an autoregressive model that relates future levels of an indicator to those in the previous periods.The use of this model is based on the assumption that the impact of the factors of revenue and operating expenses becomes apparent in time,also depending on their cumulative impact in the past.Analysis of the correlation function of a time series of the relative operating expenses revealed that only the first three coefficients of correlation were statistically significant.For modeling,we used the ARIMA-procedure provided by Minitab.We had to restrict our research with the second-order model since the algorithm had not converged for the third-order auto-regressive model:

OE t ?A 0tA 1OE t ?1tA 2OE t ?2te t ;e10Twhere t stands for time in years,OE t ,for operating expenses as percentage of revenue at the time t ,εt ,for random residuals,A 0,for an intercept term,and A i ,i =1,2,for coefficients of the model.Fitting this model to statistical data of 1991through 2004revealed a continued decrease in relative operating expenses,at least up to 2010.The estimated value for 2010is OE 2010=85.57%,slightly less than the actual observed values for the period of 2000through 2004.

The efficiency score for 2010was obtained,as before,with a DEA model given by formulas

(2),(3),and (4).The forecasted value is 96.80%-higher than the 2004value of 94.61%,yet well below the 100%mark.Thus,the problem of efficiency management arises.

As a step towards resolving the problem,we suggest finding values of DEA inputs and outputs that prove 100%efficiency.In this paper we use equal proportional changes in DEA inputs and output.To achieve the desired goal,we seek for a minimal number r N 1such that the virtual DMU obtained from that corresponding to 2010,becomes fully efficient when the 2010-inputs are divided by r and 2010-output is multiplied by r .The procedure is presented in Table 3.

Initial data for 2010is shown in the row Step 1.In Step 2,we use the value of r =1/0.9680=1.0331,the reciprocal of the efficiency score.Inputs are divided by r ;the output is increased r times.In DEA calculations we exclude 2010from the group of peers.Thus,we get 335

A.Vaninsky /Energy Economics 28(2006)326–338

new values of DEA inputs and output shown in the row Step 2in Table 3.Operating expenses are 85.57/1.0331=82.83,energy loss is 13.41/1.0331=12.98,and capacity utilization is 51.08×1.0331=52.77.The corresponding efficiency score is 101.10%.Since it is greater than 100%,the virtual DMU is overly efficient with regard to the rest of the group.

For our next step,we conduct the trial and error method with a binary search to find the coefficient of proportional change r between 1.0000and 1.0331that yields the 100%efficiency score.As shown in the last row of Table 3,this is achieved with r =1.0247.Corresponding values of DEA inputs and output are as follows:operating expenses,85.57/1.0247=83.51,energy loss,13.41/1.0247=13.09,and capacity utilization,51.08×1.0247=52.34.Roughly speaking,the desired increase in efficiency by 100?96.80=3.20percentage points would result from a 2.47%decrease in inputs and an equivalent increase in the output.The obtained values for operating expenses and capacity utilization fall within the range of historically observed data shown in Table 1.The value for energy loss however,is much higher,affirming that the 100%efficiency score in 2010is possible with a greater value of relative energy loss than the observed values of previous years.A more elaborated procedure leading to different coefficients of proportional change in DEA inputs/outputs is provided by the method DEA with a single DMU developed in Maital and Vaninsky (1999).

5.Conclusions

In this paper we estimated the relative efficiency of electric power generation in the United States in a series of consecutive years,starting in 1991through 2004,using Data Envelopment Analysis (DEA).Operating expenses and energy loss were used as DEA inputs,utilization of net capacity,as a DEA output.Our findings pointed to a relative stability in efficiency from 1994through 2000at levels of 99–100%,and a sharp plunge to 94.61%in 2004.

In order to forecast efficiency for the year 2010,an approach to apply the DEA model with expected values of DEA inputs/outputs was suggested.Based on prospective data of EIA,and using index numbers and autoregressive modeling,we received the efficiency estimation for 2010equal to 96.80%,which is greater than the efficiency score for 2004,but still well below 100%.

Our approach to efficiency management is based on a proportional change in DEA inputs and outputs.Its application to the forecasted data for 2010allowed us to determine the values of DEA inputs/outputs capable of delivering 100%efficiency.These values may be used as a benchmark for further technical –economic analysis and serve as guidelines aimed at developing measures to increase efficiency of electric power generation.What's more,the model can be further expanded to

Table 3

Finding proportional change in DEA inputs and outputs

Step Coefficient of

proportional change a Operating expenses,%

Energy loss,%Capacity utilization,%Efficiency,%DEA input

DEA input DEA output 1

85.5713.4151.0896.802

1.0331b 8

2.8312.9852.77101.103

1.0247c 83.5113.095

2.34100.00a

A divisor of DEA inputs and a factor of DEA output shown in the first row.b

Obtained as 1/0.9680.c Obtained by the trial and error method using the binary search between 1and 1.0331.

336 A.Vaninsky /Energy Economics 28(2006)326–338

accommodate interregional and international comparisons by using a small number of publicly available and manageable indicators.

Acknowledgements

The author is thankful to the Energy Information Administration of the United States,especially to Elsie Bess,Rick Farace,and Paul Hesse,for providing explanations regarding statistical indicators used in this paper,to Henry Lopez (Hostos Community College,CUNY)for his helpful assistance,and to an anonymous referee for fruitful comments that contributed to this paper.Appendix.Notes (the following information was provided by the EIA)

(1)Large quantities of new capacity were added during the period of 2000–2003.Lots of it was in the form of peaking units (combustion turbines),which have relatively low capacity factors themselves.In addition to these many peaking units,many combined cycles units were added.Because capacity was overbuilt,many of these combined cycles are also running at relatively low capacity factors.

(2)A simplistic analysis would indicate that production costs (cost of fuel,purchased power and other)probably had the largest impact on operating expenses as percent of revenue.A complicating factor is that there is a lag between when production expenses accrue and when regulated utilities are able to collect additional revenue through rate increases (to cover increased expenses)as approved by public utility commissions in those states where the electric utility industry has not been restructured or deregulated.More details are available on the web site https://www.wendangku.net/doc/f02992553.html,/cneaf/electricity/epa/epa.pdf#page=58.

Fluctuations of operating expenses could be the result of restructuring expense and/or the types of generation being used as base load units.For example,a large amount of natural gas units came online in the 1990s but also restructuring may have affected how operating costs were allocated which began in 1996.

(3)Expected rates of increase in net generation and energy consumption were obtained from the following data posted on the EIA web site https://www.wendangku.net/doc/f02992553.html, :

Release Date:December 12,2005

Electricity Generation by Fuel,1980–2030(billion kilowatt-hours)

Coal

Petroleum Natural gas Nuclear Renewable/other 2004

1976.3330117.5910699.6097788.5556358.766920102217.5550104.8182773.8234808.6948475.7432

Delivered Energy Consumption by Sector,1980–2030(quadrillion Btu)

Residential

Commercial Industrial Transportation 2004

11.435728.2639625.5595827.73526201012.24827

8.9997026.6679430.70490Generation a

Consumption a Total Increase,%Total Increase,%2004

3940.856272.994522010

4380.634611.15978.620817.708a Calculated by author.

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A.Vaninsky /Energy Economics 28(2006)326–338

338 A.Vaninsky/Energy Economics28(2006)326–338

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Hjalmarsson,L.,Veiderpass,A.,1992.Efficiency and ownership in Swedish electricity retail distribution.Journal of Productivity Analysis3,7–23.

https://www.wendangku.net/doc/f02992553.html, a web site containing DEA-related bibliography.

https://www.wendangku.net/doc/f02992553.html, a web site of the Edison Electric Institute.

https://www.wendangku.net/doc/f02992553.html, a web site of the Energy Information Administration of the United States.

Korhonen,P.J.,Syrjanen,M.J.,2003.Evaluation of cost efficiency in Finnish electricity distribution.Annals of Operations Research121(1–4),105–122.Jul.

Maital,S.,Vaninsky,A.,1999.Data envelopment analysis with a single DMU:a graphic projected-gradient approach.

European Journal of Operational Research115,518–528.

Meimodi,A.E.1998.Efficiency considerations in the electricity supply industry:the case of Iran.http://www.econ.surrey.

https://www.wendangku.net/doc/f02992553.html,/WorkingPapers/seed95.pdf.

Miliotis,P.A.,1992.Data envelopment analysis applied to electricity distribution districts.Journal of the Operational Research Society43,549–555.

Morey,M.J.,2001.Ensuring sufficient generation capacity during the transaction to competitive electricity markets.

Edison Electric https://www.wendangku.net/doc/f02992553.html,.

Nemoto,J.,Goto,M.,2003.Measurement of dynamic efficiency in production:an application of data envelopment analysis to Japanese electric utilities.Journal of Productivity Analysis19(2–3),191–210.Apr.

Pacudan,R.,de Guzman,E.,2002.Impact of energy efficiency policy to productive efficiency of electricity distribution industry in the Philippines.Energy Economics24(1),41–54.Jan.

Pahwa,A.,Feng,X.,Lubkeman,D.,2003.Closure on??Performance evaluation of electric distribution utilities based on data envelopment analysis".IEEE Transactions On Power Systems18(3),1221.AUG.

Sanhueza,R.,Rudnick,H.,2003.Discussion of??Performance evaluation of electric distribution,utilities based on data envelopment analysis".IEEE Transactions On Power Systems18(3),1220–1221.August.

Sueyoshi,T.,Goto,M.,2001.Slack-adjusted DEA for time series analysis:performance,measurement of Japanese electric power generation industry in,1984–1993.European Journal of Operational Research133(2),232–259.Sep.1. Tahvanainen,K.,Viljainen,S.,Honkapuro,S.,Lassila,J.,Partanen,J.,J?rventausta,P.,Kivikko,K.,M?kinen,A.,2004.

quality regulation in electricity distribution business.https://www.wendangku.net/doc/f02992553.html,k.fi/nordac2004/papers/nordac2004_ tahvanainen_et_al_paper.pdf.

Yunos,J.M.,Hawdon,D.,1997.The efficiency of the National Electricity Board in Malaysia:an intercountry comparison using DEA.Energy Economics19(2),255–269.