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Impact of Energy Efficiency Incentives on Electricity Distribution Companies Federico Alvarez and Hugh Rudnick, Fellow, IEEE
Abstract—An analysis is made of the impact of diverse regulatory mechanisms and financial incentives that aim at conciliating the interests of the regulating entity and distribution companies, while tending towards the implementation of energy efficiency policies on the power distribution sector. To assess the outcome of the power distributors on a given regulatory scenario, a productionpossibility model based on data envelopment analysis is developed. The methodology used adapts results gathered from international case-studies in order to ascertain the efficiency degree achieved by each regulating scheme. The analysis is subsequently applied on four representative companies of the Chilean power distribution sector, undergoing different energy efficiency levels required by the regulator. The results reveal that the introduction of white certificates of energy efficiency outperforms the other methods considered, as it succeeds on eliminating the disincentives at a minimal economic impact. Comparing the energy production-revenue decoupling mechanisms with the investment of the 1% in energy efficiency programs yields that the first method achieves betters results, provided that the regulator sets energy efficiency goals below 4% a year, whereas the second method is more effective concerning the global impact on the distributors. Index Terms—Data envelopment analysis, distribution companies, energy efficiency.
I. INTRODUCTION
W
ITH the search for energy efficiency (hereinafter EE) at the end-consumer level, the electricity sales business seems to be conflictive. The efficient use of energy could imply a decrease in energy sales for electricity firms, directly affecting their profits. Despite this, electricity-selling firms are identified as the best agents to promote EE practices among end users. The challenge is how to make them to commit to do so. On the other hand, there are entry barriers and market imperfections that prevent consumers from leveraging from the economic and environmental opportunities offered by EE. Reference [1] establishes that electricity supplying companies have a privileged position to overcome the market barriers because: • they have access to resources to finance the investments required in EE; • they are related with and trust in all the consumers in the areas in which they operate;
Manuscript received December 04, 2008; revised January 05, 2010. First published March 29, 2010; current version published October 20, 2010. This work was supported in part by Fondecyt and in part by Chilectra. Paper no. TPWRS-00983-2008. F. Alvarez is with Systep Gestión de Energía, Santiago, Chile (e-mail:
[email protected]). H. Rudnick is with the Electrical Engineering Department, Pontificia Universidad Católica de Chile, Santiago, Chile (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRS.2010.2045162
TABLE I REGULATORY SCHEMES TO PROMOTE EE
• they are aware of the opportunities existing in the field of EE; • they have a privileged position to harmoniously balance the investments on the supply and demand side [2]–[4]. In countries where the remuneration regulatory scheme is based on the benchmarking of distribution companies (Discos), there are no economic incentives that promote the development of EE programs. The regulatory framework gives them incentives to sell more electricity and to concentrate their efforts in minimizing the electricity costs and not in what the consumer pays for the service received. Thus, different regulations have created incentive mechanisms to promote EE. The basic mechanisms used in Brazil, California, and Italy are evaluated, with the schemes used summarized in Table I. It must be emphasized that those mechanisms are studied in isolation to emphasize their regulatory weight, although in their actual applications, they are part of wider actions. For example, in California, revenue decoupling has been combined with a shared-savings earnings mechanism, while Italy combines the white certificates with decoupling. In order to evaluate their performance, the following criteria are used to assess their effectiveness and harmony with the market [5], [6]: • compatibility with the objectives of proposed public policies; • level of effectiveness of the economic incentives’ structure and scheme; • the mechanism’s capability to create scale and scope economies; • the contribution it makes to the development of an EE infrastructure; • the elimination of disincentives of lost earnings due to lower energy sales; • generation of extra benefits to implement successful EE programs. The development of a mathematical model based on an analysis by efficiency boundaries is proposed, solved by using data envelopment analysis (DEA), and allowing the evaluation of the effect that the main energy efficiency regulatory mechanisms have on electricity Discos. The proposed methodology is applied to the Chilean market, simulating and determining the
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scope and impact of the implementation of each one of the regulations focused on EE and in particular for four representative companies in the market, namely, Chilectra, CGE Distribucion, Chilquinta, and Saesa. II. REGULATION MECHANISM A. Brazil: Obligation to Invest 1% In 2005, Brazil had a consumption of about 367 [TWh], energy that corresponded to almost 77% hydro generation and with high EE potential. For such purpose, in 1985, the Brazilian government created the National Electric Energy Conservation Program (PROCEL) that is executed through the Eletrobras state-owned company. One of their major projects is the electric appliance and equipment labeling project, with approximately 89% of the results obtained in EE. Historically, the measures implemented by PROCEL have had EE accrued results of about 5.3 [TWh/year] (1.8% of the annual consumption) for 1998. In 2001, there was a huge electric crisis due to severe droughts and the high water dependence in the energy mix, resulting in a strong electric curtailment of about 20% of the 2000 consumption. This crisis lasted for about eight months, and the contingency measures caused a deep drift in the country’s consumers toward EE. This took to a new law for all Discos, which obliged to contribute with at least 1% of the energy and power sales revenues for investments in EE projects focused on the end user. Of the money collected, 50% is delivered by the firms to a public/private institution that decides in which project to invest and the remaining amount is managed through the own EE departments created by the Discos. For this purpose, Discos have three alternatives: • developing EE projects and implementing them by their own; • developing EE projects jointly with institutes or universities; • hiring the energy services companies that manage the EE projects. The current results of the EE measures proposed by PROCEL have caused an “economized energy” level of 2158 [GWh/year] for year 2005 and an approximate accrued total of 22 [TWh/ year] for the 1986–2005 period. It is important to take into account that the results obtained are partly distorted by the huge electric curtailment produced in 2001, which is not in accordance with the objectives of a regulation mechanism in the spirit of efficiency and not in the spirit of energy reduction. These measures are easy to implement and they have the advantage of giving a quick implementation, with low supervision costs for the regulator’s EE investments. On the other hand, it is first necessary to determine if the 1% is the most efficient value to apply in an EE policy; is this value actually the most adequate one for the country’s reality? Finally, there are no incentives for Discos to carry out EE projects that provide a better cost-efficiency ratio. B. California: Revenue Decoupling California is one of the states that has one of the strongest EE policies in the United States. Its main aim is to decrease the per capita energy consumption. The targets proposed are the following: a reduction of 23 000 [GWh] for 2013 (estimate of
10% of the consumption) and a reduction in peak power of 7760 [MW] (it is estimated at 12% of peak power in 2013). Since the 2000–2001 crises, private firms are the ones that have the mission of implementing the EE projects, and the “California Public Utilities Commission” (CPUC) has only an enforcement and regulatory function. To attack the disincentives of the drop in energy sales, CPUC proposed “revenue decoupling” as a remuneration scheme for Discos. This is achieved by adjusting the tariff to level down revenues, using a quarterly estimation for the demand level (baseline) for the period. This computation is made by the CPUC, who, apart from the consumption baseline computation, also includes the EE goals to be achieved by Discos. Later, after ending the period and knowing actual consumption, the following methodology is used. If the actual sales were higher than the CPUC’s demand forecast, the tariff was leveled down for the following quarter and on the contrary, when the actual sales were lower than the demand forecast, the tariff was leveled up. Until today, these actual tariff adjustments have varied from 0% to 3% in-between periods. To finance the EE projects, the “Public Goods Wire Charge” was incorporated. This is a direct charge in the end user accounts with a surcharge of 1% of the total account of the former month. Discos administer these funds. In addition, flexible or hourly blocks tariffs are used, hence stimulating the consumers to decrease their peak consumption and to displace it to valley hours though price sensitivity. The execution of EE projects are subject to a cost-efficiency index, which is calculated with the “E3 Calculator” computer tool [7] developed by request of CPUC in order to have a common-base evaluation tool for all EE projects. This tool generates a list of EE investment priorities according to the level of impact of the consumption and peak power reduction in the electric system. The California achievements are directly reflected by the relationship existing between the growing Gross Domestic Product per person and a frozen growth of the energy consumption per person. In addition, a broad increase in EE project investments has been detected. This is translated into an aggregated cost-efficiency for the 2002–2006 period of an average of 63 [kWh] saved for each dollar invested. In 2004, 1869 [GWh] have been saved and 384 [MW] have been reduced in peak power. On the other hand, depending on the increase or decrease with respect to the baseline, the tariff adjustment function promotes an unclear signal to the end customer. This happens because independently if there are investments in EE or not, the accounts can increase or decrease depending on the behavior of the Disco as a whole. In addition, there are no additional incentives for Discos if they successfully fulfill their EE goals. C. Italy: White Certificates Since 2005, Italy established the use of white certificates as a financial mechanism to promote EE, becoming the first country in the world to follow this innovative mechanism. These certificates consist on the obligation for each one of the gas and electricity distribution firms to have a specific number of white certificates at the end of each year. This scheme allows trading financial elements in the market to prove the realization, measurement, and verification of investments in EE programs for
ALVAREZ AND RUDNICK: IMPACT OF ENERGY EFFICIENCY INCENTIVES ON ELECTRICITY DISTRIBUTION COMPANIES
TABLE II EE ANNUAL GOALS IN ITALY (SOURCE: GME)
TABLE III PRICE EVOLUTION OF WHITE CERTIFICATES (SOURCE: GME)
Up to October 2008.
the end customers. This instrument’s traceability and valuation properties give a correct signal to make the investments with the best cost-efficiency relationship in the deregulated market. AEEG is the agency that establishes the goals or the number of certificates to be owned by each one of the firms. In case the Discos do not fulfill their goals, they will be fined in amounts that are several times higher than the cost of having invested in EE. The unit of measurement for certificates is in equivalent tons of oil (Toe). For the electricity factor, it is necessary to apply a conversion factor that is derived from the average efficiency of Italy’s generation power stations:
Although the market has operated satisfactorily after its two first years of operation, achieving better results than the expected ones, a new decree introduced increases in the proposed goals and included the 2010–2012 period. The annual goals by energy sector established by law decree (Table II) consist on an energy efficiency of about 2% of the annual consumption in 2009 taking into account a demand growth of 1.5% per year. In a first stage, only those Discos with more than 100 000 customers can fulfill their EE goals according to their energy sales volumes. White certificates are of three major types, depending on their source: Type I (energy efficiency obtained in the electric sector), Type II (energy efficiency obtained in the natural gas sector), and Type III (energy efficiency obtained in any other energy sector). Discos can develop and implement their own EE programs and hence obtain the white certificates that later can be traded or rather they can be outsourced buying through bilateral contracts with other Discos ultimately obtaining the certificates through energy services companies who will carry out the EE program. An electric market trading stock exchange (GME) was created in Italy to allow all the agents to freely trade white certificates. With this scheme, it is possible for the market to regulate the EE program and project valuation, hence making it more economical to fulfill the goals established by the regulator.
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When issuing a white certificate, it lasts for five years, is recognized as a financial instrument, and has a monetary value. Given the fact that Discos must fulfill their goals in an annual basis, namely, they must buy the amount of certificates within a year, it is possible for the companies to have surpluses that can be traded in the market or be kept for the following year’s goals. The measurement and verification process carried out by the regulator for the Italian regulator established three methods depending on the nature of the program to be implemented. Each one of these methods is differentiated according to the level of information available and the costs to measure the impact in EE. As a result of the process, there is a huge surplus in the supply of white certificates in the electric sector, where the goals for 2006 were fulfilled, the 2007 goals were tripled, and most of the goals for 2008 have been already fulfilled. Initially, very soon after the opening of the certificates fixed by the regulator at a value of 100 [ /Toe], the transactions made the price to drop (Table III). For Type I certificates, the value reached 80 [ /Toe], Type II certificates were valued at 95 [ /Toe], and Type III certificates received a value of 35 [ /Toe]. When the price was deregulated in the market, due to the excess of Type I certificates, their price in 2007 was an average 35 [ /Toe], while Type II certificates have remained at about 84 [ /Toe]. On the other hand, as there are no compensation incentives for the Discos in the 100 rate for Type III certificates, their value continues at very low levels and far from fulfilling the goal established by the regulator. III. PROPOSED METHODOLOGY: EFFICIENCY BOUNDARIES The challenge of regulating monopolistic distribution companies through benchmarking procedures centers on generating a function cost that best represents their business model. The difficulty is in including both technical and economic company efficiency indices. If additional energy efficiency indices are needed to identify the EE mechanisms that generate the best outcomes, the task is even more difficult. A path could be to simplify the modeling of the Disco and consider it as a black box with an unknown production function, but with known input variables such as energy and power purchases. On the other hand, the outputs of this black box are the energy and power sales to end customers. Based on that approach, it becomes necessary to build a comparative efficiency index for the sample based on the relationship existing between the inputs and outputs. For this purpose, the use of the efficiency boundary scheme [8] is proposed. In particular, the data envelopment analysis mathematical programming tool is proposed, to allow the construction of an efficient production boundary, composed by the set of firms with which the sample keeps the best relationship between inputs and outputs, and the remaining firms will be inefficient in function of their distance to the boundary. A detailed explanation of the DEA mathematical model is provided in the Appendix. The model uses the following formula to estimate the efficiency index, called “E”, with a maximum value of 1: (1)
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TABLE IV INPUT AND OUTPUT VARIABLES FOR MODEL
(2) Equation (1) corresponds to the objective function, given by the weighted sum of the inputs (for example, purchased energy) divided by the weighted sum of the outputs (for example, sold are the quantities measured in the ith energy). Symbols , input and the rth output for Disco j (data obtained from the distribution companies; see Table IV); , are weighting factors is a from which the efficiency scalar measure is obtained. value between 0 and 1 that represents the efficiency result of the and Disco, obtained from the optimal solution of factors for company 0. In particular, the DEA model can configure its constraints [11], [12] to better adapt itself to the reality of a distribution industry. For this purpose, an input-oriented model is used, namely, a company is not efficient if it is possible to decrease any other input without decreasing any output. In addition, to recognize the different geographic sizes and realities of each firm, variable returns to scale (VRS) are used. With this configuration in the constraints, the outcome of the dual problem to be solved is expressed in (3):
(3) are the resultant input and output variables Variables , is the resultant efficiency measure for the for company j; evaluated company; corresponds to the vector of optimum multipliers, solution of the model for inputs and outputs , for Disco j; h are slack variables used to convert the inequalities in to equivalent equations; is a small positive real number that forces all input and output variables to be evaluated. IV. MODEL AND SIMULATION The first and most influencing step in the DEA modeling is identifying the input and output variables that allow quantifying
the impact of EE in the firms. For this purpose, through a factorial statistics process and through a principal component analysis [9], [10], the most influencing and characteristic variables in the technical and operational performance of Discos were determined. It is also important to include variables that reflect the size and geographical characteristics of the firms’ operating areas. Finally, in order to include the potential effect of EE in the firms’ performance, considering what is presented in most of the studies as disincentive for the Discos, such as a drop in energy sales, a drop in the peak hour coinciding maximum power, and the increase in investment costs, a set of six variables was obtained. • Purchased energy: This corresponds to the amount of purchased energy during the year, giving basic information to measure the EE. • Line km: This corresponds to the distribution line length owned by the firm, allowing the making of the singularities to become evident in the concession zones, hence reducing the bias from the companies that render services in extended zones. • Total cost: This is the variable that identifies the cost level incurred by the company in EE. It includes the following: (4) • aVNR: Corresponds to the value of investments incurred by the Disco to cover the demand, with annuity at 30 years and a discount rate of 10%. • CostExp: Corresponds to the annual operational costs, it includes the operating costs, network maintenance, and administration and sales associated to customer services. • CostEE: Corresponds to the annual cost or investment in EE to be incurred by the Disco • Sold energy: It corresponds to the level of energy sold during the year by the Disco and that gives basic information to measure the energy efficiency impact together with the losses level. • Maximum power at peak hours: It is possible to relate this variable to the demand factor and to include the grid usage and ultimately to represent a variable that is directly attacked by the results of the energy efficiency policies. • Number of customers: Variable that allows capturing the various firm sizes. Now, for each one of these variables, it was identified how the EE regulation mechanisms modify their values based on the results obtained from international experience, in particular, the EE implementation costs, energy reduction, and peak power and savings in investment costs achieved. From information provided by the regulatory institutions of each country, the energy and demand reduction levels can be obtained (for example, Italy created 682 913 white certificates in the year 2007, representing a reduction of demand close to 0.8% or 3,104 [MW/year]; considering an average price of 35.6 per certificate, a unit cost per saved energy of de 7.8 [ /kWh] is obtained). Then, the incurred costs to achieve that are also obtained. From those values, an index is identified that shows the average of EE policies, which allows to modify the input variable “CostEE”.
ALVAREZ AND RUDNICK: IMPACT OF ENERGY EFFICIENCY INCENTIVES ON ELECTRICITY DISTRIBUTION COMPANIES
In particular, for the California case, where there is a close follow up of the results of the EE programs, it is possible to generate a portfolio of EE projects, with their respective costs and impact on energy and peaking demand reduction. Depending on the level of required reductions in demand and energy, an investment plan in EE is defined, which has associated a cost index per unit of reduced kW and kWh, which is incorporated in variable “CostEE”. In Italy, the best source of information is the value itself of the white certificates. This value reflects directly the associated cost of the reduction in energy demand to be considered by the distribution company; thus, depending on the EE goal requested to the Disco, the value of “CostEE” will be modified, according to the cost and number of certificates. However, as it is not possible to identify which would be the price of certificates in Chile, different price scenarios are proposed to illustrate the impact on efficiency of the distribution companies. It must be emphasized that this mechanism does not aim at peak demand reduction; this variable will be constant. When the variable “Sold energy” is modified, depending on the EE levels imposed to the different Discos, it is important to maintain the initial relation with the variable “Purchased energy”, given that it reflects the percentage of energy losses of the company. It should not change, as EE programs aim at reducing final consumption. For this simulation, the information of the 33 existing Discos in 2006 in the Chilean market was used. In particular, four firms were selected. Three of them were assigned for “DEA Model” as efficient with various sizes and market shares, such as Chilectra, CGE Distribucion, and Chilquinta, and on the other hand, one inefficient firm, Saesa. For each one of these firms and in a segregated manner, their model variables were modified in order to compare the efficiency index achieved before and after implementing an adaptation of the international results and a forecast for different EE goal scenarios. The impact of changes in variables is more relevant for efficient firms than for inefficient ones; inefficiency is a broad condition in the later ones. The procedure results from modeling the current distribution market situation of the sample, creating an efficient production boundary and later applying an EE scenario to one of the four selected firms, which involves modifications in the model’s variables and compares the new position within the efficient boundary, quantifying the impact on the firm’s performance. V. RESULTS AND SIMULATION ANALYSIS The simulation results for the Chilean distribution market state that 14 firms make up the efficient boundary, where the three selected firms obtain efficiency 1 and Saesa obtains an index of 90.16%, The average for the industry is 95.1% efficiency with a standard deviation of about 5% (Fig. 1). At this time, the adaptation of the results obtained in the international experience is applied for the different scenarios, EE goals, and project’s cost-efficiency in each one and segregated four selected firms, identifying the impact of the EE policies when purchasing with the baseline scenario. A. Brazil: Obligation to Invest 1% For firms with EE, 1% of the revenues for sales were used as a fixed increase in costs through the CostEE variable. Simulated
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Fig. 1. Efficiency index, base case.
Fig. 2. Efficiency index, obligation to invest 1%.
scenarios start from 0 up to 6.1% annual reduction in consumption, in addition to a scenario that has been called “Chile” that fixes a target of 1.9% in EE, target chosen by the Chilean government. The efficiency index increases as the EE unit cost decreases and the energy efficiency goals grow (Fig. 2 shows the efficiency index increase coupled to the energy efficiency goals growth, shown for the country and a zoom for the three best companies). All Discos achieve recovering the performance obtained in the base case with annual EE goals being imposed for ranges between 5.5 and 6.1% and a unit cost in EE is obtained, to decrease to levels between 8.57 and 12.57 [$/kW]. B. California: Revenue Decoupling For the firm with EE, a cost increase was used based on the unit average value obtained in California, which is located in a reduced 14.53 [$/kWh]. Scenarios range from 0% up to 6.5% annually in consumption reduction, in addition to a scenario that has been called “Chile” that fixes a target of 1.9% in EE.
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Fig. 3. Efficiency index, revenue decoupling.
Positive results are obtained for low EE requirement levels, or about 2% annually (Fig. 3, zoom for three best companies). As EE requirements increase, the Discos’ performance considerably departs from the base case.
Fig. 4. Efficiency index, white certificates.
C. Italy: White Certificates For firms with EE, there was a cost increase depending on the number of certificates required, with different values for the white certificate price, where the lowest value is given by the 35 average observed in the Italian market in 2007 with gradual increases up to 100 per certificate. For each one of these values, EE scenarios are proposed with ranges that go from 0 up to 6.5% per year of reduction in consumption in addition to a scenario that has been called “Chile” that proposes a target of 1.9% per year in EE. For the companies in the base case that belong to the optimal boundary, in all those scenarios where the white certificate value is less than 57 , their boundary condition within the sample is maintained. This makes it evident that this financial incentive that is independent from the EE goals established in the 0 to 6.5% range does not affect the global performance of Discos provided there is a market that is adapted in the white certificate supply and demand as was captured from the Italian experience, where the white certificates stock exchange is three years old, and for 2007, the average was in 35 and the maximum was 57 . If in the market there is an increase in the certificates’ transaction value up to 80 , there is a negative effect on the performance of the firms that increases as the EE goals increase. It is important to note that for the extreme scenario with a price of about 100 for the white certificate, the efficiency index for each one of the Discos departed from what was obtained in the base case in a low percentage, all of them in about 1 to 1.6% for a highly demanding EE goal of 6.5% (Fig. 4, with zoom for graphs with 80 and 100 ). D. Comparison: “Chile” Scenario When comparing the efficiency indices in the scenarios proposed for the “Chile” scenario, it is observed that white certificates are only surpassed by the revenue decoupling mechanism when the value is higher than 90 per certificate, something that still has not happened in the Italian market. Fig. 5 shows a low impact on efficiency index for certificates and decoupling schemes. On the other hand, the 1% obligation is the worst case.
Fig. 5. Efficiency index, “Chile” scenario.
VI. CONCLUSIONS The development of a mathematical model based on the analysis by efficiency boundaries is achieved, which is solved using DEA, allowing to evaluate the effect that the main energy efficiency regulatory mechanisms, which have been successfully implemented at international level, will have on electricity Discos. The mechanisms have common performance variables that have a direct effect on a Disco, allowing to quantify and compare the performance of each one of the mechanisms and also for different EE scenarios. When evaluating each one of the mechanisms, the following results were obtained. White certificates: They achieve maintaining the efficiency levels of the firms obtained before applying EE policies. The impact on the Discos cost is low, because they allow the market to freely regulate the white certificate price, generating a resource optimization and minimizing the costs to develop EE programs and projects. However, there are external costs that the regulator must incur in
ALVAREZ AND RUDNICK: IMPACT OF ENERGY EFFICIENCY INCENTIVES ON ELECTRICITY DISTRIBUTION COMPANIES
and that have not been measured by the model, mainly enforcement costs. Revenue decoupling: This presents a low impact on the firms’ efficiency index, while the EE goals are relatively low, at around 4%. Good results are obtained given the low costs, because the regulator evaluates each one of the EE projects with a common base, hence allowing making good decisions about the best EE programs and projects. Obligation to invest 1% of the revenues on EE: This mechanism obtains good efficiency indices while the regulator imposes the fulfillment of high EE goals, in general higher than 4%. It is also necessary to have the lowest intervention from the regulator.
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programming problem by means of the Charnes and Cooper transformation, given by (9) With this, the DEA can be rewritten as follows:
APPENDIX DEA is an optimization method built to measure the relative efficiency from a group of units (DMU),1 in which the existence of multiple inputs and outputs makes difficult to compare their performance. Its formal definition is given by
(10) whose dual problem is given by
(5) Assuming that there are DMUs, each of them having inputs and outputs, the relative efficiency of the first given by [11] yields
(11)
(6)
(7) These equations are the same as (1) and (2), when terms are defined. Remark: In a fully rigorous development , would be replaced by
The optimal solution, , yields an efficiency score for a par, with ticular DMU. The process is repeated for each where represent a vector with , , similarly has components , components . DMUs for which are inefficient, while DMUs for are boundary points. which Some boundary points may be “weakly efficient” because one has nonzero slacks. This may appear to be worrisome because alternate optima may have nonzero slacks in some solutions, but not in others. However, one can avoid being worried even in such cases by invoking the following linear program in which the slacks are taken to their maximal values:
(8)
where is a non-Archimedean element smaller than any positive real number [13]. This condition guarantees that the solution will be positive. The ratio formula above yields an infinite number of soluis optimal, then is also optimal for tions; if . The denominator can be zero and render the function undefined. It is possible to narrow down the system of (6) to a linear 1Decision
Making Units.
(12) The choices of , do not affect the optimal which is determined from model (11). These developments now lead to the following definition based upon the “relative efficiency”.
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• Strong DEA Efficiency: The performance of is and fully (100%) efficient if and only if both 1) , . 2) • Weak DEA Efficiency: The performance of is and weakly efficient if and only if both 1) and/or for some and in some 2) alternative optimal. It is to be noted that the preceding development amounts to solving the following problem in two steps:
(13)
[4] L. Pagliano, P. Alari, and R. Gianluca, “The Italian Energy saving obligation to gas and electricity distribution companies,” in ECEE 2003 Summer Study—Time Turn Down Energy Demand, 2003. [5] C. Blumstein, C. Goldman, and G. y Barbose, Who Should Administer Energy-Efficiency Programs? Working paper N. CSEM-WP-115 del Center for the Study of Energy Markets, 2003. [6] M. Kushler, D. York, and P. y Witte, “Aligning utility interests with energy efficiency objectives: A review of recent efforts at decoupling and performance incentives,” in American Council for an Energy-Efficient Economy, 2006. [7] Energy and Environmental Economics, Inc., Energy and Environmental Economics Calculator. [Online]. Available: http://www.ethree. com. [8] M. J. Farrell, “The measurement of productive efficiency,” J. R. Statist. Soc. Series A (General), vol. 120, no. 3, pp. 253–290, 1957. [9] R. Sanhueza, H. Rudnick, and H. Lagunas, “DEA efficiency for the determination of the electric power distribution added value,” IEEE Trans. Power Syst., vol. 19, no. 2, pp. 919–925, May 2004. [10] M. Filippini and J. Wild, “Regional differences in electricity distribution cost and their consequences for yardstick regulation of access prices,” in Proc. 6th Regional Science Association Int. World Congr. 2000, Lugano, Switzerland, 2000. [11] A. Charnes, W. Cooper, and E. Rhodes, “Measuring the efficiency of decision-making units,” Eur. J. Oper. Res., vol. 2, pp. 429–444, 1978. [12] R. D. Banker, A. Charnes, and W. W. Cooper, “Some models for estimating technical and scale inefficiencies in data envelopment analysis,” Manage. Sci., vol. 30, no. 9, pp. 1078–1092, Sep. 1984. [13] V. Arnold, I. Bardhan, W. W. Cooper, and A. Gallegos, “Primal and dual optimality in computer codes using two-stage solution procedures in DEA,” in Operations Research Methods, Models and Applications, J. Aronson and S. Zionts, Eds. Westpost, CT: Quorum, 1998.
, are slack variables used to convert the inwhere the equalities in (11) to equivalent equations. Here, the so-called , is defined to be smaller than non-Archimedean element, any positive real number. This is equivalent to solving (11) in , where two stages by first minimizing E, then setting the slacks are to be maximized without altering the previously . Formally, this is equivalent to determined value of in granting “preemptive priority” to the determination of (10). In this manner, the fact that the non-Archimedean element is defined to be smaller than any positive real number is accommodated without having to specify the value of .
Federico Alvarez received the Industrial Electrical Engineer degree and the M.Sc. degree from Pontificia Universidad Católica de Chile, Santiago, Chile. He is presently the Development Manager at Systep GE, Santiago. His research interests involve power generation, distribution, and energy efficiency.
REFERENCES [1] P. Joskow, Programas de Eficiencia Energéticas Subsidiados por las Empresas de Electricidad, Working paper No. 176, Pontificia Univ. Católica del Perú, 1999. [2] C. Lopes, S. Thomas, and L. Pagliano, “Conciliating energy companies with demand-side management—A review of funding mechanisms in a changing market,” in Proc. Int. Conf. Electricity for a Sustainable Urban Development, Lisbonne, Portugal, 2000. [3] S. Thomas, C. Lopes, P. Alari, and L. Pagliano, “The possibilities for policy supporting DSM in the liberalized internal European electricity and gas markets,” in ECEE Summer Study—American Council for Energy Efficient, 2000.
Hugh Rudnick (F’00) received the electrical engineer degree from the University of Chile, Santiago, and the M.Sc. and Ph.D. degrees from the Victoria University of Manchester, Manchester, U.K. He is a Professor of engineering at Pontificia Universidad Católica de Chile, Santiago, and the Director of Systep Engineering. His research activities focus on the economic operation, planning, and regulation of electric power systems.
