a non paramatic approach for performance assessment of generation utilities in india

Shafali Jain, Research scholar, Electrical Department, MANIT-Bhopal, India-462003 [email protected],

Tripta Thakur, Associate Professor, Electrical Department, MANIT-Bhopal, India-462003 [email protected],

Arun Shandilya, Professor, Electrical Department, MANIT-Bhopal India-462003 [email protected]

Abstract— The technical efficiency of 30 Indian state owned Generation Utilities were investigated using Data Envelopment Analysis for the time period 2007-08. The above study provides the efficiency scores of electric utility so that they can rank themselves, identify their shortcomings, set targets, and try to achieve these targets. Input variables are: installed capacity, coal consumption, oil consumption, auxiliary consumption and energy losses and outputs are energy generated and Energy sold. In addition, slack evaluation and target evaluation for input variable has been carried out. The average overall efficiency is 84.83 % and nearly one third of the utilities lie below this average level. The above studies provides the scope for the improvement of internal efficiency of the state owned Generation Utilities which is always win to win situation for the utilities and consumers and especially relevant to the India as it needs addition in electricity generation to meet the growing demand.

Index Terms—Data Envelopment Analysis (DEA), State-owned Generation Utilities, Efficiency score, Slack analysis.

I. INTRODUCTION

Since the early 1980’s, many countries have implemented electricity sector reforms. The main objective is to improve the efficiency of the sector even though the organization of the power sectors and the approaches to reform vary across the countries. The electric power industry which had been maintained as a vertically integrated system in the past, the restructuring of electric power industry in many countries in the world has been performed in the way so as to raise efficiency by introducing competition [3]. The restructuring of electric power industry in India kept pace with the worldwide trend and started with the purpose of decreasing the electricity price and to bridge the demand-supply gap

through the introduction of competition and improvement of efficiency, but did not proceed as it planned. At this stage it is essential to have documentation of the effects of such reforms. Such documentation has been done in developed countries, however from a few case studies: the experience of developing countries remains much less researched. This documentation can be made by performance evaluation for the structural change in electric power industry. We will be able to find out the direction of the structural change in electric power industry in India by analyzing the efficiency level of power generation companies in India. Such a review of performance of existing utilities is a need for the success of any reform program. Based on efficiency analysis, benchmarks can be set, and targets for improvement may be identified. The efficiency evaluation is also necessary for generating competition and for sector regulation. This efficiency evaluation can be through by a number of approaches. Among many possible efficiency measurement methods, DEA is one method that has been used especially for the complicated systems with lots of inputs and outputs for benchmarking since its introduction by Charnes, Cooper and Rhodes in 1978 based on previous work by Farrell on production efficiency. This paper presents a case study which provides efficiency scores of generation utilities for the year 2007-08, so that they can rank themselves, identify their shortcomings, set targets and tries to achieve those targets. In addition, slack evaluation and target evaluation for input variable has been carried out.

II. METHODOLOGY DEA has been applied to calculate efficiency of different types of DMUs including schools, hospitals and power plants etc. A DMU is an entity, which we measure the efficiency levels, to be compared with other entities in the population. DEA calculates an ―efficient frontier‖ uses mathematical programming [15]. A benchmark, against which the comparative performance of all other firms or organizations that does not lie on the frontier can be judged, is created

A Non-Parametric Approach for Performance Assessment of Generation Utilities in India

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through this frontier. The efficient frontier is formed from the observed performances of the participating firms in the sample, determined by the relationships between the inputs and outputs of the firms in the sample. The technique was suggested by Charnes, Cooper and Rhodes and is built on the idea of Farrell [16]. There can be a number of input/output variables for evaluating the efficiency of electric utilities. The most important job in this efficiency analysis is the right selection of inputs and outputs. No universally applicable rational template is available for selection of variables [1]. In the context of efficiency measurement, the inputs must reflect the resources used and the outputs chosen must represent the activity levels of the utilities. . A study of standard literature reveals significant insights into the choice of variables. The most widely used variables based on international experience have been outlined in the literature. . Input variables chosen for DEA model are: installed capacity (MW), coal consumption (Million tonnes), oil consumption (Kilo litres), auxiliary consumption (GWh) ,energy losses (GWh) and the outputs are units generated (GWh) and energy sold (GWh) as shown in Table I.

TABLE I

Input Output

Installed capacity coal consumption

Units generated Energy sold

oil consumption auxiliary consumption

energy losses

In this methodology, efficiency can be evaluated either on an input-oriented or output-oriented basis. For this paper, an input-oriented or input-minimizing approach was chosen since the purpose of the analysis was to suggest benchmarks for efficiency and reduction of inputs chosen in order to produce a given output. There can be two DEA models: CCR and BCC model and both of these models are applied in this analysis. The CCR model was suggested by Charnes et al. (1978), and hence is named as CCR model and assumes constant returns to scale (CRS) assumption. If assuming data on K inputs and M outputs for each of N firms, then for the i-th firm these are represented by the column vectors xi and yi respectively. The K×N input matrix, X, and the M×N output matrix, Y, represent the data for all N firms. A measure of the ratio of all outputs over all inputs would be obtained for each firm, such as uˈyi /vˈxi, where u is an M×1 vector of output weights and v is a K×1 vector of input weights [15]. The optimal weights are obtained by solving the mathematical programming problem: maxu,v (uˈyi /vˈxi), st uˈyj /vˈxj ≤ 1, j =1,2,….N, u,v ≥ 0. (1) It is required to calculate values of u and v, such that the efficiency measure for the i-th firm is maximized, subject to

the constraints that all efficiency measures must be less than or equal to one. The difficulty in this ratio formulation is that it has an infinite number of solutions. This can be avoided by imposing the constraint vˈxi = 1, which provides: maxµ,v (µˈyi ), st vˈxi = 1, µˈyj - vˈxj ≤ 0, j =1,2,….N, µ,v ≥ 0, (2) where the notation is changed from u and v to µ and v, to stress that this is a different linear programming problem. Equation (2) is known as the multiplier form of the DEA linear programming problem. By the duality in linear programming, equivalent envelopment form of this problem can be derived as: minθ,λ θ , st -yi + Yλ ≥ 0, θ xi – Xλ ≥ 0, λ ≥ 0, (3) where θ is a scalar and λ is a N×1 vector of constants. The efficiency score for the i-th firm will be the value of θ According to the Farell (1957) definition, it will satisfy: θ ≤ 1, with a value of 1 indicating a point on the frontier and hence the firm is technically efficient firm. If the utilities do not perform at optimal scales, this CCR model can be modified to take into account variable returns to scale (VRS) conditions by adding a convexity constraint. BCC model was suggested by Banker, Charnes and Cooper (1984) investigates whether the performance of each DMU was conducted in region of increasing, constant or decreasing returns to scale in multiple outputs and multiple inputs situations. The CCR efficiency can be decomposed into the Pure technical and scale efficiency components by this BCC model, thus investigating the scale effects. According to this model an inefficient firm is only ―benchmarked‖ against firms of a similar size. The CRS linear programming problem can be easily modified to account for VRS by adding the convexity constraint: N1ˈλ=1 to (3) to provide: minθ,λ θ , st -yi + Yλ ≥ 0, θ xi – Xλ ≥ 0, N1ˈλ=1 λ ≥ 0, (4) where N1 is an N×1 vector of ones. This approach forms a convex hull of interesting planes which envelope the data points more tightly than the CRS conical hull and thus provides technical efficiency scores which are greater than or equal to those obtained using the CRS model. The VRS specification has been the most commonly used specification in the 1990s.

III. DATA COLLECTION AND COMPILATION DEA was used to derive the benchmarks based on the comparison of the 30 SOEUs in which 8 entities were the SEBs, 7 entities comprised various electricity departments (EDs), and 15 entities comprised the unbundled SOEUs. The


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physical data for various states were obtained for the different years from ―General Review‖ published by CEA [11].

Descriptive statistics of the data for year 2007-08 is presented in Table II in the form of mean, median, standard deviation, minimum and maximum values. To increase the validity of the proposed model, the assumption of the ―isotonicity‖ relationship, i.e. an increase in an input must not correspond with a decrease in an output, was examined amongst the input and output variables using correlations [1].

TABLE II

DESCRIPTIVE STATISTICS

Variables Mean Median Standard Deviation Min Max

Installed Capacity 3256.29 1754.05 3809.6 30.67 14580.46

Coal Consumptio

n 6640.3 926 9444.78 0 39385 Oil

Consumption 96543.91 8848 239836.16 0 1124510

Auxiliary Consumptio

n 910.78 195.94 1240.48 0 4704.08

Energy Losses 6201.84 4344.56 6661.42

129.74 28827.76

Units Generated 14477.57 5427.61 18407.74 21.08 72770.46

Energy Sold 16547.84 10956.17 18604.46 169.5

1 67930.96

The results indicate that the variables do not violate the isotonicity assumption. The values of correlation coefficients (Table III) indicate that the variables are reasonably correlated: neither too less of correlation nor too high a correlation.

IV. ANALYSIS OF THE RESULTS 1) Efficiency Scores CCR model measures the overall efficiency which is the efficiency measured against the CRS frontier. The results are presented in Table IV. It is evident from Table VI that Indian Electric Generation Utilities display significant variations in efficiency levels. The total efficiency had a mean score of 84.83 % for all the utilities and nearly one- third of utilities lie below this average value. Eleven utilities turned out to be the best practices. The remaining 19 utilities exhibited varying degree of inefficiencies. It is also observed that all the utilities, with the exception of the best practices and five utilities –Sikkim, Assam, Manipur, Arunachal Pradesh and Mizoram, exhibited decreasing returns to scale suggesting that the utilities exceeded their most productive scale size. This outcome supports the unbundling policy of the GoI, as envisaged in the Electricity Act. Five Utilities –Sikkim, Assam, Manipur, Arunachal Pradesh and Mizoram, exhibited increasing returns to scale, which indicates that these utilities are smaller than the most productive scale size. The management of the utilities, in general, does not have control over their scale of operation. Therefore, it is quite appropriate to assess efficiency relative to the VRS frontier. So, the technical efficiency of utilities is measured against the VRS frontier. To explore the scale effects, the BCC formulation that assumes a VRS by taking into consideration the sizes of utilities was employed. This formulation ensures that similar sized utilities are benchmarked and compared with each other. The results are presented in Table IV. The number of utilities that appear as efficient entities increased to 24, while remaining 6 utilities showed inefficiencies. The average technical efficiency is 97.9 %. The results indicate the possibility of restructuring of several utilities that display low scale efficiencies (Table IV). The low value of scale efficiencies and the fact that these utilities exhibit decreasing returns to scale indicate that these have considerable scope for improvements in their efficiencies by resizing (downsizing) their scales of operations to the optimal scale defined by more productive utilities in the sample.

TABLE III

INPUT/OUTPUT CORRELATIONS

Variables Installed Capacity Coal consumption

Oil consumption

Auxiliary Consumption Energy Losses Units

Generated

Total Energy

Sold

Installed Capacity 1



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Coal Consumption 0.939243 1

Oil Consumption 0.800981 0.790358 1

Auxiliary Consumption 0.946876 0.99216 0.753904 1

Energy Losses 0.898126 0.940558 0.746714 0.929716 1

Units Generated 0.988273 0.956928 0.813343 0.965917 0.92134 1

Energy Sold 0.977838 0.935366 0.765371 0.94689 0.92744 0.974358 1

TABLE IV

RESULTS OF CCR AND BCC MODEL

S.No. Utility Total efficiency Technical efficiency Scale efficiency Returns to scale Benchmarks 1 Haryana 0.682 0.826 0.825 DRS 9 4 5 18 8 2 Himachal Pradesh 1 1 1 - 2 3 Jammu & Kashmir 1 1 1 - 3 4 Punjab 0.969 1 0.969 DRS 4 5 Rajasthan 0.846 1 0.846 DRS 5 6 Uttar Pradesh 0.644 1 0.644 DRS 6 7 Uttrakhand 1 1 1 - 7 8 Delhi 0.837 1 0.837 DRS 8 9 Gujarat 1 1 1 - 9 10 Madhya Pradesh 0.668 0.818 0.817 DRS 8 16 9 4 21 11 Chhattisgarh 0.774 0.805 0.961 DRS 4 9 15 26 12 Maharashtra 0.855 1 0.855 DRS 12 13 Goa 1 1 1 - 13 14 Andhra Pradesh 0.88 1 0.88 DRS 14 15 Karnataka 0.909 1 0.909 DRS 15 16 Kerala 1 1 1 - 16 17 Tamil Nadu 0.835 1 0.835 DRS 17 18 Puducherry 1 1 1 - 18 19 Bihar 1 1 1 - 19 20 Jharkhand 0.508 0.941 0.54 DRS 16 18 2 8 4 21 Orissa 0.862 1 0.862 DRS 21 22 West Bengal 0.885 1 0.885 DRS 22 23 Sikkim 0.787 1 0.787 IRS 23 24 Assam 0.884 1 0.884 IRS 18 2 25 Manipur 0.485 0.994 0.488 IRS 13 27 18 26 Meghalaya 1 1 1 - 26 27 Nagaland 1 1 1 - 27 28 Tripura 1 1 1 - 28 29 Arunachal Pradesh 0.751 0.985 0.763 IRS 2 13 27 30 Mizoram 0.388 1 0.388 IRS 30

2) Slack Analysis The piece-wise linear form of the nonparametric frontier in DEA can cause a few difficulties in efficiency measurement. The problem arises because of the sections of the piece-wise linear frontier that run parallel to the axes that do not occur in most parametric functions [15]. In such cases, even the efficient point is on frontier, one can reduce the amount of the input used and still produce the same output. After the slack evaluation, directions for improvement of the relatively

inefficient units can be carried out. For this purpose BCC model has been used. The slack analysis results are shown in Table V in which only input slacks are shown, as input-oriented approach is used in this paper only input slacks are mentioned, as the model used in this paper is input-oriented. It is evident that slacks for efficient utilities with an efficiency score of 100 % are obviously zero. Even inefficient utilities, the slack



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values might not be present. There are 3 DMUs having slack in the installed capacity, 4 having slack in coal consumption, 1 in oil consumption, 3 in auxiliary consumption and 4 DMUs have input slack in energy losses. The results shown in the Table IV shows that some of the utilities are technically inefficient, which indicates excess resources are used by them than required to produce the given level of output. Slack evaluation for the input variables is carried out to determine the amount of inefficiencies.

3) Evaluation of target values

For each inefficient utility target value for input variable is calculated so as to make them efficient and shown in the

TABLE V

SLACK ANALYSIS

S.No. Utility Slack 1 (Installed

capacity) Slack 2 (Coal consumption)

Slack 3 (Oil consumption)

Slack 4 (auxiliary

consumption) Slack 5 (energy

losses) 1 Haryana 0 247.534 0 0 0 2 Himachal Pradesh 0 0 0 0 0 3 Jammu & Kashmir 0 0 0 0 0 4 Punjab 0 0 0 0 0 5 Rajasthan 0 0 0 0 0 6 Uttar Pradesh 0 0 0 0 0 7 Uttrakhand 0 0 0 0 0 8 Delhi 0 0 0 0 0 9 Gujarat 0 0 0 0 0

10 Madhya Pradesh 0 2391.401 0 0 2899.024 11 Chhattisgarh 0 2001.218 0 82.782 0 12 Maharashtra 0 0 0 0 0 13 Goa 0 0 0 0 0 14 Andhra Pradesh 0 0 0 0 0 15 Karnataka 0 0 0 0 0 16 Kerala 0 0 0 0 0 17 Tamil Nadu 0 0 0 0 0 18 Puducherry 0 0 0 0 0 19 Bihar 0 0 0 0 0 20 Jharkhand 0 772.065 0 0 0 21 Orissa 0 0 0 0 0 22 West Bengal 0 0 0 0 0 23 Sikkim 0 0 0 0 0 24 Assam 55.919 0 0 63.548 1110.468 25 Manipur 19.54 0 0 0.332 114.264 26 Meghalaya 0 0 0 0 0 27 Nagaland 0 0 0 0 0 28 Tripura 0 0 0 0 0 29 Arunachal Pradesh 14.242 0 756.182 0 93.399 30 Mizoram 0 0 0 0 0

Table VI. The target values for installed capacity, coal consumption, oil consumption, auxiliary consumption, energy losses for Haryana, Madhya Pradesh, Chhattisgarh, Jharkhand, Manipur, and Arunachal Pradesh are lower than their respective original or actual values. Let us take the case of Haryana; the input installed capacity and coal consumption should be reduced by 17 % and 20 % respectively for making it technically efficient. The mean technical efficiency of all the utilities is 97.9 % which means utilities could reduce their inputs by 2.1 % without reducing their outputs.

4) Summary of Peers

For each inefficient utility, DEA identifies a set of efficient utilities that form a peer group for that inefficient utility. There are 26 utilities which have efficiency score of one and are technically efficient. The optimal input-output mix is given by the efficient utility that forms a peer for inefficient utility [2]. For example Gujarat, Punjab, Rajasthan, Puducherry and Delhi form the peer group for Haryana. For utilities having efficiency score of one, their peers are they themselves.



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TABLE VI INPUT TARGET EVALUATION

S.No. Utility

Original values Target values

Installed Capacity

(MW)

Coal consumption (000'MT)

Oil consumptio

n (KL)


n (GWh)

Energy losses (GWh)

Installed Capacity (MW)

Coal consumption (000'MT)

Oil consumptio

n (KL)


n (GWh)

Energy losses (GWh)

1 Haryana 3159 7819 38534 1168.1 8924.6 2610.7 6213.7 31842 965.3 7374.8

2 Himachal Pradesh 926 0 0 6.7 1026.6 926.3 0 0 6.7 1026.6

3 Jammu & Kashmir 625 0 1718 5.1 5070.3 625.7 0 1718 5.1 5070.3

4 Punjab 4861 10994 16303 1623.8 8834.2 4861.3 10994 16303 1623.8 8834.2 5 Rajasthan 4519 12339 22997 1983.2 12575.6 4519.6 12339 22997 1983.2 12575. 6 Uttar Pradesh 5077 16985 63082 2244 15036.4 5077.4 16985 63082 2244 15036.4 7 Uttrakhand 1734 0 0 17.82 2624.5 1734.8 0 0 17.8 2624.5 8 Delhi 932 1718 11901 315.8 6556.3 932.4 1718 11901 315.8 6556.3 9 Gujarat 8351 22274 479022 3166.6 15650.8 8351.3 22274 479022 3166.6 15650.8 10 Madhya Pradesh 4483 11999 32274 1348.3 13066 3668.4 7425.2 26403 1103 7790.5 11 Chhattisgarh 2814 7994 24136 926.5 4503 2265.8 4434.6 19431 663.1 3625.3 12 Maharashtra 14580 39385 1124510 4704 28827.7 14580.4 39385 1124510 4704 28827.7 13 Goa 78 0 64247 7.19 684.8 78.05 0 64247 7.1 684.8 14 Andhra Pradesh 9452 17587 35782 2491.1 14110.8 9452 17587 35782 2491.1 14110.8 15 Karnataka 7625 7875 201647 1347.3 7960.9 7625.9 7875 201647 1347.3 7960.9 16 Kerala 2287 0 112394 64.1 2554.2 2287 0 112394 64.1 2554.2 17 Tamil Nadu 10606 17476 621024 2401.4 12187.4 10606.2 17476 621024 2401.4 12187.4 18 Puducherry 32 0 0 16.3 129.7 32.52 0 0 16.3 129.7 19 Bihar 590 134 4 3.7 4186 590.4 134 4 3.7 4186 20 Jharkhand 1754 3796 5795 453.4 3432.4 1650.3 2799.5 5452 426.6 3229.6 21 Orissa 2498 2650 1889 330.7 7358.9 2498.4 2650 1889 330.7 7358.9 22 West Bengal 6590 18184 36268 2610.3 7100.7 6590 18184 36268 2610.3 7100.7 23 Sikkim 44 0 22 0.01 151.5 44.11 0 22 0 151.5 24 Assam 446 0 0 76 1599.2 390.3 0 0 12.5 488.8 25 Manipur 50 0 384 0 344.2 31 0 381 0.6 227.9 26 Meghalaya 189 0 0 2.1 538.7 189 8 0 0 2.14 27 Nagaland 30 0 0 0.02 228.8 30.6 0 0 0.02 228.8 28 Tripura 148 0 0 8.7 297.8 148.3 0 0 8.7 297.8

29 Arunachal Pradesh 61 0 1745 0.2 347.3 45.9 0 962 0.2 248.7

30 Mizoram 69 0 639 0 144.6 69.3 0 639 0 144.6



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V. CONCLUSIONS The mean CRS and VRS efficiencies are 84.8 % and 97.9 % respectively. All the utilities, with the exception of the best practices and and five Utilities –Sikkim, Assam, Manipur, Arunachal Pradesh and Mizoram, exhibited decreasing returns to scale suggesting that the utilities exceeded their most productive scale size. The numbers of utilities that appear as efficient entities are 11 in case of CRS while under VRS condition, it increased to 24. This VRS formulation ensures that similar sized utilities are benchmarked and compared with each other. It is evident that slacks for efficient utilities with an efficiency score of 100 % are obviously zero. The slack values might not be present even for inefficient utilities. There are 3 DMUs having slack in the installed capacity, 4 having slack in coal consumption, 1 in oil consumption, 3 in auxiliary consumption and 4 DMUs have input slack in energy losses. For each inefficient utility target value for input variable is calculated so as to make them efficient. The target values for installed capacity, coal consumption, oil consumption, auxiliary consumption, energy losses for Haryana, Madhya Pradesh, Chhattisgarh, Jharkhand, Manipur, and Arunachal Pradesh are lower than their respective original or actual values. The mean technical efficiency of all the utilities is 97.9 % which means utilities could reduce their inputs by 2.1 % without reducing their outputs.

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a non paramatic approach for performance assessment of generation utilities in india

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