A combined methodology for evaluation of electricity distribution companies in Turkey

1 Introduction

In recent years, energy efficiency policies have become part of long-term energy plans among energy management specialists. In order to increase energy efficiency, infrastructure activities such as the feasibility of electricity transmission and distribution networks should be regularly developed. In developing countries like Turkey, energy management based on the energy efficiency concept, is a challenging issue due to limited sources such as the lack of technology, budget, and infrastructure.

After privatizations in the electricity market in Turkey, the electricity distribution task was given to twenty-one distribution companies. The electricity market is regulated with new reforms to improve the efficiency of the current market conditions. At this point, correctly determining each of the electricity companies’ performance is very critical in order to observe the current situation and take the most suitable measures.

Data Envelopment Analysis (DEA) is one of the most promising benchmarking tools in operation research. Due to its non-parametric nature, it is easily applicable. There is no need to make any pre-assumptions in the application phase of DEA. In the literature, many studies have been conducted on DEA in a wide area to evaluate the efficiency analysis of energy generation companies and the efficiency analysis of energy source technology options. Zhang et al. [1] aimed to analyze energy efficiency using super-efficiency DEA model for 30 provinces in China in 2000–2012 years. Moreno et al. [2] evaluated the efficiency of the electricity distribution companies in Brazil using network DEA. Ueasin and Wongcha [3] implemented the super-efficiency DEA to assess energy companies in Taiwan at first, then Tobit regression model used to analyze what factors identify the efficiency scores. Zhao et al. [4] analyzed the provincial energy efficiency of China employing three-stage DEA in order to identify important factors affecting energy efficiency (BCC (Banker, Charnes, and Cooper) model, Stochastic frontier analysis and then BCC model). Mahmoudi et al. [5] used the DEA approach to assess the performance of thermal power plants in Iran to improve their potential and to show an effective strategy for authorities. Hatami-Marbini et al. [6] applied interval DEA method to evaluate returns-to-scale and applied on a case study which concentrates on a combined cycle power plant includes gas and steam turbines for producing electricity with undesirable outputs for environmental efficiencies. Fernández et al. [7] evaluated energy efficiency of industrial gases facilities with DEA and Malmquist index to define reasons for inefficiencies of the industry. Song et al. [8] analyzed energy efficiency of coal-fired power units in China with DEA (Input-oriented CCR (Charnes, Cooper, and Rhodes)) for the energy conservation and emission reduction. Halkos and Tzeremes [9] evaluated the Greek renewable energy sector using bootstrapped DEA to assess the financial performance of the firms. Ren et al. [10] applied DEA in order to specify the energy efficiency of biofuel systems in China. Wu et al. [11] conducted a two-stage analysis to discover productive efficiency of wind farms in China. At first, the efficiency scores of wind farms are obtained using DEA and in the second stage, the Tobit regression is utilized to find relevance between efficiency scores and the environment variables. Zheng et al. [12] applied the DEA method to show the energy efficiency of energy service companies (ESCO) for choosing the most efficient ESCO measures in diverse sections of China. Sağlam [13] measured the efficiencies of different states of wind power in the USA by DEA in the first stage. Then, with Tobit regression, the current efficiency evaluations of the states were shed light. Lins et al. [14] conducted a DEA method to evaluate performances of alternative energy resources in the Brazilian power sector. Iribarren et al. [15] used DEA for benchmarking indicator for wind energy with regard to operational emergy-based efficiency scores. Wu et al. [16] utilized super efficiency DEA for efficiency analysis of coal-fired power plants in China. Meng et al. [17] evaluated regional low-carbon economy efficiency and low-carbon economy inefficiency performance in China with adapting a range-adjusted measure-DEA model.

According to the literature survey, there are a limited number of researches about analyzing the efficiency of the Turkish energy sector by employing DEA. Bağdadioğlu [18] evaluated the energy efficiency of Turkish electricity distribution companies using DEA. Another study of Bagdadioglu et al. [19] which analyzed the efficiency level of the merger of companies using a DEA model for the period 1999–2003. Sarica and Or [20] investigated efficiency levels of electricity generation plants owned by private and public sectors in Turkey. According to the study, the authors give extensive information about efficiency analysis on comparisons of public sector versus private sector plants, coal versus natural gas plants, and renewable versus thermal plants on the contrary of other works. Sözen et al. [21] applied DEA for efficiency analyses of hydropower facilities by performing two diverse models which consist of multiple inputs and outputs to measure their relative performances. According to the analysis, the Gökçekaya hydroelectric power facility has the maximum efficiency in both models. Çelen [22] investigated the efficiency and productivity of the Turkish electricity distribution companies performing a two-stage (DEA-Tobit) analysis. Petridis et al. [23] conducted a network DEA model for efficiency analysis of electric distribution companies in Turkey. Table 1 provides a summary of existing studies on the evaluation of energy efficiency.

The determination of the correct forecasting model is important to achieve specific targets in energy planning. The neural network is one of the soft computing methods, which is widely utilized in the energy sector due to several advantageous [24]. The adaptive and flexible nature of Artificial Neural Network (ANN) provides a more reliable predictive ability, and more successful results when compared to traditional methods. ANN is frequently employed by various researchers in the literature to estimate energy demand/consumption [25–27].

Considering the literature, it is seen that there are different application studies using ANN and DEA due to ANN’s estimation and classification feature. However, there are no studies evaluating the energy efficiency of electricity distribution companies employing DEA-ANN combination methodology. The most important contribution of this study is the complementary nature of this two-stage method which provides the opportunity to practice the new investment plans of Turkey’s electricity distribution companies in a realistic way.

Since the current situation can be analyzed by the study, future investment activities can be widely evaluated. Olanrewaju et al. [30] integrated index decomposition analysis (IDA) method, ANN and DEA for the analysis of total energy efficiency and optimization in an industrial sector. The study provides energy managers to analyze historical data, identification of the level of efficiency and thus prediction and improvement energy consumption of the industrial sector. Another study by Olanrewaju et al. [31], successfully gives knowledge on energy consumption parameters that policymakers can benefit to improve efficiency in the consumption of energy utilizing a combination of IDA-ANN-DEA methods, due to the unique advantages, in evaluating the energy potential in the South African industry. Rezaee et al. [32] applied an integrated dynamic fuzzy C-means, DEA and ANN methods for prediction of companies in the stock exchange. In the study, at first cluster members are determined and then to obtain efficiency scores financial ratios are employed and finally this efficiency scores implemented in a neural network model for predicting companies’ future performance. Shabanpour et al. [33] performed dynamic DEA and ANN methods for the efficiency of green supplier. Firstly, they predict input, output and links of green supplier utilizing ANN. Then, the forecasted data obtained from ANN are employed in DEA to assess green suppliers. Han et al. [34] used DEA-ANN approach to build a multi-input-multi-output energy optimization and prediction model in petrochemical industries. Kheirkhah et al. [35] proposed ANN-PCA and DEA approaches for a multi-staged estimation of electricity demand. ANN is used for estimation, PCA is utilized for choosing ANN inputs and DEA is used to obtain suitable ANN learning algorithms. Misiunas et al. [36] conducted a hybrid methodology which based on DEANN, for prediction of organ recipient functional status. The ANN ensures reliable predictions of the functional status of patients, while DEA divides records depend on the correlation of inputs and outputs. Vlontzos and Pardalos [37] employed DEA to calculate efficiency of EU countries primary sectors and then to foresee the performance of EU countries primary sectors on the topic of GHG emissions with applying ANN method. Azadeh et al. [38] implemented fuzzy DEA to obtain relative efficiency of solar plant units of location optimization in Iran and then the application of ANN methodology provides an assessment of potential places for further considerations. Kwon and Lee [39] implemented a two-stage production modelling based on DEA-ANN methods for U.S banks.

There are different applications in the literature that carry out DEA and ANN methodologies. According to the best of our knowledge, it is the first implementation of a unified methodology for assessing the performance analysis of the electricity distribution companies in Turkey. In this way, it will be learned which areas are inadequate/idle and how to increase efficiency, and based on the results obtained, technical, economic comprehensive investment priorities can be evaluated in the relevant regions/firms.

In this study, we aim to develop an Artificial Neural Network (ANN) model that demonstrates the efficiency of each electricity distribution company with the help of DEA and can predict the performance of existing or new electricity distribution companies. With the help of the ANN model to be developed, decision makers will be able to predict the effectiveness of electricity distribution companies based on existing data or scenarios they have created. The main contribution of the study is to combine the strengths of each method. Because, ANN is a powerful prediction method even under missing data or small sample sizes, and DEA is a successful efficiency assessment tool. The integrated DEA-ANN structure provides greater advantages over the individual use of each method. The results may give comprehensive contributions to assess the energy efficiency of the current situation or new energy investment plans for energy policymakers.

The rest of the paper is organized as follows. Section 2 explains the methods (DEA and ANN) utilized in the proposed methodology. Section 3 gives the proposed approach applied to the electricity distribution market of Turkey and the obtained results are shown in Section 4. In the last section, conclusions and future directions are presented.

In the Methodology section, the DEA and ANN methods employed are clarified in detail. Firstly CCR and BCC DEA methods are given, and then the ANN method is presented in the following section.

2.2 Artificial neural network

ANN gets its inspiration from the human brains cognitive system and it consists of layers of nerves connected to each other. These layers are divided into three layers which are input layer, hidden layer, and output layer.

NN has the ability to learn complex knowledge models and then simulate and behave like it. ANN can handle smoothly under nonlinear models and incomplete data pattern and can guarantee effective results.

The success of the ANN is dependent on a well-constructed architecture based on various parameter combinations, including the number of neurons, layers, iteration which state the connection weights, learning algorithm and transfer function. There are different types of ANN, feed-forward networks, feedback networks and supervised, unsupervised learning according to learning methods. Backpropagation ANN has mostly employed ANN technique in classification and prediction problems [45]. The core characteristic of the ANN is that it has advanced flexibility competencies in a wide variety of functional relationships from input to output. Due to the working principle, ANN performs well under uncertain, missing and unclear datasets. Furthermore, there is no need for a pre-hypothesis and a particular functional construction between input and output. It provides a great convenience in some problems. In particular, in the absence of information or assumption, ANN is a common practical option [46]. The descriptive architecture of an ANN is summarized in Fig. 1. In the ANN procedure, the sample data is divided into test and training sets. Although the test set is used to measure the performance of the model during the testing process, it learns the connection between the ANN and output layer in the training process [47].

OPEN IN VIEWER

Fig. 1

ANN architecture.

In order to construct an optimal network structure, defining an appropriate transfer function is critical. Therefore, we have utilized a sigmoid transfer function in the study.

The activation function is one of the important factors that determine neuronal behavior in artificial neural networks. This function specifies the net input to be processed in the output. The sigmoid function is given in Equation 10: y j = 1 1 + e - x j(10)

According to the working principle of the relevant algorithm (backpropagation, feedforward etc.), ANN tries to minimize mean square errors (MSE). MSE is the difference between the actual values (x _i ) and the expected values ( x ˆ i ). MSE is calculated by Equation 11, as follows: MSE = ∑ i = 1 n ( x i - x ˆ i ) 2 n(11)

The Levenberg-Marquardt algorithm, which is commonly performed to calculate the weights of the ANN in the backpropagation algorithm, is based on Newton’s method [48]. Newton’s method of minimizing the function V (x) relative to the vector x is in Equation 12 as: Δ ( x ) = - [ ∇ 2 V ( x ) ] - 1 ∇ V ( x )(12) where ∇V (x) is the gradient vector and ∇²V (x) symbolizes the Hessian matrix.

The mathematical equation of the neural network is presented in Equation 13: Y j = f ( ∑ i w ij x ij )(13) where Y _j is the output of node j, f function shows a transfer function, w _ij is the connection weight, x _ij is the input signal from node i in the lower layer.

The stages of the proposed approach are given in this section. First, input and output variables are defined in DEA. After obtaining the efficiency scores, an appropriate ANN architecture was created.

3.1 DEA application

In the first stage, DEA has been applied to twenty-one electricity distribution companies (E.D.C), which are decision making units (DMUs), to show their efficiency. All data has been taken from the Turkish Electricity Distribution Corporation (TEDC) and private electricity companies. Figure 2 shows 21 electricity distribution companies in Turkey.

OPEN IN VIEWER

Fig. 2

The map of electricity distribution companies in Turkey.

Correctly defining the input and output variables is the key point of the DEA, then the method can work properly. In this study, network length (km), transformer capacity (MWA) and loss/theft ratio are chosen as input variables while the number of customers and delivered electricity in MWh are defined as the output variables. The determination of input and output factors is an important issue, which is to measure the efficiency of decision-making units in DEA applications. When determining the correct set of input and output variables, we took into account previous energy efficiency studies [22, 49] and expert opinions in this field. These input and output variables are most widely utilized variables in the literature [22, 49].

Network length- Electricity distribution line measured in (km) [48, 49].

Transformer capacity- Maximum capacity of electrically loaded transformers to connect to the distribution system (MVA) [22, 51].

Loss/theft ratio- It is a significant element in measuring the efficiency and financial sustainability of the energy sector. It refers to the difference between the amount of electricity entering the network and the amount given to end users [22].

Number of consumers- Total number of customers receiving electricity service (person) [22, 51].

The amount of the delivered electricity - The electricity produced and delivered in MWh [22, 52].

In the energy sector, the production targets are known at the beginning of the related period, and in order to achieve the goal energy policy makers, authorities or decision makers try to reduce the inputs in order to promote efficiency. Moreover, to maintain its presence in the global world, minimizing inputs is a strategic decision in a competitive environment. In this context, an input-oriented model is a more suitable choice to define efficiency. The CCR model was implemented in the study since the CCR model takes into account overall efficiency. To measure the input usage efficiency of companies’, an input-oriented CCR model has been used with DEA-Solver Software. The efficiency scores obtained from DEA is given in Table 2.

OPEN IN VIEWER

Table 2

DEA results

Companies	Efficiency scores	Ranks
Akdeniz E.D.C	0.703454	17
AKEDC	0.574753	20
Anadolu E.D.C	0.874163	10
Aras E.D.C	0.72264	16
AYDEM E.D.C	0.731281	15
Baskent E.D.C	1	1
Bogazici E.D.C	1	1
Camlibel E.D.C	0.964887	8
Coruh E.D.C	1	1
Dicle E.D.C	0.378897	21
Firat E.D.C	0.796497	13
Gediz E.D.C	0.889613	9
Kayseri E.D.C	0.754247	14
Meram E.D.C	0.651421	19
Osmangazi E.D.C	0.802651	12
Sakarya E.D.C	1	1
Toroslar E.D.C	0.846578	11
Trakya E.D.C	1	1
Uludag E.D.C	1	1
Vangolu E.D.C	0.681526	18
Yesilirmak E.D.C	1	1

According to results, seven electricity distribution companies are efficiently utilizing their inputs (efficiency score equals to 1) while the remaining 14 companies are seen as inefficient DMUs. Bogazici, Baskent, Coruh, Sakarya, Trakya, Uludag and Yesilirmak Electricity Distribution Companies have occurred as efficient DMUs. Inefficient companies are mostly located in the eastern part of the country. In the eastern part of Turkey, the loss/theft rate is a major problem preventing efficient energy use for utilities. Loss and theft rate, which is a serious problem in electricity networks and during the distribution of electricity in the grid line. With new technological equipment and infrastructure initiatives, more durable and quality transmission lines should be established and supported. In addition, capacity expansion efforts should be encouraged consistently. Energy investments should be supported and projects on this issue should be accelerated.

3.2 Developing ANN model

The neural network toolbox in MATLAB software was used to develop the ANN model. The input and output variables in DEA, are used in the input layer of ANN. The efficiency scores obtained from DEA, are used in the output layer of ANN. The network design process starts with the determination of training, testing and validation data set. In the network design, the data of 21 companies are used. In our study, 70 percent of the data is used for the training set, 15 percent for validation set and the rest of the data (15 percent) for a test run.

The performance of the ANN depends on the proper selection of parameters. The optimal parameter set is determined by empirical studies. By checking the MSE results, an appropriate network architecture was created. Different combinations were tried until the lower MSE was achieved. MSE values were the least for both training and test datasets when the determined nodes were used in the hidden layer. To make an optimum decision about the output and performance of the network, an average approach should be indicated after several iterations.

After trying other network configurations, a two-layer feedforward network with sigmoid hidden neurons has given a consistent result. The optimized network structure consists of five input neurons (network length, transformer capacity, loss/theft ratio, the number of customers and delivered electricity in MWh), ten hidden layers and one output neuron (efficiency score). Using this network structure (in Fig. 3), new prediction models can be built to determine companies’ performances.

OPEN IN VIEWER

Fig. 3

The proposed network parameters.

In this study, we attempted to train ANN, by implementing DEA to compare each companies’ performance to increase energy efficiency. The best MSE value is obtained as 0.119 and on average, a correlation equal to 0.96 shows that the system is simulated correctly. Figure 4 displays the correlations coefficient among outputs and targets in training, validation and test sets. The R values in Fig. 4 which indicate a strong positive linear relationship between experimental values and predicted energy efficiency for training data set, validation data set and test data set. It can be seen that there is an appropriate correlation between the experimental data and the predicted data.

OPEN IN VIEWER

Fig. 4

The R-values in training, validation and test set.

There is given a comparative diagram (Fig. 5) of the predicted efficiency scores obtained by ANN and the real efficiency scores constructed by the CCR model which is given in Table 2. Figure 5 shows that there is no significant difference between the real data and the predicted results obtained from ANN model. There is a strong relationship between real and estimated data sets. In the estimation of efficiency value, R² value was found as 0.92 for the model which is established by means of ANN model that used efficiency scores obtained by the CCR model.

OPEN IN VIEWER

Fig. 5

Real efficiency scores and ANN predicted efficiency values.

The prediction success was tested using 2 efficient, 4 inefficient company data selected randomly for this identified structure. The obtained results validated that the proposed model succeeded. Table 3 shows the analyze results according to the classification of companies’ efficiency. The developed method performed well to give information about the efficiency status of the companies.

In the globalizing world, it is a common issue to make more efficient investment decisions to make electric systems work more efficiently. Recently, ANN has become a good alternative for estimating the efficiency frontier for decision makers.

In this study, DEA and ANN have been used as two complementary methods due to various superiorities of the methods individually, such as prediction/classification ability and strong benchmarking ability. The efficiency of 21 electricity distribution companies was analyzed by DEA, and then utilizing this data ANN model was developed in order to estimate efficiency levels of current or alternative companies. In this model, various scenarios or actual values can be used to estimate whether or not the electricity company will operate effectively. According to the results obtained from the model, it is seen that the energy efficiency of the companies located in the eastern part of the country is lower. First of all, energy efficiency should be improved in these areas. In addition, the government should take measures to enhance energy efficiency through energy infrastructure works, such as increasing transformer capacities, enlarging network lengths, reducing electricity loss, and theft rate. Energy investment activities should be implemented first in low-efficient regions. Loss and theft rate should be minimized and network lines should be expanded by providing energy to all regions of the country.

In this study, the model was developed for energy efficiency of electricity distribution companies and accordingly a performance evaluation was made and efficient/inefficient places were determined. This model can be applied in many fields such as education, health, information systems and tourism since it is possible for companies to survive with proper productivity studies and investment plans.

The proposed methodology can help managers to check the current situation of the energy market with respect to various scenarios with different input or output variables. The efficiency levels for new investments can already be foreseen in the light of the proposed model. For future studies, the model can be expanded and include new variables which are adapted to various application fields. An analytical approach or multi-criteria decision making tool can be integrated to make a more comprehensive and concise model.