Application Multicriteria Decision Making Method to Determine the Placement of Power Distribution System

Exploring the historical path of theories and placement models indicates the deployment in terms of effective criterions and useful approaches in various industries. The distribution of electricity is important because of different reasons and all the efforts are for the sake of decreasing casualties of this network and supplying customer needs. The following research tries to come up with a model for placement the electricity distributer posts and that only happens with the recognition of effective priorities. The following research has used measurement to collect data and samplings were executed with a nonaccidental and judgmental method. After asking 11 experts the research detected six criterions and 28 subsets. These criterions are as follows: Technical, Economical, Exploitation, Executive Surveillance and Biological. In the beginning there was a dual comparison between the factors and the effectiveness of these factors was determined by AHP approach. Then with the assessment of all the nominated factors and performing a matrix, some of the Fuzzy TOPSIS were used. In the end the following model was executed by EXCEL and a factor has been determined as the final solution.


History and Literature
The power industry is considered one of the most vital industries of a country. In the meantime, the electricity distribution networks are the confluence of electrical industry subscribers and the bugs of distribution system in the industry is considered all electricity industry problems from the perspective of consumers. Given that 53% of power industry investments relate to the distribution sector and the lack of proper design and planning system, and setting goals without projects control follow the cause of loss to national wealth, power loss, and dissatisfaction and pessimism of subscribers. Therefore, monitoring and evaluation are strongly felt in distributed systems. Generally the main goal of the design and development of electricity distribution networks is the respond to growing electricity consumption with maximum economic efficiency in a way that it does not violate the limitations of a system. Many elements in distribution networks that follow many decision variables have caused problems for designing and developing these networks (Roshan Milani, 2002).
Despite the importance of the subject, the most important challenge is the establishment of power distribution substations in optimal places which, in addition to reducing installation costs, it results in better coverage for subscribers in the region. Thus, the optimal locating of power distribution substations is one of the most important principles in order to increase their efficiency.
One of the important information that helps to achieve this goal is prioritizing candidate sites that are including greatest need to establish the power distribution substation. To achieve the target, it is required to choose a good place.

Locating
Studies about the locating have a long research history and are related to many different research areas, including research in operations, industrial engineering, geography, economics, computer science, mathematics, marketing, power engineering and urban planning (Cheng & Li, 2004 (Applebaum, 1968). e. AHP (Badri, 1999 (Nanthavanij & Yenradee, 1999).
Integer programming (Melkote & Daskin, 2001). Quadratic programming (Comley, 1995). The first scientific approach with the locating was considered by mathematicians for centuries. For example, the locating of unit device, before the seventeenth century has been in the work of mathematicians. Of course, mathematicians in the past were not involved with locating problems independently. But, they attempted to resolve the problems of extreme functions (minimum or maximum functions) with this problem. Economists have suggested many theories in relation to locating economic units that in this study, we try to point out some of them.
Lanhart in 2002 has presented his theory that he has considered great importance to transportation. From Lanhart's point of view, the ideal spot to deploy the industry is the point in which the total transportation costs will be possible in minimal including raw materials, finished products and fuel sources. In his spatial analysis, he has used the locating triangle to locate. Alfred Weber (2191) has insisted on minimizing costs, which include transportation, labor and industrial aggregation in determining the location of an economic plan. Tred Plander in 2153 has focused on the relationship between the cost of transport and the distance as well as the difference of shipping rates in the locating issue.
Agust Loucg, in the year 2149 has considered the impact of demand on choosing the right location, and this was something that did not pay attention to it in the previous theories. According to Agust Loucg, the establishment at minimum cost does not necessarily mean in maximum profit. Instead, production units sell more and earn more, and they will be able to earn more profit. He said in his theory that each manufacturer is looking to expand its sphere of influence in the market (Mehrabi Koshki, 2003). From another point of view, we can divide locating theories of the second period into two categories: one category includes conditions that create facilities from two-dimensional continues space or any x and y. These issues are mainly studied as k-median location problem.

Decision Making
Decision-making is a process that involves choosing a way or method among two or more available methods. The decision means the conscious choice that allows the person to examine the specific behavior and attitude of the set, according to a given set of conditions, and then an option will be accepted and implemented. (Yurdakul & Ic, 2004) Rarely, a person or organization decides on the basis of a benchmark. Most decisions are multi-criteria, and they were considered by managers since the Second World War and optimization problems, according to an objective function. While today, taking into account the criteria, more attention has been paid to optimization problems (Momeni, 2008). MCDM Models are divided into two categories of multiobjective decision making MADM and multi-attribute decision making MODM, so that, MODM models are used to design. However, MADM models are used in order to select the preferred option (Asgharpoor, 2010).
One of the most prominent multi-criteria decision-making approaches are analytic hierarchy process approach, which focuses on obtaining the relative weights of factors and the overall value of each option based on the weights. (Torfi, Farahani, & Rezapour, 2010) In comparison with other methods of multi-criteria decision, the AHP method is widely used in multi-criteria decision-making and in many other issues from the decision so successfully (Torfi et al., 2010 .) TOPSIS, other multi-criteria decision-based approach is the best option that has the shortest distance of the positive ideal solution (option) and the longest distance of the solution (option) of negative ideal. The positive ideal solution is solutions that maximizes profit criteria and minimize cost criteria and maximize negative ideal solution of cost criterion and minimizes the profit criterion.

Research Methodology
In this study, to collect the required data, questionnaires and interviews were used. The number of interviews Group was 11 experts in the field of electricity and to prioritize places, in this study, and to avoid ambiguity caused by uncertainty in the decision, the triangular fuzzy numbers were used. With the use of GAHP method, the weighting was done and finally, by using a fuzzy TOPSIS ranking was done. The above study steps are as follows: a. Identify the required criteria and weighting them by the Analytic Hierarchy Process b. Enter the calculated weight with a Fuzzy Topsis method to prioritize locations for power distribution substation c. Categories of candidate locations for construction of power distribution substation with the output of the Fuzzy Topsis method

Identify Needed Criteria
In the first stage, with library studies and literature available on the subject, criteria and sub-criteria affecting the ranking of candidate sites for the construction of power distribution substations were identified. The first stage questionnaire consists of three decent ranges; it is relatively good and is not suitable. Then by filling the first stage questionnaire that its example is available in Appendix 2 and interviewing with 11 experts of electricity in Qom, criteria and sub-criteria were chosen, which include (see Figure 1

Weighting the Criteria of the Study
To weight the criteria for the study 1 , the Analytic Hierarchy Process was used. AHP Process has been introduced and used for the first time by Tomas Saaty. This model is the method to decide and choose the best options, especially when there are several indicators and criteria for decision-making (Saaty, 1997). Analytical Hierarchy Process (AHP) is a logical framework that facilitates the understanding and analyzing the complex decisions by decomposing it into a hierarchical structure. (Mansor et al., 2006) Group Analytical Hierarchy Process (GAHP ) Step 1. Calculate the weighted sum vector: multiply paired comparison matrix by the column vector "relative weight" 1 Weighted sum Vector=WSV and call the new vector, the weighted sum vector.
Step 2. Calculate Consistency vector: divide elements of the weighted sum vector by the relative priority vector. Vector is called Consistency vector.
Step 3. Obtaining λ max gives the average elements of λ max Consistency vector.
Step 4. Calculate the Consistency index=CI: Consistency index for the group AHP is defined as follows: n is the number of options on an issue Step 5. Calculate the ratio of consistency: consistency ratio is obtained by dividing the consistency index to random index=RI. = . .
The consistency ratio 0.1 or less expresses the consistency in comparisons; random index derived from the chart below (Azar & Rajabzadeh, 2002).
Prioritize sites for construction of fuzzy topsis power distribution substation TOPSIS Method is broadly used in order to rank issues in real conditions. The major limitation of TOPSIS method is inability to solve vague and uncertain problems in the process of decision-making (Yu, 2002). In order to overcome this limitation, we can use fuzzy set theory with TOPSIS method that allows decision makers to determine qualitative, incomplete, non-obtainable information and detail facts with decision models. (Dağdeviren, Yavuz, & Kılınç, 2009;Kulak, Durmuşoğlu, Gumus, 2009& Kahraman, 2005 Thus, the fuzzy TOPSIS method is more appropriate and more effective than TOPSIS.
In general, algorithms for solving multi-criteria multiindex decision-making issues are provided below by fuzzy set approach.
a. The first step-Identify criteria to evaluate options, allocate appropriate linguistic variables for weighting the criteria and the allocation of points or the value of each option based on the criteria in the form of  In order to ensure compatibility between the mean of scores and the mean of weights, they must be normalized to become comparable scales. To avoid the complexity of the formula used for the classical TOPSIS normalization (Soft Euclidean), here the scale or soft line will be used to convert the scales on various criteria. As a result, normalized Fuzzy decision matrix (~ U) will be calculated (Chu, 2002). This matrix is calculated as follows.
The seventh step: Ranking the options, given the calculated proximity coefficient It is clear that, if options > * will be closer to > 0 or the positive ideal solution and will be further from > _ or the negative ideal solution, the proximity coefficient $ $ i will tend towards one. Then, based on the proximity coefficient, the rating of options can be done. In fact, the options that have more proximity coefficient, they will have higher rankings.

Evaluation Results
First phase: weighting the criteria by applying GAHP

Fitting FUZZY-TOPSIS Model
Before using, the indices of model will be defined: According to the equations that were mentioned in the second and third sections, quantities composed of k decisionmaking (D 1 , D 2 ... D k ) which are responsible for assessing the m options (A 1 , A 2 ... A m ) based on the n criteria (C 1 , C 2 ... C n ). Where 11= k is the number of decision-makers and evaluators and 8 = m is the number of candidate sites options as well as 6 = n is the number of factors and subjective and qualitative criteria.
In this section, the collected data were employed in the extended equations and the results of each step are shown in anatomical tables.
In the second part of the questionnaire, each time, the decision maker rates, according to a benchmark, to all the eight options, by using linguistic variables, in the following 7 ranges, where, VP is very poor with triangular fuzzy values (1, 0, 0), P is poor with triangular fuzzy values (3, 1, 0), MP is moderate poor with triangular fuzzy values (5, 3, 1), F is "fair" with triangular fuzzy values (7,5,3), MG is equivalent to "medium Good" with triangular fuzzy values (9, 7, 5), G is equivalent to "good" with triangular fuzzy values (01, 9, 7), and finally, the VG is equivalent to "very good" with triangular fuzzy values (10,10,9). Therefore, the second part of the questionnaire contains 29 tables (for each criterion a table).
After reviewing the questionnaires, the summarized comments of 11 decision makers are in Tables 1 and 2. The second step: Create a normalized fuzzy decision matrix The calculation of this step has been performed according to equation 3 in this study and the results are shown in Table 3: The third step: Create weighted normalized fuzzy decision matrix (WNFDM ) The calculation of this step has been performed according to equation 66 in this study and the results are shown in Table 4:     The seventh step: Ranking the options, given the calculated proximity coefficient According to the calculated proximity coefficients in the previous step, for every 8 options and compare those, the ranking of the options are as follows: MA R N > MA T N > MA N > MA N > MA U N > MA V N > MA W N > MA X N What is certain, if the option will be closer to > * or positive ideal solution, and will be further from >or negative ideal solution, the proximity coefficient will tend to one. In fact, the options with more value will have higher rankings.
Thus, the maximum amount, meaning 0.1 is characteristic of the solution. That is, among the eight options, the answer will be "Five as shown in table 7. In other words, we have:

Discussion and Conclusion
More projects that have been done in the country on locating have been done either based on the MADM methods or shipping and goal programming model, or by use of GIS. Each of these methods has its own benefits. For example, the GIS method is an appropriate method due to the complexity of the urban fabric, but it is not able to apply all kinds of descriptive information appropriately in itself particularly qualitative factors. Shipping and goal programming models do not have much application, given the circumstances of this case. Also, in this paper, it has been tried to use a method that both apply quantitative criteria and qualitative criteria appropriately. Moreover, in order to use the advantages and avoid disadvantages, the method of Fuzzy multi-attribute decision method has been used. Initially, to calculate weights, the AHP method was used and then, in order to rank the desired location, FTOPSIS method was used in combination, to select the optimal location. In fact, in this study, by using TOPSIS FUZZY method, candidate sites were ranked for the construction of power distribution substation according to known factors. Finally, the new integrated model could choose the best place of power distribution substation with checking all the criteria.