INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING & TECHNOLOGY (IJEET)

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1 INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING & TECHNOLOGY (IJEET) Proceedings of the 2 nd International Conference on Current Trends in Engineering and Management ICCTEM ISSN (Print) ISSN (Online) Volume 5, Issue 8, August (2014), pp IAEME: Journal Impact Factor (2014): (Calculated by GISI) IJEET I A E M E FUZZY-EXPERT SYSTEM BASED OPTIMAL CAPACITOR ALLOCATION IN DISTRIBUTION SYSTEM Maruthi Prasanna. H. A. 1,*, Likith Kumar. M. V. 1, T. Ananthapadmanabha 2, & A. D. Kulkarni 2 1 Research Scholar, Department of EEE, The National Institute of Engineering, Mysore, India 2 Professor, Department of EEE, The National Institute of Engineering, Mysore, India ABSTRACT A fuzzy logic approach for determining the optimal location and size of capacitors is reported in this work. The impacts of capacitors of various sizes at various locations in distribution system are evaluated with two indices viz. Power Loss Reduction Index (PLRI) and Voltage Deviation Reduction Index (VDRI). These two indices are fuzzified to obtain Placement Suitability Index (CPSI) through proposed fuzzy-expert system. The proposed method is applied for IEEE- 33bus Radial distribution system using MATLAB R2009b. The allocation of single, two and three capacitor units has been carried out. The capacitor combination which results in the minimum power loss is decided as optimal allocation. The results are compared with those existing in literature in order to prove the effectiveness of the proposed fuzzy approach. Keywords: Distribution System, s, Power loss reduction, Voltage deviation reduction, Fuzzy logic, Load flow, optimal placement. 1. INTRODUCTION Loss minimization in distribution systems has assumed greater significance recently since the trend towards distribution automation will require the most efficient operating scenario for economic viability. Studies have indicated that as much as 13% of total power generated is consumed as I 2 R losses at the distribution level. Reactive currents account for a portion of these losses. However, the losses produced by reactive currents can be reduced by the installation of shunt capacitors. In addition to the reduction of energy and peak power losses, effective capacitor installation can also release additional kva capacity from distribution apparatus and improve the system voltage profile. Reactive power compensation plays an important role in the planning of an electrical system. Its aim is principally to provide an appropriate placement of the compensation devices to ensure a satisfactory voltage profile while minimizing the cost of compensation. 86

2 Installation of shunt capacitors on distribution networks is essential for power flow control, improving system stability, power factor correction, voltage profile management and losses minimization. Therefore it is important to find optimal location and sizes of capacitors required to minimize feeder losses. The solution techniques for loss minimization can be classified into four categories: Analytical, numerical programming, heuristics and artificial intelligence based. allocation problem is a well researched topic and all earlier approached differ from each other either in their problem formulation or problem solution methods employed [1]. In large distribution networks it is very difficult to predict the optimum size and location of capacitor which finally results not only in reducing losses but also improves the overall voltage profile [2]. Though many conventional models and techniques are used for this purpose but it becomes a cumbersome task as the complexity of the system increases. [3, 4, 5] Linear and nonlinear programming methods have been proposed earlier to solve the placement problem. s are commonly used to provide reactive power support in distribution systems. The amount of reactive compensation provided is very much related to the placement of capacitors in distribution feeders. The determination of the location, size, number and type of capacitors to be placed is of great significance, as it reduces power and energy losses, increases the available capacity of the feeders and improves the feeder voltage profile. Numerous methods for solving this problem in view of minimizing losses have been suggested in the literature [6 11]. A fuzzy-expert system (FES) is developed in this paper for determining the location for connecting capacitor unit/s in distribution system to reduce the real power losses and to improve the voltage profile. The proposed fuzzy inference system is of mamdani type consisting of two fuzzy input variables and one fuzzy output variable. For determining the suitability of capacitor placement at a particular node, a set of multiple-antecedent fuzzy rules has been established. The inputs to the rules are the power loss reduction and voltage deviation reduction indices and the output is the suitability of capacitor placement. The proposed fuzzy logic approach is developed in MATLAB R2009b and in order to validate the proposed capacitor placement technique, the methodology is tested on IEEE-33 bus Radial Distribution system. Comparison of obtained results with those in recent publications showed that the proposed algorithms are capable of producing high-quality solutions with good performance of convergence, and demonstrated viability. The fuzzy based optimal capacitor placement can provide approximate global optimum solution. The organization of this paper is as follows; section 2 introduces fuzzy-expert system, section 3 defines the DG placement evaluation indices, Section 4 explains about the proposed FEM for optimal DG placement, Section 5 shows the proposed algorithm for optimal DG placement using FEM, Section 6 discusses the Results obtained by the proposed method and finally section 7 concludes the paper. 2. INTRODUCTION TO FUZZY-EXPERT SYSTEM Fuzzy logic refers to a logic system that generalizes the classical two-valued logic for reasoning under uncertainty. It is motivated by observing that human reasoning can utilize concepts and knowledge that do not have well-defined or sharp boundaries [12], [13]. Unlike the classical Boolean set allowing only 0 or 1 value, the fuzzy set is a set with a smooth boundary allowing partial membership. The degree of membership in a set is expressed by a number between 0 and 1, with 0 indicating entirely not in the set, 1 indicating completely in the set and a number in between meaning partially in the set. In this way, a smooth and gradual transition from the regions outside the set to those in the set can be described. A fuzzy set can thus be defined by a function that maps objects in the domain of concern (i.e. the universe of discourse) to their membership values in the set. Such a function is called the membership function. The two most widely used membership functions are the triangular and trapezoidal functions [12], [13]. 87

3 A fuzzy-expert system is an expert system that uses a collection of fuzzy sets and rules, instead of Boolean sets for reasoning about data. The rule in the fuzzy-expert system usually takes the form If x is low and y is high; then z = medium Where x and y are input variables, z is the output variable, and low, high and medium are membership functions defined for x, y and z respectively. The antecedent (the rule s premise) describes the degree that the rule applies, while the conclusion (the rule s consequent) assigns a membership function to the output variable. The set of rules in a fuzzy-expert system is known as the rule base or knowledge base. The computation of the output variable usually takes the following steps [12, 13] and is presented in Fig 1. Fuzzification: This step is also called Fuzzy Matching, which calculates the degree that the input data match the conditions of the fuzzy rules. Inference: Calculate the fuzzy set of the rule s conclusion based on its matching degree. There are two common approaches for the inference, namely the clipping method and the scaling method. Both methods generate conclusion by suppressing the membership function of the consequent. The extent to which they suppress the membership function depends on the degree to which the rule is matched. The lower the matching degree, the more severe the suppression of the membership functions. The clipping method cuts off the top of the membership function, whose value is higher than the matching degree. The scaling method scales down the membership function in proportion to the matching degree. The scaling method is used in this paper. Composition: Because a fuzzy rule-based system consists of a set of fuzzy rules with partially overlapping conditions, a particular input to the system often triggers multiple fuzzy rules (i.e. more than one rule will match the input to a non-zero degree). Therefore, the composition is needed to combine the inference results of all the triggered rules to form a single fuzzy subset for the output variable. The fuzzy disjunction operator Max is commonly used for constructing the output fuzzy set by taking the point-wise maximum over all the fuzzy subsets generated from the inference step. Defuzzification: This step is to convert the fuzzy set of the output variable to a crisp number. Among the various types of defuzzification methods, the Center of Area (COA or Centroid) and Maximum are the two most widely used techniques. The COA derives the crisp number by calculating the weighted average of the output fuzzy set while the Maximum method chooses the value with maximum member-ship degree as the crisp number. Fig. 1: General Fuzzy Expert System Approach. 88

4 3. CAPACITOR PLACEMENT EVALUATION INDICES In order to determine benefits from capacitor integration, two sets of indices are proposed in this paper Viz PLRI and VDRI. They are explained below. 3.1 Power Loss Reduction Index (PLRI) The total real power loss in a distribution system with N buses as a function of active and reactive power injection at all buses can be calculated using the following equation [14]. N N [ αij( PP i j + QQ i j ) + βij( Qi Pj Pi Qj )] PL= i= 1 j= 1 (1) rij rij α ij = cos( δ i δ j ) βij = sin( δ i δ j ) V Where, iv j V & iv j PL is the exact loss of the distribution system; r ij is the resistance between bus i and bus j; V i and V j is the voltage magnitude of buses i and j respectively; δ i is the voltage angle at bus i; δ j is the voltage angle at bus j; P i and Q i active and reactive power injection at bus i ; P j and Q j is the active and reactive power injection at bus j. The Power Loss Reduction Index of i th bus when capacitor is connected to that bus is given by, PL( i) PL(min) PLRI ( i) = PL( base) PL(min) (2) Where, PL(i) is the distribution system real power loss when capacitor is connected to the i th bus; PL(base) is the distribution system real power loss without capacitor; PL(min) is the minimum distribution system real power loss obtained when capacitor is connected to all the buses other than slack bus; 3.2 Voltage Deviation Reduction Index (VDRI) The voltage deviation index (VDI) of the distribution system is given by, VDI N = b i= 1 spec ( V i V i 2 ) (3) Where, V spec i is the Voltage specified in pu. In this paper, it is taken as 1 pu; V i is the Voltage at the i th bus in pu. The VDI is a measure of the voltage profile of the distribution system and it indicates how the voltage values of the distribution nodes are nearer to the specified voltage. It is expected that this value should be nearer to zero, so that all the nodes of the distribution system will be having voltage nearer to the specified voltage (1 pu). The Voltage Deviation Reduction Index (VDRI) of i th bus when capacitor is connected to that bus is given by, VDI ( i) VDI (min) VDRI ( i) = VDI ( base) VDI (min) (4) Where, VDI(i) is the voltage deviation index of distribution system when capacitor is connected to ith bus; VDI(min) is the minimum voltage deviation of distribution system of a particular bus among 89

5 all the buses when capacitor is connected to each of them other than slack bus; VDI(base) is the voltage deviation index of the distribution system without capacitor connection; 4. PROPOSED FUZZY EXPERT SYSTEM FOR OPTIMAL CAPACITOR PLACEMENT In this FES, in order to determine optimal location for capacitor integration in distribution system, two input and one output variables are proposed. Input variable-1 is power loss reduction index (PLRI) and Input variable-2 is the voltage deviation reduction index (VDRI). Output variable is placement suitability index (CPSI). The structure of proposed FES is of mamdani type. PLRI variable is fuzzified into three trapezoidal membership functions and scaled in the range from 0 to 1, as shown in Fig 2. The three membership functions of PLRI are H, M and L. The value of 0 indicates largest reduction while value of 1 indicates smallest reduction of power loss. VDRI variable is fuzzified into five triangular membership functions and scaled in the range from 0 to 1, as shown in Fig 3. The five membership functions of VDRI are H, HM, M, LM and L. The value of 0 indicates better voltage profile where as value of 1 indicates poor voltage profile of distribution system. Fig. 2: Power Loss Reduction Index (PLRI) representation The CPSI is the output fuzzy variable which is evaluated for each bus by considering PLRI and VDRI as input variables to the FES using a set of rules, which are developed from qualitative descriptions. These rules are summarized in the fuzzy decision matrix given in Table 1. CPSI is a fuzzy variable having five triangular membership functions and scaled in the range from 0 to 1, as shown in Fig 4. The five membership functions of CPSI are H, HM, M, LM and L. The minimum value of CPSI indicates the best location for capacitor placement. 90

6 Fig. 3: Voltage Deviation Reduction Index (VDRI) representation Fig. 4: Placement Suitability Index (CPSI) representation 91

7 The MAX MIN METHOD involves truncating the consequent membership function of each fired rule at the minimum membership value of all the antecedents. A final aggregated membership function is achieved by taking the union of all the truncated consequent membership functions of the fired rules [15]. For the capacitor location problem, resulting capacitor placement suitability membership function µs of node i for k fired rules is given by, µ = max (min( µ ( i), µ s k p v ( i))) µ p Where and µ v are the membership functions of the PLRI and VDRI variables respectively. The CPSI values must be defuzzified in order to determine the node suitability ranking for capacitor placement. This is achieved by Centroid method of defuzzification [15]. The capacitor placement suitability index (CPSI) is determined by (5) CPSI = µ ( z) zdz s µ ( z) dz s (6) PLRI AND Table 1: Fuzzy Decision Matrix for CPSI VDRI H HM M LM L H H H HM M LM M M M LM L L L LM LM LM L L 5. PROPOSED ALGORITHM FOR OPTIMAL CAPACITOR PLACEMENT BY FES The procedural steps that have been adopted in finding optimal location for capacitor placement in distribution system using Fuzzy-Expert System is shown in Fig SIMULATION RESULTS The proposed methodology using FES is tested on IEEE-33bus Radial Distribution System (RDS) shown in Fig. 6 [16] having following characteristics: Number of buses=33; Number of lines=32; Slack Bus no=1; Base Voltage=12.66KV; Base MVA=100 MVA; The test system is simulated in MATLAB R2009b & the proposed FES methodology has been tested, whose results are as shown below. The forward backward method of load flow (FBLF) is employed in this paper, whose details are given in [17]. The objective of this paper is to determine the optimal locations for the capacitor units to be placed in distribution system so that maximum loss reduction and voltage deviation reduction is achieved. Initially, the base case FBLF is run for the IEEE 33bus RDS and the base case voltage profile is shown in Fig 7. The base case real power loss is kw and base case VDI is pu. 92

8 Fig. 5: Optimal Placement using Fuzzy-Expert System 93

9 Fig. 6: Single line diagram of IEEE-33 bus RDS Fig. 7: Base Case Voltage Profile of IEEE-33 bus RDS In this paper, 3 scenarios of optimal capacitor placement are carried out: Scenario-1 in which a single capacitor is to be placed; Scenario-2 in which two capacitor units of unity pf are to be placed; Scenario-3 in which three capacitor units of unity pf are to be placed. The procedure of determining optimal location for capacitor units is explained in Fig 5. In each scenario, the practically available capacitor sizes are considered. The details of available capacitors can be found in [18]. The results of each scenario are tabulated in Table 2, Table 3 and Table 4 respectively. Table 2 corresponds to Scenario-1, Table 3 corresponds to Scenario-2 and Table 4 corresponds to Scenario-3. In Table 2 and Table 3, the total capacity of capacitors is restricted to 1800KVAr. In each scenario, the power loss with capacitor is compared with the base case power loss and Loss reduction in Kw by injection is tabulated and similarly the VDI with capacitor is compared with base case VDI and VDI reduction in pu by injection is tabulated. To demonstrate the validity of the proposed method, the obtained results are compared with those existing in literature. Table 5 presents the comparison of the performance parameters of the distribution system with the capacitor allocation using the proposed fuzzy approach with the other techniques present in the literature. In order to compare the different capacitor allocations, the loss savings from the capacitor allocation is evaluated as loss savings per MVAr injection of capacitor. Through this index, it is very clear from Table 5 that the proposed method yields maximum loss 94

10 reduction of Kw/MVAr with 3 capacitor units of 450KVAr optimally located at bus 33, 16, and 30 of IEEE 33 bus RDS. Fig 8 shows the distribution system loss reduction for increasing penetration of 450kvar capacitor units through each scenario. It is observed that, there will be significant reduction in power loss for each capacitor unit injection at the optimal locations of 450KVAr capacitor unit/s given in sl.no 3 of Table 2, Table 3 and Table 4 respectively. Similarly, Fig 9 shows the improvement in the voltage profile of the IEEE 33 bus RDS for increasing penetration of 450KVAr capacitor units through each scenario. It is observed that, as the VDI is reducing for each scenario, there will be an improvement in the voltage profile. Table 2: Optimal Placement Results of IEEE 33 bus RDS for Scenario-1 for various ratings Sl. no size in KVAr Optimal location Base case power loss in kw Base case VDI in pu Power loss with in kw VDI with in pu Loss reduction in kw VDI reduction in pu Table 3: Optimal Placement Results of IEEE 33 bus RDS for Scenario-2 for various ratings Sl. no size in KVAr Optimal location Base case power loss in kw Base case VDI in pu Power loss with in kw VDI with in pu Loss reduction in kw VDI reduction in pu

11 Table 4: Optimal Placement Results of IEEE 33 bus RDS for Scenario-3 for various ratings Base Base Power case VDI with Loss VDI Sl. Optimal case loss with size in power reduction reduction no location VDI in KVAr loss in in pu in kw in pu pu in kw kw Table 5: Performance of the Proposed Fuzzy-Expert System based Placement Before Optimal Allocation After Placement Placement Referen ces Losses (Kw) [19] [20] [21] [22] Propose d Method Location 8, 15, 20, 21, 24, 26, , 14, 15, 16, 31, Size in KVAr Total Size in MVA r Losses (Kw) Loss Savings in Kw Loss Savings/ MVAr injection

12 Base case 1 CAP of 450 KVAr 2 CAP of 450 KVAr 3 CAP of 450 KVAr Power loss reduction pattern Fig. 8: Reduction of Power loss in IEEE 33 bus RDS with penetration of 450KVAr s for three scenarios Voltage in Pu Distribution Network Nodes Base case 1 CAP of 450kVAr 2 CAP of 450kVAr Fig. 9: Improvement of voltage profile of IEEE 33bus RDS with penetration of 450KVAr Units for three scenarios 7. CONCLUSION A fuzzy-expert system is developed for optimal allocation of capacitor units in distribution system. The optimal locations for capacitor placement are decided in order to provide maximum power loss reduction and voltage profile improvement. The proposed fuzzy-expert system provides placement suitability index by PLRI and VDRI fuzzy variables. The proposed methodology is tested on IEEE-33bus Radial distribution system using MATLAB 9.0 for placement of single capacitor unit, two capacitor units and three capacitor units. From the results it is apparent that the proposed fuzzy-expert system provides optimal loss reduction and voltage profile improvement. The results were also compared with those existing in literature, through which, it is apparent that the proposed method provides maximum loss reduction saving per capacitor MVAr injection. 97

13 ACKNOWLEDGEMENT The authors Maruthi Prasanna. H. A. and Likith Kumar. M. V. acknowledge the Technical Education Quality Improvement Programme (TEQIP)-II of All India Council for Technical Education (AICTE), New Delhi, India and Dr. G. L. Shekar, Principal, NIE, Mysore for providing financial assistance for carrying out this research work. The author Maruthi Prasanna. H. A. also acknowledge the Karntaka Power Transmission Corporation Limited (KPTCL), Karnataka for providing leave to pursue Integrated M.Tech + PhD programme. REFERENCES [1] Sundharajan, S and Pahwa, A., Optimal Selection of s for Radial Distribution Systems using a Genetic Algorithm, IEEE Transactions on Power Systems, Vol. 9, No. 3, August 1994,pp [2] Grainger, J.J and Lee, S.H., Optimum size and location of shunt capacitors for reduction in loss in distribution systems, IEEE Transactions on Power Apparatus and Systems, Vol. PAS 100, No. 3, March 1981, pp [3] Baran, M.E. and Wu, F.F., Optimal Placement on Radial Distribution Feeders, IEEE Transactions on Power Delivery, Vol. 4, No.1, January 1989, pp [4] Chiang, H.D., Wang, J.C. and Shin, H.D., Optimal Placement in Distribution Systems: Part 1: A New Formulation and the overall problem, Part II Solution Algorithms and Numerical Results., IEEE Transactions on Power Delivery, Vol.5, No.2, April 1990, pp , and pp [5] Chis, M., Salama, M.M.A and Jayaram, S., placement in distribution systems using heuristic search strategies, IEE Proceedings Generation, Transmission and Distribution, vol. 144, no. 2, pp , May [6] Haque M H. placement in radial distribution systems for loss reduction. IEE Proc Gen Trans Dist 1999;146(5): [7] Carlisle JC, El-Keib AA. A graph search algorithm for optimal placement of fixed and switched capacitors on radial distribution systems. IEEE Trans Power Deliv 2000;15(1): [8] Prakash K, Sydulu M. A novel approach for optimal locations and sizing of capacitors on radial distribution systems using loss sensitivity factors anda-coefficients. In: IEEE PES, power system conference and exposition; p [9] Su CT, Chang CF, Chiou JP. Optimal capacitor placement in distribution systems employing ant colony search algorithm. Electric Power Compo Syst [10] 2004;33(8): [11] Venkatesh B, Ranjan B. Fuzzy EP algorithm and dynamic data structure for optimal capacitor allocation in radial distribution systems. IEE Proc Gen Trans Dist 2006;153(5):80 8. [12] Abul Wafa Ahmed R. Optimal capacitor allocation in radial distribution systems for loss reduction: a two stage method. Electric Power Syst Res 2013; 95: [13] Yen J, Langari R. Fuzzy logic: intelligence, control, and information. Englewood Cliffs, NJ: Prentice-Hall; 1999 [14] Yuan Liao a, Jong-Beom Lee, A fuzzy-expert system for classifying power quality disturbances, Electrical Power and Energy Systems 26 (2004) [15] Elgerd IO. Electric energy system theory: an introduction. New York: McGraw-Hill Inc.;

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