Minimization of Voltage Sag Costs by Optimal ... - IEEE Xplore

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 4, OCTOBER 2007

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Minimization of Voltage Sag Costs by Optimal Reconfiguration of Distribution Network Using Genetic Algorithms Sanjay Bahadoorsingh, Student Member, IEEE, Jovica V. Milanovic´, Senior Member, IEEE, Yan Zhang, Student Member, IEEE, C. P. Gupta, Member, IEEE, and Jelena Dragovic´

Abstract—The paper describes genetic-algorithm (GA)-based optimization software for reconfiguration of a distribution network in order to minimize financial losses due to voltage sags. The developed methodology starts with a selected number of switches which generate various topologies. Load flows are then performed to evaluate the feasibility of topologies. For each feasible topology, fault analysis is performed to first calculate voltage sags at different buses in the network and then to calculate financial losses incurred by voltage sags at buses with sensitive industrial processes. The result of the optimization is the topology which yields the lowest voltage sag cost to customers. The main features of the GA include double-point crossover and adaptive mutation. The developed software tool is applied to the 295-bus generic distribution system. Index Terms—Distribution networks, genetic algorithms (GAs), optimization, reconfiguration, voltage sag costs.

I. INTRODUCTION

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HE electric power system distribution network is an amazing and complex structure. The primary function of the network is to supply customers with electrical energy. Therefore, power planning engineers must design a minimal cost distribution system and operate it in the most economical manner. The design and operation of the distribution system must ensure that customers are supplied with an acceptable level of voltage magnitude, distortion-free voltage waveforms, minimal supply interruptions, and that there is minimal power loss in the system. Hence, an acceptable level of reliability and quality of supply must be sustained even in the case of a contingency although the design requirements in such cases may be relaxed. The customer suffers tangible and intangible losses when the quality of supply is inadequate for the respective customer usage. These tangible losses are generally measured in monetary units (dollars, pounds, Euros, etc.) and customers naturally want to minimize their financial losses. The costs of an ideal (disturbance free and 100% reliable) supply can be exorbitant relative to the potential losses (incurred in the case of a nonideal supply) so the utility’s revenue is affected by this Manuscript received February 28, 2006; revised January 15, 2007. This work was supported in part by the EU Framework V project DGFACTS. Paper no. TPWRD-00107-2006. The authors are with the School of Electrical and Electronic Engineering, The University of Manchester, Manchester, M60 1QD, U.K. ( 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/TPWRD.2007.899524

balance between an ideal and nonideal supply. Hence, there must be a compromise. The network design must satisfy sometimes opposing conditions and, consequently, the redundancy and mitigation design practices are suitably incorporated. By increasing the reliability and quality of supply, the costs are increased. Additionally, the problem of achieving an optimal network design is further complicated when different planning periods are considered and uncertain factors, such as load growth, are included. The GAs-based tools have been used in the past to solve the problem of network design and reconfiguration. It has been clearly demonstrated that the application of GAs to solve a dynamic multistage planning problem is both feasible and advantageous [1] and the enhanced GA-based approach can efficiently identify the optimal or near optimal network configurations [2]. The GA has also been found not only to be suitable for resolving the problem of large-scale power distribution networks planning but is also more efficient than several other methods [3]. This paper, therefore, proposes a GA-based optimization technique for the automated reconfiguration of an existing distribution network to determine the optimal topology which yields the minimum voltage sag costs to the customers. The reconfiguration process involves the opening/closure of 18 predefined switches in the 295-bus generic distribution network [4]–[8]. II. METHODOLOGY A. Optimization Technique An extensive literature survey was initially conducted to evaluate the myriad of optimization techniques which are applicable and have been successfully applied to the design of electrical distribution networks in the past. The 295-bus generic distribution system was selected for the illustration of the methodology and has been used in previous power-quality and distribution network research [4]–[8]. Many network topologies investigated in previous research contained loops and can be classified neither as completely radial nor completely meshed. Though radial networks have some advantages over meshed networks, such as lower short circuits currents and simpler switching and protection equipment [9], it is common knowledge that a meshed network provides an increased level of reliability. Hence, the authors in [9] highlighted that distribution networks are planned and built as weakly meshed networks, but operated as radial. The ability to produce a radial network topology which contains no cyclic loops is the characteristic which makes the application of tree-spanning

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techniques suitable [3], [10]. If any of the techniques outlined in [3] and [10] were implemented, this would result in switching actions which would omit topologies with loops and, thus, lead to a possibly less realistic design of large distribution network that may contain both the rural (predominately radial) and the urban (predominately meshed) 11-kV subnetworks. (Note: predominantly meshed in this context means that there are more ties between adjacent circuits in case of urban than in the case of a rural network.) The aim of the developed optimization technique is to provide optimal switching actions on the 18 existing predefined network switches in order to identify the least cost configuration with respect to voltage sag losses incurred by the customers. Since the radial constraint cannot be adhered to in this application, the GA was identified as efficient, well documented, and highly applicable for the task of optimal network reconfiguration. A canonical GA [1] is chosen even though it is a GA in its simplest form with properties, such as a fixed single-point crossover rate, fixed mutation rate, and no additional data structures nor parameters to curtail the runtime of the optimization process. However, the requirement of achieving minimal computational time was not relaxed. The following constraints/attributes of the test network were considered to reduce computational time. • The nature of the switching action permits a binary-state coding scheme implementation to represent the open and close positions of the switches. Hence, there is no need to provide any enhanced coding techniques to reduce the number of variables. • On the 295-bus generic distribution system, there are 104 lines that contained 140 switches. The assumption that loads were only connected to the secondary substations provides a reduction in the number of switches to 104. This simply meant that lines which contained more than one switch were modeled to contain only one switch. This was dependent on the status of the switches on the particular line. • The two-point crossover method has been identified as being superior to single- point crossover when dealing with reconfiguration problems in [2], [10], and [11]. However, in those papers, the radiality was enforced as a constraint on the system. • Fuzzy-controlled crossover and mutation rates discussed in [12], on the other hand, provided a reduction in computational time. This was very similar to adaptive control of the rates but with greater flexibility of adjusting parameters. In addition to the constraints/attributes just listed, the following requirements were imposed. • Each topology used in further analysis must first be deemed valid or invalid depending on the outcome of load-flow analysis which determines if any of the constraints have been violated. • The core functionality of GA must possess the ability to reinsert the best solutions from present generations into future generations. (This is known as elitism [2].) • The GA should be equipped with the functionality to create a list of infeasible topologies, similar to that of a Tabu list [13]. Such a data structure prevents the infeasible

topologies from being revisited and re-evaluated, thus improving the efficiency. • Optimization processes stagnation (i.e., no change in an optimal solution thus far) is characteristic of extensive computational times. The application of a stopping criterion, which determines whether stagnation has occurred and the optimal solution is found, curtails the extensive computational times appropriately. B. Objective Function and Constraints The objective function used in the optimization is given below [8] (1) where frequency of voltage sags at a particular site; probability of a particular load composition at the site; probability of equipment/process failure; costs associated with the tripping of the equipment/ process; number of network buses of interest. The constraints imposed are as follows: • Kirchhoff’s voltage and current laws (KVL and KCL, respectively)—ensure that the network adheres to the principle of the conservation of charge and energy; • thermal limits—ensures that there are no overloads on the transmission lines; • supply and demand balancing—ensures that the power generated can supply the load in the network; • voltage limits—ensures that the nodal voltages are within acceptable limits at the respective voltage levels. The literature reviewed suggested that power losses could have been easily implemented as another criterion for optimization. However, observations revealed that the typical monetary value of power losses for a given topology is not as significant as the costs associated with reliability and voltage sags; therefore, it was decided to omit this criterion from the optimization. C. Implementation The flowchart of the complete optimization process for selecting the optimal topology is shown in Fig. 1. The relevant modules are briefly described in the sequel. 1) Topology Generation Module : This module is responsible for toggling the switches between the open and close positions thereby producing numerous topologies. An initial population is created randomly. During the execution of the GA, the population underwent the crossover and mutation operations [1] which generated the new populations. An enhancement to this procedure is administered to prevent the existence and generation of two identical population members. The algorithm allowed a small subsequent change in the population member in such cases by mutating two bits. These

BAHADOORSINGH et al.: MINIMIZATION OF VOLTAGE SAG COSTS

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Fig. 2. Membership function for voltage limits.

Fig. 1. Flowchart of implementation highlighting the process modules.

two bits represented two of the predefined switches in the network. The mutation of these two randomly chosen bits can be interpreted as changing the status of these switches (from open to close and vice versa). Once a unique population is generated, it is passed on to the succeeding core module. 2) Topology Evaluation Module: MATPOWER [14], a MATLAB-based Power Systems Toolbox, is applied to evaluate feasibility of any given topology by performing load-flow analysis. The thermal limits for the lines were not considered at the present stage. The voltage limits were at 400 kV,

at 33 kV, 11 kV, 13.8 kV, and 275 kV, and 132 kV and 3.3 kV. Therefore, for any given topology to be valid and used in further analysis, the load flow must converge and all nodal voltages must lie within their respective limits. When this nodal voltage constraint is not satisfied, another GA was executed. This GA is embedded here in the topology evaluation module. It is designed to determine the best set of transformer tap combinations to ensure that the nodal voltages are as close to 1.0 p.u. as possible. This was instrumental to accurately determine the magnitude of the voltage sag at any given bus. The embedded GA used all 39 tap changers available in the network. The taps steps each being on those transformers can be varied in 0.05 p.u. of the nominal turns ratio. This embedded GA used a fixed single-point crossover rate, fixed mutation rate, a population of ten candidates, and a maximum of 100 generations. An enhancement is made to the stopping criterion that instantly halted this embedded GA execution if a tap setting was discovered which ensured that all voltages were within their respective limits. In order to have successful implementation (of this embedded GA), the performance of various tap setting combinations must be effectively described by one index (objective value) per population member (tap settings of all 39 transformers). Fuzzy logic was used to assist in this aspect. Such an application was also described in [2]. The membership function that determines the membership value for each bus voltage is described by Fig. 2. Hence, the suitability of each bus voltage can be evaluated in terms of a decimal value (membership value) with 1.0 indicating that the voltage is within limits and 0.0 indicating that the voltage is out of limits. Accordingly, a series of membership values can be attained for all bus voltages. The product of all membership values will produce the objective value which describes the overall performance of the population member (tap settings). The maximum and ideal objective value is 1.0 where all of the bus voltages are within their respective limits. Fig. 2 illustrates that once the bus voltage falls outside the lower and upper limits, the gradient is quite steep. This will ensure that the population members which provide acceptable and tolerable bus voltages result in an objective value very close to unity.

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Fig. 3. A 295-bus generic distribution system showing the position of the 18 switches.

At the end of 100 generations, if no tap setting was found which satisfied all bus voltages, the best tap setting solution produced by the GA was used. The fundamental flaw here manifested itself if the best tap setting solution was not acceptable enough (i.e., some voltages may still be out of the respective ranges by a given margin). A provision was made to deal with this problem. A threshold limit was set up, and this specified the tolerance on the deviation from an ideal objective value of 1.0. Hence, a comparison is made of the threshold limit to the calculated objective value of the best tap setting solution. If the comparison suggests that the calculated value is greater than the threshold limit, this would deem the given topology feasible; otherwise, this best tap setting solution is infeasible. The speci. fied threshold was decimal value 3) Fault Analysis Module: This MATLAB-based module was designed to calculate bus voltage magnitudes and phase angles following all types of faults (symmetrical and asymmetrical) at all buses in the network and at nine points along the lines in the network (11 836 faults in total is used for fault analysis). The fault calculation was based on the commonly known Z-Bus Matrix Theory. The module accepts the status of the switches and the best transformer tap settings in order to calculate the faults in network with actual prefault voltages (as close to 1 p.u. as possible). The appropriate fault rates, fault distributions, and fault durations are used in all calculations. Further details of these fault statistics can be found in [7]. The output of this module was voltage magnitudes and phase angles at every bus in the network following all 11 836 faults with corresponding fault statistics included. Hence, this module is extremely computationally intensive. 4) Voltage Sag Cost Module: This module, adopted from [6] and [8], was used to quantify the total customer losses in

monetary units due to unwanted trips of industrial/commercial processes as a result of voltage sags. The module was developed in FORTRAN using Salford FORTRAN 90/95 Compiler on a Windows platform. The software takes into account in a probabilistic manner, all of the uncertainties associated with the voltage sag calculation, sensitivity of customers’ equipment to voltage sags, the interconnection of equipment within an industrial process, customer types, and the location of the processes in the network. Detailed description of the voltage sag cost assessment module can be found in [4], [5], and [8]. The financial losses due to voltage sags in the network were calculated based on ten selected buses from different areas in the network to which sensitive industrial processes were assumed to be connected. These ten buses of interest are 16, 111, 34, 40, 66, 76, 89, 137, 243, and 247. One option in this module was the use of a different level of equipment sensitivity to voltage sags. The use of highly sensitive equipment obviously results in the highest network costs; therefore, in the optimization performed in this study, only highly sensitive equipment was considered. The GA optimization is based on selecting the switching pattern which will result in minimum financial losses in the network when all equipment applied is assumed to be highly sensitive to voltage sags. III. RESULTS AND DISCUSSION A. Influence of Setting of GA Parameters Twelve test cases (T1-T12) were used on the 295-bus generic distribution system (Fig. 3) with 18 predefined switches to find an optimal topology. The previous work performed on this test


TABLE I GA PROPERTIES FOR 12 TEST CASES

Fig. 4. Sag cost versus computation time for 12 test cases (T1–T12).

system utilized these 18 switches and, thus, in order to complement the work done in [4] and [5], the same approach is adopted here. The reason for using various test cases was to investigate the effect of varying parameters of the optimization procedure and to observe the effect on the quality of the solution found, the amount of solution space covered, and the time taken to produce the solution (see Table I). The tests were executed on a personal computer equipped with an AMD Athlon 2.09-GHz processor with 512-Mb random-access memory (RAM). When the MATLAB command bench was executed in the MATLAB command window, the personal computer was rated 17 with the maximum available rating being 40. Hence, if increased processing power is available, a rating near the maximum value will result in decreased computational time. When the tests were executed on the machine, there were no other applications in operation simultaneously. The 12 test cases produced 11 optimal topologies. The optimal topology in tests T6 and T7 was the same. This is due to the stochastic procedures involved in determining the voltage sag costs for the various topologies. Analysis of tests T1, T6, T8, and T9, where only the crossover and mutation rates were varied, showed that adaptive mutation allowed a greater solution

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space to be evaluated in the smallest number of generations but required the longest time. However, this scenario did not produce the lowest cost of these four test cases. Tests T1 and T6 produced almost identical cost results with a vast difference in time and topologies evaluated. Therefore, test T1 with fixed mutation and crossover rates performed better than test T6 with adaptive mutation and the same fixed crossover rate. Tests T8 and T9 contained different crossover rates and test T9 found the lowest cost of these four tests in the second shortest time. Tests T2, T7, T10, T11, and T12 were similar in nature to the above set. The difference being that these were allowed to run for a longer time by extending the maximum generations and stagnation criteria from 50 and 10 to 100 and 20, respectively. Test T10 searched most of the solution space than the others because of the fixed higher mutation rate. As expected, it took the longest time frame as well. Test T11 produced the lowest result and still searched quite a significant portion, approximately 75% of the solution space relative to test T10. Test T11 produced the lowest cost and the adaptive mutation began from 0.5 rather than 1.0 which was the norm in the most published literature. This was an example of how sensitive parameters can be in different applications and tuning these GA parameters can lead to more accurate results. Test T12 varied from test T11 with a slightly higher crossover rate but both used adaptive mutation rates. Test T12 searched almost the same amount as test T11 and in a similar time frame but managed to produce the highest cost of all 12 tests. The idea behind lowering the initial adaptive mutation rate was to gain a compromise between the initial haphazard searching of the solution space and analyzing local minima to gain convergence with a reduction in time. Starting at a lower initial mutation rate decreases the ability to search more areas of the solution space in a given duration. Hence, as the mutation rate decreases, the best solution could be found as large enough solution space is sampled and the GA can “slowly” analyze smaller regions of the solution space where the best solution may exist. However, the tradeoff when starting from a lower initial mutation value may be the quality of the solution, since a smaller region of the solution space is searched. (Note: In order to fully appreciate the effect that the adaptive mutation has in this particular application, further analysis is needed before a definite conclusion can be made about the behavior of the GA under these conditions.) Finally, in tests T3, T4, and T5, the maximum number of generations was increased to 200 in all tests and the stagnancy criteria was increased to 50, 75, and 150, respectively. All tests had the same fixed crossover and mutation rates and all evaluated almost the same number of topologies. The variation in the sag costs (see Fig. 4) illustrates that in test T4, the GA had not yet "discovered" the region that was "discovered" in tests T3 and T5 despite the fact that the test T4 had more time to run than test T3. Since the mutation rate was fixed, there existed the possibility that the GA would find this region, but there was no possibility to predict how soon that would occur. The computation times, illustrated in Fig. 5 for all 12 topologies, were different because of the variation in the stagnancy criteria.

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TABLE II VOLTAGE SAG COSTS RESULTS

Fig. 5. Number of topologies evaluated versus computation time for 12 test cases (T1–T12).

B. Calculated Costs of Voltage Sags The results of all 12 test cases with high sensitivity equipment showed that the calculated costs of voltage sags were within the . This represents approximately an 8.7% difrange of 2.6 and minference between the calculated maximum 32.61 imum 30.01 voltage sag costs. These results show that there could be more topologies which can produce voltage sag costs within this range. Consequently, there may be no single optimal topology but rather a group of topologies which produce very similar costs. Based on the 12 cases analyzed, it is concluded that test T11 performed the best relative to the other tests. Test T11 located the lowest voltage sag cost to customers and searched a considerable amount of the solution space relative to the other tests. The difference in the ranges of cost values for the different test cases can also be attributed to the fact that in each test, the initial random population can sample different regions in the solution space and depending on where the search began, can result in different computational execution times and a variation in the number of topologies evaluated. Compounding these factors, in each test, the GA parameters were varied. Embedded in the software was the enhancement to include two topologies that were previously used in [8] and that correspond to the cases where all switches were opened and all switches were closed. Table II illustrates the costs of voltage sags obtained in the 12 analyzed cases. The optimal topology (assumed to be the one obtained in test T11) sag cost variation with highly sensitive equipment is compared in Fig. 7, using commercially available software SIMPOW, with the variation of costs obtained using topology no. 9. Topology no. 9 was found to result in approximately average cost variation among 16 topologies obtained in previous studies, see Fig. 6, [4]–[8]. Only ten network buses, namely buses 16, 111, 34, 40, 66, 76, 89, 137, 243, and 247, are selected arbitrarily as the buses of interest at which sensitive industrial processes are running. Out of these ten buses, the first eight are 11-kV buses whereas the last two are 33-kV buses. For the stochastic assessment of process trips taking into account the voltage sag performance at the site and the sensitivity of individual equipment participating in the industrial process, there were six different generic process configurations. These configurations were comprised of series/parallel connections of four

Fig. 6. Variation in minimum and maximum sag costs obtained with 16 arbitrary chosen topologies.

Fig. 7. Variation in minimum and maximum sag costs obtained with an approximately average and the optimal topology.

types of commonly used industrial equipment—PLCs, ASDs, PCs, and ac contactors. These six configurations form 37 different processes (based on participation of individual sensitive


Fig. 8. Test 11 topology sensitivity cost curves.

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problem of network reconfiguration—in order to minimize financial losses due to voltage sags. The optimization methodology was successfully implemented in MATLAB and a software tool is developed which identifies the optimal network topology (switch configuration) that results in minimum voltage sag costs to the customers. The efficiency of the developed software tool was demonstrated on the 295-bus generic distribution system. The results from the various tests conducted also illustrated that although the enhancements made to the canonical GA aided the quality of the solution, they could compromise the computational time needed. Various parameters of the GA algorithm were varied and their influence on the efficiency of the optimization procedure is illustrated. It has been shown that the parameter settings can influence the efficiency of the optimization and that some further fine tuning of the optimization procedure might be needed in order to tackle highly complex optimization problems such as this one in a more time-efficient manner even though the time issue is not of critical importance for this type of offline study. Finally, it has been demonstrated that the developed software tool, even though reasonably simple, could be used in practice for reconfiguration of the distribution network and for selecting a distribution network topology that would lead to significant savings to both customers and utilities as a whole. The objective function of the optimization can be based on the criteria applied in this study or on different or additional criteria such as financial losses due to outages.

REFERENCES Fig. 9. Test T11 convergence properties.

equipment in them) which are randomly allocated at the ten network buses of interest through 100 individual trials. Each trial leads to different total sag costs as illustrated in Fig. 7. Further details about the procedure for sag cost assessment can be found in [4]–[6]. Fig. 8 illustrates all evaluated topologies in test T11 and their associated costs in descending order. The maximum possible voltage sag costs identified with high sensitivity equipment are and a corresponding minimum obtained in test T11 327.75 . Variation in costs obtained with both high senis 30.01 sitivity and moderate sensitivity equipment are plotted in this figure as well as the variation of associated average costs. Finally, Fig. 9 displays a step formation which is a property of good convergence. The GA moved from one solution to an improved solution gradually until the stagnation criteria halted its execution. IV. CONCLUSION The GAs identified in the past [1]–[3] as efficient, well documented, and highly applicable tools for the task of optimal network reconfiguration were applied in this study to solve the

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Yan Zhang (S’06) received the B.S. degree from the Southwest University, Mina Yang, China, in 1997 and the M.S. degree from the University of Manchester, Manchester, U.K., in 2005, where she is currently pursuing the Ph.D. degree in the area of power quality at the School of Electrical and Electronic Engineering.

Sanjay Bahadoorsingh (S’06) received the B.Sc. degree from the University of The West Indies, St. Augustine, Trinidad, in 2003 and the M.Sc. degree from the University of Manchester, Manchester, U.K., in 2005, where he is currently pursuing the Ph.D. degree in the area of reliability of insulation systems.

C. P. Gupta (M’03) received the B.E. degree from Malaviya Regional Engineering College, Jaipur, India; the M.E. degree from the University of Roorkee, Roorkee, India; and the Ph.D. degree from the Indian Institute of Technology, Kanpur, India. From 2001 to 2004, he was Research Associate and in 2005, was Academic Visitor in the School of Electrical and Electronic Engineering of the University of Manchester (formerly UMIST), Manchester, U.K. Currently, he is an Assistant Professor in the Electrical Engineering Department, Indian Institute of Technology Roorkee, Roorkee, India. His research interests include power quality, voltage instability, and power system dynamics..

Jovica V. Milanovic´ (M’95–SM’98) received the Dipl.Ing. and M.Sc. degrees in electrical engineering from the University of Belgrade, Belgrade, Yugoslavia, and the Ph.D. degree in electrical engineering from the University of Newcastle, Newcastle, Australia. Currently, he is a Professor of Electrical Power Engineering and Deputy Head of School (Research) in the School of Electrical and Electronic Engineering of the University of Manchester (formerly UMIST), Manchester, U.K.

Jelena Dragovic´ received the Dipl. Ing. degree from the University of Novi Sad, Novi Sad, Serbia and Montenegro. In 2005, she was a Research Assistant with the School of Electrical and Electronic Engineering at the University of Manchester, Manchester, U.K., working in the area of power quality and distributed generation. Currently, she is Research Assistant in the Department of Electrical and Electronic Engineering, Imperial College London, London, U.K.