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Authors: Kumar, Yogendra
Issue Date: 2006
Abstract: Due to ever increasing demand of electric power, the size and complexity of modem day power distribution system have increased significantly, which, in turn, have enhanced the likelihood of occurrence of fault and size of the area affected by the fault in the electric power distribution system significantly. Hence, to maintain the customer satisfaction and the consequent revenue earned by the power distribution company, fast restoration of power supply to the healthy out-of-service area is of profound importance. However, in the course of service restoration, several related issues must also be considered as described below. a) The power supply must be restored to the maximum possible healthy out-ofservice area. b) From economic point of view, there should be minimum loss in the system after the service restoration is accomplished. c) The topology of the distribution systems changes because of service restoration operation. However, due to various reasons such as ease of fault location, fault isolation and protective device co-ordination etc., power distribution systems are often required to operate in a radial fashion. Hence, it is important to maintain this radiality of the systems, even when the topology of the systems is undergoing changes during the service restoration process. d) Because of the varying topology and the connected loads, the bus voltages and line currents do also change during the service restoration process. To maintain the safety and security of different power system components (such as transformers and lines etc.), it is important that the bus voltages and line currents should not cross their respective operational limits. e) Service restoration is essentially accomplished by transferring the loads in the out-of-service area to the neighboring supporting feeders via 'ON-OFF' control of different switches in the distribution systems. As the time taken by the restoration process depends on the number of switching operations, it follows from the above requirement that the number of switching operations should be kept as minimum as possible. In the early days, only manually controlled switches (MCS) were used in a distribution system. Recently, these MCS are being replaced by remote, automatic control switches (ACS). As MCS have not been completely replaced by ACS in most part of the world, both these types of switches exist in almost all the power distribution systems in the world. However, the operating times ofMCS and ACS are different. Therefore, both these types of switches should be considered separately in the service restoration study. f) In any distribution system, there are always some loads, which are of highest priority (e.g. hospital). In the event of partial service restoration, the supply must be restored to highest priority customers and this fact should be reflected in the final solution of service restoration problem. g) The software run time required by the service restoration algorithm should be minimum for speedier solution. From the above discussion, it is apparent that the service restoration task is a multi-objective, multi-constraint optimization problem and therefore, following objective functions and constraints have been considered for service restoration problem in this thesis. Objective functions: 1. Minimization of out-of-service area 2. Minimization of manually controlled switches 3. Minimization of remotely controlled switches 4. Minimization of losses Constraints: 1. Radiality of the network should be maintained 2. Voltage constraint should not be violated 3. Current constraint should not be violated 4. Priority customers should always be supplied Generally, in any distribution system operation, all these objective functions are not of equally important. Depending upon the broader perspective of system operation, generally the relative importance of the objective functions is known in the power distribution systems. As a result, in this work also it is assumed that the preferential n knowledge of the objective functions considered herein is known a priori. As the customer's satisfaction is mostly affected by the availability of supply, the first objective function (minimization of out-of-service area) has been kept at the first preference. Moreover, to enhance the customer's satisfaction, the time taken for service restoration (which essentially depends on the operational times of manually controlled and remotely controlled switches) should also be minimum. Generally, the time taken for operating a manually controlled switch is significantly more than that of a remote controlled switch. Therefore, between any two solutions, the solution which requires fewer number of manual switch operations would need lesser time to complete the service restoration task as compared to the other solution. As a result, the objective function of minimization of manually controlled switch operations has been given the second preference and that of minimization of remotely controlled switch operations has been kept at the third preference. Finally the objective function of minimization of losses has been kept at the fourth preference. In the literature, different techniques such as heuristic rule-base, expert system, mathematical programming algorithms, fuzzy logic, genetic algorithm (GA) etc. have been used to solve this complex problem. However, all these methods have some or other limitations. Both the heuristic rule based approach and expert system based approach essentially attempt to capture the knowledge base of the operators which they use to determine the switching sequences for supply restoration under fault conditions. This knowledge base is typically stored in the form of 'rules', and these rules are used by these two approaches for arriving at the appropriate solution. However, acquisition of the knowledge base of the operators for this purpose is often a very difficult task. Mathematical programming approaches have been proved to be computationally very costly for large systems. In Fuzzy set approaches, out of service load, number of switching operation, bus voltage, line current, loading of transformer etc. are taken as fuzzy variables and the solution is found on the basis of maximum membership function. But it also does not guarantee the optimal solution. Off late, GA based techniques have been proposed in the literature to solve these limitations. In this approach, initially the multi-objective optimization problem is converted into a single objective optimization by using weighting factors and subsequently, GA is used to solve this single objective in optimization problem. The values of the weighting factors depend on the importance of the objective functions as well as on the scaling of the objective functions and constraints. Although the importance of the objective functions does not generally vary from network to network, the values of the objective functions and constraints vary from network to network. As a result, the scaling factors vary from network to network which, in turn, causes the variation of weighting factors for different networks. Hence, for every network, the weights are to be tuned. To alleviate the above problems, in this thesis, a Non-Dominated Sorting genetic Algorithm-II (NSGA-II) based approach is proposed for solving the service restoration problem. In this technique, the multi-objective nature of the service restoration problem is retained without using any tunable weights or parameters. As a result, the proposed methodology is generalized enough to be applicable to any power distribution network. In NSGA-II, the final solution is found out based on the rank of the solutions in the population, which is obtained by non-dominated sorting concept. In this concept, initially the dominated solutions, dominating solutions and non-dominated solutions are found from a set of solutions and subsequently, based on these solutions; a rank is given to each and every solution in the population. After each solution is given its rank, it is assigned to its corresponding front, i.e., the solution with rank 1 is assigned to front 1, the solution with rank 2 is assigned to second front and so on. After all the fronts are formed, the final solution is chosen from the first front using the preferential knowledge of the objective functions. For reducing the software run time of NSGA-II, two efficient algorithms, one for checking the radiality of the system and another for fast load flow computation of the distribution system with changing configuration have been developed, which are described below. For checking the radiality of the system, a breadth-first-search (BFS) based algorithm has been used in this work. For this purpose, the original distribution network is first mapped to a graph involving nodes and branches. The nodes of the graph represent the various zones of the original distribution system. A zone is defined by a partial network of the distribution system that does not contain any switch. The branches of the graph represent only the "ON" switches. Inside any zone (i.e. the partial network), the IV structure is radial and all the relevant network data like load data, feeder data etc. are known from the given distribution system data. As a result, the structure, whether radial or meshed, of the original distribution system network is completely determined by the structure of the graph, i.e. if the structure of the graph is radial, the original distribution system network also operates radially, whereas, if the structure of the graph is meshed, the original distribution system also operates in a meshed fashion. To check the radiality of the system, the traversal of the graph starts from the node containing the substation and if, during the traversal, any node is reached twice, the system is meshed, otherwise it is radial. For fast power flow computation of the distribution system with changing configuration, an efficient, two-way linked list based dynamic load flow technique has been developed. Because of the use of two-way linked list, the change in the configuration of the distribution system is taken care of very easily. The two way linked list stores the information regarding the configuration of the system quite effectively. After the configuration of the system is known, two matrices, which represent the topological characteristics of distribution systems, are used. The first matrix, denoted BIBC, shows the relationship between bus current injections and branch currents, and the second matrix, denoted BCBV, represents the relationship between branch currents and bus voltages. Subsequently, these two matrices are combined to form a direct approach for solving the load flow problem. As already reported in the literature, this direct method of load flow is quite fast and also, many limitations of the existing methods are avoided in this direct approach. Because of the combination of the two-way linked list and direct computation approach, the developed dynamic load flow method is both robust (takes care of the change in system configuration quite easily) and efficient (computes the power flow solution quickly). With the help of the above two algorithms, the performance of NSGA-II has been validated with a large number of simulation studies on a number of distribution systems and its performance has also been compared with that of the conventional GA. Based on these simulation results, the performance of the NSGA-II technique has been found to be better than that of the conventional GA. Moreover it has also been observed that the NSGA-II reaches the best solution quite quickly as compared to conventional GA. Also from these large simulation studies, two distinct characteristics of NSGA-II have been noticed. It has been observed that in many (in fact almost all) instances, often a drastic improvement in the solution takes place (because of the utilization of crossover, mutation operators etc.) and therefore, the best solution is reached quite quickly. However, even after the best solution is achieved, the simulation runs are still continued to attain the convergence criterion. Thus, in almost all occasions, the time needed to reach the best solution (TBS) is significantly less than the time needed for convergence (TC). Hence, in all the cases, the software continues the execution even after it reaches the best solution, which in turn, increases the time for service restoration. Hence, for enhancing the speed of service restoration further, this gap between TBS and TC must be reduced (ideally should be made zero). Because of the above observed limitation of NSGA-II, another heuristic search technique, namely Reactive Tabu Search (RTS) has been investigated for application to solve the service restoration problem. However, in a traditional RTS method, any multiobjective optimization problem first needs to be converted into a single objective optimization problem by using suitable weights. To retain the original multi-objective nature of the problem (and thereby eliminating any need of weights), in this work, the traditional RTS method has been suitably modified. In this modified version, henceforth named Multi Objective Reactive Tabu Search (MORTS) technique, the main structure of original RTS is retained. However, in MORTS, the best candidate among the neighborhood of a given solution is calculated using the non-dominated sorting concept. Upon a large number of simulation studies, two salient features of MORTS have also been observed. In contrast to NSGA-II, the drastic improvement in the solution does not take place in MORTS and as a result, the value of TBS is generally more than that achieved by NSGA-II. However, after the best solution is obtained, the MORTS algorithm reaches the convergence criterion also quite quickly. Therefore, in MORTS, the difference between TBS and TC is quite less as compared to NSGA-II. From the above discussions, it is observed that NSGA-II and MORTS are, in some sense, complimentary to each other. The advantage (limitation) of NSGA-II is manifested as limitation (advantage) in MORTS. Therefore, if NSGA-II and MORTS are combined, then it would be possible to retain the advantages (and avoid the vi > disadvantages) of both these techniques. With this objective, a combined NSGAII/ MORTS technique has been developed. In this combined method, NSGA-II is first run for three iterations and subsequently MORTS is run for single iteration. This combination of three runs of NSGA-II followed by one run of MORTS is called a cycle. This cycle is repeated till the algorithm converges and the best solution is obtained. Comparison of the results of this combined technique with those of NSGA-II and MORTS shows that both the TBS as well as the difference between TBS and TC are lower than those obtained by NSGA-II or MORTS individually. The above developed methods in this thesis to solve the service restoration problem in distribution system are fast enough. But, in a fully automatic system, it would be useful to reduce the solution time further. With that objective, in this thesis, an artificial neural network (ANN) is trained that gives service restoration solution quickly enough necessary for real time application. In this BPNN, the number of input nodes (N) is chosen to be N = 2Z+1, where Z is the number of zones in the distribution system under study. In the first 2Z nodes, the total real and reactive power loading of the zones are given. Thus, nodes 1 & 2 represent the total real and reactive power loading of zone 1, nodes 3 & 4 represent the total real and reactive power loading of zone 2 and so on. At the last node of the BPNN, the information regarding the faulted zone is given as input. The number of output nodes of the BPNN has been chosen to be equal to the number of switches in the distribution network under study. In this work, only one hidden layer has been used for the BPNN. For generating training and testing patterns, initially the loading (both real and reactive) at each bus of the distribution system under study has been varied randomly. In this process, a large number of loading patterns in the distribution network has been generated. For each of the loading patterns, a faulted bus also has been assumed randomly. Subsequently, at each of the loading patterns with its associated faulted zone, the service restoration problem is solved using the combined NSGA-II/MORTS technique thereby obtaining the corresponding status of the distribution network switches. In this process, a large number of training and testing patterns have been generated. Upon training and testing of the BPNN on a number of distribution systems, the performance of the BPNN has been found to be quite acceptable. In conclusion, following works have been carried out in this dissertation: VI1 A BFS based algorithm for networktraversinghas been developed. A robust and efficient dynamic load flow technique has been developed to compute the load flow solution quickly under changing configuration of the distribution network. A NSGA-II based approach has been developed for solving the service restoration problem. Another approach, based on MORTS has also been developed to solve the service restoration problem. A combined NSGA-II/MORTS based approach has been developed to exploit the advantages of both these methods. For on line implementation of service restoration methodology, an ANN based approach has been developed.
Other Identifiers: Ph.D
Appears in Collections:DOCTORAL THESES (Electrical Engg)

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