A Quick Judgment Method for the Infeasible Solution of Distribution Network Reconfiguration

Transcription

1 2018 International Conference on Power, Energy and Environmental Engineering (ICPEEE 2018) ISBN: A Quick Judgment Method for the Infeasible Solution of Distribution Network Reconfiguration Dong-yang YU 1 and Wan-lin GUAN 1,* 1 State Grid Heilongjiang Electric Power Company Limited Electric Power Research Institute, Harbin, Heilongjiang, , China *Corresponding author Keywords: Infeasible solution, Judgment method, Distribution network reconfiguration. Abstract. The radial and connectivity of distribution network are the constraint conditions in distribution network reconfiguration. Large numbers of infeasible solutions will be produced in the random search of Quantum particle swarm optimization (QPSO). A quick method for judging the infeasible solution of distribution network reconfiguration is presented in this paper. First, the switches in network are coded based on integer loop encoding rules. Large numbers of infeasible solutions will be eliminated through integer coded. Then, infeasible solutions are divided into two types: loop infeasible solutions and island infeasible solutions. The method named switch - loop matrix and node-layer strategy (NS) for judging infeasible solution is proposed. Finally, the judgment method is tested on IEEE33-bus distributed systems to demonstrate the performance and effectiveness of the proposed method. Introduction Network reconfiguration is the process of altering the topological structures of distribution feeders by changing the open/closed status of its sectionalizing and tie switches in order to achieve the optimal operation[1]. Artificial intelligent algorithms are applied to the distribution network reconfiguration for their global searching ability[2]. Because of network switches only have open/closed states, binary encoding are widely used in artificial intelligence algorithms. For this reason, binary coded genetic algorithm[3] and binary coded particle swarm optimization[4] are all adopted to the distribution reconfiguration.however, large numbers of infeasible solutions which can t satisfy the requirement of topology of distribution network will generate when binary coded genetic algorithm is applied. The search efficiency will greatly reduce.for example, the feasible solutions proportion of GA in initial solutions is small percentage.after crossover and mutation operations, the feasible solutions proportion will reduce to one thousandth level[5]. Ref. [6] puts forward a new decimal encoding genetic algorithm coding rule. As decimal encoding can solve the problem that binary encoding generate most infeasible solutions, so it is applied to differential evolution algorithm[7] and improved immune genetic algorithm[8].however, the evolution or crossover progress also produce most infeasible solutions. So just rely on decimal encoding can t completely solve the problem of infeasible solutions and research of the infeasible solution judgment method is still a important topic.based on existing researches, the method named switch - loop matrix and node-layer strategy (called SLNS for short) based on integer loop encoding for judging infeasible solution is proposed. This method is organic combined with quantum particle swarm optimization algorithm(qpso) and realize the distribution network reconfiguration without infeasible solutions. Integer Loop Encoding Rules Before reconfiguration, the particles need to be coded. The principle of Integer loop encoding rules has been proposed by author in Ref[1]. IEEE33-bus system is illustrated in Fig.1 and integer encoding of IEEE33-bus system is shown in Table solutions will be produced when binary encoding is adopted and infeasible solution ratio reaches 98.54%. However, integer loop encoding 171

2 only have solutions and infeasible solution ratio reduces to 74.38%. So integer encoding can produce fewer infeasible solutions and time saving than binary encoding. Loop number Figure 1. IEEE33-bus distribution network system. Table 1. Integer encoding of IEEE33-bus system. Tie switch in loop Switch number in loop ,6,5,4,3,2,20,19,18, ,13,12,11,10,9,34, ,10,9,8,7,6,5,4,3,2,21,20,19,18, ,16,15,14,13,12,11,10,9,8,7,6,25,26,27,28,29,30,31,32, ,23,22,28,27,26,25,5,4,3, Integer loop encoding of switches in loop Switch-loop Matrix and Node-layer Strategy (NS) In this paper, infeasible solutions are divided into two types: loop infeasible solution and island infeasible solution. Switch-loop matrix is defined to judge the loop infeasible solution and node-layer strategy is proposed to judge the island infeasible solution. So the method NS can judge all infeasible solutions easily. For simple single loop network, the proposed integer loop encoding is effective and the feasible solutions can reach 100%.However,if the network is multiple loop network, numbers of infeasible solutions will appear. As shown in IEEE33-bus system, loop 1 and 3,4,5 have common branches,we call it triple loop. So integer loop encoding can't eliminate the whole infeasible solutions. Swich-loop Matrix(SL) Define swich-loop matrix(sl) as the following Eq.(1). a11 a1 N SL = (1) a1 N a NN Where N is the loop number when all tie switches close; row of SL represents the loop of the network; column of SL represents the disconnect switch Number; 0 indicates the switch is included in the loop; 1 indicates the switch is not included in the loop. For example, a 23 =1 represents that the switch indicated third dimension of one particle is in loop 2. If SL is diagonal matrix, the disconnect switches are all not common switches produced by two or more loops. In this case, the network is single loop network and the solution must be feasible.however, if SL is not diagonal matrix, one of the disconnect switches must be common switches. We need to judge whether the network have the loop, if loop appears, the solution is infeasible. For example, if matrix SL has two same rows, this time loop infeasible solution will appear. The reason for this is one switches is opened two times or common switch of two loops is opened. Node-layer Strategy(NS) If matrix hasn t two same rows, the loop will not appear in the network and the solution is not loop infeasible solution. For judging whether the network has island, Node-layer strategy is proposed to judge the island infeasible solution. Original parameters of the distribution network are shown in following data formats. 172

3 Branch parameter matrix :BranchM=[First node, End node, Branch impedance parameters] Node parameter matrix:nodem = [Node number, Active load, Reactive load] Any distribution network topology can be described by matrix BranchM and NodeM. Network topology node incidence matrix NodeN (N square) can be obtained from BranchM easily and shown in the following Eq.(2). 1 Node i and j is associated Node( i, j) = (2) 0 Node i and j is not associated Where N is node numbers of network; i and j are two arbitrary nodes. Define two node-layer auxiliary matrixs: Node-layer matrix(layern) and Corresponding upper nodes matrix (UN).The size of LayerN is decided by the network layered result. Column numbers represent the layer number and elements of each column indicate the node number of this layer.un is 1 N matrix, elements of each column is the upper node of this node. If the node hasn t upper node or the network has island, the element of UN is defined as 0.Node-layer strategy will be described detail according to the IEEE16 node three feeder network(simplified equivalent) shown in Fig.2a. The network contains 14 nodes, 13 section switches and 3 tie switches. Under normal case, tie switches 14,15,16 open and all section switch close. The procedure obtains matrix NodeN according to matrix BranchM and NodeM. NodeN is symmetric matrix, so network topology relations can be decided by the upper triangular matrix of NodeN (NodeN').we will node layer according to matrix NodeN'. Step 1: Define power supply node as "1" and Take it as the first layer. LayerN=[1], UN = [ ] (3) Step 2: Search for the second layer nodes. As node "1" is contained in first layer, so procedure searches element 1 from row 1 of NodeN and store the searched column numbers into the column 2 of LayerN. 1 2 LayerN = 0 3, UN = [ ] (4) 0 4 The second layer contains nodes 2,3,4 and the upper nodes is 1. As matrix UN still has element 0 beside column 1,so some nodes have not find their upper nodes. Procedure need continue to search for the next layer nodes. Step 3: Search for the third layer nodes. As column 2 row 1 of matrix LayerN is 2, so procedure searches element 1 from row 2 of matrix NodeN and store the searched column 5, 6 into the column3 row 1 and column3 row 2 of LayerN. Column 5 and 6 of matrix UN are taken as 2. Similarly, as column 2 row 2 of matrix LayerN is 3, so procedure searches element 1 from row 3 of matrix NodeN and store the searched column 8, 11 into the column3 row 3 and column3 row 4 of LayerN. Column 5 and 6 of UN are taken as 3. Search for the whole third layer nodes according to this method and get LayerN and UN as the following Eq.(5). The second layer contains nodes 2,3,4 and the upper nodes is 1. As matrix UN still has element 0 beside column 1,so nodes 7,9,10,14 have not find their upper nodes. Procedure need continue to search for the next layer nodes LayerN = , UN = [ ] (5) 173

4 Step 4: Search for the fourth layer nodes according to the procedure of Step 3. Search for the whole third layer nodes according to this method and get LayerN and UN as the following Eq.(6) LayerN = , UN = [ ] (6) Beside column 1, all elements of UN are not 0,so the whole nodes have found their upper nodes. The network layer result can be reflected clearly from LayerN. Moreover, all peripheral nodes and the upper nodes can be find through UN. IEEE16 node network system is layered into fourth layers and shown in Fig.2b. The power flow of network will be decided after node-layer. a) Simplified equivalent network b) Node-layered network Figure 2. IEEE16-bus distribution network system. Judging Steps of Infeasible Solution Step 1: Integer loop encoding: The particles will be integer loop coded in initial state. The initial particles will be ensured infeasible. Step 2: Reversal encoding: The integer loop coded particles will be reversal encoding according to the rules of integer loop encoding. Through this, the particles will be converted into actual disconnect switches. For example, in IEEE33-bus system, if particle is [ ], after reversal encoding,the encoded particle will be [ ]. Step 3: Loop infeasible solution judgment: The procedure generates the switch - loop matrix SL for each particle. if SL appears two same rows, the solution is loop infeasible solution and procedure will go into Step 5 and gets the result of Loop infeasible solution. Otherwise, the Procedure goes into next step. Step 4: Island infeasible solution Judgment: The procedure generates matrix LayerN and UN according to node-layer strategy.after progress of node-layer is over, if matrix UN has element 0 beside column 1, the solution is judged as island infeasible solution, Otherwise, the solution is feasible solution. Step 5: Judgment conclusion: Feasible, Loop infeasible or Island infeasible solution. Experiment Result The proposed method is tested on IEEE33-bus radial distribution systems and results are obtained to evaluate its effectiveness. The 33-bus distribution system(illustratied in Fig.1) contains five tie switches 33, 34, 35, 36, 37, the solid line represents a sectionalizing switch, dotted line indicates the tie switch. Integer encoding of 33-bus system is shown in Table 1. QPSO algorithm is applied to the reconfiguration simulation. To verify the performance of the proposed infeasible solution judging method, five scheme were simulated. Judging results and time are shown in Table

5 Table 2. Judging results and time of different schemes. Scheme Encoded particle Open switches Judging result Judging time/s 1 [6,6,9,21,6] [2,9,3,36,26] Island infeasible solution [4,3,3,8,2] [4,12,9,10,23] Loop infeasible solution [5,5,14,6,5] [3,10,18,12,27] Feasible solution [2,1,12,20,1] [6,14,20,25,24] Island infeasible solution [9,2,1,15,3] [18,13,11,30,22] Feasible solution It is inferred in Tab.3 that the proposed infeasible solution judging method can determine the feasibility of the solution in a distribution network reconfiguration and the time is cost less(millisecond class).this section will detailed descript the infeasible solution judging method and take scheme 1 as an example. Step 1: Integer loop encoding :particle =[6,6,9,21,6];Step 2: Reversal encoding: Reversal coded particle =[2,9,3,36,26];Step 3: Loop infeasible solution Judgment.SL has not two same rows, so the solution is not loop infeasible solution and procedure goes into Step4. Step 4: Island infeasible solution Judgment: As can be seen from matrix LayerN, the network can be divided into 11 layers. Columns 3,23,24,25,27,28,29,30,31,32,33 of UN is 0,so the solution is judged as island infeasible solution. Nodes 3,23,24,25,27,28,29,30,31,32,33 are island nodes. So we can easily determine the island nodes through matrix UN SL = LayerN = , [ ] UN = 0 Step 5: Judgment conclusion: The solution is judged as island infeasible solution. Summary This paper has presented a method named switch - loop matrix and node-layer strategy (SLNS) for judging infeasible solution. Integer loop encoding rules is stated first. Infeasible solutions are divided into loop infeasible solutions and island infeasible solutions. Switch - loop matrix (SL) is proposed to judge loop infeasible solutions.for judging the island infeasible solution, node-layer strategy is put forward. Island infeasible solutions can be easy judged through matrixes LayerN and UN. The proposed judgment method is tested in IEEE33-bus distributed systems and the result is well. The method can satisfy the requirement of online distribution network reconfiguration. References [1] Guan WL, Tan YH, Zhang HX, et al. Distribution system feeder reconfiguration considering different model of DG sources. International Journal of Electrical Power & Energy Systems. 2015; 68: [2] Wu WC, Tsai MS. Application of enhanced integer coded particle swarm optimization for distribution system feeder reconfiguration. IEEE Transactions on Power Systems, 2011, 26(1): 1-9. [3] Huang YH, Li XM. Study on Infeasible Solution of Distribution Network Reconfiguration Genetic Algorithm. Electric Power Construction 2004, 25(3): [4] Lu ZG, Yang GL, Zhang XH, et al. Reconfiguration of distribution network based on improved particle swarm optimization. Power System Protection and Control 2009, 37(7): [5] Bi PX, Liu J, Liu CX, Zhang WY. A refined genetic algorithm for power distribution network reconfiguration [J].Automation of Electric Power Systems 2002, 26(2):

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