A New Distribution Network Reconfiguration and Restoration Path Selection Algorithm Cong Shen
Paul Kaufmann
Martin Braun
Department of Energy Management and Power System Operation University of Kassel, Germany Email:
[email protected]
Faculty for Electrical Engineering Computer Science and Mathematics University of Paderborn,Germany Email:
[email protected]
Department of Energy Management and Power System Operation University of Kassel, Germany Fraunhofer IWES, Kassel Germany Email:
[email protected]
Abstract—The distribution network restoration is one of the most important parts in the total power system restoration process. The distribution network restoration decomposes into the identification of a suitable network configuration, which is defined by the status of switches between the radially arranged power lines and the optimization of the restoration paths, which are schedules for toggling switches and booting network nodes. This paper presents a two-stage approach for the restoration process of radial high voltage distribution network (e.g.110kV). A Pareto-based multi-objective genetic algorithm (NSGA-II) is used to optimize the network configuration regarding the load that can be picked up, load priorities, and switching activity. Then, a multi-objective fuzzy decision method (FDM) selects the restoration paths. FDMs choices rely on performance indexes defined by human experts and harmonized as well as linearized by the analytic hierarchy process (AHP). In this work, the node importance degree, the load priority, the influence on already restored network, and the length of distribution lines are considered by FDM. The feasibility and efficiency of the proposed method are validated on the IEEE 30 network. Index Terms—Restoration Path, Non-dominated Genetic Algorithm (NSGA-II), Fuzzy Decision Making (FDM), Analytic Hierarchy Process (APH), Performance Indexes.
I. I NTRODUCTION
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ITH the development of modern power systems, the distribution network operation becomes more and more flexible and complex. The risk of power system blackouts still exists. If a power system totally collapses, there are two important tasks for a distribution network operator after substations in high voltage levels are reenergized. One task is to find a good distribution network configuration according to status of the network, the other is to identify the restoration paths. A distribution network can be reconfigured by changing the status of tie switches and sectionalizing [1], while a restoration path denotes the temporal operation schedule for switching and sectionalizing. Today, the choices of distribution network configuration and restoration paths depend mainly on the experience of the network operators. In recent years, many mathematical methods have been utilized to solve this problem. [2], [3] and [4] implement Paper submitted to Power Systems Computation Conference, August 1822, 2014, Wroclaw, Poland, organized by Power Systems Computation Conference and Wroclaw University of Technology.
knowledge-based expert systems. Heuristics for branch exchange based on active power loss sensitivities are presented in [5], [6], [7], [8], [9]. The algorithms have been proposed to single objective optimization only. However, the reconfiguration process of the distribution network is inherently multi-objective. Thus, [10] and [11] introduce fuzzy membership functions combined with genetic algorithms to describe the multi-objective case. The latter approaches aim on the identification of the network reconfiguration. However, the restoration paths are not considered in these approaches. Paper [12] utilizes two-stage genetic algorithm to optimize network configuration and the restoration paths. However, only restoration energy is subject to optimization. The presented paper proposes a new and more holistic way to optimize the restoration of distributed networks by considering the major decisions factors of this process. In the first stage, the NSGA-II algorithm is used to identify the network configuration. In the second stage, the Fuzzy Decision Making (FDM) is employed to select the restoration paths for the given network configuration by considering four performance indexes. In addition, the analytic hierarchy process (AHP) algorithm is applied to identify the weighting factors of the performance indexes for the FDM algorithm. The paper is organized as follows: Section II describes the network reconfiguration, defines the objective functions, and introduces the performance indexes. Section III describes the implementation of the proposed algorithm and Section IV demonstrates its feasibility and effectiveness using the IEEE 30-bus test network. Finally, the section V concludes the paper. II. G OAL F UNCTIONS F ORMALIZATION Normally, the distribution network has a radial electric topology. In this paper, we assume that the total distribution network is collapsed which is caused by the blackout of the high-level voltage network. The distribution network topology and the restoration paths should be determined anew according to the distribution network status after reenergizing of the substations in high voltage levels. The network topology, i.e., the configuration of switches is computed once at the beginning of the restoration process. The objective functions presented in Sec. II-A guide the multi-objective optimizer
where P Hi is the restoration load with high priority at the i-th substation. For computing f1 and f2 , the max flow algorithm [13] is applied to calculate the maximal load that can be restored. The number of switch operations determines the load restoration time and the probability of success. In addition, the maintenance costs of the switches depend on switch operation frequencies. With this, the last objective function can be formalized as M X (3) Ixi , f3 (Ix ) = min
Start
objective functions and constraints 1
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ident. of network configuration (NSGA-II)
analytic hierarchy process (AHP)
restoration paths update
xi =1
where Ixi is xi -th switch status, M is the total branch number. If the status of xi -th switch changes, Ixi equals one, else zero. In this paper, we assume that all switches are open after distribution network entirely collapses.
performance indexes evaluation
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calculation of decision values and ranking (FDM)
B. Constraints All paths restored? YES
Stop
Fig. 1: Structure of the proposed approach. Gray blocks are input metrics for the particular algorithms.
while constraints presented in Sec. II-B ensure the validity of network configurations. After evolving a set of non-dominated network configurations a single configuration is selected by an expert and an iterative process is started creating the restoration paths. Here, in each step an un-energized node is selected regarding the performance indexes presented in Sec. II-C for the schedule of a restoration path. This is repeated until all substations are energized again. The complete approach is illustrated in Fig. 1. A. Objective Functions The one of the most important tasks of network reconfiguration is to restore as much load as possible according to the status of the distribution network. The more load can be picked up, the better this particular reconfiguration operation is. The maximization of load restoration can be expressed as f1 (x) = max
N X
Pi ,
(1)
i=1
where x is the switch state vector (open or closed) in the distribution network, N is the total substation number, and Pi is the total restoration load at the i-th substation. During the load restoration process, the priority of loads should also be considered: N X P Hi , (2) f2 (x) = max i=1
To secure the distribution network operation, following constraints have to be satisfied during and after the reconfiguration process: 1) the configuration of the distribution network has to maintain the radial structure, 2) the voltage of each node has to be within tolerance limit, and 3) the current in each feeder has to be within the current limit which is defined by the protection devices. 4) the maximal load that can be restored in distribution network is limited by the maximal available power in upper level network. C. Performance Indexes during Reconfiguration Process Inappropriate restoration path selection can lead to the collapse of the complete restoration process. To avoid this, the restoration path selection consists of two steps. In first step, all nodes that have direct connection to the restored network are identified as candidate nodes. In second step, the candidate nodes are evaluated by following performance indexes and the best candidate node is selected as next restoration path. 1) ∆L is the total power flow variation in the distribution network caused by the restoration of the corresponding load node M X ∆Lxi , (4) ∆L = xi =1
where ∆Lxi is the power flow variation in the xi -th branch. The performance index ∆L/G is the ratio of the power flow variation to the capacity of the transformers in the high voltage level substations. 2) The node position in network determines the node importance degree. It is necessary to assess important degrees to nodes according to the surrounding network structure. The importance degree αi of node i is defined according to [14] as αi =
1 , ni e i
(5)
Parent 1
Combination
Child
Parent 2
Fig. 2: Crossover operator [15]
Child
Parent
Fig. 3: Mutation operator [15]
ei =
P
i,j∈vi
dmin,ij
ni (ni − 1)/2
.
(6)
In original network, the nodes which connect to node i are combined with node i. After the contraction, ni in Eq. 5 is the total number of nodes in the new network, ei is the ”average of the shortest distances” [14], vi is the total number of nodes in the original network, and dmin,ij is the shortest distance between node i and node j. The value ni represents the number of nodes that have direct connection with ith node. The smaller the node number after ith node contraction, the more important ith node is. The smaller ei , the more important the ith node is. 3) P Hi /Li is the ratio of the load with high priority to the total load in the i-th substation. Both parameters can be estimated by historic load curves. The more load with high priority in the substation, the more important this substation is. 4) li is the length of distribution lines between the already restored and the un-restored nodes. The length of a line influences the reactive power and voltage regulation during the reconfiguration process and can evaluate the risk of transient over-voltage.
2)
3)
III. A PPROACH FOR RESTORATION PATH SELECTION With the metrics presented in the previous section the steps of the algorithm illustrated in Fig. 1 can be explained. 1) The task of the first step is the identification of good network configurations. While most of the popular Paretobased genetic algorithms would be sufficient for solving this task, NSGA-II is selected in this work because of its popularity and good capability to find pareto front solutions. Initial Population: The W individuals of the initial population H0 are randomly created spanning trees. Each spanning tree covers the underlying distribution network topology. While there exist two classic methods for minimal spanning tree computation, namely
4) 5)
Kruskals [16] and Prims algorithms, in this paper the Kruskal algorithm is implemented. Fitness Evaluation: NSGA-II evaluates three objective functions and constraints as presented in Sec. II. Genetic Operators: Tournament selection, crossover and mutation operators are used to generate the offspring population Q0 with size W . The principle of the crossover operator for spanning trees is illustrated in Fig. 2 [15]. In the first step, the branches from two spanning trees are combined to form a graph. Then, the Kruskal algorithm is used to generate a spanning tree based on this graph. In this way, the new generated spanning tree have most branches from two parents. Similarly, the mutation operator deletes one branch randomly in a spanning tree to generate a sole node in the first step. After that, another branch in the graph is chosen to reconnect this node and form a new spanning tree. Fig. 3 shows the principle of this operation. Termination Condition: NSGA-II terminates if the variance of Pareto-vectors of non-dominated individuals is below some threshold for the last 50 generations. In the second step the restoration paths are updated. At the beginning the restoration paths are empty and each reenergized high-level voltage substation that is able to pick up load in the attached distribution network defines a restoration path. In succeeding update steps of restoration path, nodes in the distribution network that can be reenergized by nodes from a particular restoration path are added successively to this restoration path. In each update step, only one node is added to a restoration path. After the update, the selection rankings for the remaining and not energized nodes are recomputed in steps 4 and 5 of the algorithm in Fig. 1 and the restoration paths are updated again. This scheme is repeated until all nodes in the distribution network are selected for some restoration path and thus are reenergized again. To be able to select nodes for the restoration paths, all nodes have to be evaluated regarding their different performance indexes presented in the previous section. Human experts define the performance indexes and their priorities. The priorities are given as rankings for all performance index pairs. To harmonize the priority rankings and resolve priority conflicts, the analytic hierarchy process (AHP) [17] is used in step 3. AHP is an approach to transform expert knowledge into a noncontradicting importance ranking matrix and an overall linear weights decision vector. This weighting vector is used in step 5 of the algorithms in Fig. 1 to establish a linear order for a non-dominated set of solutions. In step 4 the performance indexes are evaluated. Given the performance indexes and their priorities, in step 5 a multi-objective fuzzy decision method (FDM) is executed to establish a non-dominated set and a linear ordering on it [18]. For FDM, the performance indexes have to be formalized as fuzzy membership functions. Since the values of performance indexes αi and P Hi /Li
TABLE I: The substation data of the 30-bus test network Bus 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Type source load load load load load load load load load load load load load load load load load load load load load load load load load load load source load
High Priority Load (MW) 0.0 10.0 2.4 7.6 10.0 5.6 7.8 6.5 3.2 6.0 2.2 2.4 6.8 6.2 8.2 3.5 10.0 3.2 9.6 2.2 12.6 30.0 6.2 8.7 7.6 4.6 2.4 2.8 0.0 8.2
Total Load (MW) 0.0 21.7 12.4 17.6 18.6 25.6 17.8 16.5 15.2 36.0 17.0 18.9 19.5 16.2 18.5 16.4 23.7 13.4 18.4 12.6 28.9 47.8 16.5 35.2 26.4 17.9 13.9 16.5 0.0 19.5
are lying between 0 and 1, and the higher the better, linear monotonic increased membership functions can be used. For ∆L/G and distribution line lengths, linear monotonic decreased membership functions can be employed. The line lengths have to be normalized before. FDM computes a set of non-dominated solutions and ranks the solution with the decision values. The best solution is selected to update the associated restoration path in step 2. If all branches in the final network are selected, FDM computes an empty solution set and the algorithm terminates. IV. C ASE S TUDY The IEEE 30 bus reference network [19] has been used to validate the proposed method. The modified load and branch data is given in Tab. I and Tab. II. This test network is regarded as 110kV high voltage in this paper. Fig. 4 illustrates the configuration of the 30-node test network during the normal operation. The dashed lines represent open and solid closed switches. The node numbers filled with pane represent power sources, such as high voltage substations. The other nodes are either loads or connection nodes. The number in the circles denotes substation number, whereas the number on the branch represents the serial number of the distribution line. In the experiment the nodes 1 and 29 are high voltage substations and are re-energized by the high voltage network. The rest of the distribution network remains un-energized. The high voltage level network is still under abnormal condition. The transformers in substations 1 and 29 can not pick up the
TABLE II: Network data of the 30-bus test network From 1 1 2 3 2 2 4 5 6 6 6 6 9 9 4 12 12 12 12 14 16 15 18 19 10 10 10 10 21 15 22 23 24 25 25 28 27 27 29 8 6
To 2 3 4 4 5 6 6 7 7 8 9 10 11 10 12 13 14 15 16 15 17 18 19 20 20 17 21 22 22 23 24 24 25 26 27 27 29 30 30 28 28
X (p.u) 0.06 0.19 0.17 0.04 0.20 0.18 0.04 0.12 0.08 0.04 0.21 0.56 0.21 0.11 0.26 0.14 0.26 0.13 0.20 0.20 0.19 0.22 0.13 0.07 0.21 0.08 0.07 0.15 0.02 0.20 0.18 0.27 0.33 0.38 0.21 0.40 0.42 0.60 0.45 0.20 0.06
Flow Limit (MW) 130 130 65 130 130 65 90 70 130 42 65 42 65 65 95 65 42 42 42 46 41 42 36 42 42 42 42 42 42 46 66 36 46 46 46 65 130 66 46 42 42
complete load of the distribution network. Furthermore, the branch 13 in distribution network is out of order during the restoration time. The method of this paper starts with the identification of a new network configuration. For this, NSGA-II is configured to process a population of 50 individuals and recombine as well as mutate the network configurations with the probability of 0.8 and 0.1 in step 1 of the algorithm presented in Fig. 1. After 85 iterations the algorithm terminates with two network configurations presented in Tab. III. For the first solution, the load shedding amounts to 48.5 MW, while the load shedding for case two amounts to 10.2 MW. Since the branch 13 is out of order, the computed network configurations are different from the pre-blackout network configuration. The first evolved network configuration requires nine and the second thirteen switch operations to bring the network back to the normal operation conditions. After network topology identification, restoration paths are computed in steps 2, 4 and 5 of the algorithm presented in Fig. 1. Fig. 5 and Fig. 6 illustrate the evolved network configurations and the according restoration paths. The numbered arrows represent the switch operation
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VI. ACKNOWLEDGEMENT Number of Switching Operations 9 13
sequences. The computational effort of the proposed method lies within a range of some minutes. The major share is taken by the NSGA-II algorithm while the time effort for identification of the restoration paths is negligible. For a real-world implementation the optimization methods can be significantly accelerated porting them from Matlab to a native programming language, such as C, and using parallelization. V. C ONCLUSION AND F UTURE W ORK This paper proposes an algorithm that is capable of creating quickly network configurations and restoration plans for distribution networks for restoring loads. The algorithm is able to consider up-to-date information about the error states of nodes and wires, the priorities of nodes, and the electrical properties of the distribution network topologies to minimize the probability of blackouts during restoration phases. With this, decision as well as restoration times after a network blackout can be minimized substantially. This work is part of the development of a larger tool set for network restoration process optimization in distribution network for quick decision making after large black outs to efficiently and reliably restore the electrical power system. In future work, distributed generators will be investigated to support the process of network restoration.
This work was supported by German Academic Exchange Service (DAAD) under the number A/12/94526. R EFERENCES [1] M. Kashem, “Network reconfiguration for load balancing in distribution networks,” Generation, Transmission and Distribution, IEE Proceedings, vol. 146, pp. 563 – 567, 2002. [2] C. Liu, S. Lee, and S. Venkata, “An expert system operational aid for restoration and loss reduction of distribution systems,” IEEE Transactions on Power Systems, vol. 3, pp. 619–626, 1988. [3] K. Okuda, H.Watanabe, and K. Yamazaki, “Fault restoration operation scheme in secondary power systems using case-based reasoning,” Elect. Engineer., vol. 110, pp. 47–49, 1990. [4] C. Teo and H. Gooi, “Restoration of electric power supply through an algorithm and knowledge based system,” Elect.Power System, vol. 29, pp. 171–180, 1994. [5] G. Raju and P. Ijwe, “An efficient algorithm for minimum loss reconfiguration of distribution system based on sensitivity and heuristics,” IEEE Transactions on Power Systems, vol. 3, pp. 1280 – 1287, 2008. [6] F. Gomes, S. Carneiro, and J. L. Pereira, “A new distribution system reconfiguration approach using optimal power flow technique and sensitivity anlaysis for loss reduction,” in IEEE PES General Meeting, 2005. [7] K. Akoi, H. Kuwabara, T. Sato, and M. Kanezashi, “Outage state optimal load allocation by automatic sectionalizing switches operation in distribution systems,” IEEE Transactions on Power Systems, vol. 2, pp. 1177–1185, 1987. [8] C. Ababei and R. Kavasseri, “Efficient network reconfiguration using minimum cost maximum flow-based branch exchanges and random walks-based loss estimation,” IEEE Transactions on Power Systems, vol. 26, pp. 30–37, 2011. [9] M. Baran and F. Wu, “Network reconfiguration in distribution systems for loss reduction and load balancing,” IEEE Transactions on Power Systems, vol. 4, pp. 101–102, 1989. [10] Y. Huang, “Enhanced genetic algorithm-based fuzzy multi-objective approach to distribution network reconfiguration,” IEEE Proceedings Generation Transmission Distribution, vol. 149, pp. 615–620, 2002. [11] R. King, B. Radha, and H. Rughooputh, “A fuzzy logic controlled genetic algorithm for optimal electrical distribution network reconfiguration,” in IEEE International Conference on Networking, Sensing and Control, vol. 1, 2004, pp. 577–582 Vol.1.
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[12] I. Watanabe, I. Kurihara, and Y. Nakachi, “A hybrid evolutionary algorithm for service restoration in power distribution systems,” in Computational Intelligence 293-311, 2007. [13] S. Fujishige, “A maximum flow algorithm using ma ordering,” in Elsevier Science B.V. Operations Research Letters, 2003. [14] L. Yan and G. Xueping, “Skeleton-Network Reconfiguration Based on Topological Characteristics of Scale-Free Networks and Discrete Particle Swarm Optimization,” IEEE Transactions on Power Systems, vol. 22, pp. 1267 – 1274, 2007. [15] B. Julstrom and G. Raidl, “Initialization is robust in evolutionary algorithms that encode spanning trees as sets of edges,” in in Proceedings of
[16] [17] [18] [19]
the 2002 ACM Symposium on Applied Computing. pp. 547˜n552, ACM Press, 2002. N. Srinivas and K. Deb, “Multiobjective optimization using nondominated sorting in genetic algorithm,” in Evolutionary Computation, 2002. C. Wen-Hui, “Quantitative Decision-Making Model for Distribution System Restoration,” IEEE Transactions on Power Systems, vol. 25, pp. 313 – 321, 2010. T. J. Ross, Fuzzy Logic with Engineering Applications. 3rd ed, John Wiley & Sons, 2010. “Power system test case archive,” University of Washington. [Online]. Available: http://www.ee.washington.edu/research/pstca/
