16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010 335 Distributed Load Flow using Partitioning and Equivalencing of Power Networks G A Ezhilarasi Department of Electrical Engineering Indian Institute of Technology Madras Chennai - 600036, INDIA Email: angel.ezhil@gmail.com K S Swarup Department of Electrical Engineering Indian Institute of Technology Madras Chennai - 600036, INDIA Email: swarup@ee.iitm.ac.in Abstract This paper presents a distributed load flow that can be implemented in decentralized control centres. This becomes essential for power system having geographically separated areas. The system is partitioned into two areas balancing the number of nodes in each area. This is done to balance the computational load on the system in each control center. The Boundary buses are treated as load buses and the generator buses in the internal and the external system respectively. Simulation is done on IEEE Standard 14 Bus and 30 Bus s simulation and comparison is done between the base case and the reduced load flow results. Index Terms Partitioning, Network Equivalent, Distributed Computing. I. INTRODUCTION Power system is a large interconnected complex network involving computation intensive applications and highly intensive, nonlinear dynamic entities that spread across vast area. Under normal as well as congested condition, centralized control requires powerful computing facilities and multiple high speed communication links at the control centers. During certain circumstances, a failure in remote part of the system might spread instantaneously if the control action is delayed. This lack of response may cripple the entire power system including the centralized control center itself. An effective way to monitor and control complex power system is to intervene locally at places where there is disturbance and control the problem from propagating through the network. Hence distributed computing can greatly enhance the reliability and can be used effectively in power system applications. To simulate and implement distributed computing in power system the large interconnected network must be torn into sub networks in an optimal way. The partitioning should balance between the size of the sub networks and the interconnecting tie lines in order to reduce the overall parallel execution time. Over the past decades a number of algorithms have been proposed in literature for optimal network tearing. The techniques include dynamic programming, and the heuristic clustering approaches. Some of the optimization techniques such as simulated annealing, genetic algorithm [1] and tabu search [2] have also been used for network tearing[3]. For these optimization problems the cost function is formed such that it reflects the features of parallel and distributed processing. However these methods are computation intensive and involve procedures based on natural selection crossover and mutation. It also requires a large population size and occupies more memory. As the power system is geographically distributed in nature, the optimal partitions of IEEE Standard systems is taken manually in this paper.[4] The following sections are organized as follows. Section 2 gives an overview of distributed computing of load flow in power system. The two important tasks in distributed computing are network partitioning and representing the external system by its equivalent. These two tasks are briefed in the next two sections. Section 5 discusses the implementation of the proposed methodology on IEEE 14 bus and IEEE 30 Bus s. II. DISTRIBUTED LOAD FLOW Distributed approach can greatly enhance the reliability and improve the flexibility and efficiency of power system monitoring and control.the Distributed Processing is a flexible means for the power system operators to manage the system efficiently within a limited period [5]. Control Center 1 Fig. 1. Control Center 1 Distributed Load Flow Control Center 1 Schematic Distributed Power The two main tasks in distributed computing are network partitioning and equivalencing the external network. The first step in implementing this is to divide the entire power system into a number of control areas, and then set up a lower level control center for each area. It has many advantages over the
16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010 336 centralized control like higher efficiency, economy, enhanced reliability and flexibility, even though it increases the capital investment for communication system [1]. As shown in Figure 1, each sub area communicates with the centralized control center and also among themselves. In this work, the base case load flow is used after partitioning the system and the data can be obtained offline from the centralized control center [6]. The various steps involved in this process is explained by means of a flowchart in Fig 2. The interconnected power system network is taken for study. The Base case load flow is done on the entire system under normal conditions. Then optimal partitioning of the network is done in such a way that the resulting sub network is a connected graph. The resulting partitions are treated as geographically distributed sub areas. The system under study is taken as the internal system and the other one is the external system. The external system is represented by the power flow in the tie lies obtained from the base case power flow. Then the distributed load flow is done simultaneously in the internal and the external system. The validity of this approach is justified from the error analysis on the voltage magnitude and angle at the buses and the power flow in the lines of the sub networks. Fig. 2. Network Partition Represent Equivalent Load Flow Start Read Entire Data Perform Base Case Load Flow Perform Error Analysis Stop Load Flow Flowchart for Distributed Load Flow Load Flow Study is an important application in power system, that plays a vital role in planning and designing the power system and its expansion. It plays a vital role in determining the operating state of the existing system. The principal information obtained from this study is the magnitude and phase angle of the voltage at each bus and the real and reactive power flow in the lines. The net loss in the system is also be computed from the system load flow. The conventional methods used to solve the load flow problem involve intensive computations and are time consuming [7]. A typical power flow program can handle large amount of data if the computing facilities are sufficiently large. In a restructured environment, the Independent Operator (ISO) executes load flow program to study the reliability of the system and also for transmission congestion management. The load flow results helps the ISO to examine the feasibility of the schedules in the market operations. Since electric power system is naturally distributed over a vast geographical area, distributed monitoring and control becomes essential. Distributed management consists of several clusters of computers at the sub area control centers separated miles apart [8]. This has many advantages over the centralized control of the entire system like reliability, flexibility and economy. The distributed system can provide many functions that are difficult to realize in a centralized system like online external equivalent of the other sub areas [9] III. NETWORK PARTITIONING For a integrated hierarchical architecture, it is impractical to do any power system calculation for such a huge interconnected system through centralized processing. It is ideal that each area does its own calculations under some presumed base case conditions. In decentralised processing architecture, the entire system is partitioned in to sub areas each being controlled by their own control centers [10]. All the sub areas are linked with each other by a central control centers. Apart from its own areas control, the central control centre acts a negotiator between the sub area control centres. In real time each area is geographically separated from the other areas. It needs the data at the boundary buses that are connected to the adjacent areas and governed by different control centers. In this work a simple partition scheme is employed to establish the real time geographical sub areas [11]. The singularity check is done on the partitions created. Buses in the layer are identified along with the Boundary and Boundary. The Details of the and Boundary Buses are given in Table I. TABLE I PARTITION DETAILS OF IEEE TEST CASES Test Case Boundary Boundary 14 Bus 30 Bus 1, 2, 3, 5, 8 1, 2, 3, 5, 7, 9, 11 4, 6, 7 9, 11, 12, 13 4, 6, 8, 10 12, 17, 20, 21, 22, 28 10, 14 13, 14, 15, 16, 18, 19, 23, 24, 25, 26, 27, 29, 30. The schematic of the partitions made for IEEE 14 Bus system are shown in the Figure 3. This partition has the
16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010 337 minimum number of tie lines and the number of nodes in the sub network is also well balanced. The schematic of the 1 5 4 6 7 12 11 13 and the external system. For detailed analysis of the the external system is represent by its equivalent to reduce the computational burden. The conventional techniques used for network equivalents are the WARD Equivalents [12], Radial Equivalent Independent(REI) [13] Equivalents and Linearisation. The impediments of these techniques lies in their inability to model any change in the external network [14]. The networks are valid for incremental changes within the internal networks only. In this work a simple method of representing the external system by means of the power injections at those buses is done. The overview of this approach is shown in Fig. 5 and Fig. 6. 2 8 3 10 14 Fig. 3. 9 Optimal Partition of IEEE 14 Bus into 2 Clusters partitions made for IEEE 30 Bus system are shown in the Figure 4. In this case if the network is divided into equal partitions then the connectivity of the network is lost leading to isolated node. Hence load balancing of the sub networks is not considered in this case. Boundary Tie Lines Boundary 29 27 28 Fig. 5. Schematic of Interconnected Power 30 26 25 23 24 15 18 19 17 20 Load Generation 14 16 21 22 13 12 11 9 10 Fig. 6. Schematic of Partitioned Power 1 Fig. 4. 3 4 8 6 7 2 5 Optimal Partition of IEEE 30 Bus into 2 Clusters As depicted above the boundary buses at the internal system and the external system are separated. The boundary buses in the internal system are treated a load buses with the load being the power flow in the tie lines from that bus. Similarly the boundary buses at the external system are assumed to be generator buses with the power flow in the tie lines as the generation at that bus. The slack bus [15] is taken to be the generator bus with maximum generation and voltage and angle being fixed using the base case power flow results. IV. NETWORK EQUIVALENTS Network Equivalencing methods aims to identify the internal area of the system to be fully preserved and the external area that is to reduced and represented by its equivalent. The boundary buses at the internal and the external system are also identified, which yields the tie lines between the internal V. CASE STUDY The simulations were done on IEEE 14 bus and IEEE 30 bus system. The partitions are created by sequential testing fo all possible combinations and singularity checks. The system is separated into and and the Boundary Buses are identified. The partitions created are
16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010 338 1.1 1.08 Actual Distributed 0 2 4 Actual Distributed V pu 1.06 1.04 Phase Angle δ 6 8 10 12 1.02 14 16 1 (a) Voltage Magnitude 18 (b) Phase Angle Error in V pu 0.5 x 10 3 0 0.5 1 1.5 2 2.5 3 (c) Error in Voltage Magnitude Error in δ pu 0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 (d) Error in Phase Angle Fig. 7. Comparison of IEEE 14 Bus Results already shown in section 3. Conventional load flow is done using fast decoupled load flow method and the same is applied on the partitioned system. The results are justified in terms of the error in the voltage magnitude and the angle in the system. It is found that for the system under study the error in voltage is found to be minimum. The power flow in the lines also are compared for the distributed load flow. Table II shows the simulation results of IEEE 14 Bus system. The error between the actual voltage maginitudes and the distributed system voltage magnitudes is found to be minimum. The same has been tabulated for the phase angles also. This is visualized best in the Fig 7. Comparison of voltage magnitude and phase angle of IEEE 30 Bus system is shown in Table III. The real and reactive power flows of the interconnected system is compared with that of the partitioned internal and external system. The simulation results of the test cases are found to match with minimum error as shown in Table IV. TABLE II COMPARISON OF VOLTAGE MAGNITUDE AND VOLTAGE ANGLE FOR IEEE 14 BUS SYSTEM Bus Voltage Magnitude V (p.u) Phase Angle δ (deg) No Actual Actual 1 1.0600 1.0600-0 0-2 1.0450 1.0450 - -4.9847-4.9691-3 1.0100 1.0100 - -12.7324-12.6936-4 1.0168 1.0194 - -10.3026-10.3065-5 1.0185 1.0201 - -8.7633-8.7602-6 1.0700 1.0700 - -14.2383-14.2267-7 1.0601 1.0614 - -13.3448-13.3375-8 1.0900 1.0900 - -13.3448-13.3375-9 1.0534-1.0534-14.9237 - -14.9237 10 1.0489-1.0489-15.0877 - -15.0847 11 1.0559-1.0559-14.7929 - -14.7830 12 1.0550-1.0550-15.0926 - -14.9621 13 1.0500-1.0500-15.1688 - -15.0539 14 1.0339-1.0339-16.0334 - -15.9835
16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010 339 TABLE IV COMPARISON OF REAL AND REACTIVE POWER FLOWS OF IEEE TEST CASES Test Sub Line Real Power Flow (MW) Reactive Power Flow (MVAR) Case Area No Actual Distributed Error Actual Distributed Error 1 156.9481 156.4745 0.4736-18.9364-18.8257-0.1107 2 73.2839 73.0755 0.2084 4.7514 4.7719-0.0205 3 56.1241 55.9877 0.1364-0.1910-1.6614 1.4704 4 75.4646 75.3773 0.0873 5.7274 4.9910 0.7364 5 41.5392 41.4367 0.1025 2.7448 1.8251 0.9198 6-23.2419-23.4373 0.1954 4.7678 3.2913 1.4765 7-60.9535-60.7773-0.1762 15.7813 18.1352-2.3538 16 27.3560 27.3561-0.0001-20.3621-19.7488-0.6133 18 41.2573 41.2574-0.0001-18.8539-18.2403-0.6136 19-0.0000 0.0000-0.0000-17.9711-17.2532-0.7179 11 5.1388 5.0792 0.0596 3.7088 3.7333-0.0245 12 9.3444 9.0558 0.2886 3.2825 3.4144-0.1319 13-3.8727-3.9322 0.0595-2.1218-2.0970-0.0248 14 1.6409 1.7090-0.0681 0.8178 0.7428 0.0750 15 5.7254 6.0134-0.2880 2.0735 1.9398 0.1337 1 90.6051 90.8950-0.2899 0.0249-0.0567 0.0816 2 47.9485 48.0115-0.0631-0.8178 0.1155-0.9334 3 29.1393 29.2481-0.1088-6.2992-5.1305-1.1688 4 44.6058 44.6658-0.0600-3.6685-2.7513-0.9172 5 58.0722 58.1483-0.0762 2.7810 2.7715 0.0095 6 37.8237 37.9195-0.0958-5.9643-5.5222-0.4420 7 39.1464 38.9779 0.1685 0.6047-2.4130 3.0177 8-13.0638-12.9915-0.0723 2.9639 3.3562-0.3923 9 36.2983 36.2241 0.0742 7.3140 6.9172 0.3968 10-0.7753-0.7751-0.0001 0.5347-1.4410 1.9757 35-17.9300-17.9300-0.0000-22.9920-23.2146 0.2226 36 32.5149 32.5166-0.0017 4.0216 4.0840-0.0624 38 14.8109 14.8126-0.0017-10.4738-10.6358 0.1620 39 11.8148 11.8132 0.0016-2.9580-3.0066 0.0486 11 7.6957 7.6387 0.0570 2.0309 2.0682-0.0373 12 17.5349 17.2876 0.2474 5.2617 5.3671-0.1055 13 6.7622 6.7413 0.0209 1.9212 1.9301-0.0090 14 1.4246 1.3679 0.0567 0.2831 0.3220-0.0390 15 3.2196 3.1989 0.0207 0.0316 0.0410-0.0094 16 5.6906 5.5975 0.0932 1.0477 1.0963-0.0486 17 2.4567 2.3645 0.0922 0.0787 0.1292-0.0506 18-7.0470-7.1389 0.0920-3.3288-3.2777-0.0511 23-1.5722-1.4618-0.1104-2.1263-2.1806 0.0543 24 4.8621 4.6564 0.2057 1.5944 1.6994-0.1050 25 6.1548 6.3179-0.1630 1.9051 1.8115 0.0936 26 1.6374 1.4332 0.2042-0.0555 0.0526-0.1081 27-0.9561-0.9985 0.0423-0.9274-0.9141-0.0133 28-4.5034-4.5458 0.0424-3.2988-3.2857-0.0131 29 6.1868 6.1868 0.0000 1.6627 1.6627 0.0000 30 7.0880 7.0879 0.0000 1.6553 1.6553 0.0000 31 3.7027 3.7027 0.0000 0.6039 0.6039 0.0000 34 3.5440 3.5440 0.0000 2.3657 2.3657 0.0000 37-16.9100-16.9100-0.0000-30.6924-30.6924 0.0000 41 17.0643 17.1051-0.0408-3.7942-3.8015 0.0073 IEEE 14 Bus IEEE 30 Bus
16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010 340 TABLE III COMPARISON OF VOLTAGE MAGNITUDE AND VOLTAGE ANGLE FOR IEEE 30 BUS SYSTEM Bus Voltage Magnitude V (p.u) Phase Angle δ (deg) No Actual Actual 1 1.0500 1.0500-0 0-2 1.0338 1.0338 - -2.7359-2.7456-3 1.0323 1.0306 - -4.6920-4.6835-4 1.0280 1.0259 - -5.6294-5.6190-5 1.0058 1.0058 - -8.9925-9.0107-6 1.0232 1.0224 - -6.5068-6.5146-7 1.0079 1.0074 - -8.0455-8.0578-8 1.0230 1.0230 - -6.4839-6.5047-9 1.0450 1.0445 - -8.1578-8.1679-10 1.0413 1.0407 - -10.0415-10.0535-11 1.0913 1.0913 - -6.2837-6.2929-12 1.0470-1.0470-9.2598 - -9.2598 13 1.0883-1.0883-8.0693 - -8.0693 14 1.0331-1.0331-10.1705 - -10.1604 15 1.0296-1.0296-10.2900 - -10.2692 16 1.0373-1.0373-9.8728 - -9.8702 17 1.0347-1.0347-10.2019 - -10.1968 18 1.0215-1.0215-10.9062 - -10.8714 19 1.0198-1.0198-11.0781 - -11.0349 20 1.0244-1.0244-10.8773 - -10.8298 21 1.0293-1.0293-10.5105 - -10.3996 22 1.0299-1.0299-10.5038 - -10.3946 23 1.0217-1.0217-10.7382 - -10.6889 24 1.0198-1.0198-10.9853 - -10.8979 25 1.0245-1.0246-10.9085 - -10.8121 26 1.0070-1.0070-11.3222 - -11.2258 27 1.0361-1.0361-10.5959 - -10.4939 28 1.0192-1.0192-6.9269 - -6.8163 29 1.0165-1.0165-11.7949 - -11.6929 30 1.0052-1.0052-12.6549 - -12.5528 [3] P. Kanakasabapathy and K. Swarup, Optimal Bidding Strategy for Multi-unit Pumped Storage Plant in Pool-Based Electricity Market Using Evolutionary Tristate PSO, in ICSET, 2008, pp. 95 100. [4] L. Chuang, H. Chang, C. Tu, and C. Yang, Improved binary PSO for feature selection using gene expression data, Computational Biology and Chemistry, vol. 32, no. 1, pp. 29 37, 2008. [5] H. Ding, A. El-Keib, and R. Smith, Optimal clustering of power networks using genetic algorithms* 1, Electric Power s Research, vol. 30, no. 3, pp. 209 214, 1994. [6] J. Park, K. Lee, J. Shin, and K. Lee, A particle swarm optimization for economic dispatch with nonsmooth cost functions, IEEE Transactions on Power s, vol. 20, no. 1, pp. 34 42, 2005. [7] B. Baran, E. Kaszkurewicz, and D. Falcao, Team algorithms in distributed load flow computations, IEE Proceedings-Generation, Transmission and Distribution, vol. 142, no. 6, pp. 583 588, 1995. [8] Y. Wallach and V. Conrad, Parallel solutions of load flow problems, Electrical Engineering (Archiv fur Elektrotechnik), vol. 57, no. 6, pp. 345 354, 1976. [9] H. Shayeghi, M. Mahdavi, and A. Kazemi, Discrete Particle Swarm Optimization Algorithm Used for TNEP Considering Network Adequacy Restriction, planning, vol. 5, pp. 6 12, 2009. [10] K. Chan, R. Dunn, and A. Daniels, Efficient heuristic partitioning algorithm for parallel processing of large power systems network equations. [11] X. Zhi, X. Xing, Q. Wang, L. Zhang, X. Yang, C. Zhou, and Y. Liang, A discrete PSO method for generalized TSP problem, in Machine Learning and Cybernetics, 2004. Proceedings of 2004 International Conference on, vol. 4, 2004. [12] E. Housos, G. Irisarri, R. Porter, and A. Sasson, Steady state network equivalents for power system planning applications, IEEE Transactions on Power Apparatus and s, pp. 2113 2120, 1980. [13] M. Oatts, S. Erwin, and J. Hart, Application of the REI equivalent for operations planning analysis of interchange schedules, IEEE transactions on power systems, vol. 5, no. 2, pp. 547 555, 1990. [14] Y. Phulpin, B. Miroslav, M. Petit, J. Heyberger, and D. Ernst, Evaluation of network equivalents for voltage optimization in multi-area power systems, IEEE Transactions on Power s, vol. 24, no. 2, 2009. [15] G. Jang, D. Hur, J. Park, and S. Lee, A modified power flow analysis to remove a slack bus with a sense of economic load dispatch, Electric Power s Research, vol. 73, no. 2, pp. 137 142, 2005. VI. CONCLUSION This paper presents the distributed computing approach to load flow problem in power system. Conventional Fast Decoupled Load flow is used for the solving the problem. The interconnected system is partitioned into smaller clusters and the internal external and boundary buses are identified for the partitioned system. The boundary buses in the internal system are treated as load buses and that in the external system as generator buses. The distributed load flow is done on the reduced system. The simulation is done on IEEE Standard 14 bus and 30 Bus s. The results of the base case load flow and the distributed load flow are compared. The error is found to be minimum for the test cases under study. Hence the distributed load flow study can be implemented in a restructured power system using distributed energy management system. REFERENCES [1] M. Irving and M. Sterling, Optimal network tearing using simulated annealing, IEE Proceedings C Generation, Transmission and Distribution [see also IEE Proceedings-Generation, Transmission and Distribution], vol. 137, no. 1, pp. 69 72, 1990. [2] C. Chang, L. Lu, and F. Wen, Power system network partitioning using tabu search, Electric power systems research, vol. 49, no. 1, pp. 55 61, 1999.