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| Optimal Power Flow of Three-Phase Hybrid AC-DC in Active Distribution Network Based on Second Order Cone Programming |
| Ju Yuntao, Huang Yan, Zhang Ruosi |
| College of Information and Electrical Engineering China Agricultural University Beijing 100083 China |
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Abstract The optimal power flow model of the active distribution network is non-convex, so it is difficult to ensure the global optimality and reliable convergence of the optimization results. Therefore, convex relaxation is needed to ensure that the model can be solved reliably. This paper proposes a second- order cone programming convex relaxation model which considers distributed generator, on-load voltage regulators with different connection modes, AC-DC converters, and three-phase models . Compared with the convex relaxation of Distflow model, this paper considers the effect of coupling phase-to-phase, and gives the physical characteristics of distributed generator, on-load tap-changer voltage regulators and other components. The second-order cone programming solver is used to solve the problem, and the calculation accuracy under different conditions and the calculation efficiency of different solvers are compared and analyzed. Numerical experiments based on the IEEE 13 bus system and IEEE 123 bus system show that the current optimization results can meet the constraints of power flow, which can be used as the final results for controlling. The results can also provide a good initial value for the nonconvex optimization solvers to get the solution of global optimization faster.
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Received: 11 March 2020
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[1] 李超, 苗世洪, 盛万兴, 等. 考虑动态网络重构的主动配电网优化运行策略[J]. 电工技术学报, 2019, 34(18): 3909-3919.
Li Chao, Miao Shihong, Sheng Wanxing, et al.Optimization operation strategy of active distribution network considering dynamic network reconfiguration[J]. Transactions of China Electrotechnical Society, 2019, 34(18): 3909-3919.
[2] 黄伟, 熊伟鹏, 华亮亮, 等. 基于动态调度优先级的主动配电网多目标优化调度[J]. 电工技术学报, 2018, 33(15): 3486-3498.
Huang Wei, Xiong Weipeng, Hua Liangliang, et al.Multi-objective optimization dispatch of active distribution network based on dynamic schedule priority[J]. Transactions of China Electrotechnical Society, 2018, 33(15): 3486-3498.
[3] Carpentier J.Contribution to the economic dispatch problem[J]. Bulletin de la Societe Francoise des Electriciens, 1962, 3(8): 431-447.
[4] Horst R, Pardalos P.Handbook of global optimization[M]. Berlin: Springer Science & Business Media, 2013.
[5] Hoang T.Convex analysis and global optimization[M]. Berlin: Springer, 1998.
[6] Pablo A P.Semidefinite programming relaxations for semialgebraic problems[J]. Mathematical Programming, 2003, 96(2): 293-320.
[7] Tetsuya F, Masakazu K.Semidefinite programming relaxation for nonconvex quadratic programs[J]. Journal of Global Optimization, 1997, 10(4):367-380.
[8] 林哲, 胡泽春, 宋永华. 最优潮流问题的凸松弛技术综述[J]. 中国电机工程学报, 2019, 39(13): 3717-3728.
Lin Zhe, Hu Zechun, Song Yonghua.Convex relaxation for optimal power flow problem: A recent review[J]. Proceedings of the CSEE, 2019, 39(13): 3717-3728.
[9] Jabr R A.Radial distribution load flow using conic programming[J]. IEEE Transactions on Power Systems, 2006, 21(3): 1458-1459.
[10] Jabr R A.A conic quadratic format for the load flow equations of meshed networks[J]. IEEE Transactions on Power Systems, 2007, 22(4): 2285-2286.
[11] Jabr R A.Optimal power flow using an extended conic quadratic formulation[J]. IEEE Transactions on Power Systems, 2008, 23(3): 1000-1008.
[12] Cui B, Sun X A.A new voltage stability-constrained optimal power-flow model: sufficient condition, SOCP representation, and relaxation[J]. IEEE Transactions on Power Systems, 2018, 33(5): 5092-5102.
[13] Zhang Bowen, Sun Yonghui, Zhong Yongjie, et al.Optimal energy flow of electricity-gas integrated energy system using second-order cone program[C]//2018 Chinese Control And Decision Conference (CCDC), Shenyang, 2018: 5085-5089.
[14] Farivar M, Low S H.Branch flow model: relaxations and convexification—part II[J]. IEEE Transactions on Power Systems, 2013, 28(3): 2565-2572.
[15] Farivar M, Low S H.Branch flow model: relaxations and convexification—part I[J]. IEEE Transactions on Power Systems, 2013, 28(3): 2554-2564.
[16] Gan Lingwen, Li Na, Topcu U, et al.Exact convex relaxation of optimal power flow in radial networks[J]. IEEE Transactions on Automatic Control, 2014, 60(1): 72-87.
[17] Low S H.Convex relaxation of optimal power flow-part II: exactness[J]. IEEE Transactions on Control of Network Systems, 2014, 1(2): 177-189.
[18] Low S H.Convex relaxation of optimal power flow-part I: formulations and equivalence[J]. IEEE Transactions on Control of Network Systems, 2014, 1(1): 15-27.
[19] 高红均, 刘俊勇, 沈晓东, 等. 主动配电网最优潮流研究及其应用实例[J]. 中国电机工程学报, 2017, 37(6): 1634-1645.
Gao Hongjun, Liu Junyong, Shen Xiaodong, et al.Optimal power flow research in active distribution network and its application examples[J]. Proceedings of the CSEE, 2017, 37(6): 1634-1645.
[20] Zhou Ye, Tian Yuan, Wang Keyou, et al.Robust optimisation for AC-DC power flow based on second-order cone programming[J]. The Journal of Engineering, 2017, 2017(13): 2164-2167.
[21] 韩禹歆, 陈来军, 王召健, 等. 基于自适应步长ADMM的直流配电网分布式最优潮流[J]. 电工技术学报, 2017, 32(11): 26-37.
Han Yuxin, Chen Laijun, Wang Zhaojian, et al.Distributed optimal power flow in direct current distribution network based on alternative direction method of multipliers with dynamic step size[J]. Transactions of China Electrotechnical Society, 2017, 32(11): 26-37.
[22] 刘一兵, 吴文传, 张伯明等. 基于混合整数二阶锥规划的三相有源配电网无功优化[J]. 电力系统自动化, 2014, 38(15): 58-64.
Liu Yibing, Wu Wenchuan, Zhang Boming, et al.Reactive power optimization for three-phase distribution networks with distributed generators based on mixed integer second-order cone programming[J]. Automation of Electric Power Systems, 2014, 38(15): 58-64.
[23] Sim C, Zhao G.A note on treating a second order cone program as a special case of a semidefinite program[J]. Mathematical Programming, 2005,102(3): 609-613.
[24] Martin B, Glineur F, De R P, et al.Loss reduction in a windfarm participating in primary voltage control using an extension of the convex distflow OPF[C]// 2018 Power Systems Computation Conference (PSCC), Dublin, Ireland: IEEE, 2018: 1-8.
[25] Schweitzer E, Saha S, Scaglione A, et al.Lossy distflow formulation for single and multiphase radial feeders[J]. IEEE Transactions on Power Systems, 2020, 35(3): 1758-1768.
[26] 丛鹏伟, 唐巍, 娄铖伟, 等. 含高渗透率可再生能源的主动配电网两阶段柔性软开关与联络开关协调优化控制[J]. 电工技术学报, 2019, 34(6): 1263-1272.
Cong Pengwei, Tang Wei, Lou Chengwei, et al.Two-stage coordination optimization control of soft open point and tie switch in active distribution network with high penetration renewable energy generation[J]. Transactions of China Electrotechnical Society, 2019, 34(6): 1263-1272.
[27] 李超, 苗世洪, 盛万兴, 等. 考虑动态网络重构的主动配电网优化运行策略[J]. 电工技术学报, 2019, 34(18): 3909-3919.
Li Chao, Miao Shihong, Sheng Wanxing, et al.Optimization operation strategy of active distribution network considering dynamic network reconfiguration[J]. Transactions of China Electrotechnical Society, 2019, 34(18): 3909-3919.
[28] Kocuk B, Dey S S, Sun X A.Strong SOCP relaxations for the optimal power flow problem[J]. Operations Research, 2016, 64(6): 1177-1196.
[29] Horn R A, Johnson C R.Matrix analysis[M]. Cambridge: Cambridge University Press, 2012.
[30] McCormick G P. Computability of global solutions to factorable nonconvex programs: part I-convex underestimating problems[J]. Mathematical Programming, 1976, 10(1): 147-175.
[31] Nesterov Y E, Todd M J.Primal-dual interior-point methods for self-scaled cones[J]. SIAM Journal on optimization, SIAM, 1998, 8(2): 324-364.
[32] Bai Y, Wang G, Roos C.Primal-dual interior-point algorithms for second-order cone optimization based on kernel functions[J]. Nonlinear Analysis: Theory, Methods & Applications, Elsevier, 2009, 70(10): 3584-3602.
[33] 巨云涛. 基于IEEE 13节点算例说明[EB/OL]. [2020-6-11].https://github.com/yanhuang-duoduo/-IEEE 13-.git. |
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2021, Vol. 36 
