An Extended Power Flow Calculation Model Based on Power Droop Bus and Two-Step Analysis
Feng Zhuocheng1, Jiang Tong1, Wan Kaiyao2, Li Qinxin2
1. State Key Laboratory of Alternative Electrical Power System with Renewable Energy Sources North China Electric Power University Beijing 102206 China; 2. China Electric Power Research Institute Beijing 100192 China
Abstract：Power flow calculation (PFC) is the basis of power system analysis. Ensuring the convergence of power flow plays an important role in the planning and operation of power network. Mathematically, the essence of PFC is to solve nonlinear equations, whose convergence is influenced by many factors. When improper initial value selection and unreasonable mode arrangement occur, the PFC cannot converge. The non-convergence of PFC indicates that the equation has no solution or the equation has solution but cannot be obtained due to the limitations of the solving algorithm. If the solution exists, a robust pathological power flow algorithm should be used to find the flow solution. Otherwise, the boundary conditions of power flow equations should be changed and the operating mode should be adjusted to make the power flow equations solvable and find the solution. At present, the main method of power flow adjustment is expert experience, which consumes a lot of human resources and requires a large amount of calculation. Therefore, an efficient and stable power flow adjustment strategy is urgently needed to ensure the reliable convergence of power flow. To address these issues, this paper proposed an extended power flow calculation model based on power droop bus and two-step analysis. Firstly, the power droop bus is defined to restore power flow solvability. The principle of restoring power flow solvability by bus type conversion is to intersect the characteristic curve of the converted bus with the original solvable domain manifold. The boundary of the solvable domain is composed of saddle node bifurcation (SNB) points, which is a closed curve containing the origin. According to the definition of power droop bus, the new manifold will pass through the origin of the coordinate system, and the new manifold will still pass through the original feasible region, which explains its effectiveness towards restoring solvability. An extended power flow calculation model considering power droop buses is given. The extended system is developed to restore power flow solvability by introducing power droop bus. A two-step analysis method is proposed to determine the bus conversion logic. Based on the bus voltage equation, it divides the network into PQ subnet and PV subnet. Buses need to be converted are determined by analyzing the PQ and PV subnet individually. The adjustment scheme is determined in the state backtracking procedure, which determines the action generator through calculating the left eigenvector at the backtracking point. The algorithm is tested in IEEE 118 bus system and TEXAS 2000 bus system, and compared with methods including optimal power flow (OPF) based on interior point method. In the specific scenes, 23 out of 25 unsolvable cases are adjusted into solvable cases. To verify the effectiveness and applicability of the proposed strategy, 50 unsolvable cases are constructed by increasing load randomly, and 48 cases are adjusted successfully. The simulation results indicate that proposed method achieve 92% success rate for most unsolvable cases. It can adapt to a variety of power flow situations without solutions. Further improvement should be focus on PFC problems considering direct current transmission.
冯卓诚, 姜彤, 万凯遥, 李勤新. 基于功率下垂节点与两步式分析的扩展潮流计算模型[J]. 电工技术学报, 2023, 38(9): 2335-2349.
Feng Zhuocheng, Jiang Tong, Wan Kaiyao, Li Qinxin. An Extended Power Flow Calculation Model Based on Power Droop Bus and Two-Step Analysis. Transactions of China Electrotechnical Society, 2023, 38(9): 2335-2349.
[1] 姜涛, 李雪, 李国庆, 等. 含多端柔性直流的交直流电力系统静态电压稳定域构建方法[J]. 电工技术学报, 2022, 37(7): 1746-1759. Jiang Tao, Li Xue, Li Guoqing, et al.A predictor-corrector algorithm for forming voltage stability region of hybrid AC/DC power grid with inclusion of VSC-MTDC[J]. Transactions of China Electrotechnical Society, 2022, 37(7): 1746-1759. [2] 刘明凯, 王占山, 邢彦丽. 基于强化多目标差分进化算法的电-气互联系统最优潮流计算[J]. 电工技术学报, 2021, 36(11): 2220-2232. Liu Mingkai, Wang Zhanshan, Xing Yanli.Enhanced multi-objective differential evolutionary algorithm based optimal power flow calculation for integrated electricity and gas systems[J]. Transactions of China Electrotechnical Society, 2021, 36(11): 2220-2232. [3] 王晨旭, 唐飞, 刘涤尘, 等. 基于双层代理模型的概率-区间潮流计算及灵敏度分析[J]. 电工技术学报, 2022, 37(5): 1181-1193. Wang Chenxu, Tang Fei, Liu Dichen, et al.Probabilistic-interval power flow and sensitivity analysis using double layer surrogate method[J]. Transactions of China Electrotechnical Society, 2022, 37(5): 1181-1193. [4] 胡健, 付立军, 马凡, 等. 基于仿射算术优化的不确定系统区间潮流快速分解法[J]. 电工技术学报, 2016, 31(23): 125-131. Hu Jian, Fu Lijun, Ma Fan, et al.Fast decoupled power flow calculation of uncertainty system based on interval affine arithmetic optimization[J]. Transactions of China Electrotechnical Society, 2016, 31(23): 125-131. [5] 姜涛, 张勇, 李雪, 等. 电力系统交直流潮流的全纯嵌入计算[J]. 电工技术学报, 2021, 36(21): 4429-4443, 4481. Jiang Tao, Zhang Yong, Li Xue, et al.A holomorphic embedded method for solving power flow in hybrid AC-DC power system[J]. Transactions of China Electrotechnical Society, 2021, 36(21): 4429-4443, 4481. [6] 卢志刚, 程慧琳, 冯磊. 基于支路功率选取的功率扩展潮流计算[J]. 电工技术学报, 2013, 28(6): 208-215. Lu Zhigang, Cheng Huilin, Feng Lei.Extended-power load flow calculation based on selection of branch power[J]. Transactions of China Electrotechnical Society, 2013, 28(6): 208-215. [7] 王家融, 艾欣, 王坤宇, 等. 基于增广雅可比矩阵的交直流解耦潮流新算法[J]. 电工技术学报, 2018, 33(6): 1382-1389. Wang Jiarong, Ai Xin, Wang Kunyu, et al.A novel AC-DC decoupled power flow calculation method based on the augmented Jacobian matrix[J]. Transactions of China Electrotechnical Society, 2018, 33(6): 1382-1389. [8] Overbye T J.A power flow measure for unsolvable cases[J]. IEEE Transactions on Power Systems, 1994, 9(3): 1359-1365. [9] Granville S, Mello J C O, Melo A C G. Application of interior point methods to power flow unsolvability[J]. IEEE Transactions on Power Systems, 1996, 11(2): 1096-1103. [10] Barboza L V, Salgado R.Unsolvable power flow analysis-an approach based on interior point nonlinear optimization methods[C]//2001 IEEE Porto Power Tech Proceedings (Cat. No.01EX502), Porto, Portugal, 2002, 2: 6. [11] Van Cutsem T.An approach to corrective control of voltage instability using simulation and sensitivity[J]. IEEE Transactions on Power Systems, 1995, 10(2): 616-622. [12] 陶向红, 卜广全, 王虹富, 等. 基于加权最小绝对值的大电力系统潮流可行解优化恢复方法[J]. 电力系统自动化, 2014, 38(23): 60-64, 76. Tao Xianghong, Bu Guangquan, Wang Hongfu, et al.An optimization method based on weighted least absolute value to restore power flow solvability of bulk power system[J]. Automation of Electric Power Systems, 2014, 38(23): 60-64, 76. [13] 李智欢, 韩云飞, 苏寅生, 等. 基于节点类型转换的潮流收敛性调整方法[J]. 电力系统自动化, 2015, 39(7): 188-193. Li Zhihuan, Han Yunfei, Su Yinsheng, et al.A convergence adjustment method of power flow based on node type switching[J]. Automation of Electric Power Systems, 2015, 39(7): 188-193. [14] 李敏, 陈金富, 陈海焱, 等. 一类潮流计算无解的实用性调整研究[J]. 电力系统自动化, 2006, 30(8): 11-15. Li Min, Chen Jinfu, Chen Haiyan, et al.Load flow regulation for unsolvable cases in a power system[J]. Automation of Electric Power Systems, 2006, 30(8): 11-15. [15] Jiang Tong, Feng Zhuocheng, Wan Kaiyao, et al.A power flow adjustment strategy based on weak bus identification and new bus type conversion[J]. International Journal of Electrical Power & Energy Systems, 2022, 137: 107705. [16] 王虹富, 陶向红, 李柏青, 等. 基于虚拟中点功率的潮流估算模型[J]. 中国电机工程学报, 2018, 38(21): 6305-6313, 6492. Wang Hongfu, Tao Xianghong, Li Baiqing, et al.An approximate power flow model based on virtual midpoint power[J]. Proceedings of the CSEE, 2018, 38(21): 6305-6313, 6492. [17] 张松涛, 张东霞, 黄彦浩, 等. 基于改进直流潮流算法的潮流计算收敛自动调整方法研究[J]. 电网技术, 2021, 45(1): 86-97. Zhang Songtao, Zhang Dongxia, Huang Yanhao, et al.Research on automatic power flow convergence adjustment method based on modified DC power flow algorithm[J]. Power System Technology, 2021, 45(1): 86-97. [18] 王甜婧, 汤涌, 郭强, 等. 基于知识经验和深度强化学习的大电网潮流计算收敛自动调整方法[J]. 中国电机工程学报, 2020, 40(8): 2396-2406. Wang Tianjing, Tang Yong, Guo Qiang, et al.Automatic adjustment method of power flow calculation convergence for large-scale power grid based on knowledge experience and deep reinforcement learning[J]. Proceedings of the CSEE, 2020, 40(8): 2396-2406. [19] Wu Shuang, Hu Wei, Lu Zongxiang, et al.Power system flow adjustment and sample generation based on deep reinforcement learning[J]. Journal of Modern Power Systems and Clean Energy, 2020, 8(6): 1115-1127. [20] 郭烨, 吴文传, 张伯明, 等. 节点类型扩展潮流计算的应用研究[J]. 中国电机工程学报, 2011, 31(16): 81-87. Guo Ye, Wu Wenchuan, Zhang Boming, et al.Application research on bus-type extended load flow[J]. Proceedings of the CSEE, 2011, 31(16): 81-87. [21] 郭烨, 张伯明, 吴文传. 节点类型扩展潮流计算及其可解性研究[J]. 中国电机工程学报, 2011, 31(13): 79-85. Guo Ye, Zhang Boming, Wu Wenchuan.Study on bus-type extended load flow and its solvability[J]. Proceedings of the CSEE, 2011, 31(13): 79-85. [22] 姜涛, 张明宇, 李雪, 等. 静态电压稳定域局部边界的快速搜索新方法[J]. 中国电机工程学报, 2018, 38(14): 4126-4137, 4318. Jiang Tao, Zhang Mingyu, Li Xue, et al.A novel algorithm to explore static voltage stability region boundary in power systems[J]. Proceedings of the CSEE, 2018, 38(14): 4126-4137, 4318. [23] Barboza L V, Francisco J B, Zambaldi M C.Restoring solution of electric network equations: an approach using the augmented lagrangean algorithm[J]. IEEE Latin America Transactions, 2010, 8(6): 670-677. [24] Wan Kaiyao, Jiang Tong.Augmented system for detecting the steady-state voltage stability margin[J]. IET Generation, Transmission & Distribution, 2020, 14(21): 4788-4795. [25] Jiang Tong, Wan Kaiyao, Feng Zhuocheng.Boundary-derivative direct method for com pu ting saddle node bifurcation points in voltage stability analysis[J]. International Journal of Electrical Power & Energy Systems, 2019, 112: 199-208. [26] Daniel Zimmerman R, Murillo-Sánchez C E, Thomas R J. MATPOWER: steady-state operations, planning, and analysis tools for power systems research and education[J]. IEEE Transactions on Power Systems, 2011, 26(1): 12-19.
2023, Vol. 38 
