1. School of Electrical Engineering Beijing Jiaotong University Beijing 100044 China; 2. Research and Development Center of Xuji Electric Co. Ltd Xuchang 461000 China
Abstract：Stochastic load flow is designed for power systems with uncertainties, whose fast and accurate calculation results are very important for grid operational control. In this paper, a stochastic load flow calculation method was proposed on basis of clustering and sampling. Firstly, according to history data, Monte Carlo simulation method was used to generate a large number of random variable samples. Secondly, the optimal cluster number was determined for samples by the average silhouette coefficient and sum of squared error, and the samples were clustered by using K-means. Thirdly, according to the clustering center and the average probability density of the sample in the cluster, load flow was calculated with the mean values of each cluster. Finally, the power flow calculation results and the corresponding average probability density were statistically analyzed, and the probability density function of the state variables was obtained. The modified IEEE39 system and a real regional power grid were taken as examples to analyze the calculation accuracy and calculation efficiency. The results show that the method proposed in this paper can balance calculation accuracy and calculation speed, and there are more advantageous in large systems. It provides decision basis for grid dispatching plan and operation analysis.
[1] Dopazo J F, Klitin O A, Sasson A M.Stochastic load flows[J]. IEEE Transactions on Power Apparatus and Systems, 1975, 94(2): 299-309. [2] 邵振国, 黄伟达. 考虑出力不确定性的分布式电源谐波传播计算[J]. 电工技术学报, 2019, 34(增刊2): 674-683. Shao Zhenguo, Huang Weida.A calculation method of harmonic propagation considering the uncertainty of distributed generation[J]. Transactions of China Electrotechnical Society, 2019, 34(S2): 674-683. [3] 韩佶, 苗世洪, 李超, 等. 计及相关性的电-气-热综合能源系统概率最优能量流[J]. 电工技术学报, 2019, 34(5): 1055-1067. Han Ji, Miao Shihong, Li Chao, et al.Probabilistic optimal energy flow of electricity-gas-heat integrated energy system considering correlation[J]. Transactions of China Electrotechnical Society, 2019, 34(5): 1055-1067. [4] 刘宇, 高山, 杨胜春, 等. 电力系统概率潮流算法综述[J]. 电力系统自动化, 2014, 38(23): 127-135. Liu Yu, Gao Shan, Yang Shenchun, et al.Review on algorithms for probabilistic load flow in power system[J]. Automation of Electric Power Systems, 2014, 38(23): 127-135. [5] 赵书强, 李志伟. 考虑可再生能源出力不确定性的多能源电力系统日前调度[J]. 华北电力大学学报:自然科学版, 2018, 45(5): 1-10. Zhao Shuqiang, Li Zhiwei.Day-ahead scheduling of multi-energy power system considering renewable energy uncertain output[J]. Journal of North China Electric Power University, 2018, 45(5): 1-10. [6] 朱星阳, 刘文霞, 张建华, 等. 电力系统随机潮流及其安全评估应用研究综述[J]. 电工技术学报, 2013, 28(10): 257-270. Zhu Xingyang, Liu Wenxia, Zhang Jianhua, et al.Reviews on power system stochastic load flow and its applications in safety evaluation[J]. Transactions of China Electrotechnical Society, 2013, 28(10): 257-270. [7] Amid P, Crawford C.Cumulant-based probabilistic load flow analysis of wind power and electric vehicles[C]//2016 International Conference on Probabilistic Methods Applied to Power Systems (PMAPS), IEEE, Beijing, China, 2016: 1-6. [8] 孙玲玲, 赵美超, 王宁, 等. 基于电压偏差机会约束的分布式光伏发电准入容量研究[J]. 电工技术学报, 2018, 33(7): 1560-1569. Sun Lingling, Zhao Meichao, Wang Ning, et al.Research of permitted capacity of distributed photovoltaic generation based on voltage deviation chance constrained[J]. Transactions of China Electrotechnical Society, 2018, 33(7): 1560-1569. [9] 李振坤, 崔静, 路群, 等. 基于时序动态约束的主动配电网滚动优化调度[J]. 电力系统自动化, 2019, 43(16): 17-29. Li Zhenkun, Cui Jing, Lu Qun, et al.Rolling optimal scheduling of active distribution network based on series dynamic constraints[J]. Automation of Electric Power Systems, 2019, 43(16): 17-29. [10] 石飞, 杨胜春, 冯树海, 等. 适用于超大规模电网的在线概率潮流算法[J]. 电力系统自动化, 2018, 42(21): 84-92. Shi Fei, Yang Shengchun, Feng Shuhai, et al.Online probabilistic power flow algorithm for super-large-scale power grid[J]. Automation of Electric Power Systems, 2018, 42(21): 84-92. [11] Cao Jia, Yan Zheng.Probabilistic optimal power flow considering dependences of wind speed among wind farms by pair-copula method[J]. International Journal of Electrical Power & Energy Systems, 2017, 84: 296-307. [12] Zhang H, Li P.Probabilistic analysis for optimal power flow under uncertainty[J]. IET Generation, Transmission & Distribution, 2010, 4(5): 553-561. [13] 韦鹏飞, 徐永海, 王金浩, 等. 基于拉丁超立方采样的节点敏感设备暂降免疫水平评估[J]. 电工技术学报, 2018, 33(15): 3415-3425. Wei Pengfei, Xu Yonghai, Wang Jinhao, et al.Sag immunity level evaluation of sensitive equipment at node based on Latin hypercube sampling[J]. Transactions of China Electrotechnical Society, 2018, 33(15): 3415-3425. [14] Huang Jie, Xue Yusheng, Dong Z Y, et al.An adaptive importance sampling method for probabilistic optimal power flow[C]//2011 IEEE Power and Energy Society General Meeting, IEEE, Detroit, MI, USA, 2011: 1-6. [15] Xu Xiaoyuan, Yan Z heng. Probabilistic load flow evaluation with hybrid Latin hypercube sampling and multiple linear regression[C]//2015 IEEE Power & Energy Society General Meeting, IEEE, Denver, CO, USA, 2015: 1-5. [16] Xu Qingshan, Yang Yang, Liu Yujun, et al.An improved Latin hypercube sampling method to enhance numerical stability considering the correlation of input variables[J]. IEEE Access, 2017, 5: 15197-15205. [17] 黄江宁, 郭瑞鹏, 赵舫, 等. 电力系统可靠性评估中的分层均匀抽样法[J]. 电力系统自动化, 2012, 36(20): 19-24. Huang Jiangning, Guo Ruipeng, Zhao Fang, et al.Stratified uniform sampling method for power system reliability evaluation[J]. Automation of Electric Power Systems, 2012, 36(20): 19-24. [18] Wang Jianhui, Shahidehpour M, Li Zuyi.Security-constrained unit commitment with volatile wind power generation[J]. IEEE Transactions on Power Systems, 2008, 23(3): 1319-1327. [19] 丁华杰, 宋永华, 胡泽春, 等. 基于风电场功率特性的日前风电预测误差概率分布研究[J]. 中国电机工程学报, 2013, 33(34): 136-144. Ding Huajie, Song Yonghua, Hu Zechun, et al.Probability density function of day-ahead wind power forecast errors based on power curves of wind farms[J]. Proceedings of the CSEE, 2013, 33(34): 136-144. [20] Bae K Y, Jang H S, Sung D K.Hourly solar irradiance prediction based on support vector machine and its error analysis[J]. IEEE Transactions on Power Systems, 2017, 32(2): 935-945. [21] 刘立阳, 吴军基, 孟绍良. 短期风电功率预测误差分布研究[J]. 电力系统保护与控制, 2013, 41(12): 65-70. Liu Liyang, Wu Junji, Meng Shaoliang.Research on error distribution of short-term wind power prediction[J]. Power System Protection and Control, 2013, 41(12): 65-70. [22] 隋心怡, 王瑞刚, 张鸿翔. 一种改进的K-均值聚类算法[J]. 计算机与数字工程, 2018, 46(4): 682-685. Sui Xinyi, Wang Ruigang, Zhang Hongxiang.An improved K-means clustering algorithm[J]. Computer & Digital Engineering, 2018, 46(4): 682-685. [23] 朱连江, 马炳先, 赵学泉. 基于轮廓系数的聚类有效性分析[J]. 计算机应用, 2010, 30(2): 139-141. Zhu Lianjiang, Ma Bingxian, Zhao Xuequan.Clusting validity analysis based on silhouette coefficient[J]. Journal of Computer Application, 2010, 32(2): 139-141.
2020, Vol. 35 
