Probabilistic-Interval Power Flow and Sensitivity Analysis Using Double Layer Surrogate Method
Wang Chenxu1, Tang Fei1, Liu Dichen1, Gao Xin1, Zhou Yixi2
1. School of Electrical Engineering and Automation Wuhan University Wuhan 430072 China; 2. Hangzhou Power Supply Company State Grid Zhejiang Electric Power Co. Ltd Hangzhou 310000 China
Abstract With the increasing complexity of uncertainties in power systems, the co-existence of random and interval variables makes it challenging to accurately obtain systems’ operating states by using probabilistic or interval power flow calculations. To cope with this issue, this paper proposes a double layer surrogate method for probabilistic-interval power flow analysis. The proposed method can obtain the upper and lower surrogate models based on a few times deterministic power flow calculations. Then, the surrogate models are used to solve a large number of deterministic power flow calculations required in the conventional probabilistic-interval power flow method, and the probability boxes of output variables can be obtained with high efficiency. In addition, a sensitivity index is proposed to describe the characteristics of output variables, and the sensitivity analysis is performed using the proposed method to identify the importance of input interval variables that affect output variables. The accuracy and efficiency of the proposed method are validated on the IEEE 118-bus test system by comparing the existing methods. The sensitivity analysis can identify the key interval variables for the output variables and reveal the relationship between the operating states and the input interval variables.
Wang Chenxu,Tang Fei,Liu Dichen等. Probabilistic-Interval Power Flow and Sensitivity Analysis Using Double Layer Surrogate Method[J]. Transactions of China Electrotechnical Society, 2022, 37(5): 1181-1193.
[1] Jordehi A R.How to deal with uncertainties in electric power systems? a review[J]. Renewable and Sustainable Energy Reviews, 2018, 96: 145-155. [2] 康重庆, 姚良忠. 高比例可再生能源电力系统的关键科学问题与理论研究框架[J]. 电力系统自动化, 2017, 41(9): 2-11. Kang Chongqing, Yao Liangzhong.Key scientific issues and theoretical research framework for power systems with high proportion of renewable energy[J]. Automation of Electric Power Systems, 2017, 41(9): 2-11. [3] Prusty B R, Jena D.A critical review on probabilistic load flow studies in uncertainty constrained power systems with photovoltaic generation and a new approach[J]. Renewable and Sustainable Energy Reviews, 2017, 69: 1286-1302. [4] 廖小兵, 刘开培, 乐健, 等. 电力系统区间潮流计算方法综述[J]. 中国电机工程学报, 2019, 39(2): 447-458. Liao Xiaobing, Liu Kaipei, Le Jian, et al.Review on interval power flow calculation methods in power system[J]. Proceedings of the CSEE, 2019, 39(2): 447-458. [5] 谢桦, 任超宇, 郭志星, 等. 基于聚类抽样的随机潮流计算[J]. 电工技术学报, 2020, 35(23): 4940-4948. Xie Hua, Ren Chaoyu, Guo Zhixing, et al.Stochastic load flow calculation method based on clustering and sampling[J]. Transactions of China Electrotechnical Society, 2020, 35(23): 4940-4948. [6] 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. [7] Wang Chenxu, Liu Chengxi, Tang Fei, et al.A scenario-based analytical method for probabilistic load flow analysis[J]. Electric Power Systems Research, 2020, 181: 106193. [8] 李聪聪, 王彤, 相禹维, 等. 基于改进高斯混合模型的概率潮流解析方法[J]. 电力系统保护与控制, 2020, 48(10): 146-155. Li Congcong, Wang Tong, Xiang Yuwei, et al.Analytical method based on improved Gaussian mixture model for probabilistic load flow[J]. Power System Protection and Control, 2020, 48(10): 146-155. [9] 何琨, 徐潇源, 严正, 等. 基于稀疏混沌多项式展开的孤岛微电网概率潮流计算[J]. 电力系统自动化, 2019, 43(2): 67-75. He Kun, Xu Xiaoyuan, Yan Zheng, et al.Probabilistic power flow calculation of islanded microgrid based on sparse polynomial chaos expansion[J]. Automation of Electric Power Systems, 2019, 43(2): 67-75. [10] 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. [11] 杜萍静, 杨明, 曹良晶, 等. 含电压源换流器交直流系统的仿射潮流算法[J]. 电工技术学报, 2020, 35(5): 1106-1117. Du Pingjing, Yang Ming, Cao Liangjing, et al.Affine power flow algorithm for AC/DC systems with voltage source converter[J]. Transactions of China Electrotechnical Society, 2020, 35(5): 1106-1117. [12] 廖小兵, 刘开培, 张亚超, 等. 基于区间泰勒展开的不确定性潮流分析[J]. 电工技术学报, 2018, 33(4): 750-758. Liao Xiaobing, Liu Kaipei, Zhang Yachao, et al.Uncertain power flow analysis based on interval Taylor expansion[J]. Transactions of China Electrotechnical Society, 2018, 33(4): 750-758. [13] Luo Jinqing, Shi Libao, Ni Yixin.Uncertain power flow analysis based on evidence theory and affine arithmetic[J]. IEEE Transactions on Power Systems, 2018, 33(1): 1113-1115. [14] 鲍海波, 韦化, 郭小璇, 等. 考虑风电不确定性的概率区间潮流模型与算法[J]. 中国电机工程学报, 2017, 37(19): 5633-5642. Bao Haibo, Wei Hua, Guo Xiaoxuan, et al.Model and algorithm of probabilistic interval power flow considering wind power uncertainty[J]. Proceedings of the CSEE, 2017, 37(19): 5633-5642. [15] Guo Xiaoxuan, Gong Renxi, Bao Haibo, et al.Hybrid stochastic and interval power flow considering uncertain wind power and photovoltaic power[J]. IEEE Access, 2019, 7: 85090-85097. [16] Wang Chun, Ao Xin, Fu Wenbin.Three-phase power flow calculation considering probability and interval uncertainties for power distribution systems[J]. IET Generation, Transmission & Distribution, 2019, 13(15): 3334-3345. [17] Wang Chenxu, Liu Dichen, Tang Fei, et al.A clustering-based analytical method for hybrid probabilistic and interval power flow[J]. International Journal of Electrical Power & Energy Systems, 2021, 126: 106605. [18] Hu Xiaoyun, Zhao Xia, Feng Xinxin.Probabilistic-interval energy flow analysis of regional integrated electricity and gas system considering multiple uncertainties and correlations[J]. IEEE Access, 2019, 7: 178209-178223. [19] 孙鑫, 王博, 陈金富, 等. 基于稀疏多项式混沌展开的可用输电能力不确定性量化分析[J]. 中国电机工程学报, 2019, 39(10): 1-10. Sun Xin, Wang Bo, Chen Jinfu, et al.Sparse polynomial chaos expansion based uncertainty quantification for avaiable transfer capability[J]. Proceedings of the CSEE, 2019, 39(10): 1-10. [20] 胡潇云, 赵霞, 冯欣欣. 基于稀疏多项式混沌展开的区域电-气联合系统全局灵敏度分析[J]. 电工技术学报, 2020, 35(13): 2805-2816. Hu Xiaoyun, Zhao Xia, Feng Xinxin.Global sensitivity analysis for regional integrated electricity and gas system based on sparse polynomial chaos expansion[J]. Transactions of China Electrotechnical Society, 2020, 35(13): 2805-2816. [21] 鲍海波, 郭小璇. 求解含风电相关性区间潮流的仿射变换最优场景法[J]. 电力系统保护与控制, 2020, 48(18): 114-122. Bao Haibo, Guo Xiaoxuan.Optimal scenario algorithm based on affine transformation applied interval power flow considering correlated wind power[J]. Power System Protection and Control, 2020, 48(18): 114-122. [22] Ran Xiaohong, Leng Shipeng, Liu Kaipei.A novel affine arithmetic method with missed the triangular domain with uncertainties[J]. IEEE Transactions on Smart Grid, 2020, 11(2): 1430-1439. [23] 陈丽娜, 张智晟, 于道林. 基于广义需求侧资源聚合的电力系统短期负荷预测模型[J]. 电力系统保护与控制, 2018, 46(15): 45-51. Chen Lina, Zhang Zhisheng, Yu Daolin.Short-term load forecasting model of power system based on generalized demand side resources aggregation[J]. Power System Protection and Control, 2018, 46(15): 45-51. [24] 郭茜, 匡洪海, 王建辉, 等. 单机风电功率人工智能预测模型综述[J]. 电气技术, 2020, 21(2): 1-6. Guo Qian, Kuang Honghai, Wang Jianhui, et al.Summary of artificial intelligence prediction model for single wind power[J]. Electrical Engineering, 2020, 21(2): 1-6. [25] Baghaee H R, Mirsalim M, Gharehpetian G B, et al.Fuzzy unscented transform for uncertainty quantification of correlated wind/PV microgrids: possibilistic-probabilistic power flow based on RBFNNs[J]. IET Renewable Power Generation, 2017, 11(6): 867-877. [26] Li Xu, Gong Chunlin, Gu Liangxian, et al.A sequential surrogate method for reliability analysis based on radial basis function[J]. Structural Safety, 2018, 73: 42-53. [27] Sun Xin, Tu Qingrui, Chen Jinfu, et al.Probabilistic load flow calculation based on sparse polynomial chaos expansion[J]. IET Generation, Transmission & Distribution, 2018, 12(11): 2735-2744. [28] Zimmerman R D, Murillo-Sanchez 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. [29] Bi Sifeng, Broggi M, Wei Pengfei, et al.The Bhattacharyya distance: enriching the P-box in stochastic sensitivity analysis[J]. Mechanical Systems and Signal Processing, 2019, 129: 265-281.
2022, Vol. 37 
