Static Voltage Stability Region Considering Limit Induced Bifurcation

doi:10.11930/j.issn.1004-9649.202304063

Abstract

Abstract:

With the widespread application of a high percentage of renewable energy in power systems, the volatility and randomness of renewable energy pose challenges for static voltage stability assessment of power systems. The static voltage stability region (SVSR) of power systems can comprehensively analyze and monitor the voltage stability of power systems. The key is to construct the stability region boundary quickly and accurately. To address the problems of large computational effort of the traditional continuous power flow method and nonlinear programming method, an SVSR boundary construction optimization model based on the topological properties of SVSR boundaries is proposed, in which the adjacent boundary points are directly calculated from known boundary points by a prediction-correction method based on the property that the boundaries are continuous and smooth. Based on this model, a limit induced bifurcation (LIB) identification method is proposed to construct the SVSR boundary considering LIB. Finally, the feasibility and accuracy of the proposed method are verified by case analysis.

Key words: voltage stability, static voltage stability region, saddle node bifurcation, limit induced bifurcation

Daobing LIU, Yue QI, Shichun LI, Miaosheng BAO, Yingying GUO, Juecen LI. Static Voltage Stability Region Considering Limit Induced Bifurcation[J]. Electric Power, 2024, 57(4): 118-129.

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URL: https://www.electricpower.com.cn/EN/10.11930/j.issn.1004-9649.202304063

https://www.electricpower.com.cn/EN/Y2024/V57/I4/118

Figures/Tables 16

References 26

1	谢小荣, 贺静波, 毛航银, 等. “双高” 电力系统稳定性的新问题及分类探讨[J]. 中国电机工程学报, 2021, 41 (2): 461- 475.
	XIE Xiaorong, HE Jingbo, MAO Hangyin, et al. New issues and classification of power system stability with high shares of renewables and power electronics[J]. Proceedings of the CSEE, 2021, 41 (2): 461- 475.
2	肖先勇, 郑子萱. “双碳” 目标下新能源为主体的新型电力系统: 贡献、关键技术与挑战[J]. 工程科学与技术, 2022, 54 (1): 47- 59.
	XIAO Xianyong, ZHENG Zixuan. New power systems dominated by renewable energy towards the goal of emission peak & carbon neutrality: contribution, key techniques and challenges[J]. Advanced Engineering Sciences, 2022, 54 (1): 47- 59.
3	齐金山, 姚良忠, 廖思阳, 等. 高比例新能源电力系统静态电压稳定裕度在线概率评估[J]. 电力系统保护与控制, 2023, 51 (5): 47- 57.
	QI Jinshan, YAO Liangzhong, LIAO Siyang, et al. Online probabilistic assessment of static voltage stability margin for power systems with a high proportion of renewable energy[J]. Power System Protection and Control, 2023, 51 (5): 47- 57.
4	吴亚宁, 罗毅, 雷成, 等. 基于改进型PEM和L指标的含风电场电力系统静态电压稳定评估[J]. 中国电力, 2022, 55 (9): 192- 203.
	WU Yaning, LUO Yi, LEI Cheng, et al. Steady-state voltage stability evaluation of power system containing wind farm based on improved PEM and L index[J]. Electric Power, 2022, 55 (9): 192- 203.
5	刘世超, 刘艳, 张慧, 等. 基于安全域校核的含风电系统负荷恢复优化[J]. 电网技术, 2021, 45 (8): 3061- 3069.
	LIU Shichao, LIU Yan, ZHANG Hui, et al. Load restoration optimization of wind power integrated system considering security region examination[J]. Power System Technology, 2021, 45 (8): 3061- 3069.
6	陈中, 朱政光, 严俊, 等. 基于交直流混联系统静态安全域安全校正控制后的优化调度[J]. 电力自动化设备, 2021, 41 (4): 139- 147, 169.
	CHEN Zhong, ZHU Zhengguang, YAN Jun, et al. Optimal dispatch after security correction control based on steady-state security region of AC/DC hybrid system[J]. Electric Power Automation Equipment, 2021, 41 (4): 139- 147, 169.
7	刘石川, 雷轲, 刘紫玉, 等. 基于静态安全域的含新能源输电网随机最优潮流[J]. 电力系统及其自动化学报, 2023, 35 (3): 94- 101.
	LIU Shichuan, LEI Ke, LIU Ziyu, et al. Stochastic optimal power flow in transmission grid with renewable energy based on steady-state security region[J]. Proceedings of the CSU-EPSA, 2023, 35 (3): 94- 101.
8	YU Y, LIU Y, QIN C, et al. Theory and method of power system integrated security region irrelevant to operation states: an introduction[J]. Engineering, 2020, 6 (7): 754- 777, 854–880. DOI
9	陈波, 陈秋逸, 郑富永, 等. 基于电压灵敏度的交直流电力系统静态电压安全域评估方法[J]. 智慧电力, 2022, 50 (6): 28- 34.
	CHEN Bo, CHEN Qiuyi, ZHENG Fuyong, et al. Evaluation method of static voltage security region of AC/DC power system based on voltage sensitivity[J]. Smart Power, 2022, 50 (6): 28- 34.
10	LAI Q P, LIU C X, SUN K. Analytical static voltage stability boundary based on holomorphic embedding[J]. International Journal of Electrical Power & Energy Systems, 2022, 134, 107386.
11	李雪, 张琳玮, 姜涛, 等. 基于拉格朗日乘子的电力系统安全域边界通用搜索方法[J]. 中国电机工程学报, 2021, 41 (15): 5139- 5153.
	LI Xue, ZHANG Linwei, JIANG Tao, et al. General algorithm for exploring security region boundary in power systems using Lagrange multiplier[J]. Proceedings of the CSEE, 2021, 41 (15): 5139- 5153.
12	LI X, ZHANG L W, JIANG T, et al. Relaxed decoupled direct calculation of voltage collapse points and its application in static voltage stability region boundary formation[J]. International Journal of Electrical Power & Energy Systems, 2021, 125, 106452.
13	CHIANG H D, FLUECK A J, SHAH K S, et al. CPFLOW: a practical tool for tracing power system steady-state stationary behavior due to load and generation variations[J]. IEEE Transactions on Power Systems, 1995, 10 (2): 623- 634. DOI
14	王妍, 高山. 基于改进Chord法的电力系统连续潮流计算新方法[J]. 电力系统保护与控制, 2022, 50 (4): 112- 119.
	WANG Yan, GAO Shan. A new method of power system continuous flow calculation based on an improved Chord method[J]. Power System Protection and Control, 2022, 50 (4): 112- 119.
15	金吉良, 李小腾, 梁航, 等. 基于改进连续潮流法的电压稳定极限计算方法[J]. 智慧电力, 2021, 49 (3): 46- 50, 87.
	JIN Jiliang, LI Xiaoteng, LIANG Hang, et al. Calculation method of voltage stability limit based on improved continuous power flow method[J]. Smart Power, 2021, 49 (3): 46- 50, 87.
16	QIU Y W, WU H, SONG Y H, et al. Global approximation of static voltage stability region boundaries considering generator reactive power limits[J]. IEEE Transactions on Power Systems, 2018, 33 (5): 5682- 5691. DOI
17	NEVES L S, COSTA ALBERTO L F. On the computation of the locally closest bifurcation point considering loading uncertainties and reactive power limits[J]. IEEE Transactions on Power Systems, 2020, 35 (5): 3885- 3894. DOI
18	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.
19	冯卓诚, 万凯遥, 姜彤. 基于渐近数值法的静态电压稳定域边界高阶拟合方法[J]. 电力系统自动化, 2020, 44 (7): 100- 106. DOI
	FENG Zhuocheng, WAN Kaiyao, JIANG Tong. High-order fitting method of boundary for static voltage stability region based on asymptotic numerical method[J]. Automation of Electric Power Systems, 2020, 44 (7): 100- 106. DOI
20	LIN S J, YANG Y R, LIU M B, et al. Static voltage stability margin calculation of power systems with high wind power penetration based on the interval optimisation method[J]. IET Renewable Power Generation, 2020, 14 (10): 1728- 1737. DOI
21	姜涛, 张明宇, 崔晓丹, 等. 电力系统静态电压稳定域边界快速搜索的优化模型[J]. 电工技术学报, 2018, 33 (17): 4167- 4179.
	JIANG Tao, ZHANG Mingyu, CUI Xiaodan, et al. A novel optimization model to explore static voltage stability region boundary in bulk power systems[J]. Transactions of China Electrotechnical Society, 2018, 33 (17): 4167- 4179.
22	YANG T K, YU Y X. Steady-state security region-based voltage/var optimization considering power injection uncertainties in distribution grids[J]. IEEE Transactions on Smart Grid, 2019, 10 (3): 2904- 2911. DOI
23	JIANG T, WAN K, FENG Z. Boundary derivative direct method for computing saddle node bifurcation points in voltage stability analysis[J]. International Journal of Electrical Power & Energy Systems, 2019, 112 (11): 199- 208.
24	邓慧琼, 陈心耘, 吴俊媛, 等. 兼顾电压稳定和连锁故障触发的电网预防策略研究[J]. 智慧电力, 2022, 50 (1): 1- 6, 36.
	DENG Huiqiong, CHEN Xinyun, WU Junyuan, et al. Prevention strategy of power grid considering voltage stability and cascading outage triggering[J]. Smart Power, 2022, 50 (1): 1- 6, 36.
25	李生虎, 夏伟健, 叶剑桥, 等. 静态电压稳定分析中L指标与特征值换算关系及L阈值确定方法[J]. 电网技术, 2023, 47 (9): 3828- 3837.
	LI Shenghu, XIA Weijian, YE Jianqiao, et al. Exchange relation with eigenvalues and threshold determination of L index for power system static voltage stability analysis[J]. Power System Technology, 2023, 47 (9): 3828- 3837.
26	马兆兴, 万秋兰, 李洪美. 考虑极限诱导分岔的电压稳定研究[J]. 电力系统保护与控制, 2011, 39 (20): 24- 29, 37.
	MA Zhaoxing, WAN Qiulan, LI Hongmei. Research on voltage stability analysis of limit induced bifurcation[J]. Power System Protection and Control, 2011, 39 (20): 24- 29, 37.

标号	坐标	标号	坐标
0	（0.1006, 0.0979）	12	（0.1279, 0.0843）
1	（0.0919, 0.1019）	13	（0.1378, 0.0790）
2	（0.0833, 0.1057）	14	（0.1481, 0.0732）
3	（0.0747, 0.1093）	15	（0.1589, 0.0668）
4	（0.0660, 0.1128）	16	（0.1704, 0.0598）
5	（0.0569, 0.1162）	17	（0.1825, 0.0520）
6	（0.0472, 0.1197）	18	（0.1953, 0.0434）
7	（0.0363, 0.1233）	19	（0.2087, 0.0339）
8	（0.0228, 0.1273）	20	（0.2228, 0.0235）
9	（–0.0023, 0.1327）	21	（0.2373, 0.0122）
10	（0.1094, 0.0979）	22	（0.2492, 0.0）
11	（0.1185, 0.0892）

标号	坐标	标号	坐标
0	（0.1006, 0.0979）	12	（0.1279, 0.0843）
1	（0.0919, 0.1019）	13	（0.1378, 0.0790）
2	（0.0833, 0.1057）	14	（0.1481, 0.0732）
3	（0.0747, 0.1093）	15	（0.1589, 0.0668）
4	（0.0660, 0.1128）	16	（0.1704, 0.0598）
5	（0.0569, 0.1162）	17	（0.1825, 0.0520）
6	（0.0472, 0.1197）	18	（0.1953, 0.0434）
7	（0.0363, 0.1233）	19	（0.2087, 0.0339）
8	（0.0228, 0.1273）	20	（0.2228, 0.0235）
9	（–0.0023, 0.1327）	21	（0.2373, 0.0122）
10	（0.1094, 0.0979）	22	（0.2492, 0.0）
11	（0.1185, 0.0892）

标号	最小特征值	标号	最小特征值	标号	最小特征值
1	0.0	10	0.0067	19	0.0214
2	0.0	11	0.0084	20	0.0230
3	0.0	12	0.0100	21	0.0247
4	0.0	13	0.0117	22	0.0264
5	0.0	14	0.0133	23	0.0281
6	0.0	15	0.0149	24	0.0299
7	0.0013	16	0.0165	25	0.0317
8	0.0031	17	0.0181	26	0.0336
9	0.0050	18	0.0197

标号	最小特征值	标号	最小特征值	标号	最小特征值
1	0.0	10	0.0067	19	0.0214
2	0.0	11	0.0084	20	0.0230
3	0.0	12	0.0100	21	0.0247
4	0.0	13	0.0117	22	0.0264
5	0.0	14	0.0133	23	0.0281
6	0.0	15	0.0149	24	0.0299
7	0.0013	16	0.0165	25	0.0317
8	0.0031	17	0.0181	26	0.0336
9	0.0050	18	0.0197

场景		SVSR坐标轴变量
1		负荷节点4的有功功率和无功功率
2		负荷节点7和发电机节点8的有功功率
3		负荷节点9和10的有功功率