Integrated Assessment of Transient Angle Stability and Voltage Stability Considering Renewable Energy Sources

doi:10.11930/j.issn.1004-9649.202410057

Abstract

Abstract:

Transient angle instability and transient voltage instability often occur simultaneously and interact with each other, which increases the difficulty of stability assessment and emergency control. To achieve comprehensive guidance for emergency control through stability assessment, an instability mode recongnition method is proposed. This method describes the fault severity using the critical fault clearing time, characterizes the dominance of angle instability and voltage instability based on their occurrence order, and quantifies the coupling degree with the time difference between them. A four-quadrant instability mode recongnition diagram is constructed. To achieve the integrated online assessment, an improved convolutional neural network (CNN) model based on the convolutional block attention module (CBAM) is developed, and a two-stage integrated stability assessment scheme is proposed based on this model. Finally, the New England 10-machine 39-bus system is used for simulation verification, and the results show that the proposed method can achieve comprehensiveness, effectiveness and accuracy. Further, the applicability of the proposed method in systems with renewable energy is demonstrated using a modified 10-machine 39-bus system incorporating renewable energy.

Key words: transient angle stability, transient voltage stability, convolutional block attention modul, instability mode, convolutional neural network.

BU Yuluo, WU Junyong, SHI Fashun, JI Jiashen. Integrated Assessment of Transient Angle Stability and Voltage Stability Considering Renewable Energy Sources[J]. Electric Power, 2025, 58(6): 122-136.

Add to citation manager EndNote|Ris|BibTeX

URL: https://www.electricpower.com.cn/EN/10.11930/j.issn.1004-9649.202410057

https://www.electricpower.com.cn/EN/Y2025/V58/I6/122

Figures/Tables 28

Fig.1 Post-disturbance trajectories of different cases

Fig.2 Four-quadrant diagram of instability mode recognition

Fig.3 Implementation process of IEEAC

Fig.4 Two types of curve patterns of transient angle instability

Fig.5 Two types of curve patterns of transient voltage instability

Fig.6 Instability mode recognition flow

Fig.7 Network structure of CBAM-CNN

Fig.8 Two-stage intelligent assessment flow

Table 1 Data sets obtained by time domain simulation

编号	数据集	应用场景
1	δ_G V_B	第1阶段样本标注
2	δ_G P_eG P_eG s_M T_eM T_mM	第2阶段样本标注
3	V_B θ_B	模型训练

Table 2 The first-stage confusion matrix

样本数	稳定(P)	失稳(P)
稳定(T)	N₁₁	N₁₂
失稳(T)	N₂₁	N₂₂

Table 3 The second-stage confusion matrix

样本数	GT(P)	LS(P)	GT or LS(P)	GT and LS(P)
GT(T)	N₁₁	N₁₂	N₁₃	N₁₄
LS(T)	N₂₁	N₂₂	N₂₃	N₂₄
GT or LS(T)	N₃₁	N₃₂	N₃₃	N₃₄
GT and LS(T)	N₄₁	N₄₂	N₄₃	N₄₄

Table 4 Configurations of the sample set generation

参数	具体设置	种类数
故障类型	三相短路故障	1
故障线路	交流线路（形成孤岛的线路除外）	33
故障位置	10%、30%、50%、70%、90%	5
负荷水平	80%、100%、120%	3
感应电动机占比	50%、60%、70%	3
故障持续时间	3-11周波	9

Fig.9 Visualization of control volume ratios

Fig.10 Safety control of the New England 10-machine 39-bus system

Fig.11 Schematic of the severity of system faults

Fig.12 Schematic of system dominant intensity

Table 5 Relevant information of the four cases

编号	故障线路	主导强度	故障严重程度
A	31	–0.13	–0.055
B	24	0.12	–0.069
C	16	–0.04	–0.055
D	32	–0.17	–0.107

Fig.13 Example of generator tripping (GT)

Fig.14 Example of load shedding (LS)

Fig.15 Example of GT or LS

Fig.16 Example of simultaneous GT and LS

Fig.17 Confusion matrix of TAS and TVS

Table 6 Comparison of the first-stage model training results

模型	功角评估		电压评估
模型	A₂/%	G_mean/%	A₂/%	G_mean/%
DT	94.72	94.67	94.88	94.82
MLP	95.60	95.81	95.29	94.94
GRU	97.05	97.08	96.97	96.95
RF	97.08	97.09	97.19	97.23
CNN	97.27	97.28	97.31	97.43
CBAM-CNN	97.83	97.87	97.68	97.65

Fig.18 The second-stage model training results

Table 7 Comparison of the second-stage model training results

模型	A₄/%	E_c/%
DT	91.27	6.05
MLP	92.14	5.11
GRU	93.28	4.52
RF	93.71	4.48
CNN	94.18	3.61
CBAM-CNN	95.13	2.28

Fig.19 Results of model robustness test

Table 8 The first-stage assessment results of the improved system

算法	功角稳定		电压稳定
算法	A₂/%	G_mean/%	A₂/%	G_mean/%
CBAM-CNN	97.79	97.72	97.49	97.42

Table 9 The second-stage assessment results of the improved system

算法		A₄/%		E_c/%
CBAM-CNN		94.72		4.27

References 34

1	董武, 张健, 周勤勇, 等. 中国电力系统安全稳定性演化综述[J]. 中国电力, 2025, 58 (1): 115- 127.
	DONG Wu, ZHANG Jian, ZHOU Qinyong, et al. An overview of the evolution of security and stability of China’s power system[J]. Electric Power, 2025, 58 (1): 115- 127.
2	AMJADY N. A framework of reliability assessment with consideration effect of transient and voltage stabilities[J]. IEEE Transactions on Power Systems, 2004, 19 (2): 1005- 1014.
3	叶小宁, 王彩霞, 李琼慧, 等. 国外新能源高占比电力系统电力供应保障措施及启示[J]. 中国电力, 2024, 57 (4): 61- 67.
	YE Xiaoning, WANG Caixia, LI Qionghui, et al. Power supply ensuring measures and implications of foreign countries' power systems with high proportion of new energy[J]. Electric Power, 2024, 57 (4): 61- 67.
4	CARRERAS B A, NEWMAN D E, DOBSON I. North American blackout time series statistics and implications for blackout risk[J]. IEEE Transactions on Power Systems, 2016, 31 (6): 4406- 4414.
5	OBUZ S, AYAR M, TREVIZAN R D, et al. Renewable and energy storage resources for enhancing transient stability margins: a PDE-based nonlinear control strategy[J]. International Journal of Electrical Power & Energy Systems, 2020, 116, 105510.
6	汤奕, 崔晗, 李峰, 等. 人工智能在电力系统暂态问题中的应用综述[J]. 中国电机工程学报, 2019, 39 (1): 2- 13, 315.
	TANG Yi, CUI Han, LI Feng, et al. Review on artificial intelligence in power system transient stability analysis[J]. Proceedings of the CSEE, 2019, 39 (1): 2- 13, 315.
7	SHI Z T, YAO W, LI Z P, et al. Artificial intelligence techniques for stability analysis and control in smart grids: Methodologies, applications, challenges and future directions[J]. Applied Energy, 2020, 278, 115733.
8	YANG H, ZHANG W, SHI F, et al. PMU-based model-free method for transient instability prediction and emergency generator-shedding control[J]. International Journal of Electrical Power & Energy Systems, 2019, 105, 381- 393.
9	DONG Y P, XIE X R, WANG K, et al. An emergency-demand-response based under speed load shedding scheme to improve short-term voltage stability[J]. IEEE Transactions on Power Systems, 2017, 32 (5): 3726- 3735.
10	张若愚, 吴俊勇, 李宝琴, 等. 基于迁移学习的电力系统暂态稳定自适应预测[J]. 电网技术, 2020, 44 (6): 2196- 2205.
	ZHANG Ruoyu, WU Junyong, LI Baoqin, et al. Self-adaptive power system transient stability prediction based on transfer learning[J]. Power System Technology, 2020, 44 (6): 2196- 2205.
11	吴俊勇, 张若愚, 季佳伸, 等. 计及漏判/误判代价的两阶段电力系统暂态稳定预测方法[J]. 电力系统自动化, 2020, 44 (24): 44- 52.
	WU Junyong, ZHANG Ruoyu, JI Jiashen, et al. Two-stage transient stability prediction method of power system considering cost of misdetection and false alarm[J]. Automation of Electric Power Systems, 2020, 44 (24): 44- 52.
12	刘建锋, 姚晨曦, 陈乐乐. 基于门控时空图神经网络的电力系统暂态稳定评估[J]. 电力科学与技术学报, 2023, 38 (2): 214- 223.
	LIU Jianfeng, YAO Chenxi, CHEN Lele. Power system transient stability assessment based on gating spatial temporal graph neural network[J]. Journal of Electric Power Science and Technology, 2023, 38 (2): 214- 223.
13	张建新, 蔡锱涵, 李诗旸, 等. 利用网络等值进行图降维的图注意力暂态功角稳定评估模型[J]. 南方电网技术, 2024, 18 (4): 30- 40.
	ZHANG Jianxin, CAI Zihan, LI Shiyang, et al. Transient power angle stability evaluation model for graph attention using network equivalence for graph dimensionality reduction[J]. Southern Power System Technology, 2024, 18 (4): 30- 40.
14	张晓英, 高金, 王琨, 等. 基于电压时间序列的电力系统暂态电压稳定分析[J]. 智慧电力, 2021, 49 (3): 51- 58.
	ZHANG Xiaoying, GAO Jin, WANG Kun, et al. Transient voltage stability analysis of power system based on voltage time series[J]. Smart Power, 2021, 49 (3): 51- 58.
15	SU H Y, LIU T Y. Enhanced-online-random-forest model for static voltage stability assessment using wide area measurements[J]. IEEE Transactions on Power Systems, 2018, 33 (6): 6696- 6704.
16	周挺, 杨军, 詹祥澎, 等. 一种数据驱动的暂态电压稳定评估方法及其可解释性研究[J]. 电网技术, 2021, 45 (11): 4416- 4425.
	ZHOU Ting, YANG Jun, ZHAN Xiangpeng, et al. Data-driven method and interpretability analysis for transient voltage stability assessment[J]. Power System Technology, 2021, 45 (11): 4416- 4425.
17	朱林, 张健, 陈达, 等. 面向暂态电压稳定评估的卷积神经网络输入特征构建方法[J]. 电力系统自动化, 2022, 46 (1): 85- 93.
	ZHU Lin, ZHANG Jian, CHEN Da, et al. Construction method for input features of convolutional neural network for transient voltage stability assessment[J]. Automation of Electric Power Systems, 2022, 46 (1): 85- 93.
18	黎晓, 刘崇茹, 辛蜀骏, 等. 暂态功角稳定与暂态电压稳定的耦合机理分析与耦合强度评估指标[J]. 中国电机工程学报, 2021, 41 (15): 5091- 5107.
	LI Xiao, LIU Chongru, XIN Shujun, et al. Coupling mechanism analysis and coupling strength evaluation index of transient power angle stability and transient voltage stability[J]. Proceedings of the CSEE, 2021, 41 (15): 5091- 5107.
19	吴为, 汤涌, 孙华东, 等. 电力系统暂态功角失稳与暂态电压失稳的主导性识别[J]. 中国电机工程学报, 2014, 34 (31): 5610- 5617.
	WU Wei, TANG Yong, SUN Huadong, et al. The recognition of principal mode between rotor angle instability and transient voltage instability[J]. Proceedings of the CSEE, 2014, 34 (31): 5610- 5617.
20	WANG Y H, SUN Y J, MEI S W. A method of distinguishing short-term voltage stability from rotor angle stability and its application[C]//IEEE PES Innovative Smart Grid Technologies. Tianjin, China. IEEE, 2012: 1–5.
21	HAN T, CHEN Y B, MA J, et al. Surrogate modeling-based multi-objective dynamic VAR planning considering short-term voltage stability and transient stability[J]. IEEE Transactions on Power Systems, 2018, 33 (1): 622- 633.
22	顾卓远, 汤涌. 基于响应信息的电压与功角稳定实时紧急控制方案[J]. 中国电机工程学报, 2014, 34 (28): 4876- 4885.
	GU Zhuoyuan, TANG Yong. Response-information based real-time power system voltage stability and angle stability emergency control scheme[J]. Proceedings of the CSEE, 2014, 34 (28): 4876- 4885.
23	孙黎霞, 彭嘉杰, 白景涛, 等. 结合图嵌入算法的电力系统多任务暂态稳定评估[J]. 电力系统自动化, 2022, 46 (2): 83- 91.
	SUN Lixia, PENG Jiajie, BAI Jingtao, et al. Multi-task transient stability assessment of power system incorporating graph embedding algorithm[J]. Automation of Electric Power Systems, 2022, 46 (2): 83- 91.
24	史法顺, 吴俊勇, 季佳伸, 等. 基于深度学习的电力系统暂态电压与暂态功角稳定一体化超前评估[J]. 电网技术, 2023, 47 (2): 741- 758.
	SHI Fashun, WU Junyong, JI Jiashen, et al. Integrated advance assessment of power system transient voltage and transient angle stability based on deep learning[J]. Power System Technology, 2023, 47 (2): 741- 758.
25	史法顺, 吴俊勇, 吴昊衍, 等. 基于深度学习的电力系统暂态功角与暂态电压稳定裕度一体化评估[J]. 电网技术, 2023, 47 (2): 731- 740.
	SHI Fashun, WU Junyong, WU Haoyan, et al. Integrated evaluation of power system transient power angle and transient voltage stability margin based on deep learning[J]. Power System Technology, 2023, 47 (2): 731- 740.
26	石重托, 姚伟, 黄彦浩, 等. 基于SE-CNN和仿真数据的电力系统主导失稳模式智能识别[J]. 中国电机工程学报, 2022, 42 (21): 7719- 7731.
	SHI Zhongtuo, YAO Wei, HUANG Yanhao, et al. Power system dominant instability mode identification based on convolutional neural networks with squeeze and excitation block and simulation data[J]. Proceedings of the CSEE, 2022, 42 (21): 7719- 7731.
27	ZHANG R F, YAO W, SHI Z T, et al. A graph attention networks-based model to distinguish the transient rotor angle instability and short-term voltage instability in power systems[J]. International Journal of Electrical Power & Energy Systems, 2022, 137, 107783.
28	ZHOU Y Z, XU T, YE L, et al. Transient rotor angle and voltage stability discrimination based on deep convolutional neural network with multiple inputs[C]//2021 IEEE 4th International Electrical and Energy Conference (CIEEC). Wuhan, China. IEEE, 2021: 1–6.
29	LASHGARI M, SHAHRTASH S M. Fast online decision tree-based scheme for predicting transient and short-term voltage stability status and determining driving force of instability[J]. International Journal of Electrical Power & Energy Systems, 2022, 137, 107738.
30	KUNDUR P, PASERBA J, AJJARAPU V, et al. Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions[J]. IEEE Transactions on Power Systems, 2004, 19 (3): 1387- 1401.
31	张海. 基于扩展等面积法的电力系统暂态稳定分析[D]. 太原: 太原理工大学, 2006.
	ZHANG Hai. Power system transient stability analysis based on EEAC method[D]. Taiyuan: Taiyuan University of Technology, 2006.
32	顾卓远, 汤涌, 易俊, 等. 电力系统功角失稳与局部感应电动机失稳相互影响机理分析[J]. 电网技术, 2017, 41 (8): 2499- 2505.
	GU Zhuoyuan, TANG Yong, YI Jun, et al. Study on mechanism of interrelationship between power system angle stability and induction motor stability[J]. Power System Technology, 2017, 41 (8): 2499- 2505.
33	WOO S, PARK J, LEE J Y, et al. CBAM: convolutional block attention module[M]//Computer Vision – ECCV 2018. Cham: Springer International Publishing2018: 3–19.
34	李宝琴, 吴俊勇, 邵美阳, 等. 基于集成深度置信网络的精细化电力系统暂态稳定评估[J]. 电力系统自动化, 2020, 44 (6): 17- 26.
	LI Baoqin, WU Junyong, SHAO Meiyang, et al. Refined transient stability evaluation for power system based on ensemble deep belief network[J]. Automation of Electric Power Systems, 2020, 44 (6): 17- 26.

[1]	XU Yanchun, JIANG Weijun, SUN Sihan, MI Lu. Quantitative Assessment Method for Transient Voltage of Distribution Network with High-Penetration Wind Power [J]. Electric Power, 2022, 55(7): 152-162.
[2]	CHEN Xin-qi, SUN Wei-zhen, ZHOU Yi-fen, CHEN Zhang-wei, HUANG Hong-yang. Effect of Power System Voltage Regulator on Voltage Stability of Zhejiang Power System [J]. Electric Power, 2013, 46(12): 16-19.