Optimization of Installed Wind Power Capacity Considering Dynamic Frequency Constraints and Multiple Uncertainties

doi:10.16183/j.cnki.jsjtu.2023.474

Abstract

Abstract:

As the installed capacity of wind power continues to increase, the frequency security of new power system becomes increasingly significant. To guarantee the frequency security of the system, improve the frequency regulation capability of the system, and determine an optimal wind power installed capacity, a wind power installed capacity optimization model considering dynamic frequency constraints as well as load-side inertia is proposed. First, the dynamic frequency response model with load-side inertia is derived. Then, fuzzy opportunity constraints are introduced considering the uncertainty of wind power, load, and load-side inertia. Taking into account the dynamic frequency constraints, the model incorporates multiple uncertainty fuzzy opportunity constraints, in which the uncertainty constraints are clearly converted into equivalence classes. Finally, to address the dynamic frequency-constrained nonlinear characteristic, the optimization problem is partitioned into a main problem and sub-problems for solution. The validity and feasibility of the proposed model are validated by using an improved 10-machine system.

Key words: dynamic frequency constraints, load-side inertia, fuzzy chance constraints, multiple uncertainties, optimization of installed wind power capacity

CLC Number:

TM614

YE Jing, HE Jiehui, ZHANG Lei, CAI Junwen, LIN Yuqi, XIE Jihao. Optimization of Installed Wind Power Capacity Considering Dynamic Frequency Constraints and Multiple Uncertainties[J]. Journal of Shanghai Jiao Tong University, 2025, 59(9): 1292-1303.

Figures/Tables 18

Fig.1

Fig.2

Tab.1

Tab.2

Tab.3

Tab.4

Fig.3

Fig.4

Tab.5

Tab.6

Fig.5

Fig.6

Fig.7

Tab.7

Tab.8

Tab.9

Fig.8

Fig.9

References 31

[1]	夏云峰. 部分国家2022年风电开发与利用概况[J]. 风能, 2023(2): 42-45.
	XIA Yunfeng. Overview of wind power development and utilization in some countries in 2022[J]. Wind Energy, 2023(2): 42-45.
[2]	刘福锁, 卿梦琪, 唐飞, 等. 计及风电一次调频和频率约束的风电占比极限值计算[J]. 电网技术, 2021, 45(3): 863-870.
	LIU Fusuo, QING Mengqi, TANG Fei, et al. Limit proportion calculation of wind power considering primary frequency modulation and frequency constraints[J]. Power System Technology, 2021, 45(3): 863-870.
[3]	江岳文, 陈梅森. 兼顾风电接纳与风电商利益的风电装机容量分层优化[J]. 电力自动化设备, 2017, 37(4): 52-59.
	JIANG Yuewen, CHEN Meisen. Hierarchical wind-power installation capacity optimization considering grid wind-power accommodation and wind-power supplier’s benefit[J]. Electric Power Automation Equipment, 2017, 37(4): 52-59.
[4]	韩小琪, 孙寿广, 戚庆茹. 从系统调峰角度评估电网接纳风电能力[J]. 中国电力, 2010, 43(6): 16-19.
	HAN Xiaoqi, SUN Shouguang, QI Qingru. Evaluation of wind power penetration limit from peak regulation[J]. Electric Power, 2010, 43(6): 16-19.
[5]	元博, 徐志成, 刘俊, 等. 多区域新能源接纳能力评估模型研究及应用[J]. 中国电力, 2019, 52(12): 132-139.
	YUAN Bo, XU Zhicheng, LIU Jun, et al. Research and application of multi-area new energy integration capability evaluation model[J]. Electric Power, 2019, 52(12): 132-139.
[6]	CETINAY H, KUIPERS F A, GUVEN A N. Optimal siting and sizing of wind farms[J]. Renewable Energy, 2017, 101: 51-58.
[7]	王利利, 王皓, 任洲洋, 等. 计及灵活资源调节潜力的高压配电网新能源接纳能力评估[J]. 中国电力, 2022, 55(10): 124-131.
	WANG Lili, WANG Hao, REN Zhouyang, et al. Evaluation of renewable energy accommodation capacity of high voltage distribution networks considering regulation potential of flexible resources[J]. Electric Power, 2022, 55(10): 124-131.
[8]	王宝财, 孙华东, 李文锋, 等. 考虑动态频率约束的电力系统最小惯量评估[J]. 中国电机工程学报, 2022, 42(1): 114-127.
	WANG Baocai, SUN Huadong, LI Wenfeng, et al. Minimum inertia estimation of power system considering dynamic frequency constraints[J]. Proceedings of the CSEE, 2022, 42(1): 114-127.
[9]	姜欣, 陈红坤, 向铁元, 等. 考虑调峰特性的电网风电接入能力分析[J]. 电力自动化设备, 2014, 34(12): 13-18.
	JIANG Xin, CHEN Hongkun, XIANG Tieyuan, et al. Wind power penetration capacity considering peak regulation characteristics[J]. Electric Power Automation Equipment, 2014, 34(12): 13-18.
[10]	黄杨, 陈红坤, 回俊龙, 等. 考虑风电接纳能力约束的风机装机容量优化[J]. 武汉大学学报(工学版), 2015, 48(6): 842-847.
	HUANG Yang, CHEN Hongkun, HUI Junlong, et al. Wind power capacity optimization considering accommodation of wind power constraints[J]. Engineering Journal of Wuhan University, 2015, 48(6): 842-847.
[11]	张旭, 罗先觉, 赵峥, 等. 以风电场效益最大为目标的风电装机容量优化[J]. 电网技术, 2012, 36(1): 237-240.
	ZHANG Xu, LUO Xianjue, ZHAO Zheng, et al. Installed capacity optimization of wind turbine generators considering maximum economic benefit of wind farm[J]. Power System Technology, 2012, 36(1): 237-240.
[12]	贺海磊, 张彦涛, 孙骁强, 等. 考虑频率安全约束的西北电网新能源开发及直流外送规模评估方法[J]. 中国电机工程学报, 2021, 41(14): 4753-4762.
	HE Hailei, ZHANG Yantao, SUN Xiaoqiang, et al. Evaluation method of renewable energy development scale and DC transmission scale of China northwest power grid by considering frequency security constraints[J]. Proceedings of the CSEE, 2021, 41(14): 4753-4762.
[13]	文云峰, 杨伟峰, 林晓煌. 低惯量电力系统频率稳定分析与控制研究综述及展望[J]. 电力自动化设备, 2020, 40(9): 211-222.
	WEN Yunfeng, YANG Weifeng, LIN Xiaohuang. Review and prospect of frequency stability analysis and control of low-inertia power systems[J]. Electric Power Automation Equipment, 2020, 40(9): 211-222.
[14]	王博, 杨德友, 蔡国伟. 高比例新能源接入下电力系统惯量相关问题研究综述[J]. 电网技术, 2020, 44(8): 2998-3007.
	WANG Bo, YANG Deyou, CAI Guowei. Review of research on power system inertia related issues in the context of high penetration of renewable power generation[J]. Power System Technology, 2020, 44(8): 2998-3007.
[15]	周涛, 黄菊, 韩汝帅, 等. 综合惯性控制下风机惯性支撑能力分析及等效惯量评估[J]. 上海交通大学学报, 2024, 58(12): 1915-1924. doi: 10.16183/j.cnki.jsjtu.2023.161
	ZHOU Tao, HUANG Ju, HAN Rushuai, et al. Inertial support capacity analysis and equivalent inertia estimation of wind turbines in integrated inertial control[J]. Journal of Shanghai Jiao Tong University, 2024, 58(12): 1915-1924.
[16]	周涛, 陈中, 王毅, 等. 计及异步电机频率响应的电力系统最低惯量评估[J]. 电力系统保护与控制, 2022, 50(20): 22-31.
	ZHOU Tao, CHEN Zhong, WANG Yi, et al. Evaluation of minimum inertia in power systems considering frequency response of induction machines[J]. Power System Protection & Control, 2022, 50(20): 22-31.
[17]	BIAN Y K, WYMAN-PAIN H, LI F R, et al. Demand side contributions for system inertia in the GB power system[J]. IEEE Transactions on Power Systems, 2018, 33(4): 3521-3530.
[18]	曾辉, 苏安龙, 葛延峰, 等. 考虑负荷特性的区域电网在线转动惯量快速估计算法[J]. 电网技术, 2023, 47(2): 423-436.
	ZENG Hui, SU Anlong, GE Yanfeng, et al. Fast estimation algorithm for on-line moment of inertia of regional power grid considering load characteristics[J]. Power System Technology, 2023, 47(2): 423-436.
[19]	巴文岚, 文云峰, 叶希, 等. 风电高渗透电网等效惯量概率预测方法[J]. 电力自动化设备, 2023, 43(3): 124-130.
	BA Wenlan, WEN Yunfeng, YE Xi, et al. Probability prediction method of equivalent inertia for high wind power penetration grid[J]. Electric Power Automation Equipment, 2023, 43(3): 124-130.
[20]	NURSEBO SALIH S, CHEN P Y, CARLSON O, et al. Optimizing wind power hosting capacity of distribution systems using cost benefit analysis[J]. IEEE Transactions on Power Delivery, 2014, 29(3): 1436-1445.
[21]	江岳文, 陈晓榕. 基于D-U空间混合多属性决策的风电场装机容量优化[J]. 电网技术, 2019, 43(12): 4451-4461.
	JIANG Yuewen, CHEN Xiaorong. Optimization of installed capacity of wind farm with mixed multiple attribute decisions based on D-U space[J]. Power System Technology, 2019, 43(12): 4451-4461.
[22]	姜欣, 陈红坤, 回俊龙, 等. 计及弃风的风电场最优装机容量[J]. 电工技术学报, 2016, 31(18): 160-168.
	JIANG Xin, CHEN Hongkun, HUI Junlong, et al. Optimal installed capacity of wind farm considering wind power curtailment[J]. Transactions of China Electrotechnical Society, 2016, 31(18): 160-168.
[23]	EGIDO I, FERNANDEZ-BERNAL F, CENTENO P, et al. Maximum frequency deviation calculation in small isolated power systems[J]. IEEE Transactions on Power Systems, 2009, 24(4): 1731-1738.
[24]	BADESA L, TENG F, STRBAC G. Optimal portfolio of distinct frequency response services in low-inertia systems[J]. IEEE Transactions on Power Systems, 2020, 35(6): 4459-4469.
[25]	罗纯坚, 李姚旺, 许汉平, 等. 需求响应不确定性对日前优化调度的影响分析[J]. 电力系统自动化, 2017, 41(5): 22-29.
	LUO Chunjian, LI Yaowang, XU Hanping, et al. Influence of demand response uncertainty on day-ahead optimization dispatching[J]. Automation of Electric Power Systems, 2017, 41(5): 22-29.
[26]	鄢发齐, 李姚旺, 汪旸, 等. 含CAES和多类型柔性负荷的电力系统多时间尺度电能-备用联合优化调度[J]. 电力自动化设备, 2019, 39(12): 73-81.
	YAN Faqi, LI Yaowang, WANG Yang, et al. Multi-time scale joint optimal dispatch of energy and reserve in power system with CAES and multi-type flexible load[J]. Electric Power Automation Equipment, 2019, 39(12): 73-81.
[27]	邱革非, 何超, 骆钊, 等. 考虑源、荷不确定性的工业园区电-气互联综合能源系统模糊优化调度[J]. 电力自动化设备, 2022, 42(5): 8-14.
	QIU Gefei, HE Chao, LUO Zhao, et al. Fuzzy optimal scheduling of integrated electricity and natural gas system in industrial park considering source-load uncertainty[J]. Electric Power Automation Equipment, 2022, 42(5): 8-14.
[28]	崔杨, 周慧娟, 仲悟之, 等. 考虑源荷两侧不确定性的含风电电力系统低碳调度[J]. 电力自动化设备, 2020, 40(11): 85-93.
	CUI Yang, ZHOU Huijuan, ZHONG Wuzhi, et al. Low-carbon scheduling of power system with wind power considering uncertainty of both source and load sides[J]. Electric Power Automation Equipment, 2020, 40(11): 85-93.
[29]	仲悟之, 黄思宇, 崔杨, 等. 考虑源荷不确定性的风电-光热-碳捕集虚拟电厂协调优化调度[J]. 电网技术, 2020, 44(9): 3424-3432.
	ZHONG Wuzhi, HUANG Siyu, CUI Yang, et al. W-S-C capture coordination in virtual power plant considering source-load uncertainty[J]. Power System Technology, 2020, 44(9): 3424-3432.
[30]	ONGSAKUL W, PETCHARAKS N. Unit commitment by enhanced adaptive Lagrangian relaxation[J]. IEEE Transactions on Power Systems, 2004, 19(1): 620-628.
[31]	毛颖群, 张建平, 程浩忠, 等. 考虑频率安全约束及风电综合惯性控制的电力系统机组组合[J]. 电力系统保护与控制, 2022, 50(11): 61-70.
	MAO Yingqun, ZHANG Jianping, CHENG Hao-zhong, et al. Unit commitment of a power system considering frequency safety constraint and wind power integrated inertial control[J]. Power System Protection & Control, 2022, 50(11): 61-70.

型号	P_N/MW	v_in/(m·s^-1)	v_N/(m·s^-1)	v_out/(m·s^-1)	c_in×10^-3/(美元·MW^-1)	c_pr×10^-3/(美元·MW^-1)
a	0.5	2.8	12.5	19.4	1350	36
b	1.0	3.9	11.1	25.0	1250	32
c	2.0	4.2	11.8	20.8	1120	30

机组编号	最大出力/ MW	最小出力/ MW	K_i/MW	H_a/s
1,2	455	150	25	9.3
3,4	130	20	20	8.1
5	162	25	21	8.1
6	80	20	17	5.8
7	85	25	17	5.8
8,9,10	55	10	17	5.8

模糊参数	ω₁	ω₂	ω₃	ω₄
风电	0.6	0.9	1.1	1.4
负荷	0.9	0.95	1.05	1.1
负荷侧惯量	0.9	0.95	1.05	1.1

方案	风力机类型	风电装机容量/MW	风电场净收益× 10^-9/美元
传统方案	a	741	0.816
	b	754	1.632
	c	894	1.473
本文方案	b	754	1.632

方案	风力机类型	风电装机容量/MW	风电场净收益× 10^-9/美元
1	b	754	1.632
2	b	613	1.326
3	b	683	1.479