Real-Time Voltage Calculation and Optimization Method for Wind Farms Based on Nonlinear Affine Transformation
Zhang Zhaoyi1,2, Hu Hao1,2, Wang Zijiang1,2, Shang Ben1,2, Fan Youping1,2, Shu Yinbiao1,2
1. School of Electrical Engineering and Automation Wuhan University Wuhan 430072 China; 2. Institute of Next Generation Power Systems and International Standards Wuhan University Wuhan 430072 China
Abstract：The uncertainty of wind speed leads to fluctuations in wind power, resulting in voltage fluctuations at the sending end and grid-connected point. Traditional methods for evaluating the impact of wind power fluctuations on the system state online either entail frequent power flow calculations to obtain real-time system voltages, which creates a substantial computational burden, or employ linear affine methods that yield significant errors when wind power fluctuations are large. To optimize the sending-end voltage and grid-connected point voltage considering the wind power fluctuations, centralized optimization methods require frequent optimal power flow calculations, leading to heavy computational burdens. On the other hand, distributed algorithms require advanced communication facilities, which many wind farms may struggle to meet. Therefore, this paper proposes a real-time voltage calculation and optimization method based on nonlinear affine transformation to rapidly calculate the voltage state and optimize the system voltage considering wind power fluctuations, with limited computation and communication resources. Firstly, the method establishes a multi-period dynamic reactive power optimization model to minimize the power loss and the voltage fluctuations of the grid-connected point. The cumulant method is used to analyze the sending-end voltage influenced by uncertain wind generation. Secondly, an improved interior point method, based on the analytic gradient matrix and Hessian matrix, is utilized to solve the established model, with the obtained results serving as a reference for real-time voltage optimization. Thirdly, at each moment the wind generator measures the local active power fluctuation and uses the designed event-triggered algorithm to determine whether real-time voltage optimization is necessary. Then, the nonlinear affine method is used to rapidly calculate the real-time system voltage state, and obtain the reactive power adjustment to prevent potential voltage violations at the sending end, while also reducing voltage fluctuations at the grid-connected point. Finally, the reactive power of each wind generator is regulated simultaneously by controlling the converter to achieve real-time voltage optimization of the whole wind farm. Overall, the proposed real-time voltage optimization method can improve the voltage quality of wind farms in real time. The following conclusions can be drawn from the simulation analysis: (1) The solution speed is greatly improved by adding a penalty term to the objective function of the multi-period dynamic reactive power optimization model. The improved interior point method based on analytic gradient and Hessian matrix can solve the model efficiently. (2) Based on the third-order nonlinear affine transformation of system voltage w.r.t. active/reactive power derived in this paper, the proposed method could rapidly and accurately obtain the system voltage state considering the wind power fluctuations. The computational time cost is about 0.58% of the power flow calculation, and the calculation results are more accurate compared with the linear affine method. (3) The proposed real-time voltage optimization method based on nonlinear affine transformation could effectively prevent sending-end voltage violations and further reduce the grid-connected point voltage fluctuations, thus improving the voltage quality of wind farms. Statistically, the sending-end voltage violations are eliminated throughout the simulation, and the voltage fluctuation of the grid-connected point is reduced to 35.12% of the conventional method.
张兆毅, 胡浩, 王子江, 商犇, 樊友平, 舒印彪. 基于非线性仿射的风电场电压实时计算和优化方法[J]. 电工技术学报, 2024, 39(13): 3975-3989.
Zhang Zhaoyi, Hu Hao, Wang Zijiang, Shang Ben, Fan Youping, Shu Yinbiao. Real-Time Voltage Calculation and Optimization Method for Wind Farms Based on Nonlinear Affine Transformation. Transactions of China Electrotechnical Society, 2024, 39(13): 3975-3989.
[1] 李晖, 刘栋, 姚丹阳. 面向碳达峰碳中和目标的我国电力系统发展研判[J]. 中国电机工程学报, 2021, 41(18): 6245-6259. Li Hui, Liu Dong, Yao Danyang.Analysis and reflection on the development of power system towards the goal of carbon emission peak and carbon neutrality[J]. Proceedings of the CSEE, 2021, 41(18): 6245-6259. [2] 秦世耀, 齐琛, 李少林, 等. 电压源型构网风电机组研究现状及展望[J]. 中国电机工程学报, 2023, 43(4): 1314-1334. Qin Shiyao, Qi Chen, Li Shaolin, et al.Review of the voltage-source grid forming wind turbine[J]. Proceedings of the CSEE, 2023, 43(4): 1314-1334. [3] 顾雪平, 白岩松, 李少岩, 等. 考虑风电不确定性的电力系统恢复全过程两阶段鲁棒优化方法[J]. 电工技术学报, 2022, 37(21): 5462-5477. Gu Xueping, Bai Yansong, Li Shaoyan, et al.Two stage robust optimization method for the whole-process power system restoration considering wind power uncertainty[J]. Transactions of China Electro-technical Society, 2022, 37(21): 5462-5477. [4] 王晨, 寇鹏, 王若谷, 等. 利用多空间尺度下时空相关性的点云分布多风机风速预测[J]. 电力系统自动化, 2021, 45(22): 65-73. Wang Chen, Kou Peng, Wang Ruogu, et al.Wind speed forecasting for multiple wind turbines with point cloud distribution using spatio-temporal correlation on multiple spatial scale[J]. Automation of Electric Power Systems, 2021, 45(22): 65-73. [5] 王耀翔, 戴朝波, 杨志昌, 等. 考虑风电机组无功潜力的风电场无功电压控制策略[J]. 电力系统保护与控制, 2022, 50(24): 83-90. Wang Yaoxiang, Dai Chaobo, Yang Zhichang, et al.Voltage control strategy for a wind farm considering the reactive capability of DFIGs[J]. Power System Protection and Control, 2022, 50(24): 83-90. [6] Li Shenghu, Zhang Yifan, Yu Xinyu, et al.Reactive power dispatch of DFIGs in wind farm based on multi-object optimization[J]. International Transactions on Electrical Energy Systems, 2020, 30(3): 1-16. [7] 刘其辉, 逄思敏, 吴林林, 等. 大规模风电汇集系统电压不平衡机理、因素及影响规律[J]. 电工技术学报, 2022, 37(21): 5435-5450. Liu Qihui, Pang Simin, Wu Linlin, et al.The mechanism, factors and influence rules of voltage imbalance in wind power integration areas[J]. Transactions of China Electrotechnical Society, 2022, 37(21): 5435-5450. [8] 王德胜, 颜湘武, 刘辉, 等. 基于动态无功支撑的全功率变流风电机组高电压穿越改进控制[J]. 中国电机工程学报, 2022, 42(3): 957-968. Wang Desheng, Yan Xiangwu, Liu Hui, et al.High voltage ride through improved control of full power converter wind turbines based on dynamic reactive power support[J]. Proceedings of the CSEE, 2022, 42(3): 957-968. [9] 符杨, 魏钰柠, 贾锋, 等. 分布式风电机组电压波动特性分析及平抑控制策略[J]. 中国电机工程学报, 2020, 40(14): 4496-4505, 4729. Fu Yang, Wei Yuning, Jia Feng, et al.The voltage fluctuation characteristic of distributed wind generators and its smoothing control strategy[J]. Proceedings of the CSEE, 2020, 40(14): 4496-4505, 4729. [10] 蔡游明, 李征, 蔡旭. 以并网点电压和机端电压平稳性为目标的风电场无功电压协调控制[J]. 电力自动化设备, 2018, 38(8): 166-173. Cai Youming, Li Zheng, Cai Xu.Coordinated control of reactive power and voltage for wind farm aiming at voltage stability of PCC and generator terminal[J]. Electric Power Automation Equipment, 2018, 38(8): 166-173. [11] 王渝红, 廖逸犇, 宋雨妍, 等. 风电场内部分散式无功电压优化控制策略[J]. 高电压技术, 2022, 48(12): 5047-5056. Wang Yuhong, Liao Yiben, Song Yuyan, et al.Distributed optimal control strategy of reactive power and voltage in wind farm[J]. High Voltage Engineering, 2022, 48(12): 5047-5056. [12] 朱星阳, 张建华, 刘文霞, 等. 风电并网引起电网电压波动的评价方法及应用[J]. 电工技术学报, 2013, 28(5): 88-98. Zhu Xingyang, Zhang Jianhua, Liu Wenxia, et al.Evaluation methodology and its application of voltage fluctuation in power network caused by inter-connected wind power[J]. Transactions of China Electrotechnical Society, 2013, 28(5): 88-98. [13] 王渝红, 宋雨妍, 廖建权, 等. 风电电压主动支撑技术现状与发展趋势[J]. 电网技术, 2023, 47(8): 3193-3205. Wang Yuhong, Song Yuyan, Liao Jianquan, et al.Review and development trends of DFIG-based wind power voltage active support technology[J]. Power System Technology, 2023, 47(8): 3193-3205. [14] 国家市场监督管理总局, 国家标准化管理委员会. 风电场接入电力系统技术规定第1部分:陆上风电: GB/T 19963.1—2021[S]. 北京: 中国标准出版社, 2021. [15] 张哲, 王成福, 董晓明, 等. 基于分层模型预测控制的风电场电压协调控制策略[J]. 电力系统自动化, 2019, 43(11): 34-42, 94. Zhang Zhe, Wang Chengfu, Dong Xiaoming, et al.Coordinated voltage control strategy of wind farms based on hierarchical model predictive control[J]. Automation of Electric Power Systems, 2019, 43(11): 34-42, 94. [16] 张建委, 蔺红. 考虑风电机组电压均衡性的风电场无功优化策略[J]. 水力发电, 2020, 46(9): 115-119. Zhang Jianwei, Lin Hong.Reactive power optimi-zation strategy of wind farm considering voltage balance of wind turbine[J]. Water Power, 2020, 46(9): 115-119. [17] 刘承锡, 张兆毅, 赖秋频. 考虑风电功率短期波动的风电场无功快速跟踪优化[J]. 中国电机工程学报, 2023, 43(15): 5850-5863. Liu Chengxi, Zhang Zhaoyi, Lai Qiupin.Fast-tracking optimization of reactive power for wind farm considering short-term fluctuations of wind generations[J]. Proceedings of the CSEE, 2023, 43(15): 5850-5863. [18] 胡畔, 冀肖彤, 王易, 等. 基于置信度机会约束规划的风电场无功优化技术[J]. 科学技术与工程, 2022, 22(17): 7002-7012. Hu Pan, Ji Xiaotong, Wang Yi, et al.Reactive power optimization technology of wind farm based on confidence chance-constrained programming[J]. Science Technology and Engineering, 2022, 22(17): 7002-7012. [19] 张晋华, 吴文静, 王卓然, 等. 基于降低风电场损耗的风电场优化调度研究[J]. 太阳能学报, 2018, 39(4): 1085-1096. Zhang Jinhua, Wu Wenjing, Wang Zhuoran, et al.Research of wind farm optimal scheduling based on reducing wind farm losses[J]. Acta Energiae Solaris Sinica, 2018, 39(4): 1085-1096. [20] 朱建华, 何卓林, 闫伟军, 等. 风电场自动电压控制中风机和静止无功发生器的无功分配研究[J]. 电气技术, 2022, 23(4): 31-36. Zhu Jianhua, He Zhuolin, Yan Weijun, et al.Research on reactive power distribution of wind turbine and static var generator in automatic voltage control of wind farm[J]. Electrical Engineering, 2022, 23(4): 31-36. [21] 徐询, 谢丽蓉, 梁武星, 等. 考虑风电预测误差时序性及风电可信度的双层优化模型[J]. 电工技术学报, 2023, 38(6): 1620-1632, 1661. Xu Xun, Xie Lirong, Liang Wuxing, et al.Bi-level optimization model considering time series characteristic of wind power forecast error and wind power reliability[J]. Transactions of China Electrotechnical Society, 2023, 38(6): 1620-1632, 1661. [22] Wang Licheng, Yan Ruifeng, Saha T K.Voltage management for large scale PV integration into weak distribution systems[J]. IEEE Transactions on Smart Grid, 2018, 9(5): 4128-4139. [23] 杨珺, 侯俊浩, 刘亚威, 等. 分布式协同控制方法及在电力系统中的应用综述[J]. 电工技术学报, 2021, 36(19): 4035-4049. Yang Jun, Hou Junhao, Liu Yawei, et al.Distributed cooperative control method and application in power system[J]. Transactions of China Electrotechnical Society, 2021, 36(19): 4035-4049. [24] 薛帅, 高厚磊, 郭一飞, 等. 大规模海上风电场的双层分布式有功控制[J]. 电力系统保护与控制, 2021, 49(3): 1-9. Xue Shuai, Gao Houlei, Guo Yifei, et al.Bi-level distributed active power control for a large-scale wind farm[J]. Power System Protection and Control, 2021, 49(3): 1-9. [25] 石东源, 蔡德福, 陈金富, 等. 计及输入变量相关性的半不变量法概率潮流计算[J]. 中国电机工程学报, 2012, 32(28): 104-113, 12. Shi Dongyuan, Cai Defu, Chen Jinfu, et al.Probabilistic load flow calculation based on cumulant method considering correlation between input variables[J]. Proceedings of the CSEE, 2012, 32(28): 104-113, 12. [26] 卫鹏, 刘建坤, 周前, 等. 基于半不变量和Gram-Charlier级数展开法的随机潮流算法[J]. 电力工程技术, 2017, 36(1): 34-38. Wei Peng, Liu Jiankun, Zhou Qian, et al.A probabilistic power flow algorithm based on semi-variable and gram-charlier series expansion[J]. Electric Power Engineering Technology, 2017, 36(1): 34-38. [27] Waltz R A, Morales J L, Nocedal J, et al.An interior algorithm for nonlinear optimization that combines line search and trust region steps[J]. Mathematical Programming, 2006, 107(3): 391-408. [28] Byrd R H, Gilbert J C, Nocedal J.A trust region method based on interior point techniques for nonlinear programming[J]. Mathematical Programming, 2000, 89(1): 149-185.
2024, Vol. 39 
