Control of Voltage-Dependent Loads for Grid Frequency Response Based on Hierarchical Model Predictive Control
Zhang Yuanhang1,2, Kou Peng1,2, Mei Mingyang1,2, Tian Runze1,2, Liang Deliang1,2
1. State Key Laboratory of Electrical Insulation and Power Equipment School of Electrical Engineering Xi'an Jiaotong University Xi'an 710049 China; 2. Shaanxi Key Laboratory of Smart Grid School of Electrical Engineering Xi'an Jiaotong University Xi'an 710049 China
Abstract：Driven by the national goal of “double carbon”, China's power system is accelerating the transition to a new kind of power system with high renewable energy penetration. However, the inherent intermittency and low inertia characteristics of renewable energy bring challenges to the frequency stability of the power grid. In this context, modern power systems require additional frequency regulation resources to ensure grid stability. Voltage-dependent loads are important frequency regulation resources, whose active power consumption is strongly correlated with bus voltage. For this reason, this paper proposes a control strategy for voltage-dependent loads. The proposed strategy regulates multiple reactive power devices, controlling the bus voltage of the load to change its active power consumption and contributing to frequency response. Firstly, the proposed strategy has two layers. The upper layer, employing centralized model predictive control (MPC), calculates the active power references of loads and delivers the references into the lower layer. The lower layer employs decentralized MPC to calculate the reactive power of reactive power devices based on the active power references of the loads from the upper layer. Secondly, the control problem formulation of the lower layer includes the dynamic models of voltage-dependent loads and bus voltages, thus realizing effective load active power control without violating voltage constraints. Thirdly, the lower decentralized MPC strategy consists of multiple local controllers that do not communicate with each other, and the interactions between controllers are regarded as disturbances. A tube-based robust method is used to compensate for the communication deficiencies and achieve suboptimal control, thus significantly reducing the communication burden. Simulation results on the modified IEEE 39-bus system show that, when a 522 MW load is suddenly disconnected, the grid frequency rises to 50.29 Hz at the highest level without the load support and is stabilized at 50.19 Hz in the end. If the conventional droop control is employed to regulate the voltage-dependent loads to participate in the frequency response, then the grid frequency rises to 50.22 Hz and eventually stabilizes at 50.16 Hz. In contrast, if the proposed hierarchical MPC strategy is adopted for voltage-dependent loads, the grid frequency rises to 50.18 Hz and is finally stabilized at 50.08 Hz. Based on the above analysis, it can be learned that, compared with the traditional droop control, the hierarchical MPC strategy for voltage-dependent loads reduces the peak and steady-state values of the frequency and significantly improves the frequency dynamics. We can draw the following conclusions from the simulation results: (1) When an over-frequency event occurs, the proposed hierarchical MPC strategy makes the reactive power outputs of reactive devices increase rapidly. In this way, the voltage amplitude of the entire grid rises, and thus the active power consumption of voltage-dependent loads increases, effectively mitigating the severity of the over-frequency event. (2) To realize effective frequency control, the proposed hierarchical MPC strategy takes into account the dynamic model of voltage-dependent loads, grid frequency and bus voltage, and can dynamically adjust the outputs of reactive power devices according to the specific situation. (3) During the frequency response, the hierarchical MPC strategy can still effectively limit the bus voltages within the constraints even in the absence of communication between reactive power devices. In contrast, the bus voltages under the conventional droop control strategy suffer from voltage violations.
张远航, 寇鹏, 梅铭洋, 田润泽, 梁得亮. 电压敏感型负荷参与频率响应的分层模型预测控制策略[J]. 电工技术学报, 2026, 41(1): 127-141.
Zhang Yuanhang, Kou Peng, Mei Mingyang, Tian Runze, Liang Deliang. Control of Voltage-Dependent Loads for Grid Frequency Response Based on Hierarchical Model Predictive Control. Transactions of China Electrotechnical Society, 2026, 41(1): 127-141.
[1] 李兆伟, 方勇杰, 吴雪莲, 等. 频率紧急控制中动作时延和措施量对低惯量系统控制有效性的影响[J]. 电工技术学报, 2024, 39(17): 5394-5405. Li Zhaowei, Fang Yongjie, Wu Xuelian, et al.Influence of action delay and amount on the control effectiveness of low inertia systems in frequency emergency control[J]. Transactions of China Electro-technical Society, 2024, 39(17): 5394-5405. [2] 谢开, 刘敦楠, 李竹, 等. 适应新型电力系统的多维协同电力市场体系[J]. 电力系统自动化, 2024, 48(4): 2-12. Xie Kai, Liu Dunnan, Li Zhu, et al.Multi-dimensional collaborative electricity market system for new power system[J]. Automation of Electric Power Systems, 2024, 48(4): 2-12. [3] 高倩, 杨知方, 李文沅. 电力系统混合整数线性规划问题的运筹决策关键技术综述与展望[J]. 电工技术学报, 2024, 39(11): 3291-3307. Gao Qian, Yang Zhifang, Li Wenyuan.Prospect on operations research for mixed-integer linear programming problems in power systems[J]. Transactions of China Electrotechnical Society, 2024, 39(11): 3291-3307. [4] 白国岩, 李春宝, 孟繁丞, 等. 多端柔性直流输电系统的自适应下垂控制策略研究[J]. 电气技术, 2022, 23(5): 1-8. Bai Guoyan, Li Chunbao, Meng Fancheng, et al.Research on an adaptive droop control strategy applied in voltage source converter based multi-terminal high voltage direct current transmission system[J]. Electrical Engineering, 2022, 23(5): 1-8. [5] 黄萌, 舒思睿, 李锡林, 等. 面向同步稳定性的电力电子并网变流器分析与控制研究综述[J]. 电工技术学报, 2024, 39(19): 5978-5994. Huang Meng, Shu Sirui, Li Xilin, et al.A review of synchronization-stability-oriented analysis and control of power electronic grid-connected converters[J]. Transactions of China Electrotechnical Society, 2024, 39(19): 5978-5994. [6] 刘林, 王大龙, 綦晓, 等. 基于双锁相环的海上风场综合惯量调频策略研究[J]. 发电技术, 2024, 45(2): 282-290. Liu Lin, Wang Dalong, Qi Xiao, et al.Study on double phase-locked loop on the synthetic inertia control of offshore wind farm frequency regulation[J]. Power Generation Technology, 2024, 45(2): 282-290. [7] 吴珊, 边晓燕, 张菁娴, 等. 面向新型电力系统灵活性提升的国内外辅助服务市场研究综述[J]. 电工技术学报, 2023, 38(6): 1662-1677. Wu Shan, Bian Xiaoyan, Zhang Jingxian, et al.A review of domestic and foreign ancillary services market for improving flexibility of new power system[J]. Transactions of China Electrotechnical Society, 2023, 38(6): 1662-1677. [8] 崔挺. 带电压型负荷的孤立电力系统电压和频率控制策略研究[D]. 武汉: 武汉大学, 2015. Cui Ting.Research on voltage and frequency control strategy of isolated power system with voltage load[D]. Wuhan: Wuhan University, 2015. [9] Price W W, Chiang H D, Clark H K, et al.Load representation for dynamic performance analysis (of power systems)[J]. IEEE Transactions on Power Systems, 8(2): 472-482. [10] Langwasser M, De Carne G, Liserre M, et al.Primary frequency regulation using HVDC terminals controlling voltage dependent loads[J]. IEEE Transactions on Power Delivery, 2020, 36(2): 710-720. [11] 颜湘武, 郭燕, 彭维锋, 等. 基于旋转移相变压器的电压源型无功补偿器及其控制策略[J]. 电工技术学报, 2023, 38(16): 4448-4464. Yan Xiangwu, Guo Yan, Peng Weifeng, et al.Voltage source var compensator based on rotary phase shifting transformer and its control strategy[J]. Transactions of China Electrotechnical Society, 2023, 38(16): 4448-4464. [12] Farrokhabadi M, Cañizares C A, Bhattacharya K.Frequency control in isolated/islanded microgrids through voltage regulation[J]. IEEE Transactions on Smart Grid, 2015, 8(3): 1185-1194. [13] Alghamdi B, Cañizares C.Frequency and voltage coordinated control of a grid of AC/DC microgrids[J]. Applied Energy, 2022, 310: 118427. [14] Zhong Weilin, Tzounas G, Milano F.Improving the power system dynamic response through a combined voltage-frequency control of distributed energy resources[J]. IEEE Transactions on Power Systems, 2022, 37(6): 4375-4384. [15] De Carne G, Buticchi G, Liserre M, et al.Real-time primary frequency regulation using load power control by smart transformers[C]//2020 IEEE Power & Energy Society General Meeting (PESGM), Montreal, QC, Canada, 2020: 1. [16] Wan Yong, Murad M A A, Liu Muyang, et al. Voltage frequency control using SVC devices coupled with voltage dependent loads[J]. IEEE Transactions on Power Systems, 2019, 34(2): 1589-1597. [17] Alghamdi B, Cañizares C A.Frequency regulation in isolated microgrids through optimal droop gain and voltage control[J]. IEEE Transactions on Smart Grid, 2021, 12(2): 988-998. [18] Zhang Yuanhang, Kou Peng, Zhang Zhihao, et al.Coordinated frequency and voltage optimal control of wind farm with nonlinear power constraints[J]. IEEE Systems Journal, 2023, 17(3): 4934-4945. [19] Aksland C T, Tannous P J, Wagenmaker M J, et al.Hierarchical predictive control of an unmanned aerial vehicle integrated power, propulsion, and thermal management system[J]. IEEE Transactions on Control Systems Technology, 2023, 31(3): 1280-1295. [20] Kou Peng, Liang Deliang, Gao Rong, et al.Decentralized model predictive control of hybrid distribution transformers for voltage regulation in active distribution networks[J]. IEEE Transactions on Sustainable Energy, 2019, 11(4): 2189-2200. [21] Rouhani A, Abur A.Real-time dynamic parameter estimation for an exponential dynamic load model[J]. IEEE Transactions on Smart Grid, 2016, 7(3): 1530-1536. [22] Choi B K, Chiang H D, Li Yinhong, et al.Measurement-based dynamic load models: derivation, comparison, and validation[J]. IEEE Transactions on Power Systems, 2006, 21(3): 1276-1283. [23] Liu Junwei, Xu Yan, Qiu Jing, et al.Non-network solution coordinated voltage stability enhancement with STATCOM and UVLS for wind-penetrated power system[J]. IEEE Transactions on Sustainable Energy, 2020, 11(3): 1559-1568. [24] Baldivieso Monasterios P R, Trodden P. Low-complexity distributed predictive automatic generation control with guaranteed properties[J]. IEEE Transactions on Smart Grid, 2017, 8(6): 3045-3054. [25] Mayne D Q, Seron M M, Raković S V.Robust model predictive control of constrained linear systems with bounded disturbances[J]. Automatica, 2005, 41(2): 219-224. [26] Riverso S, Farina M, Ferrari-Trecate G.Plug-and-play decentralized model predictive control for linear systems[J]. IEEE Transactions on Automatic Control, 2013, 58(10): 2608-2614. [27] Brooks J, Barooah P.Coordination of loads for ancillary services with Fourier domain consumer QoS constraints[J]. IEEE Transactions on Smart Grid, 2019, 10(6): 6148-6155. [28] Chávarro-Barrera L, Pérez-Londoño S, Mora-Flórez J.An adaptive approach for dynamic load modeling in microgrids[J]. IEEE Transactions on Smart Grid, 2021, 12(4): 2834-2843. [29] 孙凯祺, 邱伟, 李可军, 等. 面向快速频率响应系统的网络攻击防御控制策略[J]. 中国电机工程学报, 2021, 41(16): 5476-5486. Sun Kaiqi, Qiu Wei, Li Kejun, et al.Cyber attack defense control for fast frequency response system[J]. Proceedings of the CSEE, 2021, 41(16): 5476-5486. [30] Xue Nan, Chakrabortty A.Parallel identification of power system dynamic models under scheduling constraints[J]. IEEE Transactions on Power Systems, 2016, 31(6): 4584-4594. [31] Neyestanaki M K, Ranjbar A M.An adaptive PMU-based wide area backup protection scheme for power transmission lines[J]. IEEE Transactions on Smart Grid, 2015, 6(3): 1550-1559. [32] Stanojev O, Markovic U, Aristidou P, et al.MPC-based fast frequency control of voltage source converters in low-inertia power systems[J]. IEEE Transactions on Power Systems, 2022, 37(4): 3209-3220. [33] Zhang Yifu, Cortés J.Distributed bilayered control for transient frequency safety and system stability in power grids[J]. IEEE Transactions on Control of Network Systems, 2020, 7(3): 1476-1488. [34] 李春华, 张永康, 王永源, 等. 南方电网±200 Mvar静止同步补偿器人工短路试验及分析[J]. 电力系统自动化, 2013, 37(4): 125-129. Li Chunhua, Zhang Yongkang, Wang Yongyuan, et al.Artificial short circuit test and analysis of ±200 Mvar STATCOM in China Southern Power Grid[J]. Automation of Electric Power Systems, 2013, 37(4): 125-129.
2026, Vol. 41 
