Auxiliary Frequency Regulation Control Strategy of District Cooling System Based on Model Predictive Control with Terminal Constraints

doi:10.12141/j.issn.1000-565X.250017

Abstract

Abstract:

The district cooling system (DCS) belongs to a class of centralized air-conditioning loads and has frequency regulation potential. This paper proposed an auxiliary frequency regulation control strategy of DCS based on model predictive control (MPC) with terminal constraints, which controls the power consumption of the DCS by adjusting the chilled water flow rate and the number of chiller shutdowns. Firstly, the study established a dynamic model of DCS and traditional units considering the relationship between chilled water flow rate and chilled water outlet temperature, and constructed the state space expression of the system. Then, based on MPC with terminal constraints, it established a joint frequency regulation control model for DCSs and traditional units, with the objective function of minimizing frequency deviation, building temperature deviation from human comfort temperature, chilled water flow’s control instructions, and traditional unit’s control instructions. The terminal constraints include terminal cost function and terminal set. Moreover, it was proved that the MPC problem with terminal constraints is asymptotically stable by constructing the Lyapunov function of the system. Finally, simulations on a 10-unit 39-bus system and an actual power system were carried out. The results verify that adding terminal constraints can improve system stability, and the use of DCS to assist in grid frequency regulation can help the system to quickly restore the rated frequency and improve regulation performance. In addition, the participation of DCSs in grid frequency regulation have no significant impact on comfort.

Key words: district cooling system, secondary frequency regulation, model predictive control, terminal constraint, Lyapunov method

CLC Number:

TM73

LIU Mingbo, LAO Ziqing, DONG Ping. Auxiliary Frequency Regulation Control Strategy of District Cooling System Based on Model Predictive Control with Terminal Constraints[J]. Journal of South China University of Technology(Natural Science Edition), 2025, 53(9): 127-137.

Figures/Tables 12

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References 26

[1]	刘明波，曾贵华，董萍，等．氢储能系统容量双层鲁棒随机优化配置方法［J］．华南理工大学学报（自然科学版），2024，52（9）：12-23.
	LIU Mingbo， ZENG Guihua， DONG Ping，et al ．Bi-level robust stochastic optimal configuration method for hydrogen energy storage system［J］．Journal of South China University of Technology （Natural Science Edition），2024，52（9）：12-23.
[2]	康重庆，姚良忠．高比例可再生能源电力系统的关键科学问题与理论研究框架［J］．电力系统自动化，2017，41（9）：2-11.
	KANG Chongqing， YAO Liangzhong ．Key scientific issues and theoretical research framework for power systems with hight proportion of renewable energy［J］．Automation of Electric Power Systems，2017，41（9）：2-11.
[3]	张严，楚晓丽，刘永强．区域供冷系统的冷量传递控制与末端冷量调节［J］．华南理工大学学报（自然科学版），2017，45（10）：26-33.
	ZHANG Yan， CHU Xiaoli， LIU Yongqiang ．Cold transmitting control and terminal cold adjusting of district cooling system［J］．Journal of South China University of Technology （Natural Science Edition），2017，45（10）：26-33.
[4]	闫军威．区域供冷系统节能优化运行与控制方法研究及系统实现［D］．广州：华南理工大学，2012.
[5]	WANG H， WANG S， SHAN K ．Experimental study on the dynamics，quality and impacts of using variable-speed pumps in buildings for frequency regulation of smart power grids［J］．Energy，2020，199：117406/1-13.
[6]	XING L， VERONICA A， ZHENG O ．What are the impacts on the HVAC system when it provides frequency regulation? - a comprehensive case study with a multi-zone variable air volume （VAV） system［J］．Energy and Buildings，2021，243：110995/1-19.
[7]	YU P， ZHANG H， SONG Y，et al ．Frequency regulation capacity offering of district cooling system：an intrinsic-motivated reinforcement learning method［J］．IEEE Transactions on Smart Grid，2023，14（4）：2762-2773.
[8]	YU P， ZHANG H， SONG Y，et al ．District cooling system control for providing operating reserve based on safe deep reinforcement learning［J］．IEEE Transactions on Power Systems，2023，39（1）：40-52.
[9]	YADAV M K， VERMA A， PANIGRAHI B K ．Frequency regulation support from district cooling system and V2G facility in cluster of buildings［C］∥ Proceedings of the 11th IEEE International Conference on Smart Grid．Paris：IEEE，2023：289-293.
[10]	YU P， ZHANG H， SONG Y ．Equivalent system model of district cooling system in frequency domain to provide primary frequency regulation［J/OL］．CSEE Journal of Power and Energy Systems，［2025-01-08］．.
[11]	毛田，周保荣，劳子卿，等．区域供冷系统参与电力系统二次调频的控制策略［J］．南方电网技术，2024，18（11）：88-96.
	MAO Tian， ZHOU Baorong， LAO Ziqing，et al ．Control strategy for district cooling system participating in secondary frequency regulation of power systems［J］．Southern Power System Technology，2024，18（11）：88-96.
[12]	MSYNE D Q， RAWLINGS J B， RAO C V，et al ．Constrained model predictive control：stability and optimality［J］．Automatica，2000，36（6）：789-814.
[13]	KEERTHI S S， GILBERT E G.Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems：stability and moving-horizon approximations［J］．Journal of Optimization Theoryand Applications，1988，57：265-293.
[14]	RAWLINGS J B， MUSKE K R ．The stability of constrained receding horizon control［J］．IEEE Transactions on Automatic Control，1993，38（10）：1512-1516.
[15]	MICHALSKA H， MAYNE D Q ．Robust receding horizon control of constrained nonlinear systems［J］．IEEE Transactions on Automatic Control，1993，38（11）：1623-1633
[16]	CHEN H， ALLGÖWER F ．Nonlinear model predictive control schemes with guaranteed stability：nonlinear model based process control［M］．Dordrecht：Springer，1998.
[17]	HU Z， GAO B， SUN R ．An active primary frequency regulation strategy for grid integrated wind farms based on model predictive control［J］．Sustainable Energy，Grids and Networks，2022，32：100955/1-12.
[18]	LIU X， WANG C， KONG X，et al ．Tube-based distributed MPC for load frequency control of power system with high wind power penetration［J］．IEEE Transactions on Power Systems，2024，39（2）：3118-3129.
[19]	余洋，张瑞丰，陆文韬，等．基于稳定经济模型预测控制的集群电动汽车辅助电网调频控制策略［J］．电工技术学报，2022，37（23）：6025-6040.
	YU Yang， ZHANG Ruifeng， LU Wentao，et al ．Auxiliary frequency regulation control strategy of aggregated electric vehicles based on Lyapunov-based economic model predictive control［J］．Transactions of China Electrotechnical Society，2022，37（23）：6025-6040.
[20]	CHEN Z， WANG J， HAN Q ．Chiller plant operation planning via collaborative neurodynamic optimization［J］．IEEE Transactions on Systems，Man，and Cybernetics：Systems，2023，53（8）：4623-4635.
[21]	王巍巍．基于空调系统状态空间模型的MPC控制研究［D］．上海：上海交通大学，2016.
[22]	WANG H， WANG S， TANG R ．Investigation on the use of pumps in HVAC systems for providing ancillary services in smart grids［J］．Energy Procedia，2019，159：219-224.
[23]	倪以信，陈寿孙，张宝霖．动态电力系统的理论和分析［M］．北京：清华大学出版社，2002.
[24]	姜素霞，冯巧玲，丁丽芬，等．自动控制原理［M］．3版．北京：北京航空航天大学出版社，2018.
[25]	刘明波，林舜江，谢敏．电力系统电压稳定分析与控制方法［M］．北京：科学出版社，2017.
[26]	University of California ．Modelica buildings library［EB/OL］．（2024-04-09）．［2025-01-08］．
	Fluid_Chillers_Data_ElectricEIR.html#Buildings.Fluid.
	Chillers.Data.ElectricEIR.