面向电网需求响应的空调负荷异质性建模与低维广播协同调控方法

doi:10.11930/j.issn.1004-9649.202504010

中国电力 ›› 2025, Vol. 58 ›› Issue (12): 14-26.DOI: 10.11930/j.issn.1004-9649.202504010

• 协同海量分布式灵活性资源的韧性城市能源系统关键技术 • 上一篇

面向电网需求响应的空调负荷异质性建模与低维广播协同调控方法

余君一¹(), 廖思阳¹(), 柯德平¹, 张杰²

1. 武汉大学电气与自动化学院，湖北武汉　430072
2. 云南电网有限公司文山供电局，云南文山　663000

收稿日期:2025-04-07 修回日期:2025-11-11 发布日期:2025-12-27 出版日期:2025-12-28
作者简介:
余君一（2002），男，从事虚拟电厂需求响应技术研究，E-mail：yujunyi@whu.edu.cn
廖思阳（1989），男，通信作者，博士，副教授，博士生导师，从事负荷控制需求侧响应技术研究，E-mail：liaosiyang@whu.edu.cn
基金资助:
国家重点研发计划资助项目（2023YFB2407300）；中国南方电网责任有限公司科技项目（YNKJXM20222103）。

Heterogeneity Modeling and Low-Dimensional Broadcast Cooperative Control of Air Conditioning Load for Power Grid Demand Response

YU Junyi¹(), LIAO Siyang¹(), KE Deping¹, ZHANG Jie²

1. School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China
2. Yunnan Electric Power Company Wenshan Power Supply Bureau, Wenshan 663000, China

Received:2025-04-07 Revised:2025-11-11 Online:2025-12-27 Published:2025-12-28
Supported by:
This work is supported by the National Key Research and Development Program of China (No.2023YFB2407300) and the Science and Technology Project of China Southern Power Grid Co., Ltd. (No.YNKJXM20222103).

摘要/Abstract

摘要：

针对电网需求响应中大规模异构空调负荷精细化调控的需求，首先，利用二阶等效热参数模型推导空调稳态运行功率，结合高斯混合模型刻画空调参数异质性，准确计算调节容量。然后，提出“中央引导+本地自治”的低维广播信号控制策略，利用马尔可夫链模型结合增广拉格朗日函数寻找不同温度区间最优升温概率，平衡电网需求与经济成本约束。最后，通过仿真分析验证所提方法，结果表明：50000台空调异构样本集中调节容量计算准确率达97.5%，可稳定提供最大11188.12 kW的负荷削减，且广播策略能动态跟踪电网需求功率，有效缓解夏季电网高峰压力，所提方法为大规模温控负荷参与需求响应提供了理论支撑与实用化解决方案。

关键词: 空调负荷, 调节容量评估, 高斯混合模型, 马尔可夫链, 拉格朗日函数

Abstract:

To address the demand for refined regulation of large-scale heterogeneous air-conditioning loads in power grid demand response, a second-order equivalent thermal parameter model is firstly used to derive the steady-state operating power of air conditioners, and the heterogeneity of air-conditioning parameters is characterized by a Gaussian mixture model to accurately calculate the regulation capacity. Then, an innovative low-dimensional broadcast signal control strategy of "central guidance + local autonomy" is designed. A Markov chain model combined with an augmented Lagrangian function is used to find the optimal temperature rise probability in different temperature intervals, balancing the power grid demand and economic cost constraints. Finally, the proposed method is verified through simulation analysis. The results show that the calculation accuracy of regulation capacity reaches 97.5% in a heterogeneous sample set of 50000 air conditioners, which can stably provide a maximum load reduction of 11188.12 kW. Moreover, the broadcast strategy can dynamically track the grid demand power and effectively alleviate the summer grid peak pressure. The proposed method provides theoretical support and a practical solution for large-scale thermostatically controlled loads to participate in demand response.

Key words: conditioning load, regulation capacity assessment, Gaussian mixture model, Markov chain, Lagrangian function

余君一, 廖思阳, 柯德平, 张杰. 面向电网需求响应的空调负荷异质性建模与低维广播协同调控方法[J]. 中国电力, 2025, 58(12): 14-26.

YU Junyi, LIAO Siyang, KE Deping, ZHANG Jie. Heterogeneity Modeling and Low-Dimensional Broadcast Cooperative Control of Air Conditioning Load for Power Grid Demand Response[J]. Electric Power, 2025, 58(12): 14-26.

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链接本文: https://www.electricpower.com.cn/CN/10.11930/j.issn.1004-9649.202504010

https://www.electricpower.com.cn/CN/Y2025/V58/I12/14

图/表 13

图 1 二阶ETP负荷模型

Fig.1 Second-order ETP load model

图 2 广播信号实施流程

Fig.2 Broadcast signal implementation process

图 3 需求响应实施流程

Fig.3 Demand response implementation process

表 1 模型参数设置

Table 1 Model parameter settings

参数		取值
空气等效热阻${R_{\rm a}}$/(℃·(kW)^–1)		$ \mathcal{U}\left( {2,3} \right) $
材料等效热阻${R_{\rm m}}$/(℃·(kW)^–1)		$\mathcal{U}\left( {1,2} \right)$
空气等效热容${C_{\rm a}}$/((kW·h)(℃)^–1)		$\mathcal{U}\left( {4,6} \right)$
材料等效热容${C_{\rm m}}$/((kW·h)(℃)^–1)		$\mathcal{U}\left( {2,4} \right)$
制冷电功率$P$/W		$\mathcal{U}\left( {600,1\;000} \right)$
能效比${\eta _{\rm i}}$		$\mathcal{U}\left( {2.4,3.6} \right)$
温度设定值${T_{\rm set}}$/℃		$\mathcal{U}\left( {18,28} \right)$
允许温度偏差${T_{\rm dev}}$/℃		$\mathcal{U}\left( {0.5,2} \right)$
环境温度${T_{\rm o}}$/℃		$35$

图 4 高斯混合分布分量数K与BIC值的关系

Fig.4 The relationship between the number of components K of the Gaussian mixture distribution and the BIC value

图 5 抽样率与最优分量数的关系

Fig.5 The relationship between the sampling rate and the optimal number of components

图 6 抽样率与计算时间的关系

Fig.6 The relationship between the sampling rate and the calculation time

图 7 不可调节空调占比与可调节容量的关系曲线

Fig.7 The relationship curve between the proportion of non-adjustable air conditioners and the adjustable capacity

图 8 抽样率与估算的可调节容量的关系

Fig.8 The relationship between the sampling rate and the estimated adjustable capacity

表 2 5个周期内的广播参数

Table 2 Broadcast parameters within 5 cycles

温度区间/℃	1	2	3	4	5
18~19	0.96	0.95	0.88	0.86	0.85
19~20	0.92	0.87	0.79	0.75	0.72
20~21	0.85	0.74	0.68	0.62	0.6
21~22	0.76	0.63	0.56	0.58	0.48
22~23	0.72	0.65	0.62	0.63	0.68
23~24	0.63	0.72	0.65	0.62	0.52
24~25	0.56	0.45	0.42	0.39	0.32
25~26	0.32	0.28	0.25	0.21	0.16
26~27	0.18	0.09	0.09	0.07	0.04
27~28	0.05	0.05	0.04	0.03	0.03

图 9 调节功率跟踪电网需求的效果

Fig.9 The effect of regulating power to track grid demand

图 10 不同策略下的负荷削减量情况

Fig.10 Load reduction under different strategies

表 3 不同策略下关键性能指标对比

Table 3 Comparison of key performance indicators under different strategies

策略	平均负荷差率/%	平均温度偏差/℃
本文方法	1.87	0.52
固定概率	4.12	0.83
无异质性建模	5.45	0.76

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面向电网需求响应的空调负荷异质性建模与低维广播协同调控方法

Heterogeneity Modeling and Low-Dimensional Broadcast Cooperative Control of Air Conditioning Load for Power Grid Demand Response

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