基于三方Stackelberg博弈的区域制冷需求响应策略

doi:10.11930/j.issn.1004-9649.202503035

摘要/Abstract

摘要：

针对商业综合体空调负荷需求响应中用户参与度低、激励策略粗放等问题，提出融合三方Stackelberg博弈与深度学习的动态定价模型。首先，设计电网-聚合商-用户三级层级决策框架，利用神经网络挖掘用户负荷削减量和激励电价的非线性函数。其次，构建聚合商利润-风险均衡模型，引入达标率弹性约束下的惩罚机制和电网成本函数。然后，寻找最优补贴价格和负荷削减量，优化电网需求响应补贴策略。最后，以某商业综合体为实证对象，结果表明，所提模型负荷削减达标率为94.2%，用户舒适度偏离度降低至0.86，电网调峰成本优化57.14%。研究为高耗能建筑需求响应提供了兼具博弈均衡性与行为可解释性的决策工具，助力新型电力系统资源协同调控。

关键词: 区域制冷系统, 三方博弈, 需求响应, 纳什均衡, 电力市场

Abstract:

To address such issues as low user participation and coarse incentive strategies in demand response of air-conditioning loads in commercial complexes, a dynamic pricing model integrating tripartite Stackelberg game and deep learning is proposed. Firstly, a three-level hierarchical decision framework of power grid-aggregator-user is designed, and a neural network is used to mine the nonlinear function of user load reduction and incentive electricity price. Secondly, an aggregator profit-risk equilibrium model is constructed, and a penalty mechanism and power grid cost function under the elastic constraint of compliance rate are introduced. And then, the optimal subsidy price and load reduction are identified to optimize the subsidy strategy of power grid demand response. Finally, taking a commercial complex as an empirical case, the results show that the proposed model achieved a 94.2% load reduction compliance rate, reduced the user comfort deviation to 0.86, and optimized the peak-shaving cost of the power grid by 57.14% respectively. This study provides a decision-making tool that integrates game-theoretic equilibrium and behavioral interpretability for demand response in energy-intensive buildings, facilitating coordinated resource regulation in new-type power systems.

Key words: district cooling system, tripartite game, demand response, nash equilibrium, electricity market

余君一, 廖思阳, 柯德平. 基于三方Stackelberg博弈的区域制冷需求响应策略[J]. 中国电力, 2026, 59(2): 24-36.

YU Junyi, LIAO Siyang, KE Deping. District cooling demand response strategy based on tripartite Stackelberg game[J]. Electric Power, 2026, 59(2): 24-36.

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链接本文: https://www.electricpower.com.cn/CN/10.11930/j.issn.1004-9649.202503035

https://www.electricpower.com.cn/CN/Y2026/V59/I2/24

图/表 12

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参数	定义	数值
第一层	模型的第一层	160~128
第二层	模型的第二层	128~64
第三层	模型的第三层	64~16
第四层	模型的第四层	16~1
$E$	训练轮数	100
$B$	批量大小	32
$\mathcal{L}$	损失函数	—
优化器	优化算法	Adam
$\alpha $	MAE正则化系数	0.1
$\beta $	L2正则化系数	0.01
$\eta $	优化器的学习率	0.001
$\left( {{\gamma _1},{\gamma _2}} \right)$	指数衰减率对	(0.9, 0.999)

参数	定义	数值
第一层	模型的第一层	160~128
第二层	模型的第二层	128~64
第三层	模型的第三层	64~16
第四层	模型的第四层	16~1
$E$	训练轮数	100
$B$	批量大小	32
$\mathcal{L}$	损失函数	—
优化器	优化算法	Adam
$\alpha $	MAE正则化系数	0.1
$\beta $	L2正则化系数	0.01
$\eta $	优化器的学习率	0.001
$\left( {{\gamma _1},{\gamma _2}} \right)$	指数衰减率对	(0.9, 0.999)

分类	参数名称	数值
电网	目标负荷削减量 ${{\Delta }}{L_{{\text{target}}}}$/MW	1.2
	补贴价格范围 ${p_{{\text{subsidy}}}}$/(元·(kW·h)^–1)	[0.3, 2.0]
	商业电价 ${p_{{\text{base}}}}$/(元·(kW·h)^–1)	0.8
聚合商	激励价格范围 $\lambda $/(元·(kW·h)^–1)	[0.3, 2.0]
聚合商	达标率惩罚系数 ${C_{{\text{penalty}}}}$/(元·(kW·h)^–1)	2
用户	温度设定下限 ${T_{{\text{min}}}}$/°C	24
用户	温度设定上限 ${T_{{\text{max}}}}$/°C	28

分类	参数名称	数值
电网	目标负荷削减量 ${{\Delta }}{L_{{\text{target}}}}$/MW	1.2
	补贴价格范围 ${p_{{\text{subsidy}}}}$/(元·(kW·h)^–1)	[0.3, 2.0]
	商业电价 ${p_{{\text{base}}}}$/(元·(kW·h)^–1)	0.8
聚合商	激励价格范围 $\lambda $/(元·(kW·h)^–1)	[0.3, 2.0]
聚合商	达标率惩罚系数 ${C_{{\text{penalty}}}}$/(元·(kW·h)^–1)	2
用户	温度设定下限 ${T_{{\text{min}}}}$/°C	24
用户	温度设定上限 ${T_{{\text{max}}}}$/°C	28

指标	计算公式
负荷削减达标率	$ \eta =\dfrac{\displaystyle\sum {L}_{\text{actual}}}{\displaystyle\sum {L}_{\text{target}}}\times 100\text{%} $
电网成本节省率	$ \gamma = \dfrac{{{C_{{\text{base}}}} - {C_{{\text{grid}}}}}}{{{C_{{\text{base}}}}}} \times 100{\text{% }} $
用户舒适度偏离度	${{\Delta }}T = \dfrac{1}{N}\displaystyle\sum \left\| {{T_{{\text{actual}}}} - {T_{{\text{set}}}}} \right\|$