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Electric demand response and bounded rationality: mean-field control for large populations of heterogeneous bounded-rational agents
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences ( IF 5 ) Pub Date : 2021-06-07 , DOI: 10.1098/rsta.2019.0429
Andrea Marín Radoszynski 1 , Pierre Pinson 1, 2
Affiliation  

The increased penetration of renewable energy sources into existing power systems induces challenges in supply–demand balancing. Demand-side flexibility is seen as an option to accommodate variability and limited predictability from renewable energy generation. Heat pumps at residential level, if well coordinated, can be one of those flexibility sources. The complexity involved is high though, since their coordinated operation combines control, population effects and the fact agents may actually not behave as rational decision-makers. We describe here a coordinated control framework that accounts for those aspects altogether. Decentralized model predictive control for large populations of heterogeneous agents is employed. As the cost to be minimized is affected by the population behaviour as a whole through the electricity price, the decentralized control is re-thought as a mean-field game. Existence and uniqueness of a Nash equilibrium are discussed while the Picard–Banach algorithm is used as a solution approach. It is extended to the case of bounded-rational agents. The impact on system dynamics of modelling agents as bounded rational is illustrated through numerical simulations.

This article is part of the theme issue ‘The mathematics of energy systems’.



中文翻译:

电力需求响应和有界理性:大量异质有界理性主体的平均场控制

可再生能源越来越多地渗透到现有电力系统中,给供需平衡带来了挑战。需求侧的灵活性被视为适应可再生能源发电的可变性和有限可预测性的一种选择。住宅级的热泵,如果协调得当,可以成为这些灵活性来源之一。但是所涉及的复杂性很高,因为它们的协调操作结合了控制、人口效应和事实代理人实际上可能不像理性决策者那样行事。我们在这里描述了一个协调控制框架,它完全考虑了这些方面。采用了对大量异质代理的分散模型预测控制。由于要最小化的成本通过电价受整个人口行为的影响,分散控制被重新考虑为平均场游戏。讨论了纳什均衡的存在性和唯一性,同时使用 Picard-Banach 算法作为解决方法。它扩展到有界理性主体的情况。通过数值模拟说明了建模代理作为有界理性对系统动力学的影响。

这篇文章是主题问题“能量系统的数学”的一部分。

更新日期:2021-06-07
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