Mean Field Control of Thermostatically Controlled Loads as Piecewise Deterministic Markov Processes

TL;DR

This paper develops a mean-field control framework based on PDMPs for coordinating large populations of thermostatically controlled loads, ensuring comfort constraints and demonstrating effectiveness through water heater control examples.

Contribution

It introduces a PDMP-based mean-field control method tailored for TCLs, incorporating comfort constraints and a decentralized algorithm for large-scale agent coordination.

Findings

Effective control of water heaters demonstrated

Decentralized algorithm achieves coordination

Handles comfort constraints reliably

Abstract

This paper presents a mean-field control approach for Piecewise Deterministic Markov Processes (PDMPs), specifically designed for controlling a large number of agents. By modeling the interactions of a large number of agents through an aggregate cost function, the proposed method mitigates the high dimensionality of the problem by focusing on a representative agent. The contribution of this work is the application of a PDMP-based mean-field control framework to the coordination of a large population of Thermostatically Controlled Loads (TCLs). Adapting this framework to TCLs requires incorporating a quality-of-service constraint ensuring that each agent's temperature remains within a specified comfort range. To achieve this, an additional jump intensity is introduced so that agents are very likely to switch between heating and cooling modes when they reach the boundaries of their temperature range. This extension to TCLs is demonstrated through Water Heaters (WHs) control, with a decentralized algorithm based on a dual formulation and stochastic gradient descent. The numerical results obtained illustrate this approach on two examples (signal tracking and taking into account energy price).