(Online) Convex Optimization for Demand-Side Management: Application to Thermostatically Controlled Loads

To counter the challenge of integrating fluctuating renewables into the grid, devices like thermostatically controlled loads (water-heaters, air conditioners, etc.) offer flexible demand. However, efficiently controlling a large population of these devices to track desired consumption signals remains a complex challenge. Existing methods lack convergence guarantees and computational efficiency or resort to regularization techniques instead of tackling the target tracking problem directly. This work addresses these drawbacks. We propose to model the problem as a finite horizon episodic Markov decision process, enabling us to adapt convex optimization algorithms with convergence guarantees and computational efficiency. This framework also extends to online learning scenarios, where daily control decisions are made without prior knowledge of consumer behavior and with daily-changing target profiles due to fluctuations of energy production and inflexible consumption. We introduce a new algorithm, called Online Target Tracker (OTT), the first online learning load control method, for which we prove sub-linear regret. We demonstrate our claims with realistic experiments. This combination of optimization and learning lays the groundwork for more dynamic and efficient load control methods.