Robust Scheduling of Thermostatically Controlled Loads With Statistically Feasible Guarantees

Flexible resources are increasingly significant for the reliable operation of power grids due to the high penetration of renewable energy. Thermostatically controlled loads (TCLs) are one of the common flexible resources, whose control has been extensively studied. Yet, much can be improved. We investigate the scheduling of TCLs facing uncertain temperatures and dynamic prices. Classical approaches often employ the chance-constrained program or robust optimization to handle such uncertainties. However, these approaches either require specific distribution knowledge or yield too conservative solutions. The distribution knowledge can be rather challenging to obtain especially when the uncertainties from different sources are correlated. To this end, we adopt the notion of statistical feasibility and propose a robust sample-based scheduling scheme for TCLs. Such a sample-based scheme relieves the reliance on the distribution knowledge and is able to characterize the coupling effects of the two uncertainty sources. Besides, through integrating the real-time domain knowledge into uncertainty set reconstruction, we relax the solutions’ conservation by exploring the consumers’ tolerance to the room temperature. Numerical studies highlight the remarkable performance of our proposed scheme. Specifically, our approach is able to simultaneously effectively reduce the electricity bills of consumers and satisfy the consumers’ tolerance to the room temperature.