A Constrained Online Convex Optimisation Approach for Setpoint Tracking and Deviation Compensation

Abstract

Price-based demand response has been widely implemented by load aggregators to guide end-users to optimise power usage patterns. However, a key problem in practical implementation is that the current values of user price elasticity cannot be known before the current price is announced to users. To address this issue, we propose a constrained online convex optimisation (OCO) pricing strategy, which utilises the previous price adjustment and the corresponding user price elasticity to make the current price adjustment, schedule the uncertain load to track the power setpoint and combine energy storage to compensate for the tracking deviations in each round. The proposed OCO approach incorporates adversarial loss functions and adversarial constraints. Notably, these constraints are revealed only after making decisions and can tolerate instantaneous violations, yet they must be satisfied in the long term on average. Besides, dynamic Regret and dynamic Violation are introduced to guarantee the performance of the proposed approach. Finally, step and sinusoidal fluctuations are tested to validate the tracking performance. The findings highlight great application potential of the proposed constrained OCO pricing strategy in EV charging stations.