Distributed bandit online optimisation for energy management in smart grids

This paper presents a distributed optimisation algorithm based on one-point bandit feedback (OPBF) which enables the solving of energy management problems (EMPs) over directed networks. Unlike existing EMPs with known cost functions, the proposed online energy management approach considers a time-varying and unknown cost function, which creates sampling difficulty. To tackle this challenge, a random gradient-free oracle is constructed, allowing for the facilitation of output generation updates. This construction significantly mitigates the need for explicit expressions of the cost function. Furthermore, the proposed algorithm successfully enforces both the supply-demand balance constraint and the generation constraint in EMPs. In order to evaluate performance, this study introduces a performance index referred to as regret, which exhibits sublinear convergence. This finding provides additional evidence that the algorithm can achieve optimal output generation at a rapid convergence rate, subject to certain step-size conditions. Finally, the performance of the algorithm is verified on both a modified 6-bus system and an IEEE 162-bus system. The results demonstrate the effectiveness and efficiency of the proposed algorithm in solving EMPs over directed networks.