An online distributed optimisation model solving the time-coupled conundrum by the Lyapunov drift plus penalty method

With the increasing proportion of distributed energy resources, optimisation in the active distribution network becomes highly complex and challenging. To protect user privacy and perform efficient calculations, this paper proposes an online distributed optimisation between the user and the operator. To overcome the constraint non-linearity, a new linear power flow model is adopted, which can be updated online. In addition, to solve the time-coupled conundrum of energy storage, the Lyapunov drift plus penalty method is employed to transform the long-time scale optimisation problem into an instantaneous problem. Furthermore, a novel proportional integral derivative (PID)–Lagrange algorithm is proposed to improve the efficiency, where the distributed optimisation algorithm is considered as a control process, and a PID controller is used to control it. The proposed PID–Lagrange algorithm has an explicit parameter tuning strategy and significantly improves the efficiency by 54.23% in the case study.