Distributed Constrained Online Optimization for Time-Varying Economic Dispatch Under Feedback Delays

In practical economic dispatch problems, generation cost functions of generating units typically vary due to the time-varying nature of cost coefficients, while the demand balance constraints are non-fixed due to the varying generation demand and renewable energy sources. Considering the lag in obtaining information about cost coefficients, time-varying generation demand, and renewable energy, feedback signal delay is a common obstacle in the optimization process of economic dispatch. This study focuses on the time-varying economic dispatch problem with delayed feedback signals and designs a decentralized online constrained optimization approach. In every update step, each node can access its individual time-varying local objective function with a delayed time sequence and selects the appropriate local online decision-making behavior based on information from various neighboring nodes to obtain the minimal cumulative cost. It is demonstrated that, assuming the non-fixed un-balanced digraphs maintain strong connectivity, the introduced online constrained optimization algorithm ensures that the sublinearly growing static network regret, and is fundamentally associated with feedback delays and step sizes.