Distributed Economic Dispatch For Smart Grids

The last few years have witnessed a growing interest in dispatching power genera-tion for smart grids.The distributed economic dispatch problem is one of the most fun-damental problems for smart grids,which aims at distributing the total power demand among the generators to minimize the operating cost under certain security constrains.In this thesis,we study the economic dispatch problems with heterogeneous time-delay and communication uncert,ainty by employing the knowledge of graph theory,convex optimization,probability theory and Lyapunov stability theory.The main innovative works and key points are summarized as follows.First,we study the distributed economic dispatch problems with heterogeneous time-delay,in which the primary objective is to seek a distributed design that can handle heterogeneous time-delays,while preserving agents' privacy-a fundamental prerequi-site that has become gradually important for cyber-physical systems.For this purpose,we design a state predictor for each agent to compensate the effect of heterogeneous time-delays,which allows the agents to predict the missing states between two consec-utive update times.Based upon the predictor,we present a distributed gradient-descent algorithm to locally update the outputs of the generators,which guarantees that the optimal solution is attained in an asymptotic manner.Among other things,we incor-porate a privacy preservation scheme to the proposed algorithm in order to preserve agents' privacy and delicately characterize its convergence,differential privacy prop-erties,as well as accuracy.Second,we study the distributed dynamical economic dis-patch problems for smart grids,different from the above economic dispatch problem,the existence of ramp-rate constraint should not be ignored.Our primary objective is to seek a distributed scheme that can eliminate the effects of communication uncertainties.For this purpose,we design an adaptive weight-adjustment technique that enables the dispatch algorithms to choose the communication weights among neighboring gener-ating units.Based upon this technique,we present a distributed primal-dual consensus algorithm.We show that the optimal solution is achieved asymptotically under the proposed distributed optimization scheme.