Distributed multi-agent optimization protocol over energy management networks

Distributed multi-agent optimization is a key methodology to solve problems arising in large-scale networks, including recent energy management systems that consist of such many entities as suppliers, consumers, and aggregators, who behave as independent agents. In this chapter, we focus on distributed multi-agent optimization based on the linear consensus protocol and exact penalty methods, which can deal with a wide variety of convex problems with equality and inequality constraints. The agents in the network do not need to disclose their objective and constraint functions to the other agents, and the optimization is executed only by sending and receiving decision variables that are common and are needed to coincide among the agents in the network. The protocol shown in this chapter can work over unbalanced networks to obtain a Pareto optimal solution, which is applied to solve minimax problems via distributed computation. After describing the protocol, we provide a concrete proof of the convergence of the decision variables to an optimal consensus point and show numerical examples including an application to a direct-current optimal power flow problem.