Economic power dispatch in smart grids: a framework for distributed optimization and consensus dynamics

Abstract

By using the distributed consensus theory in multi-agentsystems, the strategy of economic power dispatch is studied in a smartgrid, where many generation units work cooperatively to achieve an optimal solution in a local area. The relationship between thedistributed optimization solution and consensus in multi-agentsystems is first revealed in this paper, which can serve as a general framework forfuture studies of this topic. First, without the constraints ofcapacity limitations, it is found that the total cost forall the generators in a smart grid can achieve the minimal value if theconsensus can be reached for the incremental cost of all the generation unitsand the balance between the supply and demand of powers iskept. Then, by designing a distributed consensus control protocol inmulti-agent systems with appropriateinitial conditions, incremental cost consensus can be realized and the balance for the powers can also besatisfied. Furthermore, the difficult problem for distributedoptimization of the total cost function with bounded capacitylimitations is also discussed. A reformulated barrier function isproposed to simplify the analysis, under which the total cost canreach the minimal value if consensus can be achieved for themodified incremental cost with some appropriate initial values.Thus, the distributed optimization problems for the costfunction of all generation units with and without bounded capacitylimitations can both be solved by using the idea of consensus inmulti-agent systems, whose theoretical analysis is still lackingnowadays. Finally, some simulation examples are given toverify the effectiveness of the results in this paper.