Abstract
This research focused on the design of a distributed approach using consensus theory to find an optimal solution of the economic dispatch problem (EDP) by considering the quadratic cost function along with the valve-point effect of generators and renewable energy systems (RESs). A distributed consensus approach is presented for the optimal economic dispatch under a complex valve-point effect by accounting for solar energy in addition to conventional power plants. By employing the beta distribution function and communication topology between generators, a new optimality condition for the dispatch problem was formulated. A novel distributed updation law for generation by considering the communication between generators was provided to deal with the valve-point effect. The convergence of the proposed updation law was proved analytically using Lyapunov stability and graph theory. An algorithm for ensuring a distributed economic dispatch via conventional power plants, integrated with solar energy, was addressed. To the best of the authors' knowledge, a distributed nonlinear EDP approach for dealing with the valve-point loading issue via nonlinear incremental costs has been addressed for the first time. The designed approach was simulated for benchmark systems with and without a generation capacity constraint, and the results were compared with the existing centralized and distributed strategies.