A Novel Distributed Consensus-Based Approach to Solve the Economic Dispatch Problem Incorporating the Valve-Point Effect and Solar Energy Sources

• Published in: Energies (Basel) 2023-01, Vol.16 (1), p.447
• Main Authors: Moin, Muhammad, Ahmed, Waqas, Rehan, Muhammad, Iqbal, Muhammad, Ullah, Nasim, Zeb, Kamran, Uddin, Waqar
• Format: Article
• Language: English
• Subjects: Algorithms; Alternative energy sources; Approximation; Carbon footprint; Communication; consensus; Cooperation; Cost function; distributed algorithm; Distribution functions; economic dispatch problem; Electric power distribution; Electric power systems; Energy; Energy resources; Energy sources; Generators; Genetic algorithms; Graph theory; incremental cost; Integer programming; Load dispatching; Mathematical optimization; Methods; non-smooth cost function; Optimization techniques; Photovoltaic cells; Power plants; Probability distribution functions; renewable energy sources; Renewable resources; Solar energy; Stability analysis; Topology
• ISSN: 1996-1073; 1996-1073
• DOI: 10.3390/en16010447

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.