An information gap decision theory and improved gradient-based optimizer for robust optimization of renewable energy systems in distribution network

In this paper, a robust fuzzy multi-objective framework is performed to optimize the dispersed and hybrid renewable photovoltaic-wind energy resources in a radial distribution network considering uncertainties of renewable generation and network demand. A novel multi-objective improved gradient-based optimizer (MOIGBO) enhanced with Rosenbrock's direct rotational technique to overcome premature convergence is proposed to determine the problem optimal decision variables. The deterministic optimization framework without uncertainty minimizes active energy loss, unmet customer energy, and renewable generation costs. The study also examines the impact of dispersed and hybrid renewable resources on solving the problem. In the robust optimization framework considering the deterministic obtained results, the focus is on determining the maximum uncertainty radius (MUR) of renewable resource generation and network demand based on the uncertainty risk. The MURs and system robustness are optimally determined using information gap decision theory (IGDT) and the MOIGBO, considering various uncertainty budgets under worst-case scenarios. The deterministic results indicate that the MOIGBO effectively balances the objectives and identifies the final solution within the Pareto front, according to fuzzy decision-making. The results also reveal that the dispersed case yields better objective values than the hybrid case. Furthermore, the MOIGBO outperforms MOGBO and multi-objective particle swarm optimization (MOPSO) in improving distribution network operations. The robust results show that maximum system robustness is achieved at 30% uncertainty risk due to forecasting errors, with MUR values of 0.54% for resource production and 12.56% for load demand.