Design of the Novel Fractional Order Hybrid Whale Optimizer for Thermal Wind Power Generation Systems with Integration of Chaos Infused Wind Power

Abstract

This article introduces a novel optimization approach known as fractional order whale optimization algorithm (FWOA). The proposed optimizer incorporates the idea of fractional calculus (FC) into the mathematical structure of the conventional whale optimization algorithm (WOA). To validate the efficiency of the proposed FWOA, it is applied to address the challenges associated with the economic load dispatch (ELD) problem, which is a nonconvex, nonlinear, and non-smooth optimization problem. The objectives associated with ELD such as fuel cost and wind power generation cost minimization are achieved by taking into consideration different practical constraints like valve point loading effect (VPLE), transmission line losses, generator constraints, and stochastically variation of renewable energy sources (RES) integration. RES, particularly wind energy, has garnered more attention in recent times due to a range of environmental and economic factors. Stochastic wind (SW) power is also included in the ELD problem formulation. The incomplete gamma function (IGF) quantifies the influence of wind power. To assess its efficacy, the suggested approach is applied to a range of power systems including 3 generating units, 13 generating units and 40 generating units, consisting of 37 thermal units and 3 wind power units. To further strengthen the performance of the optimizer, the FWOA is hybridized with the interior point algorithm (IPA) to further refine the outcomes of the FWOA. The FWOA and IPA are used to address the problem of ELD while including the unpredictable nature of wind power. The simulation results of the suggested technique are compared with the most advanced heuristic optimization methods available, and it has been observed that the proposed optimizer obtained a superior and refined solution when compared to other state of the art optimization techniques. Furthermore, the efficacy of the suggested strategy in enhancing the solution of the ELD issue is validated through statistical analysis in terms of minimum fitness value.

Keywords

• whale optimization algorithm
• fractional calculus
• interior point algorithm
• economic load dispatch problem
• stochastic wind