Optimized the locations and sizes of FACTS devices on electrical network involving wind power using a new hybrid stochastic algorithm

Abstract This article focuses on utilizing a new hybrid optimization algorithm called the Fitness-Distance Balance-based Archimedes Optimization Algorithm (FDB-AOA) to solve the Optimal Power Flow (OPF) problems within a recently adopted electrical transmission grid, specifically the modified IEEE-30 bus system. This system integrates thermal and wind -based generating units, including various types of Flexible AC Transmission System (FACTS) devices. Several tests are performed where the stochastic wind energy is modeled using probability density functions. The optimization goal takes into account the cost of thermal generation, the direct cost of scheduled wind power, and the penalty cost for underestimating wind power. The locations and sizing of FACTS devices are optimized with aim of reducing several fitness functions. The optimization results achieved by the proposed method in solving single objective functions were more effective in finding the optimal solution compared to several well-known algorithms. The results show the superiority of the proposed method in the majority of case studies, as it achieved a better optimum solution with a total generation cost ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mtext>gen</mml:mtext> </mml:mrow> </mml:msub> </mml:math> ) value of 806.9817 $/h, and a real power loss ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mtext>loss</mml:mtext> </mml:mrow> </mml:msub> </mml:math> ) value 1.7619 MW, also yields a competitive gross cost ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mtext>gross</mml:mtext> </mml:mrow> </mml:msub> </mml:math> ) value of 1104.6652 $/h compared to those obtained by the other algorithms. In contrast, the statistical analysis proven the superiority of this algorithm where the standard deviations (SD) required in solving the single objective problem ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mtext>gen</mml:mtext> </mml:mrow> </mml:msub> </mml:math> ) is 0.0996, which are better compared to other techniques. the simulation results demonstrate that the FDB-AOA optimizer is robust than other approaches, like the Success history based-adaptive differential evolution (SHADE) algorithm, MSA (Moth Swarm Algorithm), and ABC (artificial bee colony) integrated with the SF (superiority of feasible solutions) approach, in solving OPF problems involving the integration of both thermal and wind power plants along with FACTS devices.