Pure resistive SFCL and hybrid resistive SFCL were compared in order to determine suitable solutions for electric power systems.
Furthermore, multi-objective exergoeconomic optimization is performed using a genetic algorithm based on hybrid techniques in order to determine optimum solutions.
In order to determine feasible solutions for the problem, which appears to be a hard task for general-purpose solvers, we also develop and compare two metaheuristic approaches, namely a Tabu Search and a Variable Neighborhood Search algorithm.
In order to determine weak solutions of (1.3) in a suitable functional space E, we look for critical points of the functional J : E → R defined by J ( v ) = 1 p ∫ R N A ( x, v ) | ∇ v | p d x + 1 p ∫ R N ( b ( x ) − λ ) | v | p d x − ∫ R N F ( x, v ) d x, ∀ v ∈ E, (1.4).
In order to determine the solution of this equation, we first need to determine the solution of the following differential equation: D t m u ( x, t ) = F ( u, ∂ u ∂ x ⋯ ∂ n u ∂ x n, x, t ), t > 0, (2).
In order to determine the solution of this equation, we first need to determine the solution of the following differential equation: F ( u, D t k u, D x m u, x, t ) = 0, t > 0, (12).
In order to determine the solution of this equation, we first need to determine the solution of the following differential equation: D x m u ( x, t ) = F ( u, ∂ u ∂ t ⋯ ∂ n u ∂ t n, x, t ), t > 0, (7).
We introduce one more arbitrary boundary condition in addition to the boundary conditions (42) and (43) in order to determine the solution.
In order to determine the solution of initial-boundary values problem (9), (11 1,2, (12 2 and (13), we first take the Laplace transform [25] of Equation (9) and obtain q V ̄ ( y, q ) + λ q 2 V ̄ ( y, q ) = ν 1 + λ r q ∂ 2 V ̄ ( y, q ) ∂ y 2, (14).
