Comparison of an Improved Metaheuristic and Mathematical Optimization Based Methods to Solve the Static AC TNEP Problem

φ 1 Penalty constant when the topology use fictitious generators (10 7 ).Variables n kl Number of circuits added between nodes k and l. r P Non-supplied active power.r Q Non-supplied reactive power.V Voltage magnitude.θ Phase angle vector.P G Active power generation vector.Q G Reactive power generation vector.S f rom /S to Apparent power flow (MVA) through the branches in both terminals.n c Number of times that the fictitious generator was used in the nl contingencies.Metaheuristics Variables N I Size of population or total number of individuals.n Size of the individual.I max Max.number of iterations.F Mutation rate.C r Crossover factor.η Learning rate.N best Number of individuals with the best solutions.µ 0 , σ 0 Mean and standard deviation.p comb Combination probability.p double-mut Probability of mutation.χ Constriction factor.k 1 and k 2 Cognitive and social parameter.N R Neighbourhood radius.