Research On Multi-objective Optimal Power Flow Problem Based On Modified Firefly Algorithm

The optimal power flow(OPF)is not only a predominant technique to make the quality of power better,but also one of the most basic and important methods to ensure the safe and fair-weather operation of the power system.The main objective function of OPF problem was already formulated as fuel cost minimization in the past studies.However,the increasing demand for electricity and serious environmental problems make it take objective such as the active power losses and emission into account.In such situations,it is practicable to minimize the losses and the emission as the alternative objective functions of the OPF problem.Therefore,the OPF problem is modeled as a multi-objective optimal power flow(MOOPF)problem,and has become an indispensable potential application for power system operation planning.For the multi-objective,large-scale,and multi-constrained MOOPF problem,the following research will be done.Firstly,combined with the mathematical descriptions of multi-objective optimization problems and optimal power flow problem,the mathematical model of MOOPF problem is established,including a series of constraints and four objective functions,namely,basic fuel cost,fuel cost with valve-point effect,power loss,and emission.Because the MOOPF problem trends to be introduced with many constraints required to tackle,comparing with frequently-used penalty function based method(PFA),a novel constraint processing approach named constraints-prior Pareto-domination approach(CPA)is proposed for ensuring none violation of various inequality constraints on dependent variables.Moreover,in order to prove the feasibility and effective improvement of CPA to solve the MOOPF problem,a comparison study between MOFA-CPA and MOFA-PFA is performed on two test systems including two bi-objective optimization cases and three tri-objective optimization cases.The simulation results demonstrate the capability and superiority of the proposed CPA for dealing with inequality constraints on dependent variables.Secondly,a new multi-objective dimension-based firefly algorithm(MODFA)is proposed for the deficiency and blank of standard MOFA in the study of the MOOPF,as well as the characteristics of slow convergence and low accuracy.One modification of the MODFA algorithm is to introduce a global guiding mechanism to replace the original movement mechanism of the fireflies,the other is to adopt a dimension-based technology,where updates each firefly along different dimensions.In order to validate the performance of the proposed MODFA for multi-constrained MOOPF,the MODFA and frequently-used NSGA-III,NSGA-II,and MOPSO algorithms are implemented in three different scales of test systems with eight cases.The four algorithms adopt the optimization strategies such as the crowding distance calculation and non-dominated sorting to sustain well-distributed Pareto front(PF)and the proposed CPA to deal with the state variables under the inequality constraints.The experimental results show that the four algorithms all obtain Pareto front with uniform distribution and diversity,which verifies the rationality of the model and the effectiveness of the algorithms.Compared with NSGA-III,NSGA-II,and MOPSO,the proposed MODFA has the ability to obtain Pareto front with more uniform distribution and higher quality.The improved MODFA has better search capabilities than the standard MOFA.Finally,in order to compare the performance of NSGA-III,NSGA-II,and MOPSO,and the proposed MODFA,two performance metrics,namely,generation distance and hypervolume are considered to evaluate approximation,distribution,and diversity of Pareto front.And the statistical results have been analyzed using the Wilcoxon signed rank test.