This article presents a new efficient optimization technique namely the Multi- Objective Improved Differential Evolution Algorithm (MOIDEA) to solve the multiobjective optimal power flow problem in power systems. The main features of the Differential Evolution (DE) algorithm are simple, easy, and efficient, but sometimes, it is prone to stagnation in the local optima. This paper has proposed many improvements, in the exploration and exploitation processes, to enhance the performance of DE for solving optimal power flow (OPF) problems. The main contributions of the DE algorithm are i) the crossover rate will be changing randomly and continuously for each iteration, ii) all probabilities that have been ignored in the crossover process have been taken, and iii) in selection operation, the mathematical calculations of the mutation process have been taken. Four conflicting objective functions simultaneously have been applied to select the Pareto optimal front for the multi-objective OPF. Fuzzy set theory has been used to extract the best compromise solution. These objective functions that have been considered for setting control variables of the power system are total fuel cost (TFC), total emission (TE), real power losses (RPL), and voltage profile (VP) improvement. The IEEE 30-bus standard system has been used to validate the effectiveness and superiority of the approach proposed based on MATLAB software. Finally, to demonstrate the effectiveness and capability of the MOIDEA, the results obtained by this method will be compared with other recent methods.

Electrified railways are an example of AC single phase distribution networks. A non-negligible amount of active and nonactive power may be related to harmonics, especially for distorted highly-loaded systems. The paper considers the relevance of the harmonic power terms in order to identify distortion sources in a single-point perspective, in line with the approach of EN 50463 for the quantification of the power and energy consumption. Some single-point Harmonic Producer Indicators (HPI) based on harmonic active power direction and nonactive distortion power terms are reviewed and evaluated using pantograph voltage and current measured during several hours of runs in two European AC railways (operated at 16.7 and 50 Hz). The HPI based on active power shows to be consistent and provides detailed information of rolling stock characteristic components under variable operating conditions; those based on nonactive distortion power are global indexes and hardly can operate with complex harmonic patterns in variable operating conditions.