Document Type : Research article


Electrical Engineering Department, LES laboratory, University of August 20th, 1955, Skikda, Algeria


This paper presents a solution to the Optimal Power Flow (OPF) problem combined economic dispatch with valve-point effect and Emission Index (EI) in electrical power networks using the physics-inspired optimization method, which is the Gravitational Search Algorithm (GSA). Our main goal is to minimize the objective function necessary for the best balance between energy production and its consumption which is presented in a nonlinear function, taking into account equality and inequality constraints. The objective is to minimize the total cost of active generations, the active power losses, and the emission index. The GSA method has been examined and tested on the standard IEEE 30-bus test system with various objective functions. The simulation results of the used methods have been compared and validated with those reported in the recent literature. The results are promising and show the effectiveness and robustness of the used method. It should be mentioned that from the base case, the cost generation, the active power losses, and the emission index are significantly reduced to 823 ($/h), 6.038 (MW), and 0.227 (ton/h), which are considered 5.85%, 61.61%, and 44.63%, respectively.


  • In all multi-objective functions we use the aggregation weighting function;
  • Gravity Search Algorithm (GSA) is the recent developed meta-heuristic algorithm;
  • Nonlinear and non-smooth of the fuel costs function;
  • The change of weight factors affected directly the optimal values of the different objective functions;
  • The masses of agents are calculated using fitness evaluation.


Main Subjects