Modified Gravitational Search Algorithm with tracing-based transmission-loss allocation for Optimal Power Flow optimization in deregulated power systems

Efficient operation of deregulated electricity markets requires Optimal Power Flow (OPF) techniques that determine feasible operating conditions while minimizing network transmission losses under system constraints. Existing OPF formulations determine the optimal operating point but do not explicitly associate the optimized transmission losses with individual generators and consumers. The conventional Gravitational Search Algorithm exhibits limited convergence efficiency because its search process strongly depends on the quality of the initial population. To address this limitation, a two-stage initialized Modified Gravitational Search Algorithm (MGSA) is developed and integrated with a power flow tracing framework. The optimized transmission losses are then allocated to generators and loads using a tracing-based proportional sharing mechanism (PSM) to give the optimal loss an intuitive and fair allocation. The proposed framework is evaluated using IEEE 30-bus and Indian 24-bus benchmark systems and further compared with recent population-based optimization algorithms. With simulation and statistical analysis, MGSA provides lower transmission losses, faster convergence rates, improved computational efficiency and improved stability of solutions, and is therefore a promising approach for transparent transmission-loss allocation in deregulated electricity markets.