An optimized Lagrangian approach to reactive power compensation in nonlinear traction power-supply systems

A modified optimization method for reactive power compensation in nonlinear traction power-supply systems is presented. The proposed approach, based on the Lagrange multiplier technique, simultaneously determines the optimal capacity and installation locations of compensating capacitor banks while accounting for existing capacitive reactance and preinstalled devices. Unlike traditional methods, the developed model explicitly considers the nonlinear and time-varying load behavior typical of traction power networks. The objective function minimizes active power losses and total system costs under voltage-quality constraints. Numerical experiments demonstrate that the proposed algorithm can reduce power losses by up to 30 %, ensuring improved voltage stability and energy efficiency. The approach is computationally efficient and can be integrated into real-time reactive power control systems for traction substations.