Frequency Stability Using an Exponential Time-Weighted Cost Function with Glider Snake Optimization for Diverse Controller Structures

Load frequency control (LFC) is essential for maintaining frequency stability and regulating tie-line power in interconnected power systems. Conventional fixed-order PI and PID controllers offer limited tuning flexibility for complex multi-area systems, whereas fractional-order controllers provide additional tuning parameters at the cost of increased optimization complexity. Furthermore, the performance of optimization-based LFC schemes depends strongly on the selected objective function, as conventional integral criteria, such as the integral of time-weighted absolute error (ITAE), may not adequately distinguish between candidate responses with different error magnitudes and persistence. To address this research gap, this study investigates an exponential time-weighted cost function, termed the integral exponential time-weighted error saturation (IEMTES) criterion. Its principal contribution is the exponential transformation of the time-weighted error before integration. This preserves an ITAE-related first-order contribution while introducing higher-order nonlinear error terms; a saturation mechanism limits the exponential argument. The objective is to evaluate the effectiveness of IEMTES, in combination with the Glider Snake Optimizer (GSO), for tuning four controller structures: PI, PID, FOPID, and FOIID. Two benchmark systems are considered: a two-area non-reheat thermal system and a three-area thermal–thermal–hydro system incorporating generation rate constraints (GRCs). For the investigated GSO–FOIID configuration in the three-area system, the ITAE decreases from 76.20 with ITAE-based optimization to 69.69 with IEMTES-based optimization, corresponding to an improvement of approximately 8.5%. Additional evaluations consider random step-load patterns, larger load perturbations, and parameter variations. The findings are limited to the investigated systems, controller structures, disturbances, parameter ranges, and optimization settings.