A Discrete-Time FOLQR Framework for Centralized AGC in Multi-Area Interconnected Power Grids

This paper presents a discrete-time, centralized fractional-order linear quadratic regulator FOLQR for automatic generation control (AGC) of three-area interconnected nonreheat thermal systems. The AGC state explicitly includes the area control error (ACE) and tie-line power; a quadratic performance index penalizes ACE, its integral (IACE), and control effort. The continuous-time plant (governor–turbine dynamics and tie-line flows) is discretized at a fixed sampling interval, and a single centralized gain is obtained from the discrete algebraic Riccati equation; the fractional-order extension shapes memory in the feedback to temper rapid transients. Benchmark studies under 0.01 and 0.05 p.u. step-load disturbances show that FOLQR stabilizes the interconnection and consistently lowers peak excursions relative to a conventional discrete LQR (COQAGC) baseline—reducing frequency peaks by about 9–12% and tie-line peaks by 24–60% in the small-step case—while producing smoother actuator commands. Although FOLQR exhibits longer settling times, this trade-off is acceptable FOr multi-area AGC where limiting overshoot and tie-line excursions is operationally more critical than strict settling-time targets. The proposed controller retains a simple centralized, discrete-time structure with a modest computational burden, making it suitable FOr real-time AGC deployment in large interconnected grids and demonstrating for the first time, to our knowledge, a fractional-order LQR applied to a three-area thermal benchmark.