State-space design and analysis of load frequency control with advanced modeling and controller strategies for single, two, and three-area power systems

Load Frequency Control (LFC) is a fundamental issue in modern power systems, aimed at maintaining system frequency at its nominal value (50/60 Hz) while ensuring accurate regulation of tie-line power exchanges in interconnected areas. This study develops a comprehensive state-space modeling framework for single-area, two-area, and three-area power systems to support dynamic analysis and controller design. Integral controllers and optimal control strategies based on the Riccati equation—namely, Linear Quadratic Regulator (LQR) and Linear Quadratic Gaussian (LQG)—are implemented to enhance system performance. These controllers effectively minimize frequency and voltage deviations under varying load conditions, thereby improving power quality. To achieve faster and more precise control, a Digital Deadbeat Controller (DDC) is also proposed, ensuring rapid convergence to steady-state conditions. A comparative analysis across different system configurations highlights the steady-state frequency deviations and overall performance improvements. The study also addresses persistent challenges caused by memory-dependent nonlinearities such as backlash/deadband, which induce limit cycle (LC) oscillations and degrade system stability. Backlash nonlinearity, inherent in speed governors used in LFC, plays a significant role in these oscillations. Two methods are proposed to mitigate LC behavior: signal stabilization using deterministic or random inputs. Simulation results obtained using MATLAB/Simulink demonstrate the effectiveness of these approaches. The findings confirm that both DDC and signal stabilization techniques achieve the desired performance (Δf = 0, t→0), indicating robust and efficient control suitable for practical power system applications.