Constrained Load Frequency Control in Power Systems via Integrated Stochastic Model Predictive Control and Unscented Kalman Filter

• Published in: Proceedings of the American Control Conference pp. 729 - 735
• Main Authors: Liu, Yuqian, Ma, Tong
• Format: Conference Proceeding
• Language: English
• Published: AACC 08.07.2025
• Subjects: Costs; Frequency control; Kalman filters; Mathematical models; Power system stability; Predictive control; Scenario generation; State estimation; Uncertainty; Wind forecasting
• ISSN: 2378-5861
• DOI: 10.23919/ACC63710.2025.11107867

By incorporating the unscented Kalman filter (UKF) into the stochastic model predictive control (SMPC) architecture, a UKF-SMPC framework is formulated to solve the load frequency control (LFC) problem of a power system subject to wind resources and load disturbances. To suppress the frequency deviations resulting from the stochastic uncertainties and reduce the mechanical power cost, a finite-horizon constrained optimization problem is formulated to maintain the stability of the power system and improve the overall performance. Considering the stochastic nature of wind resources and load disturbances, the UKF is incorporated into the SMPC directly to estimate the states and to propagate the mean and covariance of the states forward in time by taking the state estimation errors and additive noise from the disturbances into consideration. The statistical description including the mean and covariance estimates of the state provided by the UKF are employed to reformulate the cost function and chance constraints. By resorting to the Chebyshev-Cantelli inequality, the chance constraints on the load frequency deviation are reformulated as deterministic ones, which are subsequently linearized at the cost of additional conservativeness. To guarantee the convergence and recursive feasibility of the UKF-SMPC framework, two kinds of terminal constraints are applied, that is, "robust horizon" and Lyapunov equation. By resorting to the Schur complement, the finite-horizon constrained optimization problem is recast as a linear one with a set of linear matrix inequalities (LMIs), which yields a Semidefinite Programming (SDP) problem. Simulation results validate the effectiveness of our approach.