Multi-Area Frequency Dynamic Constrained Unit Commitment Based on Bernstein Polynomial Approximation

Abstract

The escalating integration of renewable energy sources into modern power systems has significantly reduced system inertia, intensifying frequency stability risks. Conventional frequency-constrained unit-commitment models inadequately capture inter-area frequency disparities and consequently misrepresent regional frequency dynamics, which is a critical shortcoming in multi-area power systems with nonuniform inertia distribution. This paper proposes a multi-area frequency-constrained unit commitment (MAFCUC) model that rigorously embeds regional frequency security constraints. Bernstein polynomial approximations are used to transcribe the differential–algebraic equations describing multi-area frequency response into tractable algebraic constraints. The proposed MAFCUC is formulated as a mixed-integer linear programming model, and an adaptive bi-level decomposition algorithm is developed to improve the solution efficiency, which dynamically estimates frequency nadir timing to streamline solution processes. The tightness and effectiveness of the proposed model in ensuring multi-area frequency security are validated across multiple test systems of different scales. Compared to conventional center-of-inertia-based methods, the MAFCUC model accurately captures regional frequency oscillations and improves frequency stability.