Differential-Algebraic Equation-Constrained Frequency-Secured Stochastic Unit Commitment

With the increasing share of renewable energy, conventional synchronous generators are being replaced, which threatens the frequency security of power systems and requires a more careful plan and operations of unit commitment and primary frequency response reserve. In this paper, we propose a novel differential-algebraic equations (DAE)-constrained frequency-secured stochastic unit commitment for the first time. A continuous-time function is used to model the frequency variation and DAEs for frequency dynamics are directly incorporated into the formulation of stochastic unit commitment. To solve the established DAE-constrained optimization, we adopt Bernstein polynomial spline-based solution space transformation and operational matrices and reformulate DAEs into general algebraic constraints. Case studies demonstrate the effectiveness of the proposed method in guaranteeing frequency security.