Linearisation Based Decomposition Method for Circle Approximation in AC Network Constrained Unit Commitment

Second-order cone programming (SOCP) is one of the common methods used to solve AC network-constrained unit commitment (UC) problems. The main shortcoming of this approach is the computational complexity increasing exponentially with the system size. Additionally, under high-system loading conditions, the results may not be exact. To address these issues, we propose a decomposition algorithm. First, we linearise quadratic relaxation for the UC conic formulation. Next, we apply an outer approximation algorithm that selects optimal cuts at each iteration. Numerical experiments show the effectiveness of the algorithm compared to the standard SOCP.