An improved probability efficient point method based on outer approximation for unit commitment of multi-area power systems

• A novel PEP model for chance constraints with multiple random variables is established • An outer approximation theory is applied to accelerate converting joint chance constraints • The strengthened valid inequalities are proposed to accelerate the iteration process • The proposed method is proved efficient when the size of random variables increases The increasing penetration of renewable energy in multi-area power systems with renewable energy (MAS-RE) introduces significant uncertainties, posing substantial challenges to the unit commitment (UC) problem. Joint chance constraints (JCCs) effectively characterize the dependencies among uncertain variables, and the p -efficient point (PEP) method is effective for solving JCCs in the UC problem. However, with the increasing dimensionality and distributional heterogeneity of uncertainties, the PEP method faces challenges in maintaining accuracy and computational efficiency. To address these challenges, we propose a multi-dimensional PEP-based reformulation method for JCCs with multiple types of random variables, which leverages the additive property of distributions across different types of random variables to address the challenges posed by multi-type uncertainties. Subsequently, we apply the outer approximation method to PEP computation by categorizing and approximating the decision variables to accelerate the iterative process. Finally, case studies demonstrate that the proposed framework effectively addresses the UC problem of MAS-RE, ensuring the feasibility of the UC plan while significantly reducing the computation time.