Unit Commitment with Joint Chance Constraints in Multi-area Power Systems with Wind Power Based on Partial Sample Average Approximation

Joint chance constraints (JCCs) can ensure the consistency and correlation of stochastic variables when participating in decision-making. Sample average approximation (SAA) is the most popular method for solving JCCs in unit commitment (UC) problems. However, the typical SAA requires large Monte Carlo (MC) samples to ensure the solution accuracy, which results in large-scale mixed-integer programming (MIP) problems. To address this problem, this paper presents the partial sample average approximation (PSAA) to deal with JCCs in UC problems in multi-area power systems with wind power. PSAA partitions the stochastic variables and historical dataset, and the historical dataset is then partitioned into non-sampled and sampled sets. When approximating the expectation of stochastic variables, PSAA replaces the big-M formulation with the cumulative distribution function of the non-sampled set, thus preventing binary variables from being introduced. Finally, PSAA can transform the chance constraints to deterministic constraints with only continuous variables, avoiding the large-scale MIP problem caused by SAA. Simulation results demonstrate that PSAA has significant advantages in solution accuracy and efficiency compared with other existing methods including traditional SAA, SAA with improved big-M, SAA with Latin hypercube sampling (LHS), and the multi-stage robust optimization methods.