A hybrid approach for unit commitment with splitting technique and local search.

• Based on Lagrange duality theory and binary variable characteristics, ADMM's sub-problem is solved efficiently. • The unit status based on the solution set of ADMM is sorted, and the appropriate units are obtained for local search. • Solve UC problems with unit sizes above 1000 in the 1800 s, and the relative gap of the solution is less than 1 %. In the modern electricity market, solving the unit commitment (UC) problem becomes more challenging due to its large number of binary variables and coupling constraints. Therefore, the goal of this paper is to obtain nearly optimal solutions for such complex UC problems within specific time limits. To achieve this, a hybrid approach is presented in this paper, which incorporates a splitting technique and a local search for UC. The hybrid approach involves two steps. In the first step, the augmented Lagrange function (ALF) of UC is decomposed using a splitting technique based on the alternating direction method of multipliers (ADMM). The resulting sub-problems can be effectively solved in a distributed manner by utilizing Lagrange duality theory and binary variable characteristics. Additionally, the penalty parameters of the ALF are updated effectively with the sub-gradient method to diminish the influence of the initial penalty parameters on the algorithm. In the second step, the appropriate relaxation unit is selected using the binary variable characteristics in the current solution of ADMM. Further, the high-quality feasibility of the final solution is ensured through local search. The hybrid approach utilizes ADMM to quickly fix most binary variables in the UC model and then leverages the CPLEX solver to solve the mixed-integer linear programming (MILP) formulation of UC by fixing a large number of binary variables. Consequently, the CPLEX solver needs to branch fewer binary variables, reducing the local search time. The hybrid approach is applied to solve several power systems consisting of up to 1000 units. Compared with the CPLEX solver, the solution of the hybrid approach is found to be stable, and the relative gap of the solution is less than 1 %, demonstrating the effectiveness and performance of the proposed approach while meeting the time limit requirements of the power industry dispatching. [ABSTRACT FROM AUTHOR]