Unit commitment using Lagrangian relaxation and particle swarm optimization

Unit commitment (UC) is a NP-hard nonlinear mixed-integer optimization problem. This paper proposes ELRPSO, an algorithm to solve the UC problem using Lagrangian relaxation (LR) and particle swarm optimization (PSO). ELRPSO employs a state-of-the-art powerful PSO variant called comprehensive learning PSO to find a feasible near-optimal UC schedule. Each particle represents Lagrangian multipliers. The PSO uses a low level LR procedure, a reserve repairing heuristic, a unit decommitment heuristic, and an economic dispatch heuristic to obtain a feasible UC schedule for each particle. The reserve repairing heuristic addresses the spinning reserve and minimum up/down time constraints simultaneously. Moreover, the reserve repairing and unit decommitment heuristics consider committing/decommitting a unit for a consecutive period of hours at a time in order to reduce the total startup cost. Each particle is initialized using the Lagrangian multipliers obtained from a LR that iteratively updates the multipliers through an adaptive subgradient heuristic, because the multipliers obtained from the LR tend to be close to the optimal multipliers and have a high potential to lead to a feasible near-optimal UC schedule. Numerical results on test thermal power systems of 10, 20, 40, 60, 80, and 100 units demonstrate that ELRPSO is able to find a low-cost UC schedule in a short time and is robust in performance.