Abstract
The Lagrangian relaxation- (LR-) based methods are commonly used to solve the thermal unit commitment (UC) problem which is an important subject in power system engineering. The main drawback of this group of methods is the difference between the dual and the primal solutions which gives some significant problems on the quality of the feasible solutions. In this paper, a new approach, feasible modified subgradient (F-MSG) method which does not require finding an unconstrained global minimum of the Lagrangian function and knowing an optimal value of the problem under consideration in order to update dual variables at the each iteration, is firstly used for solving the thermal UC problem. The major advantage of the proposed approach is that it guarantees the zero duality gap and convergence independently from the size of the problem. In order to discuss the advantages of this method, the four-unit Tuncbilek thermal plant, which is located in Kutahya region in Turkey, is chosen as a small test system. The numerical results show that F-MSG gives better solutions as compared to the standard LR method.
Highlights
Solving thermal UC problem is very important for power system optimization
F-MSG method solves without any duality gap for large class of nonconvex constrained problems. This proposed approach is compared to LR method to show that F-MSG gives an optimal solution obtaining the zero duality gap value
F-MSG method is applied to the system to find the feasible results and feasible cost, dual cost, and duality gap values
Summary
Solving thermal UC problem is very important for power system optimization. The thermal UC problem, which is defined as a nonlinear, mixed-integer, and nonconvex, is considered to be an NP Nonlinear-Programming hard problem. There have been various methods for solving the thermal UC problem in the literature They are based on mathematical programming and metaheuristic-based approaches. If the LR-based methods are used for solving the UC problem, dual solution may be far away from the optimal solution. One of the methods based on dual optimization technique, F-MSG method, which has the best performance in eliminating the duality gap in the literature, is firstly used for solving the thermal UC problem as a novel approach. F-MSG method solves without any duality gap for large class of nonconvex constrained problems. This proposed approach is compared to LR method to show that F-MSG gives an optimal solution obtaining the zero duality gap value. The conclusions are presented, the main contributions of this paper are highlighted, and possible research directions are discussed
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