Unit commitment (UC) is a consistent research interest of the electric power system because of its potential economic savings. This problem is quite difficult due to its inherent high-dimensional, nonconvex, discrete, and nonlinear nature. Many methods have been developed for solving the UC problem. Besides heuristic methods, the optimization-based methods for unit commitment include dynamic programming (DP) [161, 162], Lagrangian relaxation (LR) [17, 163], integer programming, and Benders' decomposition, etc. Among these methods, dynamic programming and Lagrangian relaxation are the most extensively used. DP searches the solution space consisting of the unit status combinations for an optimal solution. The time periods of the time horizon studied are known as the stages of the DP problem. Typically each stage represents one hour of operation. The combinations of unit status within a time period are known as the states of the DP problem. DP suffers from the “curse of dimensionality” because the problem solution space grows rapidly with the number of generating units to be committed. A framework of the LR method is presented in Guan et al [17]. The basic idea of LR is to relax the systemwide constraints such as the power and spinning reserve requirements by using Lagrange multipliers, then to decompose the problem into individual unit commitment subproblems, which are much easier ...

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