Optimal long-term unit commitment in large scale systems including fuel constrained thermal and pumped-storage hydro

A method is discussed for solving a long-term unit commitment problem in a large-scale power system consisting of three types of units (1) thermal, (2) fuel-constrained thermal, and (3) pumped-storage hydro. In such a system, a long-term schedule ranging from one week to one month must be determined, because the LNG/LPG fuel is assigned to the fuel-constrained unit at weekly or monthly intervals owing to contractual restrictions and also because the operating cycle of the pumped-storage unit is one week for economical reasons. The subgradient method using the Lagrangian relaxation for a daily unit commitment is not suitable to the long-term problem, since the convergence to the dual maximum is not so good. To overcome this defect, the authors develop an algorithm for dual maximization based on the variable metric method. A numerical example is given that validates the algorithm.>