  Efficient methods for large-scale security constrained unit commitment (SCUC)
problems have long been an important research topic and a challenge especially
in market clearing computation. For large-scale SCUC, the Lagrangian relaxation
methods (LR) and the mixed integer programming methods (MIP) are most widely
adopted. However, LR usually suffers from slow convergence; and the
computational burden of MIP is heavy when the binary variable number is large.
In this paper, a variable reduction method is proposed: First, the time-coupled
constraints in the original SCUC problem are relaxed and many single-period
SCUC problems (s-UC) are obtained. Second, LR is used to solve the s-UCs.
Different from traditional LR with iterative subgradient method, it is found
that the optimal multipliers and the approximate UC solutions of s-UCs can be
obtained by solving linear programs. Third, a criterion for choosing and fixing
the UC variables in the SCUC problem is established, hence the number of binary
variables is reduced. Last, the SCUC with reduced binary variables is solved by
MIP solver to obtain the final UC solution. The proposed method is tested on
the IEEE 118-bus system and a 6484-bus system. The results show the method is
very efficient and effective.
