Global solution method for decentralised multi‐area SCUC and savings allocation based on MILP value functions

Abstract

To address the issue that Lagrangian dual function based algorithms cannot guarantee convergence and global optimality for decentralized multi-area security constrained unit commitment (M-SCUC) problems, a novel decomposition and coordination method using MILP (mixed integer linear programming) value functions is proposed in this paper. Each regional system operator sets the tie-line power injections as variational parameters in its regional SCUC model, and utilizes a finite algorithm to generate a MILP value function, which returns the optimal generation cost for any given interchange scheduling. With the value functions available from all system operators, theoretically, a coordinator is able to derive a globally optimal interchange scheduling. Since power exchanges may alter the financial position of each area considerably from what it would have been via scheduling independently, we then propose a fair savings allocation method using the values functions derived above and the Shapley value in cooperative game theory. Numerical experiments on a two-area 12-bus system and a three-area 457-bus system are carried out. The validness of the value functions based method is verified for the decentralized M-SCUC problems. The outcome of savings allocation is compared with that of the locational marginal cost based method.