  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.
