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

To address the issue that Lagrangian dual-function-based algorithms cannot guarantee convergence and global optimality for decentralised multi-area security constrained unit commitment (M-SCUC) problems, a novel decomposition and coordination method using mixed-integer linear programming (MILP) value functions is proposed. In the proposed solution method, first, each regional system operator sets the tie-line power injections as variational parameters in its regional SCUC model, and utilises a finite algorithm to generate an MILP value function, which returns the optimal generation cost for any given interchange plan. Then, with the value functions available from all system operators, theoretically, a coordinator is able to devise a globally optimal interchange plan. After the problem is solved, considering that power exchanges may alter the financial position of each area considerably from what it would have been via scheduling independently, the authors then propose a fair savings allocation method using the value 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 were carried out. The validity of the value-function-based method was verified for the decentralised M-SCUC problem. The outcome of savings allocation was compared with that of the locational marginal cost-based method.