# A Global Solution Method for Decentralized Multi-Area SCUC and Savings Allocation Based on MILP Value Functions

## TL;DR

This paper introduces a novel MILP-based decomposition and coordination method for decentralized multi-area SCUC, ensuring convergence to a global optimum and enabling fair savings allocation using cooperative game theory.

## Contribution

It proposes a MILP value function approach for decentralized SCUC, guaranteeing global optimality and introducing a fair savings allocation method based on Shapley values.

## Key findings

- Method guarantees convergence and global optimality.
- Numerical experiments validate the approach.
- Savings allocation compares favorably with LMP-based methods.

## 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.