  The tie-line scheduling problem in a multi-area power system seeks to
optimize tie-line power flows across areas that are independently operated by
different system operators (SOs). In this paper, we leverage the theory of
multi-parametric linear programming to propose algorithms for optimal tie-line
scheduling within a deterministic and a robust optimization framework. Through
a coordinator, the proposed algorithms are proved to converge to the optimal
schedule within a finite number of iterations. A key feature of the proposed
algorithms, besides their finite step convergence, is the privacy of the
information exchanges; the SO in an area does not need to reveal its dispatch
cost structure, network constraints, or the nature of the uncertainty set to
the coordinator. The performance of the algorithms is evaluated using several
power system examples.
