Zonal Reduction of Large Power Systems: Assessment of an Optimal Grid Model Accounting for Loop Flows

In development studies carried out on large power systems, a need may arise for a reduction in which whole regions are seen as the nodes of a simplified graph whose edges replace the inter-regional links. The property required from this kind of backbone representation may be that reduced load flows stay close to their physical counterpart on the full grid. In the dc approximation, such a model can consist of a set of impedances attached to each edge, along with a flow characterizing a particular state of the system. The identification of the model accommodating best a large sample of flows, representative of all of their possible diversity, is a nonconvex problem for which two partially convex reformulations are proposed. Simple ad hoc algorithms are introduced as a way to find approximate solutions satisfying first-order optimality conditions.