**Friday, 10:30 - 10:55 h, Room: MA 549**

**Stephan Lemkens**

Structural properties of power grid design

**Coauthor: Arie M.c.a. Koster**

**Abstract:**

The problem of designing a cost minimal power grid is often formulated as a mixed integer linear program using the well known DC power flow linearization. We consider its projection on the integral space, as every feasible integral point can be considered as a possible power grid design. We define the DC power grid design polytope as the convex hull of these integral points.

At first, we will consider the case in which the power flow on each line is not restricted by any means. We will show, that in this setting the convex hull is described by the connected subgraph polytope of the topology graph.

In addition, we will discuss the structural properties under the influence of bounded power flows, as every real world scenario requires bounded flows. Further, we will study the effects on the convex hull under the assumption of a metric topology.

Finally, we will discuss the impact on the stated results in the case where we use AC linear power flows instead of the DC power flow linearization.

Talk 1 of the contributed session Fri.1.MA 549

**"Power flow modelling and mechanism design"** [...]

Cluster 18

**"Optimization in energy systems"** [...]