Direct connections between nodes usually result in efficient transmission in networks. Such electric power transmission is governed by physical laws, and an assessment purely based on direct connections between nodes and shortest paths may not capture the operation of power grids
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Direct connections between nodes usually result in efficient transmission in networks. Such electric power transmission is governed by physical laws, and an assessment purely based on direct connections between nodes and shortest paths may not capture the operation of power grids. Motivated by these facts, in this chapter, we investigate the relation between the electric power transmission in a power grid and its underlying topology. Initially, we focus on synthetic power grids whose underlying topology can be structured as either a path or a complete graph. We analytically compute the impact of electric power transmission on link flows under the normal operation and under a link failure contingency using the linearised DC power flow equations. Subsequently, in various other graph types, we provide empirical results on the link flow, the voltage magnitude and the total active power loss in power grids using the nonlinear AC power flow equations. Our results show that in a path graph, as an assessment based on shortest paths holds, however, the electric power transmission can lead to substantial amount of link flows, active power loss and voltage drops, especially in large path graphs. On the other hand, adding few links to a path graph could significantly improve those performance indicators of power grids, but at a cost: the resulting meshed topology decreases the control over power grids as a direct assessment between the shortest paths and the electric power transformation is lost. Additionally, a meshed topology with loops increases the redundancy in the design to ensure a safe operation under a link failure contingency.@en