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

Metros (heavy rail transit systems) are integral parts of urban transportation systems. Failures in their operations can have serious impacts on urban mobility, and measuring their robustness is therefore critical. Moreover, as physical networks, metros can be viewed as topological entities, and as such they possess measurable network properties. In this article, by using network science and graph theory, we investigate ten theoretical and four numerical robustness metrics and their performance in quantifying the robustness of 33 metro networks under random failures or targeted attacks. We find that the ten theoretical metrics capture two distinct aspects of robustness of metro networks. First, several metrics place an emphasis on alternative paths. Second, other metrics place an emphasis on the length of the paths. To account for all aspects, we standardize all ten indicators and plot them on radar diagrams to assess the overall robustness for metro networks. Overall, we find that Tokyo and Rome are the most robust networks. Rome benefits from short transferring and Tokyo has a significant number of transfer stations, both in the city center and in the peripheral area of the city, promoting both a higher number of alternative paths and overall relatively short path-lengths.

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Electrical power grids are vulnerable to cascading failures that can lead to large blackouts. The detection and prevention of cascading failures in power grids are important problems. Currently, grid operators mainly monitor the states (loading levels) of individual components in a power grid. The complex architecture of a power grid, with its many interdependencies, makes it difficult to aggregate the data provided by local components in a meaningful and timely manner. Indeed, monitoring the resilience of an operational power grid to cascading failures is a major challenge.

This paper attempts to address this challenge. It presents a robustness metric based on the topology and operative state of a power grid to quantify the robustness of the grid. Also, it presents a distributed computation method with self-stabilizing properties that can be used for near real-time monitoring of grid robustness. The research thus provides insights into the resilience of a dynamic operational power grid to cascading failures during real-time in a manner that is both scalable and robust. Computations are pushed to the power grid network, making the results available at each node and enabling automated distributed control mechanisms to be implemented.@en

Power grid outages cause huge economical and societal costs. Disruptions in the power distribution grid are responsible for a significant fraction of electric power unavailability to customers. The impact of extreme weather conditions, continuously increasing demand, and the over-ageing of assets in the grid, deteriorates the safety of electric power delivery. Measures to analyse the robustness characteristics and to identify vulnerabilities of power grids are of utmost importance. This paper proposes a metric to quantitatively assess the robustness of power distribution grids from a topological point of view. Real-world data is used to demonstrate the applicability of the proposed metric as a tool to assess the criticality of assets in a distribution grid.@en