1 

An entropybased metric to quantify the robustness of power grids against cascading failures
The cascading failure phenomenon in a power grid is related to both the structural aspects (number and types of buses, density of transmission lines and interconnection of components), and the operative state (flow distribution and demand level). Existing studies most often focus on structural aspects, and not on operative states. This paper proposes a new metric to assess power network robustness with respect to cascading failures, in particular for cascading effects due to line overloads under targeted attacks. The metric takes both the effect of structural aspects and the effect of the operative state on network robustness into account, using an entropybased approach. IEEE test systems and real world UCTE networks are used to demonstrate the applicability of this robustness metric. © 2013 Elsevier Ltd.

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2 

Stochastic optimization in the power grid
In this thesis steps are described to determine the locations of new wind mills which minimize energy loss on the Dutch High Voltage power grid. A vindication of the used power grid model is provided; the simulation procedure for stochastic wind power is described; and the required mathematical optimization models are formally derived as well as implementedin the optimization software package Aimms. Results are shown and their relation to real life problems is discussed. The goal of the thesis is to work out a case study of power grid design where stochasticity plays a major role, and where transportation losses should be minimized. By lack of data this has not been carried out for a (perhaps more relevant) more locally oriented and Medium Voltage case, but this thesis provides a description of all crucial steps that should be taken. This thesis contains the information on power systems and the explanation of the relevant mathematical techniques for any reader to find his way in the literature on power grid design, and to address problems of a similar nature as the one treated in this thesis.

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3 

The Impact of the Topology on Cascading Failures in a Power Grid Model
Cascading failures are one of the main reasons for large scale blackouts in power transmission grids. Secure electrical power supply requires, together with careful operation, a robust design of the electrical power grid topology. Currently, the impact of the topology on grid robustness is mainly assessed by purely topological approaches, that fail to capture the essence of electric power flow. This paper proposes a metric, the effective graph resistance, to relate the topology of a power grid to its robustness against cascading failures by deliberate attacks, while also taking the fundamental characteristics of the electric power grid into account such as power flow allocation according to Kirchhoff laws. Experimental verification on synthetic power systems shows that the proposed metric reflects the grid robustness accurately. The proposed metric is used to optimize a grid topology for a higher level of robustness. To demonstrate its applicability, the metric is applied on the IEEE 118 bus power system to improve its robustness against cascading failures.

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4 

A topological investigation of phase transitions of cascading failures in power grids
Cascading failures are one of the main reasons for blackouts in electric power transmission grids. The economic cost of such failures is in the order of tens of billion dollars annually. The loading level of power system is a key aspect to determine the amount of the damage caused by cascading failures. Existing studies show that the blackout size exhibits phase transitions as the loading level increases. This paper investigates the impact of the topology of a power grid on phase transitions in its robustness. Three spectral graph metrics are considered: spectral radius, effective graph resistance and algebraic connectivity. Experimental results from a model of cascading failures in power grids on the IEEE power systems demonstrate the applicability of these metrics to design/optimise a power grid topology for an enhanced phase transition behaviour of the system. © 2014 Elsevier B.V. All rights reserved.

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5 

Applying innovative IT modelling methods to lowlevel grid information for DSO operations
Distribution system operators will gather an increasing amount of electricity data from the lower level of the grid to be able to cope with several challenges, such as an increase of distributed, heterogeneous energy production, local storage, and electric vehicles. Most DSOs are not yet prepared for collecting, storing and processing these large amounts of data. This paper introduces a method for designing, validating and implementing such a system. The most important aspect of this method is the fact that the domain expert is able to validate the constructed conceptual model, before it is used to create a working system. This validation step adds to the quality of the model, and therefore to the resulting system. We have applied our method to a use case where a DSO researcher wants to answer questions such as 'Can we recognize which appliances are present in households?' and 'How can we cluster similar households?'. © 2015 IEEE.

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6 

A network approach for power grid robustness against cascading failures
Cascading failures are one of the main reasons for blackouts in electrical power grids. Stable power supply requires a robust design of the power grid topology. Currently, the impact of the grid structure on the grid robustness is mainly assessed by purely topological metrics, that fail to capture the fundamental properties of the electrical power grids such as power flow allocation according to Kirchhoff's laws. This paper deploys the effective graph resistance as a metric to relate the topology of a grid to its robustness against cascading failures. Specifically, the effective graph resistance is deployed as a metric for network expansions (by means of transmission line additions) of an existing power grid. Four strategies based on network properties are investigated to optimize the effective graph resistance, accordingly to improve the robustness, of a given power grid at a low computational complexity. Experimental results suggest the existence of Braess's paradox in power grids: bringing an additional line into the system occasionally results in decrease of the grid robustness. This paper further investigates the impact of the topology on the Braess's paradox, and identifies specific substructures whose existence results in Braess's paradox. Careful assessment of the design and expansion choices of grid topologies incorporating the insights provided by this paper optimizes the robustness of a power grid, while avoiding the Braess's paradox in the system. © 2015 IEEE.

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