Electric power has become an essential part of daily life: we plug our electronic devices in, switch our lights on, and expect to have power. As the availability of power is usually taken for granted in modern societies, we mostly feel annoyed at its absence and perceive the importance of power during outages which have severe effects on the public order. Blackouts have had disastrous consequences for many countries and they continue to occur frequently. Such examples demonstrate the necessity for careful analysis and planning of power grids, to ultimately increase the reliability of power grids. The power grids have evolved due to economic, environmental and human-caused factors. In addition to the contingency analysis, nowadays, the operation and planning of power grids are facing many other challenges (such as demand growth, targeted attacks, cascading failures, and renewable energy integration). Thus, many questions arise, including: which buses (nodes) to connect with a new line (link)? What are the impacts of malicious attacks on power grids? How may an initial failure result in a cascade of failures? How to prepare for the integration of renewable energy? Answering such questions requires developing new concepts and tools for analysing and planning of power grids. Power grids are one of the largest and the most complex man-made systems on earth. The complex nature of power grids and its underlying structure make it possible to analyse power grids relying on network science. The applications of network science on power grids have shown the promising potential to capture the interdependencies between components and to understand the collective emergent behaviour of complex power grids. This thesis is motivated by the increasing need of reliable power grids and the merits of network science on the investigation of power grids. In this context, relying on network science, we model and analyse the power grid and its near-future challenges in terms of line removals/additions, malicious attacks, cascading failures, and renewable integration.@en

In this paper, we propose a novel technique to determine the optimal placement of wind farms, thereby taking into account wind characteristics and electrical grid constraints. We model the long-term variability of wind speed using a Weibull distribution according to wind direction intervals, and formulate the metrics that capture wind speed characteristics at a specific location, namely the arithmetic mean of wind speed, the theoretical wind power density and the capacity factor of a prospective wind power plant, to determine the feasibility of a wind power plant establishment. Furthermore, a linear optimization formulation is provided to determine the geographical locations and the installed capacities of wind farms, in order to maximize the expected annual wind power generation, while obeying the constraints from the electrical power grid and the transmission system operator. As a case study, the proposed wind speed model and the linear optimization formulation are used to evaluate the wind characteristics and the potential wind farm sites in Turkey.@en

In this paper, we study cascading failures in power grids under the nonlinear AC and linearized DC power flow models. We numerically compare the evolution of cascades after single line failures under the two flow models in four test networks. The cascade simulations demonstrate that the assumptions underlying the DC model (e.g., ignoring power losses, reactive power flows, and voltage magnitude variations) can lead to inaccurate and overly optimistic cascade predictions. Particularly, in large networks the DC model tends to overestimate the yield (the ratio of the demand supplied at the end of the cascade to the initial demand). Hence, using the DC model for cascade prediction may result in a misrepresentation of the gravity of a cascade.@en

In this paper, we compare the effects of failures in power grids under the nonlinear AC and linearized DC power flow models. First, we numerically demonstrate that when there are no failures and the assumptions underlying the DC model are valid, the DC model approximates the AC model well in four considered test networks. Then, to evaluate the validity of the DC approximation upon failures, we numerically compare the effects of single line failures and the evolution of cascades under the AC and DC flow models using different metrics, such as yield (the ratio of the demand supplied at the end of the cascade to the initial demand). We demonstrate that the effects of a single line failure on the distribution of the flows on other lines are similar under the AC and DC models. However, the cascade simulations demonstrate that the assumptions underlying the DC model (e.g., ignoring power losses, reactive power flows, and voltage magnitude variations) can lead to inaccurate and overly optimistic cascade predictions. Particularly, in large networks the DC model tends to overestimate the yield. Hence, using the DC model for cascade prediction may result in a misrepresentation of the gravity of a cascade.@en

This paper combines the fundamentals of an electrical grid, such as flow allocation according to Kirchhoff’s laws and the effect of transmission line reactances with spectral graph theory, and expresses the linearized power flow behaviour in slack-bus independent weighted graph matrices to assess the relation between the topological structure and the physical behaviour of a power grid. Based on the pseudoinverse of the weighted network Laplacian, the paper further analytically calculates the effective resistance (Thevenin) matrix and the sensitivities of active power flows to the changes in network topology by means of transmission line removal and addition. Numerical results for the IEEE 118-bus power system are demonstrated to identify the critical components to cascading failures, node isolation, and Braess’ paradox in a power grid.@en

Due to the open data policies, nowadays, some countries have their power grid data available online. This may bring a new concern to the power grid operators in terms of malicious threats. In this paper, we assess the vulnerability of power grids to targeted attacks based on network science. By employing two graph models for power grids as simple and weighted graphs, we first calculate the centrality metrics of each node in a power grid. Subsequently, we formulate different node-attack strategies based on those centrality metrics, and empirically analyse the impact of targeted attacks on the structural and the operational performance of power grids. We demonstrate our methodology in the high-voltage transmission networks of 5 European countries and in commonly used IEEE test power grids.@en

Many countries aim to integrate a substantial amount of wind energy in the near future. This requires meticulous planning, which is challenging due to the uncertainty in wind profiles. In this paper, we propose a novel framework to discover and investigate those geographic areas that are well suited for building wind farms. We combine the key indicators of wind farm investment using fuzzy sets, and employ multiple-criteria decision analysis to obtain a coarse wind farm suitability value. We further demonstrate how this suitability value can be refined by a Markov Random Field (MRF) that takes the dependencies between adjacent areas into account. As a proof of concept, we take wind farm planning in Turkey, and demonstrate that our MRF modeling can accurately find promising areas@en

We study the electrodynamic impedance of percolating conductors with a predefined network topology using a scanning microwave impedance microscope at gigahertz frequencies. For a given percolation number we observe strong spatial variations across a sample that correlate with the connected regions (clusters) in the network when the resistivity is low such as in aluminum. For the more-resistive material (Nb,Ti)N, the impedance becomes dominated by the local structure of the percolating network (connectivity). The results can be qualitatively understood and reproduced with a network current-spreading model based on the pseudoinverse Laplacian of the underlying network graph.@en

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

Determining a set of "important" nodes in a network constitutes a basic endeavor in network science. Inspired by electrical flows in a resistor network, we propose the best conducting node j in a graph G as the minimizer of the diagonal element Qjj† of the pseudoinverse matrix Q† of the weighted Laplacian matrix of the graph G. We propose a new graph metric that complements the effective graph resistance RG and that specifies the heterogeneity of the nodal spreading capacity in a graph. Various formulas and bounds for the diagonal element Qjj† are presented. Finally, we compute the pseudoinverse matrix of the Laplacian of star, path, and cycle graphs and derive an expansion and lower bound of the effective graph resistance RG based on the complement of the graph G.@en