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.

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.

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.