No Arabic abstract
Power Grids and other delivery networks has been attracted some attention by the network literature last decades. Despite the Power Grids dynamics has been controlled by computer systems and human operators, the static features of this type of network can be studied and analyzed. The topology of the Brazilian Power Grid (BPG) was studied in this work. We obtained the spatial structure of the BPG from the ONS (electric systems national operator), consisting of high-voltage transmission lines, generating stations and substations. The local low-voltage substations and local power delivery as well the dynamic features of the network were neglected. We analyze the complex network of the BPG and identify the main topological information, such as the mean degree, the degree distribution, the network size and the clustering coefficient to caracterize the complex network. We also detected the critical locations on the network and, therefore, the more susceptible points to lead to a cascading failure and even to a blackouts. Surprisely, due to the characteristic of the topology and physical structure of the network, we show that the BPG is resilient against random failures, since the random removal of links does not affect significantly the size of the largest cluster. We observe that when a fraction of the links are randomly removed, the network may disintegrates into smaller and disconnected parts, however, the power grid largest component remains connected. We believe that the even a static study of the network topology can help to identify the critical situations and also prevent failures and possible blackouts on the network.
The dynamics of power-grid networks is becoming an increasingly active area of research within the physics and network science communities. The results from such studies are typically insightful and illustrative, but are often based on simplifying assumptions that can be either difficult to assess or not fully justified for realistic applications. Here we perform a comprehensive comparative analysis of three leading models recently used to study synchronization dynamics in power-grid networks -- a fundamental problem of practical significance given that frequency synchronization of all power generators in the same interconnection is a necessary condition for a power grid to operate. We show that each of these models can be derived from first principles within a common framework based on the classical model of a generator, thereby clarifying all assumptions involved. This framework allows us to view power grids as complex networks of coupled second-order phase oscillators with both forcing and damping terms. Using simple illustrative examples, test systems, and real power-grid datasets, we study the inherent frequencies of the oscillators as well as their coupling structure, comparing across the different models. We demonstrate, in particular, that if the network structure is not homogeneous, generators with identical parameters need to be modeled as non-identical oscillators in general. We also discuss an approach to estimate the required (dynamical) parameters that are unavailable in typical power-grid datasets, their use for computing the constants of each of the three models, and an open-source MATLAB toolbox that we provide for these computations.
Power grids exhibit patterns of reaction to outages similar to complex networks. Blackout sequences follow power laws, as complex systems operating near a critical point. Here, the tolerance of electric power grids to both accidental and malicious outages is analyzed in the framework of complex network theory. In particular, the quantity known as efficiency is modified by introducing a new concept of distance between nodes. As a result, a new parameter called net-ability is proposed to evaluate the performance of power grids. A comparison between efficiency and net-ability is provided by estimating the vulnerability of sample networks, in terms of both the metrics.
This paper explores a variety of strategies for understanding the formation, structure, efficiency and vulnerability of water distribution networks. Water supply systems are studied as spatially organized networks for which the practical applications of abstract evaluation methods are critically evaluated. Empirical data from benchmark networks are used to study the interplay between network structure and operational efficiency, reliability and robustness. Structural measurements are undertaken to quantify properties such as redundancy and optimal-connectivity, herein proposed as constraints in network design optimization problems. The role of the supply-demand structure towards system efficiency is studied and an assessment of the vulnerability to failures based on the disconnection of nodes from the source(s) is undertaken. The absence of conventional degree-based hubs (observed through uncorrelated non-heterogeneous sparse topologies) prompts an alternative approach to studying structural vulnerability based on the identification of network cut-sets and optimal connectivity invariants. A discussion on the scope, limitations and possible future directions of this research is provided.
Many partitioning methods may be used to partition a network into smaller clusters while minimizing the number of cuts needed. However, other considerations must also be taken into account when a network represents a real system such as a power grid. In this paper we use a simulated annealing Monte Carlo (MC) method to optimize initial clusters on the Florida high-voltage power-grid network that were formed by associating each load with its closest generator. The clusters are optimized to maximize internal connectivity within the individual clusters and minimize the power deficiency or surplus that clusters may otherwise have.
An imperative condition for the functioning of a power-grid network is that its power generators remain synchronized. Disturbances can prompt desynchronization, which is a process that has been involved in large power outages. Here we derive a condition under which the desired synchronous state of a power grid is stable, and use this condition to identify tunable parameters of the generators that are determinants of spontaneous synchronization. Our analysis gives rise to an approach to specify parameter assignments that can enhance synchronization of any given network, which we demonstrate for a selection of both test systems and real power grids. Because our results concern spontaneous synchronization, they are relevant both for reducing dependence on conventional control devices, thus offering an additional layer of protection given that most power outages involve equipment or operational errors, and for contributing to the development of smart grids that can recover from failures in real time.