The traditional Power Grid has been designed in a hierarchical fashion, with Energy pushed from the large scale production facilities towards the end users. But with the increasing availability of micro and medium scale generating facilities, the situation is changing. Many end users can now produce energy and share it over the Power Grid. Naturally, end users need to have incentives to do so and might want to be able to act in an open decentralized energy market. In the present work, we offer a novel analysis of the Medium and Low Voltage Power Grids of the North Netherlands using statistical tools from the Complex Network Analysis field. We use a weighted model based on actual Grid data and propose a set of statistical measures to evaluate the adequacy of the current infrastructure for a decentralized energy market. Further, we use the insight gained by the analysis to propose parameters that tie the statistical topological measures to economic factors that might influence the attractiveness to the end users in participating in such a decentralized energy market, thus identifying what are the important topological parameters to work on to facilitate such open decentralized markets.
Rosato @cite_26 analyse the same network samples studied in @cite_33 to investigate the main topological properties of these Grids (i.e., Italian, French and Spanish Grids). The contributions of this work include the comparison of the Grid of three different countries, the identification of the most vulnerable edges, and the damage of an attack and achievable improvements based on adding edges. It also studies the node degree distribution and the shortest path length distribution for these samples. It is interesting to note how the authors clearly show the correlation between country geography and topological measures. The sample used is notably small; in addition there is no use of weights to characterize the edges.
@cite_26 @cite_33
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The topological properties of high-voltage electrical power transmission networks in several UE countries (the Italian 380 kV, the French 400 kV and the Spanish 400 kV networks) have been studied from available data. An assessment of the vulnerability of the networks has been given by measuring the level of damage introduced by a controlled removal of links. Topological studies could be useful to make vulnerability assessment and to design specific action to reduce topological weaknesses. Numerous recent papers have found important relationships between network structure and risks within networks. These results indicate that network structure can dramatically affect the relative effectiveness of risk identification and mitigation methods. With this in mind this paper provides a comparative analysis of the topological and electrical structure of the IEEE 300 bus and the Eastern United States power grids. Specifically we compare the topology of these grids with that of random [1], preferential-attachment [2] and small-world [3] networks of equivalent sizes and find that power grids differ substantially from these abstract models in degree distribution, clustering, diameter and assortativity, and thus conclude that these abstract models do not provide substantial utility for modeling power grids. To better represent the topological properties of power grids we introduce a new graph generating algorithm, the minimum distance graph, that produces networks with properties that more nearly match those of known power grids. While these topological comparisons are useful, they do not account for the physical laws that govern flows in electricity networks. To elucidate the electrical structure of power grids, we propose a new method for representing electrical structure as a weighted graph. This analogous representation is based on electrical distance rather than topological connections. A comparison of these two representations of the test power grids reveals dramatic differences between the electrical and topological structure of electrical power systems. We report a study of the correlations among topological, weighted and spatial properties of large infrastructure networks. We review the empirical results obtained for the air-transportation infrastructure that motivates a network modeling approach which integrates the various attributes of this network. In particular, we describe a class of models which include a weight-topology coupling and the introduction of geographical attributes during the network evolution. The inclusion of spatial features is able to capture the appearance of non-trivial correlations between the traffic flows, the connectivity pattern and the actual distances of vertices. The anomalous fluctuations in the betweenness-degree correlation function observed in empirical studies are also recovered in the model. The presented results suggest that the interplay between topology, weights and geographical constraints is a key ingredient in order to understand the structure and evolution of many real-world networks. We study the statistical properties of the sampled networks by a random walker. We compare topological properties of the sampled networks such as degree distribution, degree-degree correlation, and clustering coefficient with those of the original networks. From the numerical results, we find that most of topological properties of the sampled networks are almost the same as those of the original networks for @math . In contrast, we find that the degree distribution exponent of the sampled networks for @math somewhat deviates from that of the original networks when the ratio of the sampled network size to the original network size becomes smaller. We also apply the sampling method to various real networks such as collaboration of movie actor, Worldwide Web, and peer-to-peer networks. All topological properties of the sampled networks are essentially the same as those of the original real networks.