We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

This paper reviews the current status and implementation of battery chargers, charging power levels, and infrastructure for plug-in electric vehicles and hybrids. Charger systems are categorized into off-board and on-board types with unidirectional or bidirectional power flow. Unidirectional charging limits hardware requirements and simplifies interconnection issues. Bidirectional charging supports battery energy injection back to the grid. Typical on-board chargers restrict power because of weight, space, and cost constraints. They can be integrated with the electric drive to avoid these problems. The availability of charging infrastructure reduces on-board energy storage requirements and costs. On-board charger systems can be conductive or inductive. An off-board charger can be designed for high charging rates and is less constrained by size and weight. Level 1 (convenience), Level 2 (primary), and Level 3 (fast) power levels are discussed. Future aspects such as roadbed charging are presented. Various power level chargers and infrastructure configurations are presented, compared, and evaluated based on amount of power, charging time and location, cost, equipment, and other factors.

/pdf/review-of-battery-charger-topologies-charging-power-levels-85yy2igx2w.pdf

Review of Battery Charger Topologies, Charging Power Levels, and Infrastructure for Plug-In Electric and Hybrid Vehicles

The rapid rise of shale gas development through horizontal drilling and high volume hydraulic fracturing has expanded the extraction of hydrocarbon resources in the U.S. The rise of shale gas development has triggered an intense public debate regarding the potential environmental and human health effects from hydraulic fracturing. This paper provides a critical review of the potential risks that shale gas operations pose to water resources, with an emphasis on case studies mostly from the U.S. Four potential risks for water resources are identified: (1) the contamination of shallow aquifers with fugitive hydrocarbon gases (i.e., stray gas contamination), which can also potentially lead to the salinization of shallow groundwater through leaking natural gas wells and subsurface flow; (2) the contamination of surface water and shallow groundwater from spills, leaks, and/or the disposal of inadequately treated shale gas wastewater; (3) the accumulation of toxic and radioactive elements in soil or stream sediments near disposal or spill sites; and (4) the overextraction of water resources for high-volume hydraulic fracturing that could induce water shortages or conflicts with other water users, particularly in water-scarce areas. Analysis of published data (through January 2014) reveals evidence for stray gas contamination, surface water impacts in areas of intensive shale gas development, and the accumulation of radium isotopes in some disposal and spill sites. The direct contamination of shallow groundwater from hydraulic fracturing fluids and deep formation waters by hydraulic fracturing itself, however, remains controversial.

/pdf/a-critical-review-of-the-risks-to-water-resources-from-2v7n5hmzlz.pdf

A Critical Review of the Risks to Water Resources from Unconventional Shale Gas Development and Hydraulic Fracturing in the United States

The National Academy of Sciences founded The National Academies Press (NAP) with the goal of publishing reports of all four national academies. Annually, NAP publishes more than 200 books from the fields of science, engineering and medicine and offers more than 4000 titles in PDF on its website (http://www.nap.edu/) free of charge.

/pdf/the-national-academies-press-3oqc1apmt7.pdf

The National Academies Press

As the number of plug-in hybrid vehicles (PHEVs) increases, so might the impacts on the power system performance, such as overloading, reduced efficiency, power quality, and voltage regulation particularly at the distribution level. Coordinated charging of PHEVs is a possible solution to these problems. In this work, the relationship between feeder losses, load factor, and load variance is explored in the context of coordinated PHEV charging. From these relationships, three optimal charging algorithms are developed which minimize the impacts of PHEV charging on the connected distribution system. The application of the algorithms to two test systems verifies these relationships approximately hold independent of system topology. They also show the additional benefits of reduced computation time and problem convexity when using load factor or load variance as the objective function rather than system losses. This is important for real-time dispatching of PHEVs.

Coordinated Charging of Plug-In Hybrid Electric Vehicles to Minimize Distribution System Losses

In order to identify the extent to which results from topological graph models are useful for modeling vulnerability in electricity infrastructure, we measure the susceptibility of power networks to random failures and directed attacks using three measures of vulnerability: characteristic path lengths, connectivity loss, and blackout sizes. The first two are purely topological metrics. The blackout size calculation results from a model of cascading failure in power networks. Testing the response of 40 areas within the Eastern U.S. power grid and a standard IEEE test case to a variety of attack/failure vectors indicates that directed attacks result in larger failures using all three vulnerability measures, but the attack-vectors that appear to cause the most damage depend on the measure chosen. While the topological metrics and the power grid model show some similar trends, the vulnerability metrics for individual simulations show only a mild correlation. We conclude that evaluating vulnerability in power networks using purely topological metrics can be misleading.

Do topological models provide good information about electricity infrastructure vulnerability

Identifying coherent sub-graphs in networks is important in many applications. In power systems, large systems are divided into areas and zones to aid in planning and control applications. But not every partitioning is equally good for all applications; different applications have different goals, or attributes, against which solutions should be evaluated. This paper presents a hybrid method that combines a conventional graph partitioning algorithm with an evolutionary algorithm to partition a power network to optimize a multi-attribute objective function based on electrical distances, cluster sizes, the number of clusters, and cluster connectedness. Results for the IEEE RTS-96 show that clusters produced by this method can be used to identify buses with dynamically coherent voltage angles, without the need for dynamic simulation. Application of the method to the IEEE 118-bus and a 2383-bus case indicates that when a network is well partitioned into zones, intra-zone transactions have less impact on power flows outside of the zone; i.e., good partitioning reduces loop flows. This property is particularly useful for power system applications where ensuring deliverability is important, such as transmission planning or determination of synchronous reserve zones.

https://ir.library.oregonstate.edu/xmlui/bitstream/handle/1957/45758/Cotilla-SanchezEduardoElectricalEngineeringComputerScienceMultiAttributePartitioning.pdf;sequence=1

Multi-Attribute Partitioning of Power Networks Based on Electrical Distance

The topological (graph) structure of complex networks often provides valuable information about the performance and vulnerability of the network. However, there are multiple ways to represent a given network as a graph. Electric power transmission and distribution networks have a topological structure that is straightforward to represent and analyze as a graph. However, simple graph models neglect the comprehensive connections between components that result from Ohm's and Kirchhoff's laws. This paper describes the structure of the three North American electric power interconnections, from the perspective of both topological and electrical connectivity. We compare the simple topology of these networks with that of random, preferential-attachment, and small-world 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 topological forms may be misleading as models of power systems. To study the electrical connectivity of power systems, we propose a new method for representing electrical structure using electrical distances rather than geographic connections. Comparisons of these two representations of the North American power networks reveal notable differences between the electrical and topological structures of electric power networks.

Comparing the Topological and Electrical Structure of the North American Electric Power Infrastructure

In order to identify the extent to which results from topological graph models are useful for modeling vulnerability in electricity infrastructure, we measure the susceptibility of power networks to random failures and directed attacks using three measures of vulnerability: characteristic path lengths, connectivity loss and blackout sizes. The first two are purely topological metrics. The blackout size calculation results from a model of cascading failure in power networks. Testing the response of 40 areas within the Eastern US power grid and a standard IEEE test case to a variety of attack/failure vectors indicates that directed attacks result in larger failures using all three vulnerability measures, but the attack vectors that appear to cause the most damage depend on the measure chosen. While our topological and power grid model results show some trends that are similar, there is only a mild correlation between the vulnerability measures for individual simulations. We conclude that evaluating vulnerability in power networks using purely topological metrics can be misleading.

Do topological models provide good information about vulnerability in electric power networks

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.

Seth Blumsack

Papers

Do topological models provide good information about electricity infrastructure vulnerability

Multi-Attribute Partitioning of Power Networks Based on Electrical Distance

Comparing the Topological and Electrical Structure of the North American Electric Power Infrastructure

Do topological models provide good information about vulnerability in electric power networks

The Topological and Electrical Structure of Power Grids