There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

The Smart Grid, regarded as the next generation power grid, uses two-way flows of electricity and information to create a widely distributed automated energy delivery network. In this article, we survey the literature till 2011 on the enabling technologies for the Smart Grid. We explore three major systems, namely the smart infrastructure system, the smart management system, and the smart protection system. We also propose possible future directions in each system. colorred{Specifically, for the smart infrastructure system, we explore the smart energy subsystem, the smart information subsystem, and the smart communication subsystem.} For the smart management system, we explore various management objectives, such as improving energy efficiency, profiling demand, maximizing utility, reducing cost, and controlling emission. We also explore various management methods to achieve these objectives. For the smart protection system, we explore various failure protection mechanisms which improve the reliability of the Smart Grid, and explore the security and privacy issues in the Smart Grid.

/pdf/smart-grid-the-new-and-improved-power-grid-a-survey-4jypbbgv3j.pdf

Smart Grid — The New and Improved Power Grid: A Survey

Smart Grid - The New and Improved Power Grid:

Transactions of the Institute of British Geographers

Are Power Line Communications (PLC) a good candidate for Smart Grid applications? The objective of this paper is to address this important question. To do so, we provide an overview of what PLC can deliver today by surveying its history and describing the most recent technological advances in the area. We then address Smart Grid applications as instances of sensor networking and network control problems and discuss the main conclusions one can draw from the literature on these subjects. The application scenario of PLC within the Smart Grid is then analyzed in detail. Because a necessary ingredient of network planning is modeling, we also discuss two aspects of engineering modeling that relate to our question. The first aspect is modeling the PLC channel through fading models. The second aspect we review is the Smart Grid control and traffic modeling problem which allows us to achieve a better understanding of the communications requirements. Finally, this paper reports recent studies on the electrical and topological properties of a sample power distribution network. Power grid topological studies are very important for PLC networking as the power grid is not only the information source but also the information delivery system-a unique feature when PLC is used for the Smart Grid.

/pdf/for-the-grid-and-through-the-grid-the-role-of-power-line-u1a0j36lkc.pdf

For the Grid and Through the Grid: The Role of Power Line Communications in the Smart Grid

What will the neighbors think? Cultural norms and ecological design

In order to design an efficient communication scheme and examine the efficiency of any networked control architecture in smart grid applications, we need to characterize statistically its information source, namely the power grid itself. Investigating the statistical properties of power grids has the immediate benefit of providing a natural simulation platform, producing a large number of power grid test cases with realistic topologies, with scalable network size, and with realistic electrical parameter settings. The second benefit is that one can start analyzing the performance of decentralized control algorithms over information networks whose topology matches that of the underlying power network and use network scientific approaches to determine analytically if these architectures would scale well. With these motivations, in this paper we study both the topological and electrical characteristics of power grid networks based on a number of synthetic and real-world power systems. The most interesting discoveries include: the power grid is sparsely connected with obvious small-world properties; its nodal degree distribution can be well fitted by a mixture distribution coming from the sum of a truncated geometric random variable and an irregular discrete random variable; the power grid has very distinctive graph spectral density and its algebraic connectivity scales as a power function of the network size; the line impedance has a heavy-tailed distribution, which can be captured quite accurately by a clipped double Pareto lognormal distribution. Based on the discoveries mentioned above, we propose an algorithm that generates random topology power grids featuring the same topology and electrical characteristics found from the real data.

Generating Statistically Correct Random Topologies for Testing Smart Grid Communication and Control Networks

The design of the Smart Grid requires solving a complex problem of combined sensing, communications and control and, thus, the problem of choosing a networking technology cannot be addressed without also taking into consideration requirements related to sensor networking and distributed control. These requirements are today still somewhat undefined so that it is not possible yet to give quantitative guidelines on how to choose one communication technology over the other. In this paper, we make a first qualitative attempt to better understand the role that Power Line Communications (PLCs) can have in the Smart Grid. Furthermore, we here report recent results on the electrical and topological properties of the power distribution network. The topological characterization of the power grid is not only important because it allows us to model the grid as an information source, but also because the grid becomes the actual physical information delivery infrastructure when PLCs are used.

/pdf/power-line-communications-and-the-smart-grid-2tsdmmrd7e.pdf

Power Line Communications and the Smart Grid

Centrality measures are used in network science to rank the relative importance of nodes and edges of a graph. Here we define new measures of centrality for power grid structure that are based on its functionality. We show that the relative importance analysis based on centrality in graph theory can be generalized to power grid network with its electrical parameters taken into account. In the paper we experiment with the proposed electrical centrality measures on the NYISO-2935 system and the IEEE 300-bus system. We analyze the centrality distribution in order to identify important nodes or branches in the system which are of essential importance in terms of system vulnerability. We also present and discuss a number of interesting discoveries regarding the importance rank of power grid nodes and branches.

/pdf/electrical-centrality-measures-for-electric-power-grid-168n9hpb8j.pdf

Zhifang Wang

Papers

For the Grid and Through the Grid: The Role of Power Line Communications in the Smart Grid

What will the neighbors think? Cultural norms and ecological design

Generating Statistically Correct Random Topologies for Testing Smart Grid Communication and Control Networks

Power Line Communications and the Smart Grid

Electrical centrality measures for electric power grid vulnerability analysis