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

MATPOWER is an open-source Matlab-based power system simulation package that provides a high-level set of power flow, optimal power flow (OPF), and other tools targeted toward researchers, educators, and students. The OPF architecture is designed to be extensible, making it easy to add user-defined variables, costs, and constraints to the standard OPF problem. This paper presents the details of the network modeling and problem formulations used by MATPOWER, including its extensible OPF architecture. This structure is used internally to implement several extensions to the standard OPF problem, including piece-wise linear cost functions, dispatchable loads, generator capability curves, and branch angle difference limits. Simulation results are presented for a number of test cases comparing the performance of several available OPF solvers and demonstrating MATPOWER's ability to solve large-scale AC and DC OPF problems.

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MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education

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.

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

The increasing interest in integrating intermittent renewable energy sources into microgrids presents major challenges from the viewpoints of reliable operation and control. In this paper, the major issues and challenges in microgrid control are discussed, and a review of state-of-the-art control strategies and trends is presented; a general overview of the main control principles (e.g., droop control, model predictive control, multi-agent systems) is also included. The paper classifies microgrid control strategies into three levels: primary, secondary, and tertiary, where primary and secondary levels are associated with the operation of the microgrid itself, and tertiary level pertains to the coordinated operation of the microgrid and the host grid. Each control level is discussed in detail in view of the relevant existing technical literature.

Trends in Microgrid Control

Smart Grid - The New and Improved Power Grid:

In this paper we numerically study the topology robustness of power grids under random and selective node breakdowns, and analytically estimate the critical node-removal thresholds to disintegrate a system, based on the available US power grid data. We also present an analysis on the node degree distribution in power grids because it closely relates with the topology robustness. It is found that the node degree in a power grid can be well fitted by a mixture distribution coming from the sum of a truncated Geometric random variable and an irregular Discrete random variable. With the findings we obtain better estimates of the threshold under selective node breakdowns which predict the numerical thresholds more correctly.

/pdf/the-node-degree-distribution-in-power-grid-and-its-topology-36o9q4r8ye.pdf

The Node Degree Distribution in Power Grid and Its Topology Robustness under Random and Selective Node Removals

It is well known that given a network that can become constrained on voltage or real power flows, reserves must also be spatially located in order to handle all credible contingencies. However, to date, there is no credible science-based method for assigning and pricing reserves in this way. Presented in this paper is a new scheduling algorithm incorporating constraints imposed by grid security considerations, which include one base case (intact system) and a list of possible contingencies (line-out, unit-lost, and load-growth) of the system. By following a cost-minimizing co-optimization procedure, both power and reserve are allocated spatially for the combined energy and reserve markets. With the Lagrange multipliers (dual variables) obtained, the scheduling algorithm also reveals the locational shadow prices for the reserve and energy requirements. Unlike other pricing and scheduling methods in use, which are usually ad-hoc and are based on engineering judgment and experience, this proposed formulation is likely to perform better in restructured markets when market power is a potential problem. An illustrative example of a modified IEEE 30-bus system is used to introduce concepts and present results.

/pdf/locational-pricing-and-scheduling-for-an-integrated-energy-1khqekvv1v.pdf

Locational pricing and scheduling for an integrated energy-reserve market

In this paper, the concepts of transiently chaotic swings and windowed Lyapunov exponents in power system dynamics are described. An efficient computer method to detect a transiently chaotic swing from a set of real-time phasor measurements is presented. The method estimates the largest windowed Lyapunov exponent, /spl lambda//spl circ//sub [N/spl Delta/T]//sup 1/ as a detection index. In simulation results, it is shown that the proposed method has the potential to detect a transiently chaotic swing and the estimated /spl lambda//spl circ//sub [N/spl Delta/T]//sup 1/ can be used as an online stability index to predict multi-swing transient instability. >

Detection of transiently chaotic swings in power systems using real-time phasor measurements

The dynamic characteristics of power system loads are critical to obtaining quality operating point-prediction and stability calculations. The composition of components at a load bus makes the aggregated behavior too complicated to be expressed by a simple form. Armed with the theorems recently developed on the approximation capability of artificial neural networks, the authors devise a load model to describe the complex dynamic behavior of loads. Real field data are used to train and test this model. The results verify that this model can emulate load dynamics well and should therefore be suitable as a representation of load for stability analysis. >

Power system dynamic load modeling using artificial neural networks

The short-term forecasting of real-time locational marginal price (LMP) and network congestion is considered from a system operator perspective. A new probabilistic forecasting technique is proposed based on a multiparametric programming formulation that partitions the uncertainty parameter space into critical regions from which the conditional probability distribution of the real-time LMP/congestion is obtained. The proposed method incorporates load/generation forecast, time varying operation constraints, and contingency models. By shifting the computation cost associated with multiparametric programs offline, the online computation cost is significantly reduced. An online simulation technique by generating critical regions dynamically is also proposed, which results in several orders of magnitude improvement in the computational cost over standard Monte Carlo methods.

Robert J. Thomas

Papers

The Node Degree Distribution in Power Grid and Its Topology Robustness under Random and Selective Node Removals

Locational pricing and scheduling for an integrated energy-reserve market

Detection of transiently chaotic swings in power systems using real-time phasor measurements

Power system dynamic load modeling using artificial neural networks

Probabilistic Forecast of Real-Time LMP and Network Congestion