Power Grid Network Research Articles

Rumors in a Network: Who's the Culprit?

We provide a systematic study of the problem of finding the source of a rumor in a network. We model rumor spreading in a network with the popular susceptible-infected (SI) model and then construct an estimator for the rumor source. This estimator is based upon a novel topological quantity which we term rumor centrality. We establish that this is a maximum likelihood (ML) estimator for a class of graphs. We find the following surprising threshold phenomenon: on trees which grow faster than a line, the estimator always has nontrivial detection probability, whereas on trees that grow like a line, the detection probability will go to 0 as the network grows. Simulations performed on synthetic networks such as the popular small-world and scale-free networks, and on real networks such as an internet AS network and the U.S. electric power grid network, show that the estimator either finds the source exactly or within a few hops of the true source across different network topologies. We compare rumor centrality to another common network centrality notion known as distance centrality. We prove that on trees, the rumor center and distance center are equivalent, but on general networks, they may differ. Indeed, simulations show that rumor centrality outperforms distance centrality in finding rumor sources in networks which are not tree-like.

Parallel and Scalable Transient Simulator for Power Grids via Waveform Relaxation (PTS-PWR)

This paper presents a fast algorithm for transient simulation of power grids in very large scale integration systems using waveform relaxation (WR) techniques. Novel partitioning methods and convergence accelerators are developed for fast convergence of WR iterations when applied to power grid networks. Unlike the direct solvers, the new method is highly parallelizable and scales well with the increasing number of CPUs, leading to significant speed-ups. Numerical examples are presented to demonstrate the validity and efficiency of the proposed method.

The exponential degree distribution in complex networks: Non-equilibrium network theory, numerical simulation and empirical data

The exponential degree distribution has been found in many real world complex networks, based on which, the random growing process has been introduced to analyze the formation principle of such kinds of networks. Inspired from the non-equilibrium network theory, we construct the network according to two mechanisms: growing and adjacent random attachment. By using the Kolmogorov–Smirnov Test (KST), for the same number of nodes and edges, we find the simulation results are remarkably consistent with the predictions of the non-equilibrium network theory, and also surprisingly match the empirical databases, such as the Worldwide Marine Transportation Network (WMTN), the Email Network of University at Rovira i Virgili (ENURV) in Spain and the North American Power Grid Network (NAPGN). Our work may shed light on interpreting the exponential degree distribution and the evolution mechanism of the complex networks.

Distributed Optimization for Model Predictive Control of Linear Dynamic Networks With Control-Input and Output Constraints

A linear dynamic network is a system of subsystems that approximates the dynamic model of large, geographically distributed systems such as the power grid and traffic networks. A favorite technique to operate such networks is distributed model predictive control (DMPC), which advocates the distribution of decision-making while handling constraints in a systematic way. This paper contributes to the state-of-the-art of DMPC of linear dynamic networks in two ways. First, it extends a baseline model by introducing constraints on the output of the subsystems and by letting subsystem dynamics to depend on the state besides the control signals of the subsystems in the neighborhood. With these extensions, constraints on queue lengths and delayed dynamic effects can be modeled in traffic networks. Second, this paper develops a distributed interior-point algorithm for solving DMPC optimization problems with a network of agents, one for each subsystem, which is shown to converge to an optimal solution. In a traffic network, this distributed algorithm permits the subsystem of an intersection to be reconfigured by only coordinating with the subsystems in its vicinity.

Stochastic Non-homogeneous Arnoldi Method for Analysis of On-Chip Power Grid Networks under Process Variations

In this paper, a Stochastic Non-Homogeneous ARnoldi (SNHAR) method is proposed for the analysis of the on-chip power grid networks in the presence of process variations. In SNHAR method, the polynomial chaos based stochastic method is employed to handle the variations of power grids. Different from the existing StoEKS method which uses extended Krylov Subspace (EKS) method to compute the coefficients of the polynomial chaos, a computation-efficient and numerically stable Non-Homogeneous ARnoldi (NHAR) method is employed in SNHAR method to compute the coefficients of the polynomial chaos. Compared with EKS method, NHAR method has superior numerical stability and can achieve remarkably higher accuracy with even lower computational cost. As a result, SNHAR can capture the stochastic characteristics of the on-chip power grid networks with higher accuracy, but even lower computational cost than StoEKS.

Floridian high-voltage power-grid network partitioning and cluster optimization using simulated annealing

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 highvoltage 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.

Detecting sources of computer viruses in networks

We provide a systematic study of the problem of finding the source of a computer virus in a network. We model virus spreading in a network with a variant of the popular SIR model and then construct an estimator for the virus source. This estimator is based upon a novel combinatorial quantity which we term rumor centrality. We establish that this is an ML estimator for a class of graphs. We find the following surprising threshold phenomenon: on trees which grow faster than a line, the estimator always has non-trivial detection probability, whereas on trees that grow like a line, the detection probability will go to 0 as the network grows. Simulations performed on synthetic networks such as the popular small-world and scale-free networks, and on real networks such as an internet AS network and the U.S. electric power grid network, show that the estimator either finds the source exactly or within a few hops in different network topologies. We compare rumor centrality to another common network centrality notion known as distance centrality. We prove that on trees, the rumor center and distance center are equivalent, but on general networks, they may differ. Indeed, simulations show that rumor centrality outperforms distance centrality in finding virus sources in networks which are not tree-like.

Optimal transport on supply-demand networks

In the literature, transport networks are usually treated as homogeneous networks, that is, every node has the same function, simultaneously providing and requiring resources. However, some real networks, such as power grids and supply chain networks, show a far different scenario in which nodes are classified into two categories: supply nodes provide some kinds of services, while demand nodes require them. In this paper, we propose a general transport model for these supply-demand networks, associated with a criterion to quantify their transport capacities. In a supply-demand network with heterogeneous degree distribution, its transport capacity strongly depends on the locations of supply nodes. We therefore design a simulated annealing algorithm to find the near optimal configuration of supply nodes, which remarkably enhances the transport capacity compared with a random configuration and outperforms the degree target algorithm, the betweenness target algorithm, and the greedy method. This work provides a start point for systematically analyzing and optimizing transport dynamics on supply-demand networks.

IR-Drop Management in FPGAs

This paper presents novel computer-aided design (CAD) techniques for mitigating IR-drops in field-programmable gate arrays (FPGAs). The proposed placement and routing relies on reducing the switching activities in local regions in the FPGA fabric to improve the profile of the supply voltage distribution. The proposed techniques reduce IR-drops and the variance of the supply voltage distribution across all the nodes in the power grid network. The proposed CAD techniques are efficient as they do not require solving the power grid model at every placement and routing iteration. A reduction of up to 53% in maximum IR-drop and up to 66% reduction in standard deviation of is obtained from the design techniques proposed in this paper with an average impact of 3% on circuit delay.

Good cooperation demands good coordination: coordinated cooperative communications [Message from the Editor in Chief

Dear Readers, In my message in the last issue, I listed a few interesting areas of wireless technologies: wireless health (mobile health or m-Health), mobile social networks, and smart environments. Another important area of paramount importance is the power grid or energy networks, which have been attracting significant attention in the past few years as you can see from the column from the industrial perspective in this issue. Although these few areas are indeed interesting, we have often been asked where the research or innovations are as an engineer or a researcher. It seems that we already have the technologies to address all the problems we could face in these important areas. The problem is that we have too many problems when we apply the current technologies to address those problems.

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

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 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">small-world</i> 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.

Vulnerability of complex networks

We consider normalized average edge betweenness of a network as a metric of network vulnerability. We suggest that normalized average edge betweenness together with is relative difference when certain number of nodes and/or edges are removed from the network is a measure of network vulnerability, called vulnerability index. Vulnerability index is calculated for four synthetic networks: Erdős–Rényi (ER) random networks, Barabási–Albert (BA) model of scale-free networks, Watts–Strogatz (WS) model of small-world networks, and geometric random networks. Real-world networks for which vulnerability index is calculated include: two human brain networks, three urban networks, one collaboration network, and two power grid networks. We find that WS model of small-world networks and biological networks (human brain networks) are the most robust networks among all networks studied in the paper.

Statistical analysis of large on-chip power grid networks by variational reduction scheme

One of the most critical challenges in today's CMOS VLSI design is the lack of predictability in chip performance at design stage. One of the process variabilities comes from the voltage drop variations in on-chip power distribution networks. In this paper, we present a novel analysis approach for computing voltage drops of large power grid networks under process variations. The new algorithm is very efficient and scalable for huge networks with a large number of variational variables. This approach, called variational extended truncated balanced realization ( varETBR), is based on model order reduction techniques to reduce the circuit matrices before the variational simulation. It performs the parameterized reduction on the original system using variation-bearing subspaces. After the reduction, Monte Carlo based statistical simulation is performed on the reduced system and the statistical responses of the original system are obtained thereafter. varETBR calculates variational response Grammians by Monte Carlo based numerical integration considering both system and input source variations in generating the projection subspace. varETBR is very scalable for the number of variables and flexible for different variational distributions and ranges as demonstrated in experimental results. Experimental results, on a number of IBM benchmark circuits up to 1.6 million nodes, show that the varETBR can be 1900 X faster than the Monte Carlo method and is much more scalable than one of the recently proposed approaches.

Re-thinking the power transmission model for sub-Saharan Africa

A vision for a United States of Africa has been advocated since the dawn of independence by, among others, pioneers like Kwame Nkrumah, Gamal Abdel Nasser and Julius Nyerere. More recently the idea gained new momentum, through such initiatives as the New Partnership for African Development (NEPAD) and the African Union (AU) to create a single market of Africa’s 750 million people that is competitive within itself and within the global economy. This would be achieved through a deliberate, systematic and concerted effort to integrate, upgrade and modernize infrastructure that would offer the required catalyst for economic growth. However, the prioritization by African policy makers of a grand plan to link up the entire African continent’s electric power grid networks would appear to be incompatible with 21st century thinking. The specifications for a centrally managed power grid were made by Nicola Tesla in 1883 and have served the power industry for over 125 years but are now obsolete in the era of digital micro-electronics and smart grid concepts. This paper examines some issues that surround the evolution of sub-Sahara African regional power pools and highlights the anomalies and perhaps wrong timing around the conceptualization and prioritization of grand inter-state power grids. The authors then propose an alternative model that conforms to a new and more sustainable paradigm in electricity supply economics. The proposals are however not meant to provide a panacea but it is hoped that the article will ignite a debate that will lead to a lasting solution.

On Modeling Random Topology Power Grids for Testing Decentralized Network Control Strategies

An electrical power grid is a critical infrastructure. Its reliable, robust, and efficient operation inevitably depends on underlying telecommunication networks. In order to design an efficient communication scheme and examine the efficiency of any networked control architecture, we need to characterize statistically its information source, namely the power grid itself. In this paper we studied both the topological and electrical characteristics of power grid networks based on a number of synthetic and real-world power systems. We made several interesting discoveries: the power grids are sparsely connected and the average nodal degree is very stable regardless of network size; the nodal degrees distribution has exponential tails, which can be approximated with a shifted Geometric distribution; the algebraic connectivity scales as a power function of network size with the power index lying between that of one-dimensional and two-dimensional lattice; the line impedance has a heavy-tailed distribution, which can be captured quite accurately by a Double Pareto LogNormal distribution. Based on the discoveries mentioned above, we propose an algorithm that generates random power grids featuring the same topology and electrical characteristics we found from the real data.

Statistical Analysis of On-Chip Power Delivery Networks Considering Lognormal Leakage Current Variations With Spatial Correlation

As the technology scales into 90 nm and below, process-induced variations become more pronounced. In this paper, we propose an efficient stochastic method for analyzing the voltage drop variations of on-chip power grid networks, considering log-normal leakage current variations with spatial correlation. The new analysis is based on the Hermite polynomial chaos (PC) representation of random processes. Different from the existing Hermite PC based method for power grid analysis (Ghanta <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">al</i> ., 2005), which models all the random variations as Gaussian processes without considering spatial correlation, the new method consider both wire variations and subthreshold leakage current variations, which are modeled as log-normal distribution random variables, on the power grid voltage variations. To consider the spatial correlation, we apply orthogonal decomposition to map the correlated random variables into independent variables. Our experiment results show that the new method is more accurate than the Gaussian-only Hermite PC method using the Taylor expansion method for analyzing leakage current variations. It is two orders of magnitude faster than the Monte Carlo method with small variance errors. We also show that the spatial correlation may lead to large errors if not being considered in the statistical analysis.

Statistical power supply dynamic noise prediction in hierarchical power grid and package networks

One of the most crucial high performance systems-on-chip design challenge is to front their power supply noise sufferance due to high frequencies, huge number of functional blocks and technology scaling down. Marking a difference from traditional post physical-design static voltage drop analysis, a priori dynamic voltage drop evaluation is the focus of this work. It takes into account transient currents and on-chip and package RLC parasitics while exploring the power grid design solution space: Design countermeasures can be thus early defined and long post physical-design verification cycles can be shortened. As shown by an extensive set of results, a carefully extracted and modular grid library assures realistic evaluation of parasitics impact on noise and facilitates the power network construction; furthermore statistical analysis guarantees a correct current envelope evaluation and Spice simulations endorse reliable results.

Transmit the light fantastic [HVDC power transmission

This paper looks at the current state of the electrical energy sector in the People&apos;s Republic of China in the face of a massive rate of economic growth. More than 120 GW of generating capacity is under construction including the 18.2 GW Three Gorges hydroelectric project, which is due for eventual expansion to 22.4 GW. However, even with this rate of growth within the electrical energy sector, new generating capacity is unlikely to meet demand in most areas for at least another 12 months. Despite efforts to reform the electricity sector, strengthening the country&apos;s power grid networks remains a key objective. Fortunately, the pace of technological development in the power transmission sector is also gathering momentum. Awaiting approval is a project to construct the world&apos;s first ultra high voltage direct current (UHVDC) transmission system. This is part of the effort to upgrade and reinforce the existing nine west-to-east links which import bulk power.

05/02540 Earnings management under price regulation: Empirical evidence from the Spanish electricity industry

This paper proposes mathematical models based on the electrical properties of smart grids for conducting vulnerability analyses and predicting brownouts and blackouts. Definitions of pseudo-Laplacian, pseudo-adjacency and pseudo-degree matrices for smart grids are introduced to specify new centrality measures with electrical interpretations. The centrality measures are used to rank the relative importance of nodes (e.g., generating stations or substations) and edges (e.g., transmission lines or buses) of a graph corresponding to a power grid network and to assess the overall vulnerability of the network. The reliability of using the centrality measures to predict brownouts and blackouts is demonstrated in the face of random and targeted attacks. Monte-Carlo simulations are used to analyze attacks on smart grid networks and to assess the performance of the centrality measures. The simulations employ the IEEE 30-bus, IEEE 57-bus and IEEE 300-bus networks as well as the WSCC 4941-bus real power grid. Every scenario in the Monte-Carlo simulations involves the removal of a subset of buses and performing a complete nonlinear Newton–Raphson power flow analysis to compute the power traffic matrix and the corresponding centrality. The Monte-Carlo simulations conclusively demonstrate that electrical centrality measures based on the power traffic matrix are reliable indicators of the total unsatisfied load ratio (i.e., the load taken offline due to an attack divided by the total load demand). A key result is that, if the total centrality score of the removed buses exceeds a threshold estimated via Monte-Carlo simulation, then a sudden and dramatic jump to a blackout situation is ensured.

Modelling and Analysing Impacts of Wind Power on Transient Stability of Power Systems

This paper considers the impact of increasingly large numbers of wind turbine generators on the stability of power grid networks. Most modern wind turbines do not have conventional grid coupled synchronous generators, as is the case with most other technologies for electrical power generation. Instead, squirrel cage induction generators are used, or generators that are grid coupled with power electronic converters. Consequently, wind turbines interact with the power system in a way that differs from conventional generators. In the paper, the interaction between wind turbines and the power system is investigated using simulations of a widely used representative dynamics test system in which a high wind power penetration is assumed. It is concluded that the impact of wind power on power system transient stability varies much when either constant or variable speed wind turbines are used.