Eduardo Cotilla-Sanchez

Do topological models provide good information about electricity infrastructure vulnerability

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.

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

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 Ohms and Kirchhoffs 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.

Multi-Attribute Partitioning of Power Networks Based on Electrical Distance

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.

Predicting Critical Transitions From Time Series Synchrophasor Data

The dynamical behavior of power systems under stress frequently deviates from the predictions of deterministic models. Model-free methods for detecting signs of excessive stress before instability occurs would therefore be valuable. The mathematical frameworks of “fast-slow systems” and “critical slowing down” can describe the statistical behavior of dynamical systems that are subjected to random perturbations as they approach points of instability. This paper builds from existing literature on fast-slow systems to provide evidence that time series data alone can be useful to estimate the temporal distance of a power system to a critical transition, such as voltage collapse. Our method is based on identifying evidence of critical slowing down in a single stream of synchronized phasor measurements. Results from a single machine, stochastic infinite bus model, a three machine/nine bus system and the Western North American disturbance of 10 August 1996 illustrate the utility of the proposed method.

Dynamic Modeling of Cascading Failure in Power Systems

The modeling of cascading failure in power systems is difficult because of the many different mechanisms involved; no single model captures all of these mechanisms. Understanding the relative importance of these different mechanisms is important for choosing which mechanisms need to be modeled for particular applications. This work presents a dynamic simulation model of both power networks and protection systems, which can simulate a wider variety of cascading outage mechanisms relative to existing quasi-steady-state (QSS) models. This paper describes the model and demonstrates how different mechanisms interact. In order to test the model, we simulated a batch of randomly selected N-2 contingencies for several different static load configurations, and found that the distributions of blackout sizes and event lengths from the simulator correlate well with historical trends. The results also show that load models have significant impacts on the cascading risks. Finally, the dynamic model was compared against a simple dc-power-flow based QSS model; we find that the two models tend to agree for the early stages of cascading but produce substantially different results for later stages.

Dual Graph and "Random Chemistry" Methods for Cascading Failure Analysis

This paper describes two new approaches to cascading failure analysis in power systems that can combine large amounts of data about cascading blackouts to produce information about the ways that cascades may propagate. In the first, we evaluate methods for representing cascading failure information in the form of a graph. We refer to these graphs as “dual graphs” because the vertices are the transmission lines (the physical links), rather than the more conventional approach of representing power system buses as vertices. Examples of these ideas using the IEEE 30 bus system indicate that the “dual graph” methods can provide useful insight into how cascades propagate. In the second part of the paper we describe a random chemistry algorithm that can search through the enormous space of possible combinations of potential component outages to efficiently find large collections of the most dangerous combinations. This method was applied to a power grid with 2896 transmission branches, and provides insight into component outages that are notably more likely than others to trigger a cascading failure. In the conclusions we discuss potential uses of these methods for power systems planning and operations.

Topological Models and Critical Slowing down: Two Approaches to Power System Blackout Risk Analysis

This paper describes results from the analysis of two approaches to blackout risk analysis in electric power systems. In the first analysis, we compare two topological (graph-theoretic) methods for finding vulnerable locations in a power grid, to a simple model of cascading outage. This comparison indicates that topological models can lead to misleading conclusions about vulnerability. In the second analysis, we describe preliminary results indicating that both a simple dynamic power system model and frequency data from the August 10, 1996 disturbance in North America show evidence of critical slowing down as the system approaches a failure point. In both examples, autocorrelation in the time- domain signals (frequency and phase angle), significantly increases before reaching the critical point. These results indicate that critical slowing down could be a useful indicator of increased blackout risk.

Understanding Early Indicators of Critical Transitions in Power Systems From Autocorrelation Functions

Many dynamical systems, including power systems, recover from perturbations more slowly as they approach critical transitions - a phenomenon known as critical slowing down. If the system is stochastically forced, autocorrelation and variance in time-series data from the system often increase before the transition, potentially providing an early warning of coming danger. In some cases, these statistical patterns are sufficiently strong, and occur sufficiently far from the transition, that they can be used to predict the distance between the current operating state and the critical point. In other cases CSD comes too late to be a good indicator. In order to better understand the extent to which CSD can be used as an indicator of proximity to bifurcation in power systems, this paper derives autocorrelation functions for three small power system models, using the stochastic differential algebraic equations (SDAE) associated with each. The analytical results, along with numerical results from a larger system, show that, although CSD does occur in power systems, its signs sometimes appear only when the system is very close to transition. On the other hand, the variance in voltage magnitudes consistently shows up as a good early warning of voltage collapse.

Benchmarking and Validation of Cascading Failure Analysis Tools

Cascading failure in electric power systems is a complicated problem for which a variety of models, software tools, and analytical tools have been proposed but are difficult to verify. Benchmarking and validation are necessary to understand how closely a particular modeling method corresponds to reality, what engineering conclusions may be drawn from a particular tool, and what improvements need to be made to the tool in order to reach valid conclusions. The community needs to develop the test cases tailored to cascading that are central to practical benchmarking and validation. In this paper, the IEEE PES working group on cascading failure reviews and synthesizes how benchmarking and validation can be done for cascading failure analysis, summarizes and reviews the cascading test cases that are available to the international community, and makes recommendations for improving the state of the art.

Developing a dynamic model of cascading failure for high performance computing using trilinos

This paper describes work-in-progress toward the development of a dynamic model of cascading failure in power systems that is suitable for High Performance Computing simulation environments. Doing so involves simulating a power grid as a set of differential, algebraic and discrete equations. We describe the general form of the algorithm in use for this simulation and provide details about the implementation using the Trilinos software libraries. Several computational tests illustrate how the proposed approach can be leveraged to optimize the computational efficiency of cascading failure simulation.