Saleh Soltan

Cascading failures in power grids: analysis and algorithms

This paper focuses on cascading line failures in the transmission system of the power grid. Recent large-scale power outages demonstrated the limitations of percolation- and epidemic-based tools in modeling cascades. Hence, we study cascades by using computational tools and a linearized power flow model. We first obtain results regarding the Moore-Penrose pseudo-inverse of the power grid admittance matrix. Based on these results, we study the impact of a single line failure on the flows on other lines. We also illustrate via simulation the impact of the distance and resistance distance on the flow increase following a failure, and discuss the difference from the epidemic models. We use the pseudo-inverse of admittance matrix to develop an efficient algorithm to identify the cascading failure evolution, which can be a building block for cascade mitigation. Finally, we show that finding the set of lines whose removal results in the minimum yield (the fraction of demand satisfied after the cascade) is NP-Hard and introduce a simple heuristic for finding such a set. Overall, the results demonstrate that using the resistance distance and the pseudo-inverse of admittance matrix provides important insights and can support the development of efficient algorithms.

Analysis of Failures in Power Grids

This paper focuses on line failures in the transmission system of power grids. Recent large-scale power outages demonstrated the limitations of percolation- and epidemic-based tools in modeling failures and cascades in power grids. Hence, we study failures and cascades by using computational tools and a linearized power-flow model. We first obtain results regarding the Moore-Penrose pseudoinverse of the power grid admittance matrix. Based on these results, we analytically study the impact of a single-line failure on the flows on other lines and introduce metrics to evaluate the robustness of grids to failures. We also illustrate via simulation the impact of the distance and resistance distance on the flow increase following a failure, and discuss the difference from the epidemic models. We use the pseudoinverse of admittance matrix to develop an efficient algorithm to identify the cascading failure evolution, which can be a building block for cascade mitigation. Finally, we show that finding the lines whose removal results in the minimum yield (the fraction of demand satisfied after the cascade) is NP-Hard and present a simple heuristic for finding such a set. Overall, the results demonstrate that using the resistance distance and the pseudoinverse of the admittance matrix provides important insights and can support the development of algorithms for designing robust power grids and controlling the evolution of a cascade upon failures.

Joint Cyber and Physical Attacks on Power Grids: Graph Theoretical Approaches for Information Recovery

Recent events demonstrated the vulnerability of power grids to cyber attacks and to physical attacks. Therefore, we focus on joint cyber and physical attacks and develop methods to retrieve the grid state information following such an attack. We consider a model in which an adversary attacks a zone by physically disconnecting some of its power lines and blocking the information flow from the zone to the grids control center. We use tools from linear algebra and graph theory and leverage the properties of the power flow DC approximation to develop methods for information recovery. Using information observed outside the attacked zone, these methods recover information about the disconnected lines and the phase angles at the buses. We identify sufficient conditions on the zone structure and constraints on the attack characteristics such that these methods can recover the information. We also show that it is NP-hard to find an approximate solution to the problem of partitioning the power grid into the minimum number of attack-resilient zones. However, since power grids can often be represented by planar graphs, we develop a constant approximation partitioning algorithm for these graphs. Finally, we numerically study the relationships between the grids resilience and its structural properties, and demonstrate the partitioning algorithm on real power grids. The results can provide insights into the design of a secure control network for the smart grid.

Power Grid State Estimation Following a Joint Cyber and Physical Attack

This paper focuses on joint cyber and physical attacks on power grids and presents methods to retrieve the grid state information following such an attack. We consider a model where an adversary attacks a zone by physically disconnecting some of its power lines and blocking the information flow from the zone to the grids control center. We use tools from linear algebra and graph theory and leverage the properties of the linearized power flow model to develop methods for information recovery. Using information observed outside the attacked zone, these methods recover information about the disconnected lines and the phase angles at the buses. We identify sufficient conditions on the zone structure and constraints on the attack characteristics such that these methods can recover the information. We also show that it is NP-hard to find an approximate solution to the problem of partitioning the power grid into the minimum number of attack-resilient zones. However, since power grids can often be represented by planar graphs, we develop a constant approximation partitioning algorithm for these graphs and numerically demonstrate its performance on real power grids.

Computational analysis of cascading failures in power networks

This paper focuses on cascading line failures in the transmission system of the power grid. Such a cascade may have a devastating effect not only on the power grid but also on the interconnected communication networks. Recent large-scale power outages demonstrated the limitations of epidemic- and percolation-based tools in modeling the cascade evolution. Hence, based on a linearized power flow model (that substantially differs from the classical packet flow models), we obtain results regarding the various properties of a cascade. Specifically, we consider performance metrics such as the the distance between failures, the length of the cascade, and the fraction of demand (load) satisfied after the cascade. We show, for example, that due to the unique properties of the model: (i) the distance between subsequent failures can be arbitrarily large and the cascade may be arbitrarily long, (ii) a large set of initial line failures may have a smaller effect than a failure of one of the lines in the set, and (iii) minor changes to the network parameters may have a significant impact. Moreover, we show that finding the set of lines whose removal has the most significant impact (under various metrics) is NP-Hard. Moreover, we develop a fast algorithm to recompute the flows at each step of the cascade. The results can provide insight into the design of smart grid measurement and control algorithms that can mitigate a cascade.

Generation of synthetic spatially embedded power grid networks

The development of algorithms for enhancing the resilience and efficiency of the power grid requires evaluation with topologies of real transmission networks. However, due to security reasons, such topologies and particularly the locations of the substations and lines are usually not publicly available. Therefore, we study the structural properties of the North American grids and present an algorithm for generating synthetic spatially embedded networks with similar properties to a given grid. The algorithm has several tunable parameters that allow generating grids similar to any given grid. We apply it to the Western Interconnection (WI) and to grids that operate under the SERC Reliability Corporation (SERC) and the Florida Reliability Coordinating Council (FRCC), and show that the generated grids have similar structural and spatial properties to these grids. To the best of our knowledge, this is the first attempt to consider the spatial distribution of the nodes and lines and its importance in generating synthetic grids.

Comparing the Effects of Failures in Power Grids under the AC and DC Power Flow Models

In this paper, we compare the effects of failures in power grids under the nonlinear AC and linearized DC power flow models. First, we numerically demonstrate that when there are no failures and the assumptions underlying the DC model are valid, the DC model approximates the AC model well in four considered test networks. Then, to evaluate the validity of the DC approximation upon failures, we numerically compare the effects of single line failures and the evolution of cascades under the AC and DC flow models using different metrics, such as yield (the ratio of the demand supplied at the end of the cascade to the initial demand). We demonstrate that the effects of a single line failure on the distribution of the flows on other lines are similar under the AC and DC models. However, the cascade simulations demonstrate that the assumptions underlying the DC model (e.g., ignoring power losses, reactive power flows, and voltage magnitude variations) can lead to inaccurate and overly optimistic cascade predictions. Particularly, in large networks the DC model tends to overestimate the yield. Hence, using the DC model for cascade prediction may result in a misrepresentation of the gravity of a cascade.

Quantifying the effect of k-line failures in power grids

In this paper, we quantify the effect of k-line failures on flow changes using the DC power flow model. We demonstrate that our approach results in efficient tools that can be used to reduce both the total number of cases needed to be analyzed and the computational complexity in power grid contingency analysis. After providing an analytical update of the pseudo-inverse of the admittance matrix following a k-line failure, we compute the k-line outage distribution matrix. The k-line outage distribution matrix is a generalization to the line outage distribution factor for single line failures. We obtain a matrix equation based on the submatrices of the matrix of equivalent reactance values, relating changes in power flows to the initial flows on the failed lines. We also define and analytically compute the disturbance value of a failure - the weighted sum of squares of the flow changes - and show that it can be computed for any set of failures in O(1) independent of the size of the power grid. Finally, we numerically compute disturbance values for all possible choices of 3-line failures in IEEE 118-bus and 300-bus systems and show that the disturbance values provide a clear separation between failures with higher impact and lower impact.

A study of cascading failures in real and synthetic power grid topologies

Using the linearized DC power flow model, we study cascading failures and their spatial and temporal properties in the US Western Interconnect (USWI) power grid. We also introduce the preferential Degree And Distance Attachment (DADA) model, with similar degree distributions, resistances, and currents to the USWI. We investigate the behavior of both grids resulting from the failure of a single line. We find that the DADA model and the USWI model react very similarly to that failure, and that their blackout characteristics resemble each other. In many cases, the failure of a single line can cause cascading failures, which impact the entire grid. We characterize the resilience of the grid by three parameters, the most important of which is tolerance

Algorithms for Power Grid State Estimation after Cyber-Physical Attacks

{\alpha}