arXiv subjects

Emma S. Johnson

Publications and source records attributed to Emma S. Johnson.

4 recordsLinked to original sources

arXiv2021

A Trilevel Model for Segmentation of the Power Transmission Grid Cyber Network

Network segmentation of a power grid's communication system is one way to make the grid more resilient to cyber attacks. We develop a novel trilevel programming model to optimally segment a grid communication system, taking into account the actions of an information technology (IT) administrator, attacker, and grid operator. The IT administrator is given an allowance to segment existing networks, and the attacker is given a fixed budget to attack the segmented communication system in an attempt to inflict damage on the grid. Finally, the grid operator is allowed to redispatch the grid after the attack in order to minimize damage. The resulting problem is a trilevel interdiction problem, which we solve by leveraging current research in bilevel branch and bound. We demonstrate the benefits of optimal network segmentation through case studies on the 9-bus WSCC system and the 30-bus IEEE system. These examples illustrate that network segmentation can significantly reduce the threat.

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arXiv2021

A Scalable Lower Bound for the Worst-Case Relay Attack Problem on the Transmission Grid

We consider a bilevel attacker-defender problem to find the worst-case attack on the relays that control the transmission grid. The attacker maximizes load shed by infiltrating a number of relays and rendering the components connected to them inoperable. The defender responds by minimizing the load shed, re-dispatching using a DC optimal power flow (DCOPF) problem on the remaining network. Though worst-case interdiction problems on the transmission grid are well-studied, there remains a need for exact and scalable methods. Methods based on using duality on the inner problem rely on the bounds of the dual variables of the defender problem in order to reformulate the bilevel problem as a mixed integer linear problem. Valid dual bounds tend to be large, resulting in weak linear programming relaxations and making the problem difficult to solve at scale. Often smaller heuristic bounds are used, resulting in a lower bound. In this work we also consider a lower bound, where instead of bounding the dual variables, we drop the constraints corresponding to Ohm's law, relaxing DCOPF to capacitated network flow. We present theoretical results showing that, for uncongested networks, approximating DCOPF with network flow yields the same set of injections, which suggests that this restriction likely gives a high-quality lower bound in the uncongested case. Furthermore, we show that in the network flow relaxation of the defender problem, the duals are bounded by 1, so we can solve our restriction exactly. Last, we see empirically that this formulation scales well computationally. Through experiments on 16 networks with up to 6468 buses, we find that this bound is almost always as tight as we can get from guessing the dual bounds, even for congested networks. In addition, calculating the bound is approximately 150 times faster than achieving the same bound with the reformulation guessing the dual bounds.

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arXiv2021

A K-Nearest Neighbor Heuristic for Real-Time DC Optimal Transmission Switching

While transmission switching is known to reduce power generation costs, the difficulty of solving even DC optimal transmission switching (DCOTS) has prevented optimal transmission switching from becoming commonplace in real-time power systems operation. In this paper, we present a k-nearest neighbors (KNN) heuristic for DCOTS which relies on the insight that, for routine operations on a fixed network, the DCOTS solutions for similar load profiles and generation cost profiles will likely turn off similar sets of lines. We take a data-driven approach and assume that we have DCOTS solutions for many historical instances, which is realistic given that the problem is solved every 5 minutes in practice. Given a new instance, we find a set of "close" instances from the past and return the best of their solutions for the new instance. We present a case study on 7 test networks ranging in size from 118 to 3,375 buses. We compare the proposed heuristic to DCOTS heuristics from the literature, commercial solver heuristics, and a simple greedy local search algorithm. In most cases, we find better quality solutions in less computational time. In addition, the computational time is within the limits imposed by real-time operations, even on larger networks. Last, we present an empirical study of our training data to understand why the heuristic works well.

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arXiv2019

An Exact and Scalable Problem Decomposition for Security-Constrained Optimal Power Flow

In this paper, we present decomposition techniques for solving large-scale instances of the security-constrained optimal power flow (SCOPF) problem with primary response. Specifically, under each contingency state, we require that the nodal demands are met and that the synchronized units generating below their limits follow a linear model for primary response. The resulting formulation is a mixed-integer linear program since the primary response model introduces disjunctions to the SCOPF problem. Unfortunately, exact methods relying on traditional Benders' decomposition do not scale well. As an alternative, we propose a decomposition scheme based on the column-and-constraint-generation algorithm where we iteratively add disjunctions and cuts. We provide procedures for preprocessing dedicated cuts and for numerically determining the post-contingency responses based on the master problem solutions. We also discuss heuristics to generate high-quality primal solutions and upper bounds for the method. Finally, we demonstrate the efficiency of the proposed method on large-scale systems.

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