Evaluación de la vulnerabilidad de sistemas eléctricos por medio de programación multinivel: una revisión bibliográfica

Vulnerability studies can identify critical elements in electric power systems in order to take protective measures against possible scenarios that may result in load shedding, which can be caused by natural events or deliberate attacks. This article is a literature review on the latter kind, i.e., the interdiction problem, which assumes there is a disruptive agent whose objective is to maximize the damage to the system, while the network operator acts as a defensive agent. The non-simultaneous interaction of these two agents creates a multilevel optimization problem, and the literature has reported several interdiction models and solution methods to address it. The main contribution of this paper is presenting the considerations that should be taken into account to analyze, model, and solve the interdiction problem, including the most common solution techniques, applied methodologies, and future studies. This literature review found that most research in this area is focused on the analysis of transmission systems considering linear approximations of the network, and a few interdiction studies use an AC model of the network or directly treat distribution networks from a multilevel standpoint. Future challenges in this field include modeling and incorporating new defense options for the network operator, such as distributed generation, demand response, and the topological reconfiguration of the system.f the system.Los estudios de vulnerabilidad pueden identificar elementos críticos en los sistemas de distribución de potencia eléctrica con el fin de tomar medidas de protección contra posibles escenarios que pueden resultar en desconexión de carga (también llamado deslastre de carga), que puede ser ocasionada por eventos naturales o ataques deliberados. Este artículo es una reseña bibliográfica sobre el segundo tipo de casos, es decir, los del problema de interdicción, en el que se asume la existencia de un agente disruptivo cuyo objetivo es maximizar los daños ocasionados al sistema mientras el operador de red actúa como agente de defensa del mismo. La interacción no simultánea de estos dos agentes crea un problema de optimización multinivel y en la bibliografía se reportan varios modelos de interdicción y soluciones para abordar el problema. La contribución principal de este artículo es la presentación de consideraciones que deben tomarse en cuenta para analizar, modelar y resolver el problema de la interdicción, incluyendo las soluciones, métodos y técnicas más comunes para solucionarlo, así como futuros estudios al respecto. Esta revisión encontró que la mayoría de la investigación en el tema se enfoca en el análisis de los sistemas de transmisión, considerando las aproximaciones lineales de la red; algunos estudios en interdicción usan un modelo AC de la red o tratan las redes de distribución directamente desde un enfoque multinivel. Algunos retos en este campo son el modelado y la inclusión de nuevas opciones de defensa para el operador de la red, como la generación distribuida, la respuesta a la demanda y la reconfiguración topológica del sistema.&nbsp

Solution Techniques for Large-Scale Optimization Problems on the Transmission Grid

In this thesis, we are interested in solution techniques and primal heuristics for several large-scale optimization problems on the transmission grid. While some of these problems have been studied for a long time, none of the techniques proposed previously allowed them to be solved exactly on large-scale networks, rendering them of little use in practice. We will present methodology which yields high quality solutions on large networks. In Chapter 2, we consider the DC optimal transmission switching (DCOTS) problem. In this problem, we simultaneously optimize the grid topology (i.e., choose which lines are on and off) and the generator dispatch, using a DC optimal power flow (DCOPF) model. It is well-known that transmission switching is an affordable way to reduce congestion in the grid, reducing generation costs. However, DCOTS has so far been a prohibitively difficult model to solve, particularly given that dispatch problems are solved every 5 to 10 minutes for most independent system operators. We present a data-driven approach which assumes that DCOTS has been solved to optimality offline for a variety of demand profiles. We then use the k-nearest neighbors (KNN) method as a primal heuristic, directly mapping from demand profiles to topologies. This scales well since the computational time is dominated by the time to solve k linear programs. We find that we can generate high-quality primal solutions within the time constraints imposed by real-time operations. In addition, we find that defining the feature space for KNN differently can also yield equally good results: In particular, using dual information from the DCOPF problem can be effective. In Chapter 3, we propose a scalable lower bound for a worst-case attack on transmission grid relays. This is a bilevel interdiction problem in which an attacker first targets relays within an attack budget, compromising all components controlled by the relays he chooses, and aiming to maximize load shed. Then, a defender redispatches the generators, solving a DCOPF model and minimizing the load shed. Since the inner problem is convex, it is possible to dualize it, resulting in a mixed-integer single-level reformulation. However, the difficulty arises in linearizing this reformulation. Without bounds on the dual variables of DCOPF, this is not possible to do exactly. Prior literature has used heuristic bounds on the duals. However, in addition to providing a lower bound only, this comes at a computational cost: The more conservatively the bounds are chosen, the larger the big-M values are in the resulting mixed-integer programming (MIP) formulation. This worsens the continuous relaxation and makes it increasingly difficult for even commercial solvers. Instead, we propose using a different lower bound: We relax DCOPF to capacitated network flow, dropping the constraints corresponding to Ohm's law. We show that, on uncongested networks, the injections we get from solving this relaxation are a good approximation of those from solving DCOPF. We can again dualize this problem, creating a single-level formulation. The duals of the relaxed defender problem are bounded in absolute value by 1, meaning we can linearize the single-level formulation and solve it exactly. Furthermore this MIP scales extremely well when solving with a commercial solver. Last, in Chapter 4, we present methodology to solve a trilevel interdiction problem where the inner bilevel problem is the worst-case relay attack problem from Chapter 3. In this problem, we optimize the design of the Supervisory Control and Data Acquisition (SCADA) network controlling the transmission grid in order to minimize the impact of a worst-case cyberattack. Specifically, we decide where the cyber networks in the SCADA system should be subdivided, with communication limited between these subdivisions, a technique called network segmentation. The resulting problem is a trilevel interdiction model with pure integer first and second player problems and a convex third-player problem. We show that it can be solved for large-scale power networks using a covering decomposition approach in which we iteratively fix a network design and generate a worst-case attack. We then find a new design that makes all the generated attacks infeasible. When there is no such design, then the design corresponding to the least-damaging attack generated so far is optimal. We show empirically that this method is scalable for large power networks and moderate network designer and attacker budgets.Ph.D