Paradigm and paradox in power networks

Well known in the theory of network flows, Braess paradox states that adding path(s) to a congested road network may increase overall journey time. In transportation networks, the phenomenon results from selfish routing. In power systems, an analogous increase in congestion can arise as a consequence of Kirchhoff's laws, suggesting opportunities to optimize grid topology. The thesis starts with the discussion of Braess-like congestion phenomena in linear circuits. We prove that adding electrical path(s) always increases congestion in networks powered by voltage sources, while the opposite in networks driven by current sources. Although such predictability is not present in networks controlled by a mixture of voltage and current sources, our results offer a clean decomposition that completely separates the effect of current sources and voltage sources on total loss. The culmination of this research is a set of four equivalent methods of computing I^2R loss in mixed-source networks. We go on to explore network decomposition in combination with greedy sequential line switching heuristics to address the NP-hardness of power grid topology control. By means of some low order examples, it is shown that within a reasonably large class of greedy heuristics, none can be found that perform better than the others across all grid topologies. Despite this cautionary tale, statistical evidence indicates that, among three most representative heuristics, the global greedy heuristic is most computationally intensive but has the best chance of reducing generation cost while enforcing connectivity. The final part of the thesis presents a new approach to grid decomposition using vertex cut sets. We show that each vertex cut set and corresponding grid decomposition establishes a natural upper bound on the interactions between subgrids as nodal injections are regulated within each. Using such decomposition, it becomes possible to isolate congestion effects to a relatively small subgrid. A fast grid decomposition heuristic based on vertex cut sets and locational marginal prices is then proposed and studied through simulations on IEEE 118-bus system. On average, the computational cost is significantly reduced and the generation cost saving is similar to what is obtained with a global greedy algorithm

A Novel Decomposition for Control of DC Circuits and Grid Models with Heterogeneous Energy Sources

The way in which electric power depends on the topology of circuits with mixed voltage and current sources is examined. The power flowing in any steady-state DC circuit is shown to depend on a minimal set of key variables called fundamental node voltages and fundamental edge currents. Every steady-state DC circuit can be decomposed into a voltage controlled subcircuit and a current controlled subcircuit. In terms of such a decomposition, the I^2R losses of a mixed source circuit are always the sum of losses on the voltage controlled subcircuit and the current controlled subcircuit. The paper concludes by showing that the total power flowing in a mixed source circuit can be found as critical points of the power expressed in terms of the key voltage and current variables mentioned above. The possible relationship to topology control of electric grid operations is discussed

Paradigm and paradox in topology control of power grids

Corrective Transmission Switching can be used by the grid operator to relieve line overloading and voltage violations, improve system reliability, and reduce system losses. Power grid optimization by means of line switching is typically formulated as a mixed integer programming problem (MIP). Such problems are known to be computationally intractable, and accordingly, a number of heuristic approaches to grid topology reconfiguration have been proposed in the power systems literature. By means of some low order examples (3-bus systems), it is shown that within a reasonably large class of “greedy” heuristics, none can be found that perform better than the others across all grid topologies. Despite this cautionary tale, statistical evidence based on a large number of simulations using IEEE 118-bus systems indicates that among three heuristics, a globally greedy heuristic is the most computationally intensive, but has the best chance of reducing generation costs while enforcing N-1 connectivity. It is argued that, among all iterative methods, the locally optimal switches at each stage have a better chance in not only approximating a global optimal solution but also greatly limiting the number of lines that are switched.First author draf

Paradigm and Paradox in Topology Control of Power Grids

Corrective Transmission Switching can be used by the grid operator to relieve line overloading and voltage violations, improve system reliability, and reduce system losses. Power grid optimization by means of line switching is typically formulated as a mixed integer programming problem (MIP). Such problems are known to be computationally intractable, and accordingly, a number of heuristic approaches to grid topology reconfiguration have been proposed in the power systems literature. By means of some low order examples (3-bus systems), it is shown that within a reasonably large class of greedy heuristics, none can be found that perform better than the others across all grid topologies. Despite this cautionary tale, statistical evidence based on a large number of simulations using using IEEE 118- bus systems indicates that among three heuristics, a globally greedy heuristic is the most computationally intensive, but has the best chance of reducing generation costs while enforcing N-1 connectivity. It is argued that, among all iterative methods, the locally optimal switches at each stage have a better chance in not only approximating a global optimal solution but also greatly limiting the number of lines that are switched

Power Grid Decomposition Based on Vertex Cut Sets and Its Applications to Topology Control and Power Trading

It is well known that the reserves/redundancies built into the transmission grid in order to address a variety of contingencies over a long planning horizon may, in the short run, cause economic dispatch inefficiency. Accordingly, power grid optimization by means of short term line switching has been proposed and is typically formulated as a mixed integer programming problem by treating the state of the transmission lines as a binary decision variable, i.e. in-service or out-of-service, in the optimal power flow problem. To handle the combinatorial explosion, a number of heuristic approaches to grid topology reconfiguration have been proposed in the literature. This paper extends our recent results on the iterative heuristics and proposes a fast grid decomposition algorithm based on vertex cut sets with the purpose of further reducing the computational cost. The paper concludes with a discussion of the possible relationship between vertex cut sets in transmission networks and power trading

Power Flow and Optimal Power Flow via Physics-Informed Typed Graph Neural Networks

Esta tesis explora las redes neuronales de grafos tipados informadas por la física aplicadas al modelado de redes de transporte de energía eléctrica, concretamente a los problemas de flujo de potencia y flujo de potencia óptimo. Las redes de transporte de energía eléctrica son complejos sistemas interconectados, cruciales para garantizar un suministro estable de electricidad. Para lograr la transición hacia sistemas energéticos asequibles, fiables y sostenibles, la electrificación de diversos sectores económicos y la integración de fuentes de energía renovable en la red de transmisión han aumentado significativamente. La mayoría de las tecnologías para la generación de energía renovable añaden fluctuación e incertidumbre a la generación de electricidad, por lo que, para garantizar un suministro eléctrico eficiente y estable en todo momento, los operadores de la red de transporte deben realizar frecuentes simulaciones de flujo de potencia y de flujo de potencia óptimo para evaluar el estado de la red. Por estas razones es necesario investigar técnicas nuevas, flexibles y más eficientes para resolver estos análisis. Los recientes avances en el aprendizaje automático, y en particular en las redes neuronales artificiales, indican que estos métodos tienen potencial para resolver problemas de análisis de redes eléctricas de forma rápida y fiable. Hasta la fecha, pocos trabajos han intentado aprovechar las capacidades de aprendizaje de las redes neuronales artificiales para abordar estos temas. Sin embargo, la mayoría de los trabajos publicados no resuelven dos grandes retos: en primer lugar, la necesidad de grandes cantidades de datos de entrenamiento y, en segundo lugar, la falta de capacidad de generalización para analizar redes de transporte realistas con topología variable. En esta tesis, se superan estos inconvenientes introduciendo redes neuronales de grafos tipados, que están especializados para procesar datos estructurados en forma de grafos con distintos tipos de elementos. La red de transmisión puede representarse directamente como un grafo, y al asignar distintos tipos de nodos para representar los diferentes elementos de la red de transmisión, se incrementa la precisión y la interpretabilidad del modelo propuesto. El modelo resultante es un modelo de red de transporte adaptable que puede aplicarse a diversos problemas, como las aplicaciones de flujo de potencia y flujo de potencia óptimo que se presentan en esta tesis. El esquema de aprendizaje presentado está informado por la física, de forma que el entrenamiento no está supervisado, sino que incorpora información de las leyes físicas del sistema subyacente en la función de costo. Además, el modelo resultante puede probarse en redes eléctricas con diferentes configuraciones y, en el caso del flujo de potencia, con redes de diferentes tamaños. Se demuestra que el método propuesto, con las aplicaciones consideradas, consigue resultados similares a los obtenidos con un método convencional pero hasta cuatro órdenes de magnitud más rápido, sin necesidad de datos de entrenamiento y con capacidad de generalización a diferentes redes de transporte. Se puede concluir, por tanto, que el trabajo presentado en esta tesis ofrece un método basado en redes neuronales para agilizar la resolución del complejo sistema de ecuaciones no lineales presente en el problema de flujo de potencia, así como el problema de optimización con restricciones presente en el problema de flujo de potencia óptimo. Estos resultados proporcionan un valioso paso hacia el desarrollo de un sistema general para ayudar a los operadores de sistemas de transmisión a optimizar la integración de nuevas tecnologías en la red convencional, y mejorar la fiabilidad y sostenibilidad de los sistemas eléctricos.<br /

Resilience of power grids and other supply networks: structural stability, cascading failures and optimal topologies

The consequences of the climate crisis are already present and can be expected to become more severe in the future. To mitigate long-term consequences, a major part of the world's countries has committed to limit the temperature rise via the Paris Agreement in the year 2015. To achieve this goal, the energy production needs to decarbonise, which results in fundamental changes in many societal aspects. In particular, the electrical power production is shifting from fossil fuels to renewable energy sources to limit greenhouse gas emissions. The electrical power transmission grid plays a crucial role in this transformation. Notably, the storage and long-distance transport of electrical power becomes increasingly important, since variable renewable energy sources (VRES) are subjected to external factors such as weather conditions and their power production is therefore regionally and temporally diverse. As a result, the transmission grid experiences higher loadings and bottlenecks appear. In a highly-loaded grid, a single transmission line or generator outage can trigger overloads on other components via flow rerouting. These may in turn trigger additional rerouting and overloads, until, finally, parts of the grid become disconnected. Such cascading failures can result in large-scale power blackouts, which bear enormous risks, as almost all infrastructures and economic activities depend on a reliable supply of electric power. Thus, it is essential to understand how networks react to local failures, how flow is rerouted after failures and how cascades emerge and spread in different power transmission grids to ensure a stable power grid operation. In this thesis, I examine how the network topology shapes the resilience of power grids and other supply networks. First, I analyse how flow is rerouted after the failure of a single or a few links and derive mathematically rigorous results on the decay of flow changes with different network-based distance measures. Furthermore, I demonstrate that the impact of single link failures follows a universal statistics throughout different topologies and introduce a stochastic model for cascading failures that incorporates crucial aspects of flow redistribution. Based on this improved understanding of link failures, I propose network modifications that attenuate or completely suppress the impact of link failures in parts of the network and thereby significantly reduce the risk of cascading failures. In a next step, I compare the topological characteristics of different kinds of supply networks to analyse how the trade-off between efficiency and resilience determines the structure of optimal supply networks. Finally, I examine what shapes the risk of incurring large scale cascading failures in a realistic power system model to assess the effects of the energy transition in Europe