Investment in Electricity Networks with Transmission Switching

We consider the application of Dantzig-Wolfe decomposition to stochastic integer programming problems arising in the capacity planning of electricity trans-mission networks that have some switchable transmission elements. The decomposition enables a column-generation algorithm to be applied, which allows the solution of large problem instances. The methodology is illustrated by its application to a problem of determining the optimal investment in switching equipment and transmission capacity for an existing network. Computational tests on IEEE test networks with 73 nodes and 118 nodes confirm the efficiency of the approach

A Cycle-Based Formulation and Valid Inequalities for DC Power Transmission Problems with Switching

It is well-known that optimizing network topology by switching on and off transmission lines improves the efficiency of power delivery in electrical networks. In fact, the USA Energy Policy Act of 2005 (Section 1223) states that the U.S. should "encourage, as appropriate, the deployment of advanced transmission technologies" including "optimized transmission line configurations". As such, many authors have studied the problem of determining an optimal set of transmission lines to switch off to minimize the cost of meeting a given power demand under the direct current (DC) model of power flow. This problem is known in the literature as the Direct-Current Optimal Transmission Switching Problem (DC-OTS). Most research on DC-OTS has focused on heuristic algorithms for generating quality solutions or on the application of DC-OTS to crucial operational and strategic problems such as contingency correction, real-time dispatch, and transmission expansion. The mathematical theory of the DC-OTS problem is less well-developed. In this work, we formally establish that DC-OTS is NP-Hard, even if the power network is a series-parallel graph with at most one load/demand pair. Inspired by Kirchoff's Voltage Law, we give a cycle-based formulation for DC-OTS, and we use the new formulation to build a cycle-induced relaxation. We characterize the convex hull of the cycle-induced relaxation, and the characterization provides strong valid inequalities that can be used in a cutting-plane approach to solve the DC-OTS. We give details of a practical implementation, and we show promising computational results on standard benchmark instances

A strategic decision support system framework for energy-efficient technology investments

Energy systems optimization under uncertainty is increasing in its importance due to on-going global de-regulation of the energy sector and the setting of environmental and efficiency targets which generate new multi-agent risks requiring a model-based stakeholders dialogue and new systemic regulations. This paper develops an integrated framework for decision support systems (DSS) for the optimal planning and operation of a building infrastructure under appearing systemic de-regulations and risks. The DSS relies on a new two-stage, dynamic stochastic optimization model with moving random time horizons bounded by stopping time moments. This allows to model impacts of potential extreme events and structural changes emerging from a stakeholders dialogue, which may occur at any moment of the decision making process. The stopping time moments induce endogenous risk aversion in strategic decisions in a form of dynamic VaR-type systemic risk measures dependent on the system’s structure. The DSS implementation via an algebraic modeling language (AML) provides an environment that enforces the necessary stakeholders dialogue for robust planning and operation of a building infrastructure. Such a framework allows the representation and solution of building infrastructure systems optimization problems, to be implemented at the building level to confront rising systemic economic and environmental global changes

Optimization Methods in Electric Power Systems: Global Solutions for Optimal Power Flow and Algorithms for Resilient Design under Geomagnetic Disturbances

An electric power system is a network of various components that generates and delivers power to end users. Since 1881, U.S. electric utilities have supplied power to billions of industrial, commercial, public, and residential customers continuously. Given the rapid growth of power utilities, power system optimization has evolved with developments in computing and optimization theory. In this dissertation, we focus on two optimization problems associated with power system planning: the AC optimal power flow (ACOPF) problem and the optimal transmission line switching (OTS) problem under geomagnetic disturbances (GMDs). The former problem is formulated as a nonlinear, non-convex network optimization problem, while the latter is the network design version of the ACOPF problem that allows topology reconfiguration and considers space weather-induced effects on power systems. Overall, the goal of this research includes: (1) developing computationally efficient approaches for the ACOPF problem in order to improve power dispatch efficiency and (2) identifying an optimal topology configuration to help ISO operate power systems reliably and efficiently under geomagnetic disturbances. Chapter 1 introduces the problems we are studying and motivates the proposed research. We present the ACOPF problem and the state-of-the-art solution methods developed in recent years. Next, we introduce geomagnetic disturbances and describe how they can impact electrical power systems. In Chapter 2, we revisit the polar power-voltage formulation of the ACOPF problem and focus on convex relaxation methods to develop lower bounds on the problem objective. Based on these approaches, we propose an adaptive, multivariate partitioning algorithm with bound tightening and heuristic branching strategies that progressively improves these relaxations and, given sufficient time, converges to the globally optimal solution. Computational results show that our methodology provides a computationally tractable approach to obtain tight relaxation bounds for hard ACOPF cases from the literature. In Chapter 3, we focus on the impact that extreme GMD events could potentially have on the ability of a power system to deliver power reliably. We develop a mixed-integer, nonlinear model which captures and mitigates GMD effects through line switching, generator dispatch, and load shedding. In addition, we present a heuristic algorithm that provides high-quality solutions quickly. Our work demonstrates that line switching is an effective way to mitigate GIC impacts. In Chapter 4, we extend the preliminary study presented in Chapter 3 and further consider the uncertain nature of GMD events. We propose a two-stage distributionally robust (DR) optimization model that captures geo-electric fields induced by uncertain GMDs. Additionally, we present a reformulation of a two-stage DRO that creates a decomposition framework for solving our problem. Computational results show that our DRO approach provides solutions that are robust to errors in GMD event predictions. Finally, in Chapter 5, we summarize the research contributions of our work and provide directions for future research

Optimization Algorithms for Power Grid Planning and Operational Problems.

The modern electrical grid is an engineering marvel. The power grid is an incredibly complex system that largely functions very reliably. However, aging infrastructure and changing power consumption and generation trends will necessitate that new investments be made and new operational regimes be explored to maintain this level of reliability. One of the primary difficulties in power grid planning is the presence of uncertainty. In this thesis, we address short-term (i.e., day-ahead) and long-term power system planning problems where there is uncertainty in the forecasted demand for power, future renewable generation levels, and/or possible component failures. We initially consider a network capacity design problem where there is uncertainty in the nodal supplies and demands. This robust single-commodity network design problem underlies several applications including power transmission networks. Minimum cost capacity expansion decisions are made to ensure that there exists a feasible network flow solution for alpha% of the demand scenarios in the given set, where alpha is a parameter specified by the user. We next consider a day-ahead planning problem that is specifically applicable to the power grid. We present an extension of the traditional unit commitment problem where we additionally consider (1) a more stringent security requirement and (2) a more flexible set of recovery actions. We require that feasible operation is possible for any simultaneous failure of k generators and/or transmission lines (i.e., N-k security), and transmission switching may be used to recover from a failure event. Finally, we consider a transmission expansion planning problem where there is uncertainty in future loads, renewal generation outputs and line failures, and transmission switching is also allowed as a recovery action. We propose a robust optimization model where feasible operation is required for all loads and renewable generation levels within given ranges, and for all single transmission line failures. For all three of these problems, novel algorithms are presented that enable these problems to be solved even when straight-forward formulations are too large to be tractable. Computational results are presented for each algorithm to provide insight into the advantages and limitations of these algorithms in practicePHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/107076/1/kaschu_1.pd

Contributions à l'amélioration de la performance statique des réseaux T & D intégrés en présence des REDs

Avec la croissance des nouvelles technologies émergentes dans les réseaux de distribution, tels que les éoliennes, les panneaux solaires, les véhicules électriques et les sources de génération distribuées, la nécessité d'étudier simultanément les réseaux de transmission et de distribution (T&D) et leurs interactions bilatérales ne peut plus être négligée. Une forte pénétration des sources d'énergie renouvelable, naturellement stochastiques, peut inverser le flux d'énergie, ce qui ne rentre pas dans le paradigme d’un écoulement de puissance à flux descendant qui caractérise les systèmes d'alimentation conventionnels. Par conséquent, les méthodes d'étude de réseaux telles que le fux de puissance optimal (Optimal Power Flow), l'engagement des groupes de production (unit commitment) et l'analyse de la stabilité doivent être revisitées. Cette thèse propose l'application de systèmes de stockage d'énergie sur batterie (BESS) dans un cadre intégré de T&D minimisant les impacts négatifs des énergies renouvelables insérées dans le réseau de distribution ou chez le client. Les BESS peuvent être interprétés comme des équipements flexibles supplémentaires, contrôlés à distance et/ou localement, qui absorbent ou libèrent des puissances actives et réactives et améliorent l'efficacité globale du système T&D au complet du point de vue de la stabilité et de la performance dynamique. Selon la pratique courante, les études des systèmes T&D intégrés peuvent être classées en sous-groupes d’études dynamiques vs stationnaires ou en sous-groupes d’études de cooptimisation vs co-simulation. Suivant la même approche, l’analyse à l’état d’équilibre est d’abord lancée par un nouvel outil d’allocation optimisée stochastique de BESS (VSCSOBA) à contrainte de stabilité de tension. L'outil d'optimisation développé basé sur GAMS à deux niveaux prend en compte les BESS et des modèles détaillés de ressources énergétiques distribuées stochastiques tout en minimisant principalement les pertes de puissance active, mais les écarts de tension, les coûts de délestage, l'augmentation de la capacité de charge (chargeabilité ou « loadbility ») ainsi que la réduction de la vulnérabilité sont aussi des fonctions objectives qui ont été considérées. L’applicabilité de l’outil proposé a été confirmée sur des cas d’utilisation basés sur des réseaux T&D benchmark de l’IEEE comportant des centaines de variables et contraintes. Dans la partie suivante, l'architecture du framework de co-simulation, ainsi que les différents acteurs clés qui y participent seront examinés. Les objectifs de cette partie sont les suivants : développer, simuler et résoudre des équations algébriques de chaque niveau indépendamment, à l'aide de simulateurs bien connus, spécifiques à un domaine (c’est-à-dire, transport vs distribution), tout en assurant une interface externe pour l'échange de données. L'outil d'interface devrait établir une connexion de partage de données robuste, fiable et bilatérale entre deux niveaux de système. Les idées et les méthodologies proposées seront discutées. Pour completer cette étude, La commutation optimale de réseaux de transport (Optimal Transmission Switching) en tant que nouvelle méthode de réduction des coûts d'exploitation est considérée d'un point de vue de la sécurité, en assument ou non la présence des BESS. De toute évidence, l'OTS est un moyen efficace (tout comme la référence de tension ou le contrôle des références de puissances P-Q) qui s’avère nécessaire dans le cadre T&D intégré, tel que nous le démontrons à travers divers cas d'utilisation. Pour ce faire, afin de préserver la sécurité des systèmes de transport d'électricité contre les attaques ou les catastrophes naturelles telles que les ouragans et les pannes, un problème OTS stochastique orienté vulnérabilité (VO-SOTS) est également introduit dans cette thèse tout en considérant l'incertitude des charges via une approche par échantillonage de scénarios respectant la distribution statistique des incertitudes.With the growing trend of emerging new technologies in distribution networks, such as wind turbines, solar panels, electric vehicles, and distributed generations, the need for simultaneously studying Transmission & Distribution (T&D) networks and their bilateral interactions cannot be overlooked anymore. High penetration of naturally stochastic renewable energy sources may reverse the energy flow which does not fit in the top-down energy transfer paradigm of conventional power systems. Consequently, network study methods such as optimal power flow, unit commitment, and static stability analysis need to be revised. This thesis proposes application of battery energy storage systems (BESS) within integrated T&D framework minimizing the adverse impacts of renewable energy resources. The BESSs can be interpreted as additional flexible equipment, remotely and/or locally controlled, which absorb or release both active and reactive powers and improve the overall efficiency of the complete T&D system from both steady-state and dynamic viewpoints. As a common practice, the integrated T&D framework studies are categorized into either dynamic and steady-state subcases or co-optimization framework and co-simulation framework. Following the same approach, the steady-state analysis is first initiated by a novel voltage stability constrained stochastic optimal BESS allocation (VSC-SOBA) tool. The developed bi-level GAMS-based optimization tool takes into account BESSs and detailed models of stochastic distributed energy resources while minimizing active power losses, voltage deviation, load shedding costs, increasing loadability, and vulnerability mitigation are objective functions. The applicability of proposed tool has been confirmed over large IEEE recognized T&D benchmarks with hundreds of variables and constraints. In the next part, the architecture of co-simulation framework and different key players will be investigated. The objectives of this part are set as: developing, simulating, and solving differential and algebraic equations of each level independently, using existing well-known domain-specific simulators, while externally-interfaced for exchanging data. The interface tool should stablish a robust, reliable, and bilateral data sharing connection between two levels of system. The ideas and proposed methodologies will be discussed. To complete this study, optimal transmission switching (OTS) as a new method for reduction of operation costs is next considered from a security point of view. It is shown clearly that OTS is an effective mean (just like voltage reference or P-Q reference control), which is necessary in the integrated T&D framework to make it useful in dealing with various emerging use cases. To do so without impeding the security of power transmission systems against attacks or natural disasters such as hurricane and outages, a vulnerability oriented stochastic OTS (VO-SOTS) problem is also introduced in this thesis, while considering the loads uncertainty via a scenario-based approach