Vulnerability Analysis of Modern Electric Grids: A Mathematical Optimization Approach

Electrical power must be transmitted through a vast and complicated network of interconnected grids to arrive at one’s fingertips. The US electric grid network and its components are rapidly advancing and adapting to the advent of smart technologies. Production of electricity is transitioning to sustainable processes derived from renewable energy sources like wind and solar power to decrease dependence on nonrenewable fossil fuels. These newly pervasive natures of smart technology and the variable power supply of renewable energy introduce previously unexamined vulnerabilities into the modern electric grid. Disruption of grid operations is not uncommon, and the effects can be economically and societally severe. Thus, a vulnerability analysis can provide decision makers with the ability to characterize points of improvement in the networks they supervise. This thesis performs a vulnerability analysis of electric grid operations including storage. This vulnerability analysis is achieved through a set of numerical experiments on a multi-period optimal power flow model including storage and variable demand. This model resulted in an analysis indicating storage is helpful in increasing resilience in networks with excess generation, no matter how severe the disruption. Networks with constrained generation benefit little, if at all, from storage. This analysis allows us to conclude careful implementation is the best way to improve electric grid security in the face of widespread use of renewable energy and smart technology

Linear Optimal Power Flow Using Cycle Flows

Linear optimal power flow (LOPF) algorithms use a linearization of the alternating current (AC) load flow equations to optimize generator dispatch in a network subject to the loading constraints of the network branches. Common algorithms use the voltage angles at the buses as optimization variables, but alternatives can be computationally advantageous. In this article we provide a review of existing methods and describe a new formulation that expresses the loading constraints directly in terms of the flows themselves, using a decomposition of the network graph into a spanning tree and closed cycles. We provide a comprehensive study of the computational performance of the various formulations, in settings that include computationally challenging applications such as multi-period LOPF with storage dispatch and generation capacity expansion. We show that the new formulation of the LOPF solves up to 7 times faster than the angle formulation using a commercial linear programming solver, while another existing cycle-based formulation solves up to 20 times faster, with an average speed-up of factor 3 for the standard networks considered here. If generation capacities are also optimized, the average speed-up rises to a factor of 12, reaching up to factor 213 in a particular instance. The speed-up is largest for networks with many buses and decentral generators throughout the network, which is highly relevant given the rise of distributed renewable generation and the computational challenge of operation and planning in such networks.Comment: 11 pages, 5 figures; version 2 includes results for generation capacity optimization; version 3 is the final accepted journal versio

Hierarchical Predictive Control Algorithms for Optimal Design and Operation of Microgrids

In recent years, microgrids, i.e., disconnected distribution systems, have received increasing interest from power system utilities to support the economic and resiliency posture of their systems. The economics of long distance transmission lines prevent many remote communities from connecting to bulk transmission systems and these communities rely on off-grid microgrid technology. Furthermore, communities that are connected to the bulk transmission system are investigating microgrid technologies that will support their ability to disconnect and operate independently during extreme events. In each of these cases, it is important to develop methodologies that support the capability to design and operate microgrids in the absence of transmission over long periods of time. Unfortunately, such planning problems tend to be computationally difficult to solve and those that are straightforward to solve often lack the modeling fidelity that inspires confidence in the results. To address these issues, we first develop a high fidelity model for design and operations of a microgrid that include component efficiencies, component operating limits, battery modeling, unit commitment, capacity expansion, and power flow physics; the resulting model is a mixed-integer quadratically-constrained quadratic program (MIQCQP). We then develop an iterative algorithm, referred to as the Model Predictive Control (MPC) algorithm, that allows us to solve the resulting MIQCQP. We show, through extensive computational experiments, that the MPC-based method can scale to problems that have a very long planning horizon and provide high quality solutions that lie within 5\% of optimal.Comment: To appear in "Power Systems Computation Conference", Dublin, Irelan

Flexible management and decarbonisation of rural networks using multi-objective battery control

To support the electrification of heat and transport, distribution network operators are looking to adopt network management solutions which can exploit local flexibility to advance their decarbonisation efforts in line with the evolving management requirements of the network. This paper develops a multi-functional battery control strategy that integrates constraint management with carbon-intensity linked control dispatch – carbon control – to support decarbonisation of rural distribution networks in Scotland by displacing last resort backup diesel generation and facilitating low carbon network balancing in the drive towards self-sustaining local distribution networks. The interplay between the different functionalities is considered to understand the challenges, and opportunities, of adopting multi-functional battery storage as an alternative management solution based on an operational distribution network in Scotland. Case studies are presented which consider network constraints at different times of day and year for various generation, demand and carbon intensity profiles to support this investigation. The findings of this work provide for the near-term, realisation of self-sustaining carbon-neutral local distribution networks that are in keeping with both the operational objectives of incumbent network operators, smart local energy systems and also low carbon policy objectives

Advances in Energy System Optimization

The papers presented in this open access book address diverse challenges in decarbonizing energy systems, ranging from operational to investment planning problems, from market economics to technical and environmental considerations, from distribution grids to transmission grids, and from theoretical considerations to data provision concerns and applied case studies. While most papers have a clear methodological focus, they address policy-relevant questions at the same time. The target audience therefore includes academics and experts in industry as well as policy makers, who are interested in state-of-the-art quantitative modelling of policy relevant problems in energy systems. The 2nd International Symposium on Energy System Optimization (ISESO 2018) was held at the Karlsruhe Institute of Technology (KIT) under the symposium theme “Bridging the Gap Between Mathematical Modelling and Policy Support” on October 10th and 11th 2018. ISESO 2018 was organized by the KIT, the Heidelberg Institute for Theoretical Studies (HITS), the Heidelberg University, the German Aerospace Center and the University of Stuttgart

Essays on the ACOPF Problem: Formulations, Approximations, and Applications in the Electricity Markets

The alternating current optimal power flow (ACOPF) problem, also referred to as the optimal power flow (OPF) problem, is at the core of competitive wholesale electricity markets and vertically integrated utility operations. ACOPF simultaneously co-optimizes real and reactive power. First formulated over half a century ago in 1962 by Carpentier, the ACOPF is the most representative mathematical programming-based formulation of steady-state operations in AC networks. However the ACOPF is not solved in practice due to the nonconvex structure of the problem, which is known to be NP-hard. Instead, least-cost unit commitment and generation dispatch in the day-ahead, intra-day, and real-time markets is determined with numerous simplifications of the ACOPF constraint set. This work presents a series of essays on the ACOPF problem, which include formulations, approximations, and applications in the electricity markets. The main themes center around ACOPF modeling fundamentals, followed by local and global solution methods for a variety of applications in the electricity markets. Original contributions of these essays include an alternative formulation of the ACOPF, a successive linear programming algorithm to solving the ACOPF for the real-time energy market, an outer approximation method to solving integrated ACOPF-unit commitment as a mixed-integer linear program for the day-ahead market, and applications of convex relaxations to the ACOPF and its approximations for the purpose of globally optimal storage integration. These contributions are concluded with a discussion of potential future directions for work

Model-Predictive Control for Alleviating Transmission Overloads and Voltage Collapse in Large-Scale Electric Power Systems

Emergency control in electric power systems requires rapid identification and implementation of corrective actions. Typically, system operators have performed this service while relying on rules-of-thumb and predetermined control sequences with limited decision support tools. Automatic control schemes offer the potential to improve this process by quickly analyzing large, complex problems to identify the most effective actions. Model-predictive control (MPC) is one such scheme which has a strong record of success in the process industry and has begun receiving attention in power systems applications. Incorporating flexibility into the MPC model using energy storage and temperature-based transmission line limits has shown promising results for relieving transmission overloads on small networks with linear active power models. Separately, MPC has demonstrated its capabilities in correcting transformer-driven voltage collapse behaviors. However, a comprehensive solution combines both aspects into a single controller formulation with knowledge of active and reactive power and voltage magnitude and angle. Additionally, most power system networks are large and result in computationally challenging problem formulations. This work considers these practical limitations and suggests techniques to enable an MPC process capable of operating reliably in the real-world. A new linear controller model is proposed which considers voltage magnitude and angle and both active and reactive power. The new model provides greater accuracy when predicting system behavior and better identifies the actual control needs of the system. The problem size is reduced by limiting the model to only those devices which are significantly affected by the emergency conditions. The new approach is shown to identify controls more rapidly and better suppresses undesirable thermal behavior on overloaded transmission lines while avoiding potential voltage collapse situations.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/137120/1/jandrewm_1.pd

Modélisation fréquentielle analytique de convertisseurs statiques en vue du dimensionnement de systèmes par optimisation

For the design of static energy conversion systems from power grids, harmonic standards have to berespected. To characterize them, frequency modeling approaches, either numerical or semi-analytical. Thesecond one is more advisable for the sizing by optimization of systems, where a fast model is required and manyconstraints have to be carried out. However, the main difficulties happen in the analytical modeling of powerelectronics structures, especially those with soft commutations.This thesis proposes a semi-analytical modeling approach where the solving of implicit equations iscarried out by Newton-Raphson or SQP. The convergence difficulties are analyzed in two viewpoints:numerically and according the operating mode of the static converters. Then, alternatives are proposed to solvethem.To illustrate the problematic, applications with diode rectifiers (widely used in railway electrical gridsubstations or airline electrical grid) are used. Especially, the sizing of power channel of « new generation» of anAirbus, is made by optimization, using the proposed modelling approach.Dans le cadre du dimensionnement des systèmes de conversion statique d’énergie implantés dans des réseaux électriques, il est important de respecter certaines normes harmoniques. Pour caractériser celles-ci, on doit utiliser des approches des modélisations fréquentielles : soit numérique, soit semi-analytique. La deuxième est préférable pour à une procédure de dimensionnement par optimisation de système, qui requiert un modèle rapide et peut accepter beaucoup de contraintes. Cependant, la difficulté principale apparaît lors de la modélisation analytique des structures d’électronique de puissance, notamment celles ayant de la commutation naturelle.Cette thèse propose une approche de modélisation semi-analytique où la résolution des équations implicites est faite par Newton-Raphson ou SQP. Cependant, cette approche pose des difficultés de convergence de la méthode utilisée du point de vue numérique et du point de vue du mode de fonctionnement du convertisseur statique. Ainsi, cette thèse propose différentes alternatives pour les résoudre.En terme d’illustrations, cette thèse s’appuie particulièrement sur des applications avec des redresseurs à diodes qui sont largement utilisés dans les sous-stations de réseaux ferroviaires ou dans les réseaux d’avion,Notamment, un canal de puissance typique d’un Airbus de « nouvelle génération » sert d’application du point de vue de dimensionnement par optimisation

Solving Large-Scale AC Optimal Power Flow Problems Including Energy Storage, Renewable Generation, and Forecast Uncertainty

Renewable generation and energy storage are playing an ever increasing role in power systems. Hence, there is a growing need for integrating these resources into the optimal power flow (OPF) problem. While storage devices are important for mitigating renewable variability, they introduce temporal coupling in the OPF constraints, resulting in a multiperiod OPF formulation. This work explores a solution method for multiperiod AC OPF problems that combines a successive quadratic programming approach (AC-QP) with a second-order cone programming (SOCP) relaxation of the OPF problem. The solution of the SOCP relaxation is used to initialize the AC-QP OPF algorithm. Additionally, the lower bound on the objective value obtained from the SOCP relaxation provides a measure of solution quality. Compared to other initialization schemes, the SOCP-based approach offers improved convergence rate, execution time and solution quality. A reformulation of the the AC-QP OPF method that includes wind generation uncertainty is then presented. The resulting stochastic optimization problem is solved using a scenario based algorithm that is based on randomized methods that provide probabilistic guarantees of the solution. This approach produces an AC-feasible solution while satisfying reasonable reliability criteria. The proposed algorithm improves on techniques in prior work, as it does not rely upon model approximations and maintains scalability with respect to the number of scenarios considered in the OPF problem. The optimality of the proposed method is assessed using the lower bound from the solution of an SOCP relaxation and is shown to be sufficiently close to the globally optimal solution. Moreover, the reliability of the OPF solution is validated via Monte Carlo simulation and is demonstrated to fall within acceptable violation levels. Timing results are provided to emphasize the scalability of the method with respect to the number of scenarios considered and demonstrate its utility for real-time applications. Several extensions of this stochastic OPF are then developed for both operational and planning purposes. The first is to include the cost of generator reserve capacity in the objective of the stochastic OPF problem. The need for the increased accuracy provided by the AC OPF is highlighted by a case study that compares the reliability levels achieved by the AC-QP algorithm to those from the solution of a stochastic DC OPF. Next, the problem is extended to a planning context, determining the maximum wind penetration that can be added in a network while maintaining acceptable reliability criteria. The scalability of this planning method with respect not only to large numbers of wind scenarios but also to moderate network size is demonstrated. Finally, a formulation that minimizes both the cost of generation and the cost of reserve capacity while maximizing the wind generation added in the network is investigated. The proposed framework is then used to explore the inherent tradeoff between these competing objectives. A sensitivity study is then conducted to explore how the cost placed on generator reserve capacity can significantly impact the maximum wind penetration that can be reliably added in a network.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138664/1/jkfelder_1.pd