The Promise of EV-Aware Multi-Period OPF Problem: Cost and Emission Benefits

In this paper, we study the Multi-Period Optimal Power Flow problem (MOPF) with electric vehicles (EV) under emission considerations. We integrate three different real-world datasets: household electricity consumption, marginal emission factors, and EV driving profiles. We present a systematic solution approach based on second-order cone programming to find globally optimal solutions for the resulting nonconvex optimization problem. To the best of our knowledge, our paper is the first to propose such a comprehensive model integrating multiple real datasets and a promising solution method for the EV-aware MOPF problem. Our computational experiments on various instances with up to 2000 buses demonstrate that our solution approach leads to high-quality feasible solutions with provably small optimality gaps. In addition, we show the importance of coordinated EV charging to achieve significant emission savings and reductions in cost. In turn, our findings can provide insights to decision-makers on how to incentivize EV drivers depending on the trade-off between cost and emission.Comment: 10 pages, 6 figures, 2 table

BATTPOWER Toolbox: Memory-Efficient and High-Performance Multi-Period AC Optimal Power Flow Solver

With the introduction of massive renewable energy sources and storage devices, the traditional process of grid operation must be improved in order to be safe, reliable, fast responsive and cost efficient, and in this regard power flow solvers are indispensable. In this paper, we introduce an Interior Point-based (IP) Multi-Period AC Optimal Power Flow (MPOPF) solver for the integration of Stationary Energy Storage Systems (SESS) and Electric Vehicles (EV). The primary methodology is based on: 1) analytic and exact calculation of partial differential equations of the Lagrangian sub-problem, and 2) exploiting the sparse structure and pattern of the coefficient matrix of Newton-Raphson approach in the IP algorithm. Extensive results of the application of proposed methods on several benchmark test systems are presented and elaborated, where the advantages and disadvantages of different existing algorithms for the solution of MPOPF, from the standpoint of computational efficiency, are brought forward. We compare the computational performance of the proposed Schur-Complement algorithm with a direct sparse LU solver. The comparison is performed for two different applicational purposes: SESS and EV. The results suggest the substantial computational performance of Schur-Complement algorithm in comparison with that of a direct LU solver when the number of storage devices and optimisation horizon increase for both cases of SESS and EV. Also, some situations where computational performance is inferior are discussed.Comment: 24 pages, 15 figures, Accepted for publication in IEEE Transactions on Power System

Modeling and Analysis of Remote, Off-grid Microgrids

Over the past century the electric power industry has evolved to support the delivery of power over long distances with highly interconnected transmission systems. Despite this evolution, some remote communities are not connected to these systems. These communities rely on small, disconnected distribution systems, i.e., microgrids, to deliver power. Power distribution in most of these remote communities often depend on a type of microgrid called off-grid microgrids\u27\u27. However, as microgrids often are not held to the same reliability standards as transmission grids, remote communities can be at risk to experience extended blackouts. Recent trends have also shown an increased use of renewable energy resources in power systems for remote communities. The increased penetration of renewable resources in power generation will require complex decision making when designing a resilient power system. This is mainly due to the stochastic nature of renewable resources that can lead to loss of load or line overload during their operations. In the first part of this thesis, we develop an optimization model and accompanying solution algorithm for capacity planning and operating microgrids that include N-1 security and other practical modeling features (e.g., AC power flow physics, component efficiencies and thermal limits). We demonstrate the effectiveness of our model and solution approach on two test systems: a modified version of the IEEE 13 node test feeder and a model of a distribution system in a remote Alaskan community. Once a tractable algorithm was identified to solve the above problem, we develop a mathematical model that includes topology design of microgrids. The topology design includes building new lines, making redundant lines, and analyzing N-1 contingencies on generators and lines. We develop a rolling horizon algorithm to efficiently analyze the model and demonstrate the strength of our algorithm in the same network. Finally, we develop a stochastic model that considers generation uncertainties along with N-1 security on generation assets. We develop a chance-constrained model to analyze the efficacy of the problem under consideration and present a case study on an adapted IEEE-13 node network. A successful implementation of this research could help remote communities around the world to enhance their quality of life by providing them with cost-effective, reliable electricity

Application de l’optimisation conique au problème d’écoulement de puissance optimal

RÉSUMÉ: Le problème d’écoulement de puissance optimal consiste à déterminer, sur les bases des consommations et productions prévues, un plan de fonctionnement d’un réseau électrique qui optimise un certain objectif tout en respectant les contraintes physiques et sécuritaires. Sa formulation classique est un problème d’optimisation non convexe et très difficile à résoudre. Récemment, quelques relaxations convexes telles que la relaxation semidéfinie, la relaxation conique du second-ordre, la relaxation quadratique convexe, ont montré un intérêt significatif dans la communauté scientifique. La relaxation semidéfinie est plus forte que la plupart d’entre elles et il existe des applications numériques où elle est exacte. Toutefois, sa résolution s’avère trop coûteuse comparativement à celle de la relaxation conique du second ordre pour un réseau de grande taille. Dans ce travail, nous proposons une nouvelle relaxation conique qui s’avère être un bon compromis entre la relaxation semidéfinie et la relaxation conique du second ordre pour des réseaux de grande taille en termes de gap d’optimalité et de temps de résolution. En effet, des résultats numériques sur des réseaux comportant jusqu’à 6515 noeuds montrent que la nouvelle relaxation est plus forte que la relaxation conique du second ordre et que sa résolution est beaucoup moins coûteuse que celle de la relaxation semidéfinie. Ensuite, nous considérons le problème de répartition optimale de puissance réactive. Ce problème est en fait un problème d’écoulement de puissance optimal où les composants qui permettent de contrôler le flux de puissance réactive dans le réseau, tels que les condensateurs shunts, les transformateurs, sont pris en compte. Le problème de répartition optimale de puissance réactive est un problème mixte en nombres entiers, donc plus complexe que le problème classique. Pour le résoudre, nous utilisons la technique de l’arrondi combinée à une relaxation conique. Cette approche appliquée à des réseaux avec jusqu’à 3375 noeuds donne des meilleurs résultats que si l’on avait considéré une simple relaxation continue du problème, qui est non convexe. En effet, les solutions optimales obtenues sont quasi globales. En pratique, le problème d’écoulement de puissance optimal est un problème multi-période à cause, notamment, de la variation horaire de la consommation. D’autre part, le temps de résolution et la qualité de la solution représentent un besoin clé pour des algorithmes du problème d’écoulement de puissance optimal. En réalité, ce dernier est résolu toutes les 5-10 minutes afin de répondre aux besoins horaires des consommateurs. Dans la dernière partie de ce travail, nous montrons que la relaxation développée dans la première partie peut être exacte. Par la suite, nous l’extrapolons au problème multi-période et les résultats numériques sur des réseaux ayant jusqu’à 500 noeuds montrent que la relaxation multi-période est prometteuse pour des applications réelles.----------ABSTRACT: The classical alternating current optimal power flow (ACOPF) problem is highly nonconvex and generally hard to solve. Convex relaxations, in particular semidefinite, second-order cone, convex quadratic, and linear relaxations, have recently attracted significant interest. The semidefinite relaxation is the strongest among them and is exact for many cases. However, the computational efficiency for solving large-scale semidefinite optimization is lower than for second-order cone optimization. In this work, we first propose a conic relaxation obtained by combining semidefinite optimization with the reformulation-linearization technique, commonly known as RLT. The proposed relaxation, called tight-and-cheap relaxation (TCR), is stronger than the second-order cone relaxation and nearly as tight as the standard semidefinite relaxation. Computational experiments using standard test cases with up to 6515 buses show that the time to solve the new conic relaxation is up to one order of magnitude lower than for the chordal relaxation, a semidefinite relaxation technique that exploits the sparsity of power networks. In the second part of this work, we consider the optimal reactive power dispatch (ORPD) problem, which is anACOPF problem where discrete control devices for regulating the reactive power, such as shunt elements and tap changers, are considered. The ORPD problem is modelled as a mixed-integer nonlinear optimization problem and its complexity is increased compared to the ACOPF problem. We show that a round-off technique applied with a tight conic relaxation of the ORPD problem leads to near-global optimal solutions with very small guaranteed optimality gaps, unlike with the nonconvex continuous relaxation. We report computational results on selected MATPOWER test cases with up to 3375 buses. Many power system applications that require solving an OPF problem are multi-period because of several reasons such as the evolution of market prices or the behavior of the demand. On the oher hand, computational speed and global optimality are a key need for pratical OPF algorithms. In fact, in real-time applications, an OPF problem is run every few minutes to meet the daily requirements optimally in every hour. In the last part of this work, we show that TCR can be exact and can provide a global optimal solution for the ACOPF problem, theoretically and numerically. Thereafter, we propose a multi-period TCR for the multi-period ACOPF problem and computational experiments using MATPOWER test cases with up to 500 buses show that this new relaxation is promising for real-life applications

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

Global Optimization of Multi-period Optimal Power Flow

In this work, we extend the algorithm proposed in [1] to solve multi-period optimal power flow (MOPF) problems to global optimality. The multi-period version of the OPF is time coupled due to the integration of storage systems into the network, and ramp constraints on the generators. The global optimization algorithm is based on the spatial branch and bound framework with lower bounds on the optimal objective function value calculated by solving a semidefinite programming (SDP) relaxation of the MOPF. The proposed approach does not assume convexity and is more general than the ones presented previously for the solution of MOPF. We present a case study of the IEEE 57 bus instance with a time varying demand profile. The integration of storage in the network helps to satisfy loads during high demands and the ramp constraints ensure smooth generation profiles. The SDP relaxation does not satisfy the rank condition, and our optimization algorithm is able to guarantee global optimality within reasonable computational time