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Abstract : This work proposes a Mixed Integer Second Order Cone Programming (MISOCP) model for Distribution Optimal Power Flow (DOPF) by incorporating conic model of voltage control through a Load Tap Changer (LTC) as discrete control. A novel algorithm, Sequential Bound Tightening Algorithm (SBTA), is also developed to solve the proposed model. The algorithm improves accuracy and the formulation along with the algorithm permits computational tractability on practical-sized systems. The proposed model and the algorithm are tested and benchmarked against the results from a standard Mixed Integer Nonlinear Programming (MINLP) model. The results show that the model is sufficiently accurate and scales well on larger systems. Additionally, a Mixed Integer Conic Reformulation of the UC problem is also proposed whose computational efficiency is further enhanced by incorporating convex hull of difficult inter-temporal constraints. The results show that the proposed model outperforms MINLP by a large factor and it even outperforms commonly used MILP model on larger systems.
This volume in the SpringerBriefs in Energy series offers a systematic review of unit commitment (UC) problems in electrical power generation. It updates texts written in the late 1990s and early 2000s by including the fundamentals of both UC and state-of-the-art modeling as well as solution algorithms and highlighting stochastic models and mixed-integer programming techniques. The UC problems are mostly formulated as mixed-integer linear programs, although there are many variants. A number of algorithms have been developed for, or applied to, UC problems, including dynamic programming, Lagrangian relaxation, general mixed-integer programming algorithms, and Benders decomposition. In addition the book discusses the recent trends in solving UC problems, especially stochastic programming models, and advanced techniques to handle large numbers of integer- decision variables due to scenario propagation
In this talk, I will give an overview of mixed integer linear programming (MILP) formulations and extensions thereof which enable the effective solution of the unit commitment problem (UC) when paired with a commercial MILP solver. First, we will place UC in context, stressing the importance of achieving a (near) optimal solution. Then we will discuss the importance of perfect and "good-enough" formulations for individual generators / market participants. Some of these formulations enable symmetry-aware reformulations for identical market participants, which can be critical when symmetry is present. Finally, we will discuss approximations of AC power flow currently used in practice, and the challenges with including these approximations within the UC formulation.
This handbook gathers state-of-the-art research on optimization problems in power distribution systems, covering classical problems as well as the challenges introduced by distributed power generation and smart grid resources. It also presents recent models, solution techniques and computational tools to solve planning problems for power distribution systems and explains how to apply them in distributed and variable energy generation resources. As such, the book therefore is a valuable tool to leverage the expansion and operation planning of electricity distribution networks.
The techniques described in this monograph form the basis of running an optimally efficient modern day power system. It is a must-read for all students and researchers working on the cutting edge of electric power systems.
An authoritative guide to large-scale energy storage technologies and applications for power system planning and operation To reduce the dependence on fossil energy, renewable energy generation (represented by wind power and photovoltaic power generation) is a growing field worldwide. Energy Storage for Power System Planning and Operation offers an authoritative introduction to the rapidly evolving field of energy storage systems. Written by a noted expert on the topic, the book outlines a valuable framework for understanding the existing and most recent advances in technologies for integrating energy storage applications with power systems. Filled with full-color illustrations, the book reviews the state-of-the-art of energy storage systems and includes illustrative system models and simulations. The author explores the various techniques that can be employed for energy storage that is compatible with renewable energy generation. Designed as a practical resource, the book examines in detail the aspects of system optimization, planning, and dispatch. This important book, Provides an introduction to the systematically different energy storage techniques with deployment potential in power systems Models various energy storage systems for mathematical formulation and simulations Contains a review of the techniques for integrating and operating energy storage with renewable energy generation Analyses how to optimize power systems with energy storage, at both the transmission and distribution system levels Shows how to optimize planning, siting, and sizing of energy storage for a range of purposes Written for power system engineers and researchers, Energy Storage for Power System Planning and Operation introduces the application of large-scale energy storage for the optimal operation and planning of power systems.
Mixed integer programming (MIP) maximizes (or minimizes) a linear objective subject to a set of constraints. In particular, one of the constraints for a MIP is that at least one of the variables can only take integer values. This technique has been widely studied in operations research and a MIP can be solved efficiently by commercial solvers. In this dissertation, two power system problems namely, an interdiction problem and a unit commitment problem, are formulated and solved with MIP techniques. The studies presented in this dissertation focus on extracting the special features embedded in the problems and formulating the problems such that they can be solved using the available MIP techniques. The objective of an interdiction problem in a power system is to find a set of the most critical or vulnerable components to secure and reliable operation. Before formulating the problem, we need to study the outages and their impacts in power systems in depth. Once a critical component of a power system fails, the outages including generator and load trips can sequentially spread and frequently lead to large blackouts. The efforts to develop a model to analyze cascading outages is first summarized. Reports about cyber attacks on the Ukraine power grid revealed that one or more malwares were deliberately developed to attack industrial facilities, with power systems as one of the major targets. Another potential cyber threat to secure operation of power transmission grids involves Internet of Things (IoT) demand attacks. Increasingly, Internet connections are available to devices with high energy consumption such as air conditioners and water heaters. However, these new connections expose the control of new electric loads to potential manipulation by attackers. To help assess the effects of cyber attacks, we develop numerical experiments and define different types of cyber attacks to simulate Ukraine-style cyber attacks and IoT demand attacks to study the system responses in a North American regional interconnection system. Based on the studies in cascading outage analysis and cyber attack simulations, an interaction problem between a defender (e.g. system operator) and an attacker (e.g. terrorist) in a power system is formulated as a MIP and a "short-term" impact of an attack is considered using a cascading outage anylsis (COA) tool. A demonstrative case study with an existing method is presented and numeric studies with "short-term" impacts with COA model are ongoing. The unit commitment (UC) problem in a power system is another MIP problem. UC determines the start-up and shut down schedules of generating units to meet forecast demand in a short term future (few hours to few days). It is critical to precisely represent the generating units in a UC problem to maximize the social welfare, which is the objective of the problem. The formulation of two types of unit namely, combined-cycle gas units and pumped-storage hydro units in a UC problem are presented in this dissertation. In recent years, combined-cycle units (CCUs) have been operated as providers of flexibility needed due to the increasing shares of renewables. Consequently, optimization models have been proposed to determine the configuration of CCUs. However, most of the existing models assume that any transition between configurations finishes in a single interval. This assumption is often violated in reality, as a transition might last up to a few hours during which the CCU has limited dispatchability. In this work, a mixed-integer programming formulation that represents the transition ramping of CCUs is summarized and the formulations of ramping constraints are discussed. Numerical studies are performed on an illustrative test system and a Mid-continent Independent System Operator (MISO) system. As one of the mature technologies for energy storage, pumped-storage hydro is able to provide services in a time range from minutes to days. Particularly, pumped storage hydro units are useful for enhancing the integration of renewable generations that are naturally intermittent. Optimization models have been proposed to determine strategies to dispatch a energy storage unit in the system. However, most of existing work assumes the output from a energy storage unit is continuous. This assumption is not true for a pumped storage hydro unit. Inspired by the work of modeling a combined cycle unit in the unit commitment problem, this work proposes a configuration based pumped storage hydro model that removes the invalid continuous outputs assumption in order to enhance the use of pumped storage hydro resources in the system. By introducing three "configurations," namely, pumping, generating and "alloff" or off-line, for a pumped storage hydro unit, the proposed model can more accurately reflect the practical operations of pumped storage hydro units in the day-ahead market. A comprehensive review of the existing pumped storage hydro models and industry practices is presented. The definition of configurations of a pumped storage hydro unit and the transitions between the configurations during operation are revealed and discussed in detail to describe the proposed model. A case study is presented to illustrate the proposed model
This book provides an overview of state-of-the-art research on “Systems and Optimization Aspects of Smart Grid Challenges.” The authors have compiled and integrated different aspects of applied systems optimization research to smart grids, and also describe some of its critical challenges and requirements. The promise of a smarter electricity grid could significantly change how consumers use and pay for their electrical power, and could fundamentally reshape the current Industry. Gaining increasing interest and acceptance, Smart Grid technologies combine power generation and delivery systems with advanced communication systems to help save energy, reduce energy costs and improve reliability. Taken together, these technologies support new approaches for load balancing and power distribution, allowing optimal runtime power routing and cost management. Such unprecedented capabilities, however, also present a set of new problems and challenges at the technical and regulatory levels that must be addressed by Industry and the Research Community.
Disjunctive Programming is a technique and a discipline initiated by the author in the early 1970's, which has become a central tool for solving nonconvex optimization problems like pure or mixed integer programs, through convexification (cutting plane) procedures combined with enumeration. It has played a major role in the revolution in the state of the art of Integer Programming that took place roughly during the period 1990-2010. The main benefit that the reader may acquire from reading this book is a deeper understanding of the theoretical underpinnings and of the applications potential of disjunctive programming, which range from more efficient problem formulation to enhanced modeling capability and improved solution methods for integer and combinatorial optimization. Egon Balas is University Professor and Lord Professor of Operations Research at Carnegie Mellon University's Tepper School of Business.
This book addresses the uncertainties of wind power modeled as interval numbers and assesses the physical modeling and methods for interval power flow, interval economic dispatch and interval robust economic dispatch. In particular, the optimization models are set up to address these topics and the state-of-the-art methods are employed to efficiently solve the proposed models. Several standard IEEE test systems as well as real-world large-scale Polish power systems have been tested to verify the effectiveness of the proposed models and methods. These methods can be further applied to other research fields that are involved with uncertainty.