Introduction to stochastic programming

The smart grid concept continues to evolve and various methods have been developed to enhance the energy efficiency of the electricity infrastructure. Demand Response (DR) is considered as the most cost-effective and reliable solution for the smoothing of the demand curve, when the system is under stress. DR refers to a procedure that is applied to motivate changes in the customers' power consumption habits, in response to incentives regarding the electricity prices. In this paper, we provide a comprehensive review of various DR schemes and programs, based on the motivations offered to the consumers to participate in the program. We classify the proposed DR schemes according to their control mechanism, to the motivations offered to reduce the power consumption and to the DR decision variable. We also present various optimization models for the optimal control of the DR strategies that have been proposed so far. These models are also categorized, based on the target of the optimization procedure. The key aspects that should be considered in the optimization problem are the system's constraints and the computational complexity of the applied optimization algorithm.

A Survey on Demand Response Programs in Smart Grids: Pricing Methods and Optimization Algorithms

'Satisfiability (SAT) related topics have attracted researchers from various disciplines: logic, applied areas such as planning, scheduling, operations research and combinatorial optimization, but also theoretical issues on the theme of complexity and much more, they all are connected through SAT. My personal interest in SAT stems from actual solving: The increase in power of modern SAT solvers over the past 15 years has been phenomenal. It has become the key enabling technology in automated verification of both computer hardware and software' - Edmund M. Clarke (FORE Systems University Professor of Computer Science and Professor of Electrical and Computer Engineering at Carnegie Mellon University). 'Bounded Model Checking (BMC) of computer hardware is now probably the most widely used model checking technique. The counterexamples that it finds are just satisfying instances of a Boolean formula obtained by unwinding to some fixed depth a sequential circuit and its specification in linear temporal logic. Extending model checking to software verification is a much more difficult problem on the frontier of current research. One promising approach for languages like C with finite word-length integers is to use the same idea as in BMC but with a decision procedure for the theory of bit-vectors instead of SAT. All decision procedures for bit-vectors that I am familiar with ultimately make use of a fast SAT solver to handle complex formulas' - Edmund M. Clarke (FORE Systems University Professor of Computer Science and Professor of Electrical and Computer Engineering at Carnegie Mellon University). 'Decision procedures for more complicated theories, like linear real and integer arithmetic, are also used in program verification. Most of them use powerful SAT solvers in an essential way. Clearly, efficient SAT solving is a key technology for 21st century computer science. I expect this collection of papers on all theoretical and practical aspects of SAT solving will be extremely useful to both students and researchers and will lead to many further advances in the field' - Edmund M. Clarke (FORE Systems University Professor of Computer Science and Professor of Electrical and Computer Engineering at Carnegie Mellon University).

/pdf/handbook-of-satisfiability-2dsvkz551d.pdf

Handbook of Satisfiability

http://www.optimization-online.org/DB_FILE/2012/02/3378.pdf

Non-convex mixed-integer nonlinear programming: A survey

Over the past half-century, Optimal Power Flow (OPF) has become one of the most important and widely studied nonlinear optimization problems. In general, OPF seeks to optimize the operation of electric power generation, transmission, and distribution networks subject to system constraints and control limits. Within this framework, however, there is an extremely wide variety of OPF formulations and solution methods. Moreover, the nature of OPF continues to evolve due to modern electricity markets and renewable resource integration. In this two-part survey, we survey both the classical and recent OPF literature in order to provide a sound context for the state of the art in OPF formulation and solution methods. The survey contributes a comprehensive discussion of specific optimization techniques that have been applied to OPF, with an emphasis on the advantages, disadvantages, and computational characteristics of each. Part I of the survey (this article) provides an introduction and surveys the deterministic optimization methods that have been applied to OPF. Part II of the survey examines the recent trend towards stochastic, or non-deterministic, search techniques and hybrid methods for OPF.

Optimal power flow: a bibliographic survey I

This paper examines the polytope of feasible power generation schedules in the unit commitment (UC) problem. We provide computational results comparing formulations for the UC problem commonly found in the literature. We introduce a new class of inequalities, giving a tighter description of feasible operating schedules for generators. Computational results show that these inequalities can significantly reduce overall solution times.

http://atmtn.persiangig.com/Article/Tight%20Mixed%20Integer%20Linear%20Programming.pdf

Tight Mixed Integer Linear Programming Formulations for the Unit Commitment Problem

Introduction to Semidefinite, Conic and Polynomial Optimization.- The Approach of Moments for Polynomial Equations.- Algebraic Degree in Semidefinite and Polynomial Optimization.- Semidefinite Representation of Convex Sets and Convex Hulls.- Convex Hulls of Algebraic Sets.- Convex Relations and Integrality Gaps.- Relaxations of Combinatorial Problems via Association Schemes.- Copositive Programming.- Invariant Semidefinite Programs.- A "Joint+Marginal" Approach in Optimization.- An Introduction to Formally Real Jordan Algebras and Their Applications in Optimization.- Complementarity Problems Over Symmetric Conics: A Survey of Recent Developments in Several Aspects.- Convexity and Semidefinite Programming in Dimension-Free Matrix Unknowns.- Positivity and Optimization: Beyond Polynomials.- Self-Regular Interior-Point Methods for Semidefinite Optimization.- Elementary Optimality Conditions for Nonlinear SDPs.- Recent Progress in Interior-Point Methods: Cutting Plane Algorithms and Warm Starts.- Exploiting Sparsity in SDP Relaxation of Polynomial Optimization Problems.- Block Coordinate Descent Methods for Semidefinite Programming.- Projection Methods in Conic Optimization.- SDP Relaxations for Non-Commutative Polynomial Optimization.- Semidefinite Programming and Constraint Programming.- The State-of-the-Art in Conic Optimization Software.- Latest Developments in SDPA Family for Solving Large-Scale SDPs.- On the Implementation and Usage of SDPT3: A MATLAB Software Package for Semidefinite-Quadratic-Linear Programming, Version 4.0.- PENNON: Software for Linear and Nonlinear Matrix Inequalities.- SDP Relaxations for Some Combinatorial Optimization Problems.- Computational Approaches to Max-Cut.- Global Approaches for Facility Layout and VLSI Floorplanning.- Euclidean Distance Matrices and Applications.- Sparse PCA: Convex Relaxations, Algorithms and Applications.

/pdf/handbook-on-semidefinite-conic-and-polynomial-optimization-46u7v88xp2.pdf

Handbook on semidefinite, conic and polynomial optimization

This paper presents a system architecture for load management in smart buildings which enables autonomous demand side load management in the smart grid. Being of a layered structure composed of three main modules for admission control, load balancing, and demand response management, this architecture can encapsulate the system functionality, assure the interoperability between various components, allow the integration of different energy sources, and ease maintenance and upgrading. Hence it is capable of handling autonomous energy consumption management for systems with heterogeneous dynamics in multiple time-scales and allows seamless integration of diverse techniques for online operation control, optimal scheduling, and dynamic pricing. The design of a home energy manager based on this architecture is illustrated and the simulation results with Matlab/Simulink confirm the viability and efficiency of the proposed framework.

A System Architecture for Autonomous Demand Side Load Management in Smart Buildings

This paper proposes a two-level framework for the operation of a competitive market for reactive power ancillary services. It is argued that the first-level, i.e., reactive power procurement, be on a seasonal basis while the second-level, i.e., reactive power dispatch, be close to real-time operation. To this effect, a reactive power procurement market model is proposed here taking into consideration system security aspects. This procurement procedure is based on a two-step optimization model. First, the marginal benefits of reactive power supply from each provider with respect to system security are obtained by solving an optimal power flow (OPF) that maximizes system loadability subject to transmission security constraints imposed by voltage limits, thermal limits, and stability limits. Second, the selected set of generators is then determined by solving an OPF-based auction to maximize a societal advantage function comprising generators' offers and their corresponding marginal benefits with respect to system security, considering all transmission system constraints. The proposed procedure yields the selected set of generators and zonal price components, which would form the basis for seasonal contracts between the system operator and the selected reactive power service providers.

Miguel F. Anjos

Papers

Tight Mixed Integer Linear Programming Formulations for the Unit Commitment Problem

Handbook on semidefinite, conic and polynomial optimization

A System Architecture for Autonomous Demand Side Load Management in Smart Buildings

A Procurement Market Model for Reactive Power Services Considering System Security

A semidefinite optimization approach for the single-row layout problem with unequal dimensions