Semidefinite Programming. methods and algorithms for energy management

La présente thèse a pour objet d explorer les potentialités d une méthode prometteuse de l optimisation conique, la programmation semi-définie positive (SDP), pour les problèmes de management d énergie, à savoir relatifs à la satisfaction des équilibres offre-demande électrique et gazier.Nos travaux se déclinent selon deux axes. Tout d abord nous nous intéressons à l utilisation de la SDP pour produire des relaxations de problèmes combinatoires et quadratiques. Si une relaxation SDP dite standard peut être élaborée très simplement, il est généralement souhaitable de la renforcer par des coupes, pouvant être déterminées par l'étude de la structure du problème ou à l'aide de méthodes plus systématiques. Nous mettons en œuvre ces deux approches sur différentes modélisations du problème de planification des arrêts nucléaires, réputé pour sa difficulté combinatoire. Nous terminons sur ce sujet par une expérimentation de la hiérarchie de Lasserre, donnant lieu à une suite de SDP dont la valeur optimale tend vers la solution du problème initial.Le second axe de la thèse porte sur l'application de la SDP à la prise en compte de l'incertitude. Nous mettons en œuvre une approche originale dénommée optimisation distributionnellement robuste , pouvant être vue comme un compromis entre optimisation stochastique et optimisation robuste et menant à des approximations sous forme de SDP. Nous nous appliquons à estimer l'apport de cette approche sur un problème d'équilibre offre-demande avec incertitude. Puis, nous présentons une relaxation SDP pour les problèmes MISOCP. Cette relaxation se révèle être de très bonne qualité, tout en ne nécessitant qu un temps de calcul raisonnable. La SDP se confirme donc être une méthode d optimisation prometteuse qui offre de nombreuses opportunités d'innovation en management d énergie.The present thesis aims at exploring the potentialities of a powerful optimization technique, namely Semidefinite Programming, for addressing some difficult problems of energy management. We pursue two main objectives. The first one consists of using SDP to provide tight relaxations of combinatorial and quadratic problems. A first relaxation, called standard can be derived in a generic way but it is generally desirable to reinforce them, by means of tailor-made tools or in a systematic fashion. These two approaches are implemented on different models of the Nuclear Outages Scheduling Problem, a famous combinatorial problem. We conclude this topic by experimenting the Lasserre's hierarchy on this problem, leading to a sequence of semidefinite relaxations whose optimal values tends to the optimal value of the initial problem.The second objective deals with the use of SDP for the treatment of uncertainty. We investigate an original approach called distributionnally robust optimization , that can be seen as a compromise between stochastic and robust optimization and admits approximations under the form of a SDP. We compare the benefits of this method w.r.t classical approaches on a demand/supply equilibrium problem. Finally, we propose a scheme for deriving SDP relaxations of MISOCP and we report promising computational results indicating that the semidefinite relaxation improves significantly the continuous relaxation, while requiring a reasonable computational effort.SDP therefore proves to be a promising optimization method that offers great opportunities for innovation in energy management.PARIS11-SCD-Bib. électronique (914719901) / SudocSudocFranceF

Large-scale unit commitment under uncertainty: an updated literature survey

The Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115--171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject

Secure and cost-effective operation of low carbon power systems under multiple uncertainties

Power system decarbonisation is driving the rapid deployment of renewable energy sources (RES) like wind and solar at the transmission and distribution level. Their differences from the synchronous thermal plants they are displacing make secure and efficient grid operation challenging. Frequency stability is of particular concern due to the current lack of provision of frequency ancillary services like inertia or response from RES generators. Furthermore, the weather dependency of RES generation coupled with the proliferation of distributed energy resources (DER) like small-scale solar or electric vehicles permeates future low-carbon systems with uncertainty under which legacy scheduling methods are inadequate. Overly cautious approaches to this uncertainty can lead to inefficient and expensive systems, whilst naive methods jeopardise system security. This thesis significantly advances the frequency-constrained scheduling literature by developing frameworks that explicitly account for multiple new uncertainties. This is in addition to RES forecast uncertainty which is the exclusive focus of most previous works. The frameworks take the form of convex constraints that are useful in many market and scheduling problems. The constraints equip system operators with tools to explicitly guarantee their preferred level of system security whilst unlocking substantial value from emerging and abundant DERs. A major contribution is to address the exclusion of DERs from the provision of ancillary services due to their intrinsic uncertainty from aggregation. This is done by incorporating the uncertainty into the system frequency dynamics, from which deterministic convex constraints are derived. In addition to managing uncertainty to facilitate emerging DERs to provide legacy frequency services, a novel frequency containment service is designed. The framework allows a small amount of load shedding to assist with frequency containment during high RES low inertia periods. The expected cost of this service is probabilistic as it is proportional to the probability of a contingency occurring. The framework optimally balances the potentially higher expected costs of an outage against the operational cost benefits of lower ancillary service requirements day-to-day. The developed frameworks are applied extensively to several case studies. These validate their security and demonstrate their significant economic and emission-saving benefits.Open Acces

Advanced Optimization and Data-Driven Control in Smart Grid

The power grids are continuously evolving over the past decades, where new challenges and opportunities are embraced at the same time. On one hand, the penetration of renewable generations and other distributed energy resources (DER) is growing rapidly, whose different generation and control patterns could significantly impact the daily operation. On the other hand, the new communication, monitoring and regulating devices are gradually installed, which enable more control abilities of the generations, demands, and grids, and the feasibility to deploy more sophisticated control schemes.To leverage the new technique and overcome the new challenges in the smart girds, different optimization and control problems need to be solved for different roles including the system operator, demand, and financial traders. For the system operators, it is critical to maximizing the total social welfare while satisfying the operational constraints. To better coordinate the DER and improve the efficiency of distribution systems, the three-phase optimal power flow (OPF) problem algorithms are developed including the DCOPF algorithm for robustness and the ACOPF algorithm for optimality. Moreover, the deep reinforcement learning-based Volt-VAR control schemes are proposed to better maintain the voltage stability and electricity service quality.For demands resources, minimizing their energy bills will satisfy the energy needs is always their goal. Providing ancillary services by proactively adjusting their total demand is one of the potential choices. Through the provision of the services, the demands can not only receiving incentives from the system operators but also help to improve the reliability and stability of power grids. We develop control schemes specifically for the data centers to provide the phase balancing service in the distribution system and the frequency regulation service in the transmission system. The financial traders, it is desired to maximize their total profits. A better trading strategy with a more accurate forecast model can help increase the traders' gain and further improve the price convergence of the electricity market. Our machine learning based trading framework outperforms the existing approach and lays the foundation for market efficiency evaluation across the markets

Large-Scale Optimization for Interdependent Infrastructure Systems

The primary focus of this thesis is to develop decomposition methods for solving large-scale optimization problems, especially those arising in interconnected infrastructure systems. Several factors (e.g., the Internet-of-Things) are driving infrastructure systems to become more interdependent. As a result, these complex systems are increasingly exposed to a variety of risks and demand elaborate optimization modeling that allows risk-informed decision-making. The resulting optimization models, however, are often of large-scale and have computationally challenging properties. In this regard, this thesis studies how to formulate optimization models mitigating their risks and develop decomposition methods for solving these models with improved computational properties. We first present a network planning problem for electricity distribution grids and their associated communication networks. The problem is formulated as a two-stage mixed-integer linear program and is of large-scale, since it captures hundreds of potential disaster scenarios as well as grids’ dependencies on the communication systems. To deal with its vast size, we develop a branch-and-price algorithm that features a tight lower bound and various acceleration schemes that address degeneracy. The model and algorithm were evaluated on a variety of test cases, the results of which demonstrate the impact of the risk- aware planning decisions as well as the computational benefits of the proposed solution approach. Next, we propose a unit scheduling problem of electric grids. We introduce gas network awareness into the scheduling problem to alleviate risks from natural gas networks. The resulting optimization model is formulated as a bi-level optimization problem. To address inherent computational challenges in solving bilevel problems, we develop a dedicated Benders decomposition method for solving a certain class of bilevel problems (discrete-continuous bilevel problems), which subsumes the proposed model. The algorithm features a Benders subproblem decomposition technique that breaks down the Benders subproblem into two more tractable problems. We test the model and the solution approach on a practically-relevant network data set. The results demonstrate that the risk-aware opera- tional decision is instrumental in avoiding disruptions caused by gas system insecurity. It is also demonstrated that the proposed decomposition algorithm not only improves the computational performance of existing solution methods but also allows intuitive interpretation of Benders cuts.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155075/1/gbyeon_1.pd

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