Why Methods for Optimization Problems with Time-Consuming Function Evaluations and Integer Variables Should Use Global Approximation Models

This paper advocates the use of methods based on global approximation models for optimization problems with time-consuming function evaluations and integer variables.We show that methods based on local approximations may lead to the integer rounding of the optimal solution of the continuous problem, and even to worse solutions.Then we discuss a method based on global approximations.Test results show that such a method performs well, both for theoretical and practical examples, without suffering the disadvantages of methods based on local approximations.approximation models;black-box optimization;integer optimization

Impact of Equipment Failures and Wind Correlation on Generation Expansion Planning

Generation expansion planning has become a complex problem within a deregulated electricity market environment due to all the uncertainties affecting the profitability of a given investment. Current expansion models usually overlook some of these uncertainties in order to reduce the computational burden. In this paper, we raise a flag on the importance of both equipment failures (units and lines) and wind power correlation on generation expansion decisions. For this purpose, we use a bilevel stochastic optimization problem, which models the sequential and noncooperative game between the generating company (GENCO) and the system operator. The upper-level problem maximizes the GENCO's expected profit, while the lower-level problem simulates an hourly market-clearing procedure, through which LMPs are determined. The uncertainty pertaining to failures and wind power correlation are characterized by a scenario set, and their impact on generation expansion decisions are quantified and discussed for a 24-bus power system

An Integrated Market for Electricity and Natural Gas Systems with Stochastic Power Producers

In energy systems with high shares of weather-driven renewable power sources, gas-fired power plants can serve as a back-up technology to ensure security of supply and provide short-term flexibility. Therefore, a tighter coordination between electricity and natural gas networks is foreseen. In this work, we examine different levels of coordination in terms of system integration and time coupling of trading floors. We propose an integrated operational model for electricity and natural gas systems under uncertain power supply by applying two-stage stochastic programming. This formulation co-optimizes day-ahead and real-time dispatch of both energy systems and aims at minimizing the total expected cost. Additionally, two deterministic models, one of an integrated energy system and one that treats the two systems independently, are presented. We utilize a formulation that considers the linepack of the natural gas system, while it results in a tractable mixed-integer linear programming (MILP) model. Our analysis demonstrates the effectiveness of the proposed model in accommodating high shares of renewables and the importance of proper natural gas system modeling in short-term operations to reveal valuable flexibility of the natural gas system. Moreover, we identify the coordination parameters between the two markets and show their impact on the system's operation and dispatch

Why Methods for Optimization Problems with Time-Consuming Function Evaluations and Integer Variables Should Use Global Approximation Models

This paper advocates the use of methods based on global approximation models for optimization problems with time-consuming function evaluations and integer variables.We show that methods based on local approximations may lead to the integer rounding of the optimal solution of the continuous problem, and even to worse solutions.Then we discuss a method based on global approximations.Test results show that such a method performs well, both for theoretical and practical examples, without suffering the disadvantages of methods based on local approximations.

Active network management for electrical distribution systems: problem formulation, benchmark, and approximate solution

With the increasing share of renewable and distributed generation in electrical distribution systems, Active Network Management (ANM) becomes a valuable option for a distribution system operator to operate his system in a secure and cost-effective way without relying solely on network reinforcement. ANM strategies are short-term policies that control the power injected by generators and/or taken off by loads in order to avoid congestion or voltage issues. Advanced ANM strategies imply that the system operator has to solve large-scale optimal sequential decision-making problems under uncertainty. For example, decisions taken at a given moment constrain the future decisions that can be taken and uncertainty must be explicitly accounted for because neither demand nor generation can be accurately forecasted. We first formulate the ANM problem, which in addition to be sequential and uncertain, has a nonlinear nature stemming from the power flow equations and a discrete nature arising from the activation of power modulation signals. This ANM problem is then cast as a stochastic mixed-integer nonlinear program, as well as second-order cone and linear counterparts, for which we provide quantitative results using state of the art solvers and perform a sensitivity analysis over the size of the system, the amount of available flexibility, and the number of scenarios considered in the deterministic equivalent of the stochastic program. To foster further research on this problem, we make available at http://www.montefiore.ulg.ac.be/~anm/ three test beds based on distribution networks of 5, 33, and 77 buses. These test beds contain a simulator of the distribution system, with stochastic models for the generation and consumption devices, and callbacks to implement and test various ANM strategies

Operation and planning of distribution networks with integration of renewable distributed generators considering uncertainties: a review

YesDistributed generators (DGs) are a reliable solution to supply economic and reliable electricity to customers. It is the last stage in delivery of electric power which can be defined as an electric power source connected directly to the distribution network or on the customer site. It is necessary to allocate DGs optimally (size, placement and the type) to obtain commercial, technical, environmental and regulatory advantages of power systems. In this context, a comprehensive literature review of uncertainty modeling methods used for modeling uncertain parameters related to renewable DGs as well as methodologies used for the planning and operation of DGs integration into distribution network.This work was supported in part by the SITARA project funded by the British Council and the Department for Business, Innovation and Skills, UK and in part by the University of Bradford, UK under the CCIP grant 66052/000000

Modern control concepts in hydrology

Two approaches to an identification problem in hydrology are presented based upon concepts from modern control and estimation theory. The first approach treats the identification of unknown parameters in a hydrologic system subject to noisy inputs as an adaptive linear stochastic control problem; the second approach alters the model equation to account for the random part in the inputs, and then uses a nonlinear estimation scheme to estimate the unknown parameters. Both approaches use state-space concepts. The identification schemes are sequential and adaptive and can handle either time invariant or time dependent parameters. They are used to identify parameters in the Prasad model of rainfall-runoff. The results obtained are encouraging and conform with results from two previous studies; the first using numerical integration of the model equation along with a trial-and-error procedure, and the second, by using a quasi-linearization technique. The proposed approaches offer a systematic way of analyzing the rainfall-runoff process when the input data are imbedded in noise

Multistage Expansion Planning of Active Distribution Systems: Towards Network Integration of Distributed Energy Resources

Over the last few years, driven by several technical and environmental factors, there has been a growing interest in the concept of active distribution networks (ADNs). Based on this new concept, traditional passive distribution networks will evolve into modern active ones by employing distributed energy resources (DERs) such as distributed generators (DGs), energy storage systems (ESSs), and demand responsive loads (DRLs). Such a transition from passive to active networks poses serious challenges to distribution system planners. On the one hand, the ability of DGs to directly inject active and reactive powers into the system nodes leads to bidirectional power flows through the distribution feeders. This issue, if not adequately addressed at the design stage, can adversely affect various operational aspects of ADNs, specifically the reactive power balance and voltage regulation. Therefore, the new context where DGs come into play necessitates the development of a planning methodology which incorporates an accurate network model reflecting realistic operational characteristics of the system. On the other hand, large-scale integration of renewable DGs results in the intermittent and highly volatile nodal power injections and the implementation of demand response programs further complicates the long-term predictability of the load growth. These factors introduce a tremendous amount of uncertainty to the planning process of ADNs. As a result, effective approaches must also be devised to properly model the major sources of uncertainty. Based on the above discussion, successful transition from traditional passive distribution networks to modern active ones requires a planning methodology that firstly includes an accurate network model, and secondly accounts for the major sources of uncertainty. However, incorporating these two features into the planning process of ADNs is a very complex task and requires sophisticated mathematical programming techniques that are not currently available in the literature. Therefore, this research project aim to develop a comprehensive planning methodology for ADNs, which is capable of dealing with different types of DERs (i.e., DGs, ESSs, and DRLs), while giving full consideration to the above-mentioned two key features. To achieve this objective, five major steps are defined for the project. Step 1 develops a deterministic mixed-integer linear programming (MILP) model for integrated expansion planning of distribution network and renewable/conventional DGs, which includes a highly accurate network model based on a linear format of AC power flow equations. This MILP model can be solved using standard off-the-shelf mathematical programming solvers that not only guarantee convergence to the global optimal solution, but also provide a measure of the distance to the global optimum during the solution process. Step 2 proposes a distributionally robust chance-constrained programming approach to characterize the inherent uncertainties of renewable DGs and loads. The key advantage of this approach is that it requires limited information about the uncertain parameters, rather than perfect knowledge of their probability distribution functions. Step 3 devises a fast Benders decomposition-based solution procedure that paves the way for effective incorporation of ESSs and DRLs into the developed planning methodology. To this end, two effective acceleration strategies are proposed to significantly enhance the computational performance of the classical Benders decomposition algorithm. Eventually, Steps 4 and 5 propose appropriate models for ESSs and DRLs and integrate them into the developed planning methodology. In this regard, a sequential-time power flow simulation method is also proposed to incorporate the short-term operation analysis of ADNs into their long-term planning studies. By completing the above-defined steps, the planning model developed in Step 1 will be gradually evolved, so that Step 5 will yield the final comprehensive planning methodology for ADNs

Unit Commitment with uncertainties - State of the art

International audienceThe increasing share of variable renewable energy generation (VG), as a response to environmental concerns,brings along new challenges to conciliate economics with security in power system supply. Nowadays, the more developed VGsources are wind and solar, which have low controllability and a variable output that is only partially predictable. This paperpresents an overview on recent developments in Unit Commitment (UC) problems in order to take into account theuncertainty in the demand-generation balance. This subject has been widely discussed in literature over the last years inhundreds of scientific publications, mainly related to the impact of deregulation and the management of forecast errors. Awide variety of approaches to include uncertainties in conventional generation day-ahead optimization, and to representthese uncertainties has been proposed in literature. These include modifications in the objective function, enhanced securityconstraints and solution methods that improve computational speed. In this paper we analyse the development presented inthe literature in order to identify evolution trends in UC models to achieve more robust solutionsL’insertion des énergies renouvelables (EnR) variables pose de nouveaux défis aux gestionnaires de réseaux (GR)pour concilier l’optimisation économique, la sécurité et la qualité de fourniture. Aujourd'hui, l’éolien et le photovoltaïque(PV) sont les EnR avec la plus forte croissance, mais elles s’accompagnent d’une variabilité peu contrôlable et d’uneimprévisibilité partielle de leur production, ce qui impacte, entre autres, la gestion du parc de production. Ce travail présentedifférentes méthodes pour la prise en compte de ces incertitudes dans le placement de la production à cout-terme, définicomme la solution d’un problème d’optimisation, souvent désigné Unit Commitment (UC). Au cours des dix dernières années,les travaux présentés dans la littérature ont eu pour objectif non seulement la représentation des incertitudes sous forme decontraintes supplémentaires dans la fonction objectif, mais également la conception d’une algorithmique avancée pouratteindre des temps acceptables de résolution de cette fonction objectif modifiée y compris pour les grands systèmes. Dans cepapier nous présentons une analyse des évolutions récentes du modèle UC de façon à identifier des nouvelles tendances