Mathematical Programming bounds for Large-Scale Unit Commitment Problems in Medium-Term Energy System Simulations

We consider a large-scale unit commitment problem arising in medium-term simulation of energy networks, stemming from a joint project between the University of Milan and a major energy research centre in Italy. Optimal plans must be computed for a set of thermal and hydroelectric power plants, located in one or more countries, over a time horizon spanning from a few months to one year, with a hour-by-hour resolution. We propose a mixed-integer linear programming model for the problem. Since the complexity of this unit commitment problem and the size of real-world instances make it impractical to directly optimise this model using general purpose solvers, we devise ad-hoc heuristics and relaxations to obtain approximated solutions and quality estimations. We exploit an incremental approach: at first, a linear relaxation of an aggregated model is solved. Then, the model is disaggregated and the full linear relaxation is computed. Finally, a tighter linear relaxation of an extended formulation is obtained using column generation. At each stage, metaheuristics are run to obtain good integer solutions. Experimental tests on real-world data reveal that accurate results can be obtained by our framework in affordable time, making it suitable for efficient scenario simulations

Water-related modelling in electric power systems: WATERFLEX Exploratory Research Project: version 1

Water is needed for energy. For instance, hydropower is the technology that generates more electricity worldwide after the fossil-fuelled power plants and its production depends on water availability and variability. Additionally, thermal power plants need water for cooling and thus generate electricity. On the other hand, energy is also needed for water. Given the increase of additional hydropower potential worldwide in the coming years, the high dependence of electricity generation with fossil-fuelled power plants, and the implications of the climate change, relevant international organisations have paid attention to the water-energy nexus (or more explicitly within a power system context, the water-power nexus). The Joint Research Centre of the European Commission, the United States Department of Energy, the Institute for Advanced Sustainability Studies, the Midwest Energy Research Consortium and the Water Council, or the Organisation for Economic Co-operation and Development, among others, have raised awareness about this nexus and its analysis as an integrated system. In order to properly analyse such linkages between the power and water sectors, there is a need for appropriate modelling frameworks and mathematical approaches. This report comprises the water-constrained models in electric power systems developed within the WATERFLEX Exploratory Research Project of the European Commission’s Joint Research Centre in order to analyse the water-power interactions. All these models are deemed modules of the Dispa-SET modelling tool. The version 1 of the medium-term hydrothermal coordination module is presented with some modelling extensions, namely the incorporation of transmission network constraints, water demands, and ecological flows. Another salient feature of this version of Dispa-SET is the modelling of the stochastic medium-term hydrothermal coordination problem. The stochastic problem is solved by using an efficient scenario-based decomposition technique, the so-called Progressive Hedging algorithm. This technique is an Augmented-Lagrangian-based decomposition method that decomposes the original problem into smaller subproblems per scenario. The Progressive Hedging algorithm has multiple advantages: — It is easy parallelizable due to its inherent structure. — It provides solution stability and better computational performance compared to Benders-like decomposition techniques (node-based decomposition). — It scales better for large-scale stochastic programming problems. — It has been widely used in the technical literature, thus demonstrating its efficiency. Its implementation has been carried out through the PySP software package which is part of the Coopr open-source Python repository for optimisation. This report also describes the cooling-related constraints included in the unit commitment and dispatch module of Dispa-SET. The cooling-related constraints encompass limitations on allowable maximum water withdrawals of thermal power plants and modelling of the power produced in terms of the river water temperature of the power plant inlet. Limitations on thermal releases or water withdrawals could be imposed due to physical or policy reasons. Finally, an offline and decoupled modelling framework is presented to link such modules with the rainfall-runoff hydrological LISFLOOD model. This modelling framework is able to accurately capture the water-power interactions. Some challenges and barriers to properly address the water-power nexus are also highlighted in the report.JRC.C.7-Knowledge for the Energy Unio

ALGORITHMS FOR THE LARGE-SCALE UNIT COMMITMENT PROBLEM IN THE SIMULATION OF POWER SYSTEMS

Lo Unit Commitment Problem (UCP) \ue8 un problema di programmazione matematica dove un insieme di impianti termoelettrici deve essere programmato per soddisfare la domanda di energia e altri vincoli di sistema. Il modello \ue8 impiegato da decenni per supportare la pianificazione operazionale di breve termine dei sistemi elettrici. In questo lavoro affrontiamo il problema di risolvere UCP lineari di larga-scala per realizzare simulazioni accurate di sistemi elettrici, con i requisiti aggiuntivi di impiegare capacit\ue0 di calcolo convenzionali, ad esempio i personal computers, ed un tempo di soluzione di poche ore. Il problema, sotto le medesime condizioni, \ue8 affrontato abitualmente dal nostro partner industriale RSE S.p.A. (Ricerche Sistema Energetico), uno dei principali centri ricerche industriali su sistemi energetici in Italia. L\u2019ottimizzazione diretta di queste formulazioni con solutori generici \ue8 impraticabile. Nonostante sia possibile calcolare buone soluzioni euristiche, ovvero con un gap di ottimalit\ue0 sotto il 10%, in tempi ragionevoli per UCP di larga scala, si richiedono soluzioni pi\uf9 accurate, per esempio con gap sotto l\u20191%, per migliorare l\u2019affidabilit\ue0 delle simulazioni ed aiutare gli esperti di dominio, che potrebbero non essere familiari con i dettagli dei metodi di programmazione matematica, a supportare meglio le loro analisi. Tra le idee che abbiamo esplorato i seguenti metodi risultano i pi\uf9 promettenti: una mateuristica per calcolare efficientemente buone soluzioni e due metodi esatti di bounding: column generation e Benders decomposition. Questi metodi decompongono il problema disaccoppiando il commitment degli impianti termoelettrici, rappresentati da variabili discrete, e il loro livello di produzione, rappresentato da variabili continue. I nostri esperimenti dimostrano che il modello possiede propriet\ue0 intrinseche come degenerazione e forma della funzione obbiettivo piatta che ostacolano o impediscono la convergenza in risolutori allo stato dell\u2019arte. Tuttavia, i metodi che abbiamo sviluppato, sfruttando efficacemente le propriet\ue0 strutturali del modello, permettono di raggiungere soluzioni quasi ottime in poche iterazioni per la maggior parte delle istanze.The Unit Commitment Problem (UCP) is a mathematical programming problem where a set of power plants needs to be scheduled to satisfy energy demand and other system-wide constraints. It has been employed for decades to support short-term operational planning of power plants. In this work we tackle the problem of solving large-scale linear UCPs to perform accurate medium-term power systems simulations, with the additional requirements of employing conventional computing power, such as personal computers, and a solution time of a few hours. The problem, under such conditions, is routinely faced by our industry partner, the Energy Systems Development department at RSE S.p.A. (Ricerche Sistema Energetico), a major industrial research centre on power systems in Italy. The direct optimization of these formulations via general-purpose solvers is impractical. While good heuristic solutions, that is with an optimality gap below 10%, can be found for large-scale UCPs in affordable time, more accurate solutions, for example with a gap below 1%, are sought to improve the reliability of the simulations and help domain experts, who may not be familiar with the details of mathematical programming methods, to better support their analysis. Among the ideas we explored, the following methods are the most promising: a matheuristic to efficiently compute good solutions and two exact bounding methods: column generation and Benders decomposition. These methods decompose the problem by decoupling the commitment of thermal plants, represented by discrete variables, and their level of production, represented by continuous variables. Our experiments proved that the model posses inherent properties as degeneracy and objective flatness which hinder or prevent convergence in state-of-the-art solvers. On the other hand, the methods we devised, by effectively exploiting structural properties of the model, allow to reach quasi-optimal solutions within a few iterations on most instances

OATS : Optimisation and Analysis Toolbox for power Systems

Optimisation and Analysis Toolbox for power Systems analysis (OATS) is an open-source simulation tool for steady-state analyses of power systems problems distributed under the GNU General Public License (GPLv3). It contains implementations of classical steady-state problems, e.g. load flow, optimal power flow (OPF) and unit commitment, as well as enhancements to these classical models relative to the features available in widely used open-source tools. Enhancements implemented in the current release of OATS include: a model of voltage regulating on-load tap-changing transformers; load shedding in OPF; allowing a user to build a contingency list in the security constrained OPF analysis; implementation of a distributed slack bus; and the ability to model zonal transfer limits in unit commitment. The mathematical optimisation models are written in an open-source algebraic modelling language, which offers high-level symbolic syntax for describing optimisation problems. The flexibility offered by OATS makes it an ideal tool for teaching and academic research. This paper presents novel aspects of OATS and discusses, through demonstrative examples, how OATS can be extended to new problem classes in the area of steady-state power systems analysis

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

WIND POWER PROBABILISTIC PREDICTION AND UNCERTAINTY MODELING FOR OPERATION OF LARGE-SCALE POWER SYSTEMS

Over the last decade, large scale renewable energy generation has been integrated into power systems. Wind power generation is known as a widely-used and interesting kind of renewable energy generation around the world. However, the high uncertainty of wind power generation leads to some unavoidable error in wind power prediction process; consequently, it makes the optimal operation and control of power systems very challenging. Since wind power prediction error cannot be entirely removed, providing accurate models for wind power uncertainty can assist power system operators in mitigating its negative effects on decision making conditions. There are efficient ways to show the wind power uncertainty, (i) accurate wind power prediction error probability distribution modeling in the form of probability density functions and (ii) construction of reliable and sharp prediction intervals. Construction of accurate probability density functions and high-quality prediction intervals are difficult because wind power time series is non-stationary. In addition, incorporation of probability density functions and prediction intervals in power systems’ decision-making problems are challenging. In this thesis, the goal is to propose comprehensive frameworks for wind power uncertainty modeling in the form of both probability density functions and prediction intervals and incorporation of each model in power systems’ decision-making problems such as look-ahead economic dispatch. To accurately quantify the uncertainty of wind power generation, different approaches are studied, and a comprehensive framework is then proposed to construct the probability density functions using a mixture of beta kernels. The framework outperforms benchmarks because it can validly capture the actual features of wind power probability density function such as main mass, boundaries, high skewness, and fat tails from the wind power sample moments. Also, using the proposed framework, a generic convex model is proposed for chance-constrained look-ahead economic dispatch problems. It allows power system operators to use piecewise linearization techniques to convert the problem to a mixed-integer linear programming problem. Numerical simulations using IEEE 118-bus test system show that compared with widely used sequential linear programming approaches, the proposed mixed-integer linear programming model leads to less system’s total cost. A framework based on the concept of bandwidth selection for a new and flexible kernel density estimator is proposed for construction of prediction intervals. Unlike previous related works, the proposed framework uses neither a cost function-based optimization problem nor point prediction results; rather, a diffusion-based kernel density estimator is utilized to achieve high-quality prediction intervals for non-stationary wind power time series. The proposed prediction interval construction framework is also founded based on a parallel computing procedure to promote the computational efficiency for practical applications in power systems. Simulation results demonstrate the high performance of the proposed framework compared to well-known conventional benchmarks such as bootstrap extreme learning machine, lower upper bound estimation, quantile regression, auto-regressive integrated moving average, and linear programming-based quantile regression. Finally, a new adjustable robust optimization approach is used to incorporate the constructed prediction intervals with the proposed fuzzy and adaptive diffusion estimator-based prediction interval construction framework. However, to accurately model the correlation and dependence structure of wind farms, especially in high dimensional cases, C-Vine copula models are used for prediction interval construction. The simulation results show that uncertainty modeling using C-Vine copula can lead the system operators to get more realistic sense about the level of overall uncertainty in the system, and consequently more conservative results for energy and reserve scheduling are obtained

Decentralised Optimisation and Control in Electrical Power Systems

Emerging smart-grid-enabling technologies will allow an unprecedented degree of observability and control at all levels in a power system. Combined with flexible demand devices (e.g. electric vehicles or various household appliances), increased distributed generation, and the potential development of small scale distributed storage, they could allow procuring energy at minimum cost and environmental impact. That however presupposes real-time coordination of demand of individual households and industries down at the distribution level, with generation and renewables at the transmission level. In turn this implies the need to solve energy management problems of a much larger scale compared to the one we currently solve today. This of course raises significant computational and communications challenges. The need for an answer to these problems is reflected in today’s power systems literature where a significant number of papers cover subjects such as generation and/or demand management at both transmission and/or distribution, electric vehicle charging, voltage control devices setting, etc. The methods used are centralized or decentralized, handling continuous and/or discrete controls, approximate or exact, and incorporate a wide range of problem formulations. All these papers tackle aspects of the same problem, i.e. the close to real-time determination of operating set-points for all controllable devices available in a power system. Yet, a consensus regarding the associated formulation and time-scale of application has not been reached. Of course, given the large scale of the problem, decentralization is unavoidably part of the solution. In this work we explore the existing and developing trends in energy management and place them into perspective through a complete framework that allows optimizing energy usage at all levels in a power system