Models and algorithms for the efficient operation and planning of energy production systems

Abstract

Since the last four decades the electrical industry has been characterized by important and rapid changes around the world, regarding generation, transmission and distribution of electricity. These changes create the need for more e cient operation and planning of energy generation systems. Global energy demand is increasing, but most of the energy sources which are used to produce electricity nowadays are characterized by a limited scope, and electric energy is not suitable to be stored. Performing proper operation and planning of energy generation systems leads to a more e cient utilization of the available resources and to a limitation in the global environmental impact. The recent changes of electrical market structures, like privatization, restructuring and dereg- ulation lead to maximize the expected value of the electricity market pro ts. Moreover, the inte- gration of di erent types of energy sources in conventional electrical systems is assuming growing importance, like renewable sources such as wind and solar energy. These aspects have to be consid- ered to perform a proper energy production scheduling, taking into account both the uncertainty related to energy demand load forecast and the uncertainty related to not conventional energy. For these issues researchers from mathematics, operations research and engineering have fo- cused for many years on applying mathematical modeling and optimization techniques, in order to solve the optimization problems related to energy generation systems. Di erent types of optimization problems are considered and solved, according to the energy industry process that is involved; typically, generation, transmission and distribution of electricity, or a combination of them. These optimization problems are characterized by an objective function, variables and constraints. Generally, the economic e ciency or the utilities pro ts are represented by the objective function, system operating and technical requirements are represented by the constraints, while the variables are used to model decisions, which can be taken in long-term, medium-term, short-term or on-line periods. In a long-term period (months and years), the Power Expansion Problem is solved, in order to determine the type, the capacity and the number of generating units that the energy system should have. In a medium-term period (days and weeks), the objective is to determine the best combina- tion of generating units in terms of their status (committed or uncommitted) and their output (power). This schedule has to satisfy the forecast demand at minimum total production cost, under the operating, technical and environmental system constraints. This problem is known as Unit Commitment Problem (UC). In a short-term and on-line period (hours and minutes), the Economic Dispatch Problem (ED) is solved, in order to determine the power that each unit, scheduled in the previous phase (solving the UC problem) must produce in order to meet the system demand at real time. Part of our research activities focused on analyzing the modeling aspects related with the production and the scheduling of electrical systems. In particular, we have studied the limits and the simpli cations mainly used in the classical UC models presented in the literature, in order to develop more realistic formulations for this problem. UC models are usually characterized by a combination of several di culties like the presence of continuous and binary decision variables at the same time, a very large-scale dimension, several non-linearities (for instance, in fuel costs modeling) and uncertainty of the problem data (for example, in load demand forecasts, fuel pricing models, stream ows to reservoirs and generating units failures). For these reasons, numerous simpli ed variants of models and algorithms for UC have been proposed in the literature. Traditional UC models are based on two main hypotheses. First, the power can be instanta- neously adjusted. Second, the power output is constant in an assigned time interval (i.e. 1 hour), so that the energy produced in each hour is equal to the power level multiplied by 1 hour. These assumptions greatly simplify the model, because energy and power can be represented by the same entity even if they are di erent from a physical point of view; nevertheless the model does not properly re ect the realistic operating behavior of the generating units. For this reason, in our research activities we have de ned more realistic mathematical formu- lations for the UC than the ones proposed in the literature, in order to overcome most of their main drawbacks. In particular, we propose new Mixed-Integer Quadratic Programming (MIQP) models for UC, based on power instead of energy. We have also de ned and proposed new UC models integrated with the ED problem, where the variables are associated with the power levels, that are assumed to change linearly in each time period, while the energy levels are then computed accordingly. We have thus derived more realistic models that e ectively represent the constraints imposed on the units in order to avoid mechanical stresses to the rotors for conventional units, or to avoid the use of more units in peak hours. Conventional electrical systems are highly fossil fuel dependent, being the major contributors to the greenhouse gas emissions and to the depletion of global fossil fuel resources which are characterized by more volatile prices. For this reason, the use of clean renewable energy sources for electricity generation is acquiring global relevance. Several world countries actively support the growing use of renewable energy sources, such as wind, in order to meet Kyoto Protocol targets for reducing greenhouse gas emissions. Wind energy contributes to this target with a signi cant percentage. In some world and European countries, such as Italy, Spain, Germany, and Denmark, wind is an important part of the electricity supply. Nevertheless, the integration of wind energy into the electrical systems is complex and sig- ni cantly challenging, especially when large amounts of variable wind generation are introduced. Even if there exist positive aspects related with the utilization of wind energy, it is necessary to take into account some practical considerations. For instance, when wind power plants are connected to the electrical network, it is necessary to improve transmission lines, in order to avoid grid stability problems, needing additional operational costs. Furthermore, when the uncertainty associated with the electricity produced by wind energy sources becomes greater than the uncer- tainty of the demand, it is no longer possible to maintain the same power system reliability with the conventional power plant scheduling techniques. For these reasons, even if the integration of wind energy sources into conventional electrical system is growing in importance - due to its economical and environmental development bene ts - particular attention must be devoted to the related practical operational aspects. This leads to the necessity to modify the current industry procedures, such as the UC and the ED, to take into account large amounts of wind power production. Even if an exhaustive literature exists on the general UC problem, focused on how improve its mathematical formulation and its solution algorithm, the research that considers the UC problem in presence of wind energy resources is limited. Part of our research activities has then focused on the development of new UC models in presence of wind energy sources. The objective of the new proposed UC models is to integrate renewable energy sources in a conventional electrical system. These models formulate and solve the problem of determining the best con guration (optimal mix) of available thermal, hydro and wind power plants. The ongoing integration and deregulation of electricity markets in Europe and in the world requires that part of the electricity production is traded daily on power pools where producers state how much electricity they will provide up to 36 hours in advance. This market structure induces additional costs for wind power producers due to the greater unpredictability of wind power at these time horizons. These issues motivate the importance of wind power forecasting techniques that are fundamental to provide accurate forecasts on wind production. In particular, wind generation requires complex forecasting techniques which take into account wind speed, wind direction, hub height, geographical conditions, wind farm size, wind turbine technical and operational characteristics and so on. Since the use of wind energy sources and its integration into power generation systems is as- suming increasing importance, new generation models for synthetic wind data are needed, in order to properly generate forecasts of wind speed and power. This data is fundamental in simulations carried out to analyze and improve the performances of wind generating units, individuating the technical parameters of wind turbines that directly a ect power production. Part of our research activities focused also on developing a new model in order to generate real- istic synthetic wind data. In this model, wind speed is assumed to behave as aWeibull distribution, while wind speed forecast error is simulated using First-Order Auto-Regressive Moving Average - ARMA time-series models. Mathematical Operations Research formulations of the Assignment Problem are used to model wind speed persistence features, which, as shown by simulation results, are essential to properly obtain wind speed and power output forecasts. Furthermore, wind synthetic data, generated with the new generation model proposed, has been used to carry out simulations studies to individuate wind turbines operational parameters that mainly a ect wind generators performances. In particular, an experimental function which expresses the average energy produced by a wind turbine in a 24 hours time horizon in a typical day has been determined, considering the main simulation parameters related withWeibull distribution and wind turbines. Below we describe the structure of this dissertation. In Part I we describe how conventional electrical systems work, focusing our attention on the UC problem which is solved for their e cient operation and planning. In particular, in Chapter 1 we present the main characteristics of a conventional electrical system and we illustrate how the energy is traded in the electrical market and how the electricity production is properly scheduled. Chapter 2 and Chapter 3 illustrate the basic features of the UC, presenting the state of the art of the models and for methods use to solve this problem, respectively. Part II deals with the new proposed models for the UC, which represent an improvement of the conventional electrical systems, since - as previously anticipated - they are based on novel assumptions which have been neglected in the literature so far. In particular, Chapter 4 illustrates the novel formulations for the UC with power variables, while in Chapter 5 the new model for the UC integrated with the ED is presented. In Part III, the integration of wind energy sources into conventional electrical systems is treated. In particular, the problems and the challenges that this integration imposes to the already existing systems are presented in Chapter 6, where the new model for the UC in presence of wind energy sources is proposed. The importance of wind speed and power output forecasts for a proper energy production scheduling is described in Chapter 7, where the new model to generate synthetic wind data is presented. Chapter 8 describes how this new generation model can be applied to properly compute the average energy of a typical wind turbine, illustrating the main parameters of the wind generator that a ect the calculation of the energy. Finally, in the last part of this dissertation, conclusions are drawn and interesting directions for future research are discussed.