Electric Vehicles and Renewable Generation

This chapter provides an overview of the operation and planning problems that power system operators, planners, and participants will face in future power systems. The decision framework of each problem is also discussed. The main challenges of power systems are pointed out, focusing on the role of renewable energies and electric vehicles.

This chapter describes some modeling aspects that are recommended to be known by the readers of this book to fully understand the decision-making models that are presented in Chaps. 4–12. In particular, this chapter describes the modeling of the operation of power systems, as well as the energy production processes of wind and solar photovoltaic power plants and the energy consumption of electric vehicles. The temporal characterization of long-term planning horizons is also analyzed in this chapter.

This chapter describes some specific mathematical tools that are used throughout this book. First, two decision-making under uncertainty tools are analyzed: stochastic programming and robust optimization. Next, the linear decision rules approach is presented. This technique allows to establish linear relationships between the optimization variables and the uncertain parameters, which allows to reduce the computational size of optimization problems. The linear decision rules approach is specially convenient in multi-stage programming problems under uncertainty. Finally, the practical implementation of the Benders’ decomposition is described in detail. This decomposition technique is of special interest for those large-scale optimization problems that can be decomposed easily if the values of some variables are fixed. Note that this chapter intends to provide basic concepts of some mathematical tools of interest. Those readers familiar with these tools may skip this chapter.

This chapter describes a two-stage stochastic problem that models the day-ahead energy and reserve scheduling of a renewable-dominated power system considering the uncertainty in the balancing market. The system operator perspective is adopted such that the total operating cost is minimized taking into account the technical constraints of dispatchable, intermittent renewable, and storage units, as well as of the transmission lines. The uncertainty of the hourly demand and wind and solar power is modeled through a set of scenarios. The resulting model is formulated as a mixed-integer stochastic problem that incorporates the unit commitment variables of dispatchable units. Illustrative examples allow to better understand the main ideas of the proposed model. Then, a realistic case study based on the European power system is studied and multiple numerical results show how a real power system with high penetration of renewable energies is scheduled in the short-term horizon.

This chapter studies the problem of the market clearing with high presence of electric vehicles. In particular, it is presented an optimization model describing the day-ahead market, where energy and reserve capacity is scheduled, and the real-time operation, where the reserve capacity is deployed to counteract the deviations in the demand and renewable power with respect to the predictions made the day ahead of delivery. It is considered that electric vehicles can provide reserve services when connected considering the capacity of the battery and the final state requirement. The uncertainty of the demand, the intermittent renewable power, and the use of the electric vehicle batteries is modeled through a set of scenarios. Therefore, the model is formulated as a mixed-integer two-stage stochastic programming problem. Illustrative examples explain in a simple way the proposed formulations, while a realistic case study based on the power system of Lanzarote and Fuerteventura in Spain provides a deep numerical analysis.

This chapter analyzes the bidding strategy problem of an aggregator managing a set of electric vehicles. The electric vehicle aggregator determines the bidding decisions in the market that minimize the charging costs of electric vehicles and, at the same time, meets the driving requirements of electric vehicle users. The models developed in this chapter take into account the uncertainty in both market prices and driving needs using a set of scenarios, which allows formulating the problem using a stochastic programming approach. The impact of the bidding decisions of the electric vehicle aggregator on market prices is also addressed in the decision-making tool. A number of illustrative examples explain how to formulate and solve this type of problems.

This chapter describes and formulates the selling price determination problem faced by an electricity supplier. We assume that this supplier provides the power demand of a set of small consumers that do not participate in the electricity markets. We also consider that these consumers are electric vehicle users. In this problem, the electricity supplier has to handle a number of uncertainties: (i) the electricity price in the pool market, (ii) the consumption patterns of electric vehicles, and (iii) the selling prices offered by rival suppliers. Additionally, electricity suppliers must anticipate the response of their potential clients to the offered selling price. For these reasons, the selling price determination by electricity suppliers can be considered challenging from the modeling point of view.

This chapter analyzes the generation expansion planning problem of a power system with renewable energies. The problem is formulated under the perspective of a central planner that aims at determining the generation expansion plans that minimize both the investment and operation costs. Then, this central planner promotes the building of the most suitable generating units among private profit-oriented investors. Uncertain variables are modeled using both scenarios and confidence bounds, which allows formulating the generation expansion planning problem using stochastic programming and robust optimization approaches. A static approach is adopted, where investment decisions are made at the beginning of the planning horizon. This chapter includes a number of illustrative examples that easily explain how the proposed approaches work and a case study based on the European power system.

This chapter describes a generation expansion problem in which investment decisions can be made at different stages along the planning horizon. This planning problem usually consists of a long-term decision process that is subject to multiple uncertain sources. Therefore, a precise representation of the evolution of the uncertain parameters helps the decision maker to adopt the optimal solutions considering its final targets. In this chapter, a multi-stage investment model in generation capacity considering long-term uncertainties is presented. Specifically, the demand growth per year and the investment costs of the units are characterized as random variables. The proposed model is formulated using two different approaches, namely stochastic programming and linear decision rules. These approaches differ in how the uncertain parameters are represented. Illustrative examples are provided to ease the understanding of the proposed formulations. A realistic case study based on the European power system is solved. The outcomes obtained from the stochastic and linear decision rules approaches are compared for different number of decision stages.

This chapter studies the generation expansion problem considering explicitly the presence of electric vehicles. The demand associated with the charge of electric vehicles may change substantially the shape of the system demand curve and can influence the determination of the generation mix of future power systems. The model described in this chapter considers the possibility of using financial incentives to modify the consumption patterns of electric vehicle users. The aim of this financial tool is to place the charge of vehicles in convenient periods from the perspective of the power system operator. Therefore, it is assumed that electric vehicle users will be willing to leave the charge of their vehicles in hands of the power system operator if a high-enough financial incentive is offered to them. Price-quota curves are used to model the willingness of electric vehicle users to give the control of the charge/discharge of their vehicles to the system operator. The formulation of these curves implies the use of binary variables. The model analyzed in this chapter considers uncertainties such as the annual demand growth, the capital costs of generating and storage units and the number of electric vehicles. As a result, a two-stage stochastic programming problem is formulated. In this model, generation and storage capacity investments and financial incentives for electric vehicle users are decided in the first stage, whereas operating decisions are made in the second stage. The Benders’ decomposition technique is applied to solve the resulting mathematical problem in reasonable computational times. A number of illustrative examples and a realistic case study are included in this chapter to show the performance of the described formulation. The realistic case study included at the end of the chapter is based on the isolated power system comprising Lanzarote and Fuerteventura islands in Spain.

This chapter studies the transmission expansion problem considering the presence of renewable energies and electric vehicles. The expected replacement of a relatively small number of high-capacity thermal units by a large number of renewable energy units with smaller capacity per unit may change substantially the utilization of the transmission network. Additionally, the incorporation of a large number of electric vehicle chargers may increase significantly the energy load at specific periods in some buses and may require the reinforcement of the transmission system. Then, a two-stage stochastic programming formulation is described in this chapter to decide the investments in transmission lines to face the increase of renewable power and the number of electric vehicles. A number of illustrative examples and a realistic case study are included in this chapter to show the performance of the described formulation. The realistic case study included at the end of the chapter is based on the isolated power system of Gran Canaria island in Spain.

This chapter studies the distribution expansion problem considering the existence of a large number of chargers of electric vehicles connected to a low-voltage distribution network. The presence of electric vehicle chargers may change substantially the energy load at some locations and may require the reinforcement of the distribution system to preserve its adequate operation. We assume the role of a distribution system operator that desires to determine the distribution lines to reinforce to avoid voltage drops and congestion problems considering the additional power consumption of electric vehicle chargers. A number of illustrative examples are included to describe the performance of the formulation of the distribution expansion problem. Additionally, a case study based on a realistic distribution network is presented at the end of the chapter.