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## Energy management of a small-size electric energy system with electric vehicles, flexible demands, and renewable generating units

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This chapter describes the energy-management problem of a small-size electric energy system (SSEES), which comprises a set of electric vehicles (EVs); a set of flexible demands that can shift their energy consumption according to the system needs; and renewable generating units, such as solaror wind-powered units. We consider an energy-management system (EMS) in charge of all the components in the SSEES. This EMS determines the power scheduling of each component and guarantees that all the technical and economic constraints of these components are satisfied. Moreover, the EMS guarantees that the technical constraints of the SSEES are met. In order to compensate the energy deviations, the SSEES is connected to the main grid from which the EMS can buy/sell the deficit/surplus energy to the electricity market. Particularly, we model the day-ahead (DA) market. The considered problem is characterized by a number of uncertainties including the energy market prices and the production of renewable generating units. These uncertainties are modeled using a set of scenarios. Therefore, the resulting problem is formulated as a two-stage stochastic programming problem. In the first stage, the EMS decides the power bought from/sold to the DA market. In the second stage, and once the actual realization of the different uncertainty sources is known, the EMS decides the actual power scheduling of each component in the SSEES.

Chapter Contents:

• 6.1 Introduction
• 6.2 Notation
• 6.2.1 Indices
• 6.2.2 Sets
• 6.2.3 Parameters
• 6.2.4 Optimization variables
• 6.3 Modeling of electric vehicles
• 6.3.1 Individual modeling
• 6.3.2 EV aggregator
• 6.4 Deterministic energy-management problem
• 6.4.1 Objective function
• 6.4.2 Power balance constraints
• 6.4.3 Network constraints
• 6.4.4 Electric vehicle constraints
• 6.4.5 Demand constraints
• 6.4.6 Renewable production constraints
• 6.4.7 Formulation
• 6.5 Uncertainty characterization
• 6.6 Stochastic energy-management problem
• 6.7 Summary and conclusions
• 6.8 GAMS codes
• 6.8.1 Illustrative example 6.1
• 6.8.2 Illustrative example 6.2
• 6.8.3 Illustrative example 6.3
• 6.8.4 Illustrative example 6.5
• References

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