**Impact of Different Charging Strategies for Electric Vehicles in an Austrian Office Site**

### **Carlo Corinaldesi \* , Georg Lettner, Daniel Schwabeneder, Amela Ajanovic and Hans Auer**

Energy Economics Group (EEG), Vienna University of Technology, Gußhausstraße 25-29, E370-3, 1040 Vienna, Austria; lettner@eeg.tuwien.ac.at (G.L.); schwabeneder@eeg.tuwien.ac.at (D.S.); ajanovic@eeg.tuwien.ac.at (A.A.); auer@eeg.tuwien.ac.at (H.A.)

**\*** Correspondence: corinaldesi@eeg.tuwien.ac.at; Tel.: +43-(0)1-58801-370370

Received: 1 October 2020; Accepted: 3 November 2020; Published: 10 November 2020

**Abstract:** Electric vehicles represent a necessary alternative for wheeled transportation to meet the global and national targets specified in the Paris Agreement of 2016. However, the high concentration of electric vehicles exposes their harmful effects on the power grid. This reflects negatively on electricity market prices, making the charging of electric vehicles less cost-effective. This study investigates the economic potential of different charging strategies for an existing office site in Austria with multiple charging infrastructures. For this purpose, a proper mathematical representation of the investigated case study is needed in order to define multiple optimization problems that are able to determine the financial potential of different charging strategies. This paper presents a method to implement electric vehicles and stationary battery storage in optimization problems with the exclusive use of linear relationships and applies it to a real-life use case with measured data to prove its effectiveness. Multiple aspects of four charging strategies are investigated, and sensitivity analyses are performed. The results show that the management of the electric vehicles charging processes leads to overall costs reduction of more than 30% and an increase in specific power-related grid prices makes the charging processes management more convenient.

**Keywords:** electric mobility; charging strategies; economics; promotion policies; mixed-integer optimization; flexible systems

### **1. Introduction**

The global warming and the increasing GHG emission challenges in recent years are expected to be an accelerator for the deployment of electric vehicles (EVs) as a more sustainable alternative for wheeled transportation around the world [1–4]. The European Environment Agency recognizes transport as a critical source of environmental pressures in the European Union, and it has a decisive influence on climate change and air pollution. The transport sector consumes one-third of the final energy in the European Union and is responsible for a large share of the European's greenhouse gas emissions. This makes transport one of the major contributors to climate change [5]. The Intergovernmental Panel on Climate Change (IPCC) affirms that wheeled transportation produces more than 70% of the overall greenhouse gas emissions from transport [6]. Because of their significant environmental advantages, numerous countries are working on different strategies to make EVs monetarily more convenient than traditional wheeled vehicles [7].

However, as the number of EVs increases, the negative effects of their charging on the power grid become more evident, especially at the low-voltage level. In fact, high concentrations of EVs have various harmful effects due to the overlap between EV charging, residential peak loads and renewable generation [8–10]. For these reasons, the growing number of EVs, in parallel with the growing penetration of renewable energy sources, leads the power grid facing a challenging future [11,12]. Charging management systems and different charging strategies of EVs have been extensively studied in order to reduce the greenhouse gas emissions, to improve the power grid operation and to reduce the electricity costs for end-users [13–16]. In the last decade, several unidirectional and bidirectional charging strategies of EVs have been investigated in different contributions [17–20]. Furthermore, the possibility of combining stationary battery storages (SBSs) with the charging infrastructures has also been studied in-depth, in order to further reduce the peak load power and the electricity costs and allow the fast charging of EVs even with low grid connection power [21,22].

The core objective of this study is to investigate the economic potential of different charging strategies of EVs for an existing office site in Austria with multiple charging infrastructures. The economic potential is given by trading electricity in the Day-Ahead (DA) spot market considering the overall power and energy procurement costs of the office site's charging infrastructures. Profit opportunities could incentivize the end-users to apply flexible electricity consumption patterns to their EVs charging schedules, and they could also incentivize the office site to install further SBSs.

In this paper, multiple optimization problems are defined in order to determine the monetary potential of different operating strategies for managing the EVs' charging processes. The optimization approach aims to define the power flows between the EVs, the SBSs and the power grid, in order to minimize the electricity costs and to best allocate the flexibility of the Austrian office site. However, a detailed description of the technical operation of the above-mentioned components is needed in order to implement them in a mathematical model. In this work, the components of the Austrian office site are described with the exclusive use of linear relationships, which can be implemented in mixed-integer optimization problems. The optimization problems are modeled using the *Python* toolbox *Pyomo* [23] and solved with the *Gurobi* solver [24].

The paper is organized as follows. Section 2 provides an overview of the state of the art in the scientific literature. Next, Section 3 describes the mathematical representation of the Austrian office site, including the EVs and the SBSs in the optimization problem and its objective function, which aims to minimize the overall costs. Section 4 illustrates the description of the investigated real-life use case in Austria with measured data used to simulate the different charging strategies. Section 5 presents the comprehensive results and sensitivity analyses of the case study. Finally, Section 6 concludes the paper and discusses possible directions for future research.

### **2. State of the Art**

The growing share of renewable energy sources, such as wind and solar photovoltaic, increases the volatility of electricity generation in the power grid [25–27]. At the same time, the increasing integration of high-power consumption loads, such as EVs, are setting new challenges for the distribution system operators [28,29]. Hence, the active participation of the demand-side can play a crucial role in the European transition to a carbon-free energy sector [30–32]. For this reason, nowadays, one of the key challenges is to enhance the use of the potential flexible demand in the power grid. An EV represents a flexible load type, and the growing number of grid-connected EVs accords to them a growing flexibility potential for the power grid [33]. Flexibility is the electrical components capability to alter their scheduled consumption in reaction to external signals, for example, spot market prices or grid costs [34]. However, an exhaustive mathematical description of the flexible components, such as EVs and SBSs, is needed in order to efficiently coordinate and aggregate multiple flexible load types.

In several studies, for example [33,35,36], the flexibility of EVs is utilized in order to support the variable renewable energy injection and minimize the overall system costs. Weis et al. [37] quantify the benefits of managed charging of EVs achieving 1.5–2.3% cost savings in the simulations. Sheikhi et al. [38] introduce a charging management strategy for EVs aimed to reduce peak loads. The benefits and the drawbacks of bidirectional charging of EVs are thoroughly investigated in [39–41]. In several simulations, the electricity cost reductions achieved through the vehicle-to-grid charging are overcompensated by higher battery degradation costs. If the higher battery degradation costs are not considered, the overall costs reduction could reach 13.6% [39]. However, managed charging and

vehicle-to-grid charging of EVs are able to alleviate congestion in the power grid [42]. In the last decade, different methods were developed in order to mathematically represent flexible loads in optimization frameworks. In Hao et al. [43], a method to describe the flexibilities of different technologies as virtual batteries is presented. In this work, flexibilities are represented in a mixed-integer optimization problem with the exclusive use of linear relationships, which makes the model scalable and able to handle a growing amount of components.

This paper presents the mathematical implementation of EVs and SBSs in optimization problems, which aim to minimize the overall costs of their operation, applying peak shaving and load shifting to aggregated charging infrastructures. Furthermore, in this work different charging strategies are defined and compared in order to determine the optimal charging strategy for an office site of an electric utility company in Austria with multiple charging infrastructures. The simulated period covers the entire year 2019. The main contributions of this paper beyond the-state-of-the-art are as follows.


### **3. Methods**

The real operation of EVs and SBSs is characterized by non-linear relationships, which lead to non scalability of the calculations. In Section 3.1, a simplified method to implement EVs and SBSs in optimization problems as linear systems is developed. Moreover, the optimization problem and its cost function are presented in Section 3.2. Lastly, in Section 3.3, the investigated EV charging strategies are defined.

### *3.1. Components*

A mathematical description of SBSs and EVs is needed in order to efficiently implement them in a mixed-integer optimization problem and define the optimal allocation of their power flows using a linear optimization model. In the following Sections 3.1.1 and 3.1.2, the mathematical representations of SBSs and EVs are presented. In this work, the time is considered as discrete, and the optimized time range T is divided into a number of constant time intervals Δ*t*.

### 3.1.1. Stationary Battery Storage (SBS)

The operation of a SBS is bounded to its physical limits such as power and capacity limits. The input and output power (*pSBS*,*in <sup>t</sup>* and *<sup>p</sup>SBS*,*out <sup>t</sup>* ) are confined between 0 and the maximum input and output power (*pSBS*,*in max* and *pSBS*,*out max* ) are specified as follows.

$$0 \le p\_t^{\text{SBS,in}} \le p\_{\text{max}}^{\text{SBS,in}} \tag{1}$$

$$0 \le p\_t^{\text{SBS}, \text{out}} \le p\_{\text{max}}^{\text{SBS}, \text{out}} \tag{2}$$

The capacity limits bound the state of charge of the SBS (*soc*SBS *<sup>t</sup>* ) between 0 and its nominal capacity (*E*SBS) as mathematically described below.

$$0 \le soc\_t^{\text{SBS}} \le E^{\text{SBS}} \tag{3}$$

If the charging and discharging efficiency (*ηSBS*,*in* and *ηSBS*,*out*) and the standby losses percentage (*ESBS Loss*%) are taken into account, the energy balance of an SBS can be defined in each time period in T as follows.

$$\text{score}\_{t}^{\text{SBS}} = \text{soc}\_{t-1}^{\text{SBS}} \cdot \left(1 - E\_{\text{Loss}, \%}^{\text{SBS}}\right) + \left(p\_{t}^{\text{SBS,in}} \cdot \eta^{\text{SBS,in}} - \frac{p\_{t}^{\text{SBS,out}}}{\eta^{\text{SBS,out}}}\right) \cdot \Delta t \tag{4}$$

Furthermore, the costs of the operation of the SBS can be implemented in the optimization problem using the levelized cost of storage (LCOS) method [44]. LCOS can be described as the cost per unit of charged electricity for a specific storage technology. It can be formally defined as follows.

$$LCOS = \frac{C\_{Inv}^{\text{SBS}}}{n \cdot E^{\text{SBS}}} \tag{5}$$

where *C*SBS *Inv* indicates the investment costs of the SBS and *n* the number of charging cycles that the SBS is able to support before its capacity falls under 80% of its original capacity [45]. Hence, the total costs of storage *C*SBS *LCOS* within the optimized time range T can be described as the LCOS multiplied by the SBS's cumulative delivered electricity and can be expressed as below.

$$\mathbf{C}\_{LCOS}^{\text{SBS}} = L\text{COS} \cdot \sum\_{t=1}^{T} \left( p\_t^{\text{SBS}, \text{in}} \right) \tag{6}$$

According to the physical limits and the total costs of storage, the optimization algorithm determines the optimal input and output power (*pSBS*,*in <sup>t</sup>* and *<sup>p</sup>SBS*,*out <sup>t</sup>* ) and the state of charge (*soc*SBS *<sup>t</sup>* ) of the SBS, hence defining its optimal operation.

### 3.1.2. Electric Vehicle (EV)

In this paper, we consider different possibilities of charging EVs: managed charging (MC) and vehicle-to-grid (V2G). The flexibility available from a charging cycle can vary in terms of duration and amount of energy. In fact, EV batteries are only available for a limited period of time, or rather only when they are connected to the charging infrastructure. Hence, the operation of a charging cycle is bounded to its physical limits such as power, capacity and time limits. The time limits are given by the connection time (*S*EV) and the disconnection time (*D*EV) of the EV at the charging infrastructure. We formally consider the initial state of charge (*soc*EV *<sup>S</sup>*EV ) equal to 0, since most of today's charging infrastructures do not allow to know the state of charge of an EV when it is connected to one of them. Formally, the state of charge of an EV is confined as follows.

$$
bar{c}\_{\text{SFV}}^{\text{EV}} = 0\tag{7}$$

$$\text{soc}\_{D^{\text{EV}}}^{\text{EV}} = E^{\text{EV}} \tag{8}$$

$$0 \le \text{soc}\_t^{\text{EV}} \le E^{\text{EV}} \qquad\qquad\qquad\forall t \in \left(S^{\text{EV}}, D^{\text{EV}}\right) \tag{9}$$

The input and output power (*pEV*,*in <sup>t</sup>* and *<sup>p</sup>EV*,*out <sup>t</sup>* ) are confined between 0 and the maximum input and output power (*pEV*,*in max* and *pEV*,*out max* ) as formally described below.

$$0 \le p\_t^{\text{EV,in}} \le p\_{\text{max}}^{\text{EV,in}} \tag{10} \\ \qquad \qquad \qquad \forall t \in \left(S^{\text{EV}}, D^{\text{EV}}\right) \tag{10}$$

$$0 \le p\_t^{\text{EV,out}} \le p\_{\text{max}}^{\text{EV,out}} \qquad \qquad \forall t \in (S^{\text{EV}}, D^{\text{EV}}) \tag{11}$$

*Energies* **2020**, *13*, 5858

If V2G is not considered, the maximum output power (*p*EV,out *max* ) is formally set to 0. Moreover, when the EV is not connected to the charging station, the input and output power is set to 0 as specified below.

$$p\_t^{\text{EV,in}} = 0 \tag{1} \tag{12}$$

$$p\_t^{\text{EV,out}} = 0 \tag{13}$$
 
$$\forall t \notin \left(\text{S}^{\text{EV}}, \text{D}^{\text{EV}}\right) \tag{13}$$

If the charging and discharging efficiency (*ηEV*,*in* and *ηEV*,*out*) and the standby losses percentage (*EEV Loss*%) are considered, the energy balance of an EV could be formally defined in the optimization problem in each time period in T as follows.

$$\text{soc}\_{t}^{\text{EV}} = \text{soc}\_{t-1}^{\text{EV}} \cdot \left(1 - \mathbb{E}\_{\text{Loss}}^{\text{EV}}\right) + \left(p\_{t}^{\text{EVin}} \cdot \eta^{\text{EVin}} - \frac{p\_{t}^{\text{EVout}}}{\eta^{\text{EVout}}}\right) \cdot \Delta t \qquad \qquad \forall t \in (\text{S}^{\text{EV}}, \text{D^{EV}}) \tag{14}$$

where the AC-DC and the DC-AC conversion losses are included in the charging and discharging efficiency factors (*ηEV*,*in* and *ηEV*,*out*). A graphical representation and the associated power flows of the flexibility of a charging process of an EV are shown in Figure 1.
