## 1. Introduction

Increasing environmental awareness, technical improvements, and favorable regulatory conditions have all allowed the market for electric vehicles (EVs) in Germany and worldwide to experience an upturn [

1,

2]. Simultaneously, an increasing number of electricity consumers are investing in renewable energy sources. Photovoltaic (PV) power generators especially benefit from a growing popularity in residential homes, allowing these customers to reduce electricity costs and rendering them as prosumers [

3]. A home energy storage system (HES) can be added to further increase self-consumption and self-sufficiency rates [

4].

In literature, HESs and EVs are well-researched topics [

4,

5,

6], however, combined approaches of both storage systems are still a very young research field [

7]. While recent literature presents a novel energy management system (EMS) for residential buildings with HES and EV, the contribution comes short on analyzing the technical characteristics of the battery energy storage systems (BESSs) at varying charging schemes [

7]. In this work, we analyze how the aforementioned trends may interact, conduct a full techno-economic system analysis and reveal how prosumers with an EV may be able to optimize their electricity expenses. In particular, the degradation and efficiency of the HES and the EV’s BESS are discussed. In addition, operating expenses (OPEX) are analyzed in the context of electricity costs for both the building and the vehicle. To increase the comparability of the results, a vehicle with an internal combustion engine (ICE) serves as a reference case.

As illustrated in

Figure 1, three different charging strategies for the EV are analyzed and compared: Simple charging (SC) and optimized charging (OC) schemes, which both allow unidirectional power flows from the building to the vehicle, and the vehicle-to-building (V2B) strategy, which is an extension of the OC scheme allowing bidirectional power flows [

6,

8]. It is known that vehicle usage patterns may vary strongly [

9]. For this reason, to make more valid statements about the degradation behavior, efficiency, and OPEX, the vehicle utilization patterns of a commuter and a supplementary vehicle are investigated. These vehicles are characterized by varying plug-in times at the power outlet of the prosumer’s residence. As an additional degree of freedom, interaction between the EV battery and an optional stationary HES is examined. Particularly, the influence on the degradation and the efficiency of such a scenario considering two BESSs (EV and HES) is discussed. For the sake of simplicity, throughout this work, a typical German household with corresponding load and PV generator profiles is utilized and price signals of the German energy market are incorporated. However, the methodology can be applied to other profile data and the conclusive results drawn in this contribution are valid for other regions worldwide. An overview of the discussed simulation structure is visualized in

Figure 1.

The investigated scenarios in this work are simulated using a two-step approach. First, the residential power flow (RPF) model with an underlying linear programming (LP) algorithm optimizes the power flows within the residential multi-node system. Next, the optimized power flows are transferred to the open source simulation tool

SimSES in order to model the resulting battery degradation and system efficiency [

10].

This paper is structured as follows:

Section 2 explains the optimization and simulation models as well as the system’s topology,

Section 3 presents the simulation results, and

Section 4 concludes with a summary and discussion.

## 2. Methods

In order to optimize the electricity exchange between components and analyze the storage systems in a detailed fashion, two solution methods are combined, as is illustrated in

Figure 2. First, the power flows between the individual technical units are optimized using the RPF model. The underlying algorithm is based on LP, derived from the MATLAB optimization toolbox and the Gurobi optimizer [

11]. Then, the simulation tool

SimSES is used, which is capable of simulating the technical parameters of an energy storage system [

10]. The results of the linear optimization are transferred to

SimSES and represent the inputted alternating current (AC) power values of the energy storage system’s inverter. By using

SimSES’ integrated operation strategy

PowerFollow, the predefined time-discrete power values are implemented, and a detailed simulation is carried out. Both tools, the RPF model and the

SimSES simulations are conducted in MathWorks MATLAB R2018b, operating at a sampling rate of 15 min [

5].

The profit of a residential electricity prosumer in Germany is computed by simulating several different system configurations: Optional HES, optional EV, three different EV charging schemes, and two vehicle usage patterns.

Depending on the scenario, the RPF model of the investigated household consists of up to six main components, which are illustrated in

Figure 3. The household is equipped with a PV generator with 8 kWp peak power, which is a common size for an average German household [

12]. The PV generator system is composed of the PV panels, maximum power point tracker (MPPT), and inverter that converts the generator’s direct current (DC) power into AC power. The one-year data measured from a PV system installed in Munich, Germany is used as the PV generating profile. To implement the degradation of the PV system, a degradation factor of 0.5% of the PV’s peak power per year is assumed [

4,

13].

In order to consider the electricity demand of a typical household, a representative one-year load profile (

profile 31) out of a freely available set of smart-meter derived household load profiles is used in this study [

14]. The annual electricity demand (only of the building, excluding that of the EV) of the considered household is set to 6000 kWh, a value taken from literature and well-suited to an average German household [

12].

Further parameters and technical specifications of the household and its stationary HES can be taken from

Table 1. The eligibility requirements, according to the German Federal Ministry of Economics and Technology, stipulate a feed-in limitation of 50% for PV generators that are operated in combination with a stationary or decentralized BESS [

15]. Furthermore, a fixed feed-in remuneration price of

$0.123$ EUR/kWh is utilized, which is fixed and guaranteed for a period of twenty years [

13]. Due to the projected electricity price of

$0.437$ EUR/kWh in 2030 and the electricity price of

$0.294$ EUR/kWh in 2018, a compound annual growth rate (CAGR) of 3.35% is assumed for the electricity purchase price in the simulation [

16].

lithium ion batteries (LIBs) are assumed for both the EV and HES. The cell chemistry chosen for the stationary HES within the building is based on a lithium iron phosphate (LFP) cathode and graphite anode. This chemistry allows a high cyclic stability [

18], which makes it a suitable candidate for stationary applications [

17].

The average German household with a HES has a usable energy content of

$8.1$ kWh [

12]. From this the nominal energy content of 9 kWh is derived with the state of charge (SOC) limitations of 5% and 95% [

17]. Furthermore, a self-discharge rate of 0.6% of the nominal energy content per month is assumed for the LFP cell [

17]. Efficiency losses during charge and discharge processes of the battery are calculated via

SimSES’ equivalent circuit model, which depends on charging and discharging current, battery temperature, and SOC [

10].

The semi-empirical degradation model of the LFP cell is also incorporated in

SimSES. Degradation analysis is based on a superposition of calendar and cycling-related capacity fade [

19]. During idle periods only calendar degradation, whereas during load periods also cyclic degradation is occurring [

20]. This cyclic degradation is a function of multiple factors, including the depth of cycle (DOC), current, SOC range, and temperature [

10]. A constant ambient temperature of 25

${}^{\circ}\mathrm{C}$ is assumed throughout the simulation period as the HES is installed within the building.

Since the AC coupling topology is the dominant topology for HESs in Germany [

12], this setup is also used in this work. One of the major advantages of this topology over a DC coupling to the PV generator is an easy integration into a building with an existing PV generator, thus ensuring a high level of flexibility [

21].

For the power-electronics efficiency, a simplified constant value of 95% is assumed in the RPF model. In order to make more accurate statements about the efficiency of the BESSs, the

SimSES simulation tool takes into account a concave efficiency curve, which is derived from previous literature [

4,

22]. This curve considers the dependence on the inverter’s output power and the fact that values below 10% of the rated inverter power result in a significantly lower efficiency.

Analogous to the procedure for the stationary HES, the power flows to and from the EV are optimized using the RPF model and then validated in

SimSES. For all simulations of the EV and the ICE vehicle, a

B-segment small car is considered [

23,

24,

25]. An overview of the technical characteristics for the considered vehicles can be found in

Table 2.

A nickel manganese cobalt (NMC) based cathode cell chemistry is chosen for the EV’s BESS. Compared to other LIB cell chemistries, the NMC cell offers a higher energy density. The nominal and usable energy contents of the chosen EV battery,

$21.6$ kWh and

$18.8$ kWh, are closely linked to numbers often stated for EVs widely used in Germany. Derived from the nominal and usable energy contents, SOC boundaries of 8% and 95% are defined [

17]. Similar to the LFP cell of the HES, the self-discharge rate of the NMC cell is set to 0.6% of the nominal energy content per month. Both the RPF model and detailed simulations using

SimSES assume a round-trip efficiency of 95% for the EV battery [

26].

In comparison to the highly sophisticated battery model of the LFP cell, the EV’s battery is modelled using a more generic approach within

SimSES [

10]. Similar to previous work, a Wöhler curve (i.e., stress-number (S-N) curve) based fatigue model is used as the underlying method to estimate cycling-induced stress in the battery [

4]. This method leads to an exponential weighting of DOC, i.e., an increased DOC leads to an overproportional increase in battery stress level, which again results in a reduced amount of equivalent full cycles (EFC) compared to low DOC values; thus, resulting in a shortened battery lifetime [

27].

The annual mileage of a passenger car is based on the German average, which is 13,922 km [

29]. Therefore, a comparable EV, which consumes

$12.9$ kWh/100 km, requires approximately 1800 kWh annually [

28]. In this paper, a gasoline-powered vehicle with an average fuel consumption of

$5.3$ L/100 km is used [

30]. Analogous to the electricity costs, a temporally dynamic behavior is also assumed for the fuel price: An initial price of

$1.45$ EUR/L fuel is assumed for the start of the simulation. Due to the projected gasoline price of

$1.89$ EUR/L in 2030 and the gasoline price of

$1.45$ EUR/L in 2018, a CAGR of 2.25% is assumed for fuel prices in the simulation [

16].

As part of this work, two EV profiles are created synthetically. The profiles for the two considered EVs (commuter and supplementary vehicle) are based on the US06 driving cycle and 83 charging profiles provided by the Forschungsstelle für Energiewirtschaft e. V., which are used in the federal study

Mobility in Germany [

9,

31,

32]. Both vehicle utilization patterns consist of a driving profile and a binary time series, which indicates whether the vehicle is connected to the power outlet of the building. It is assumed that the EV is only charged at the residential building and this additional electricity demand is directly allocated to the total electricity consumption of the household.

In

Figure 4 an exemplary week (Monday to Sunday) in early summer is illustrated. The dashed areas in the two lower subplots show the plug-in times of the two utilization patterns, where the respective EV is connected to the building. As is immediately apparent, both profiles differ strongly in terms of their total plug-in time and respective daytime behavior: The commuter profile is only rarely connected to the building’s power outlet during times of high solar irradiation on weekdays, which makes it more difficult for this vehicle user to directly utilize surplus PV power. Instead, the cumulative plug-in time of the supplementary car is much higher, so the potential of optimizing the power flows between building and vehicle is assumed to be higher.

In order to bring the difference of the vehicle utilization types into a quantifiable context, the quotient between plug-in time and the residual power is formed. Residual power is defined as the difference between PV power and demanded power. For the two types of examined profiles, the resulting correlation coefficients are 7% for the commuter vehicle and 28% for the supplementary car. With the increased plug-in time, the BESS availability of the EV is increased, which increases the degree of freedom for power flow optimization. This increased utilization coefficient leads to a reduction in electricity purchases, which in turn lowers the OPEX of the prosumer. Based on this theory, this metric is introduced and discussed further in the following sections.

In addition to the two aforementioned vehicle utilization patterns, three different EV charging schemes are introduced. All three strategies are discussed in the context of storage system efficiency, degradation, and economic impact:

simple charging (SC): A simple rule-based charging of the EV is applied, where power is delivered unidirectionally from the power outlet of the building to the vehicle. As long as the vehicle is connected to the building and the EV’s battery SOC has not reached the maximum SOC limit, the EV gets charged at the maximum allowed charge rate. The RPF model, as well as the simulation tool SimSES, are considering constraints for the respective SOC and C-Rate boundaries.

optimized charging (OC): Similar to SC the power outlet is used for unidirectional vehicle charging only. An advanced strategy is used that optimizes and controls the amount of energy and the timing of the EV’s charging. The controller is fed by input values such as power flows within the building and the plug-in times of the EV.

vehicle-to-building (V2B): As an extension of the OC strategy, V2B enables a bidirectional power flow between the EV and building.

The RPF model’s objective is to maximize the profit from the electricity sold and purchased throughout the simulation period. This comes down to a minimization of the OPEX of the prosumer. All scenarios use the following base objective function:

whereby

${E}_{i}^{\mathrm{r}}$ denotes the amount of electricity that is sold to the superordinate electricity grid at time step

i. The purchased electricity per time step is defined by the variable

${E}_{i}^{\mathrm{p}}$. The price signals

${p}_{i}^{\mathrm{r}}$ and

${p}_{i}^{\mathrm{p}}$ describe the remuneration and purchasing price at time

i. Considering changing electricity prices over time, price signals are time-dependent. Besides the objective function, inequality constraints for the BESSs’ SOC and C-Rate, as well as equality constraints for the power flows at each node are considered and derived from a previous contribution [

33].

Literature shows that the total cost of ownership (TCO) for an EV in Germany depends on many factors [

25]. Due to the perennial lifetime of modern BESSs and the complex estimation of future BESS investment costs, capital expenditures (CAPEX) are neglected. In order to make the results as comprehensible as possible, only electricity costs and fuel costs are taken into account.