# Modeling the Total Cost of Ownership of an Electric Car Using a Residential Photovoltaic Generator and a Battery Storage Unit—An Italian Case Study

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## Abstract

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## 1. Introduction

## 2. Literature Review

## 3. Methodology

#### 3.1. Estimating the Levelized Cost of Recharged Energy with Photovoltaics

_{0}(kWh/kWp/year) is the yield of the plant, ${d}_{r}$ (%/year) is the degradation rate of the PV modules, N is the project lifetime (years), and CRF (%) is the capital recovery factor that can be computed as:

#### 3.2. Estimating the Levelized Cost of Storage of a Battery Storage System

#### 3.3. EV Driving Profile Model

_{min}, X

_{max}), where X denotes the current value. We examine, hereafter, in detail, the simulation parameters.

#### 3.3.1. Workdays and Day Trips

#### 3.3.2. Long-Distance Holidays

#### 3.4. Energy Flows Model

_{charge}), then the remaining part is delivered to the storage, if SoC < 1 (where SoC is the State of Charge), otherwise to the LV grid. If there is no sunlight, the storage charges the car, until it is empty, and then the power is drawn from the LV grid. The value SoC

_{min}represents the minimum possible SoC. Finally, if there is no sunlight and the car is not present, no action takes place. Table 3 summarizes this model in detail.

_{charge}. ∆PV power denotes the difference (PV power−P

_{charge}) delivered to storage if PV power > P

_{charge}. Items (1—Storage power to car) and (2—LV grid power to car) in the same cell denote an order of activation. If the storage power is not sufficient to charge the car, then the LV grid provides the required additional power. Note that, when the car is fully charged, the algorithm jumps from case A to case B and from case C to case D, respectively. A fully charged car is equivalent to an absent car. In the same way, when either SoC < 1 becomes SoC = 1 or SoC > SoC

_{min}becomes SoC = SoC

_{min}, the algorithm jumps to the group of cells below.

#### Solar-Forecast-Based Charging Strategy

- During work days, the system checks the weather forecast at evening. If the next-day morning sunlight is high enough, the car is charged by storage and LV grid until 90% of full charge. In the morning, the PV power will top off the charge before the user takes the car.
- If the user expects to remain at home next day, then the car is not charged at all during evening and night. The PV power will charge the car during the next day, and then the remaining part is redirected to storage and LV grid.

#### 3.5. The PV–BS Electricity Cost

#### 3.6. Total Cost of Ownership Model

## 4. Case Study

#### 4.1. PV Module

- Technical assumptions: ${P}_{n}$: 4 kWp; degradation rate $\text{}{d}_{r}$: 0.90% per year;
- Economic assumptions: PV overnight capital costs (OCS): 2000 €/kWp + 10%VAT; fiscal incentives: 50% tax rebate on the OCS; fixed operation and maintenance costs (FO&MC): 2.5% of the initial costs; guaranteed lifespan: 30 years; the capital structure is 50% equity with 1% cost of equity and 50% debt with a 5% cost of debt, which results in a weighted average cost of capital (WACC) rate of 3%; price recognized by the DSO (PR) = 0.0398 €/kWh.

#### 4.2. Battery Storage

- Technical assumptions: nameplate and usable capacity: 10 kWh;
- Economic assumptions: battery price: 700 €/kWh + 10% VAT; fiscal incentives: 50% tax refund; guaranteed lifespan: 10 years.

#### 4.3. EV and ICEV

- Nissan Leaf. Concerning the initial costs, we use the following values: MSRP: €39,475; battery capacity of 40 kWh; registration costs (RC): €522; government subsidies (SUB): €6000 in line with the recent Italian policies, supporting EV uptake. Concerning the annual operating costs, we assume the following values: insurance premium is highly affected not only by factors related to vehicle’s features but also by driver’s characteristics (e.g., past accidents history), residential area, and the commercial strategy of the insurance company. In this analysis, we assume as a reference user a 40-year-old man living in the Friuli Venezia Giulia Region. We use quotes obtained from “facile.it”, a website comparing the most important Italian insurance companies obtaining a value INS = €359; repair and maintenance cost (MAINT): 0.05 €/km, assuming a value 30% lower than that of ICEVs because of regenerative breaking, no oil change, spark plugs, or transmission fluids; circulation tax (CT): €0 (in Italy EVs are exempt from the annual circulation tax); home charging equipment (HC): €1000; resale value: η = 20% of the MSRP after a period of ownership T = 8 years, electricity consumption in urban areas: 14.2 kWh/100 km; electricity consumption in extra-urban areas: 20.6 kWh/100 km; weather-adjustment factor (γ): 1.15, i.e., we assume for EVs a 30% decrease in electricity efficiency when driving at very high (in summer) or very low (in winter) temperatures; electricity price from the electrical grid (net of the fixed costs and including taxes on variable costs): 0.119 €/kWh.
- Nissan Qashqai: MSRP: €29,000; registration costs (RC): €577; circulation tax (CT): €270; insurance premium (INS): €412; repair and maintenance cost (MAINT): 0.07 €/km; resale value: η = 40% of the MSRP after a period of ownership T = 8 years; fuel efficiency in urban areas: 7 l/100 km; fuel efficiency in extra-urban areas: 5 l/100 km; petrol price = €1.645 (the value is kept constant over the vehicle lifetime).

#### 4.4. Financial Assumptions

## 5. Results

- The percentage of the electricity drawn directly from PV with respect to the total electricity needed to charge the EV (%PV2EV);
- The percentage of electricity from storage to EV (%BS2EV);
- The percentage of electricity withdrawn from the electrical grid (%Grid2EV);
- The percentage of electricity produced by PV and self-consumed for the household domestic load (%PV2HDL);
- The percentage of electricity produced by PV and discharged into the electrical grid (%PV2Grid);
- The levelized cost of the photovoltaic recharge (LCOPR);
- The levelized cost of storage (LCOS);
- The PV–BS electricity cost;
- The TCO/km of the EV coupled with a PV–BS system (EV
_{PV–BS}); - The TCO/km of the EV charged only from the electrical grid (EV
_{grid}); - The TCO/km of the petrol fueled ICEV.

#### 5.1. Base-Case Scenario without the Solar-Forecast-Based Charging Strategy

#### 5.2. Base Case Scenario with the Solar-Forecast-Based Charging Strategy

#### 5.3. Simulative Scenarios

#### 5.3.1. Simulative Scenario 1: 50% Reduction of the Storage Capacity

_{PV–BS}is competitive with the ICEV when the ADT is above 9000 km. This finding highlights the trade-off between the economic and the energy self-sufficiency goals and the need to optimize the PV–BS–EV system according to the specific driving profile of the user. We plan to analyze this issue in more depth in a future research project.

#### 5.3.2. Simulative Scenario 2: Removing Purchase Subsidies on EV and Tax Deductions on the PV and BS Equipment

_{PV–BS}has a lower TCO/km relative to the ICEV only when ADT is higher than 25,000 km.

## 6. Discussion and Conclusions

_{PV–BS}cost competitive with the ICEV. Therefore, we argue that the economic viability of the PV–BS–EV bundle is still heavily dependent on fiscal incentives, as previously argued by [14].

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature (NA: Not Applicable)

UNIT | ||

AAOC | Average annual operating costs | € |

ADT | Annual distance traveled | km |

AIC | Annualized initial cost | € |

AOC | Annual operating costs | € |

APR | Annual percentage rate | % |

BC | Battery capacity | kWh |

BS | Battery storage | NA |

CRF | Capital recovery factor | % |

CT | Circulation tax | € |

DARV | Discounted and annualized residual value | € |

dr | Photovoltaic module degradation rate | %/year |

DSO | Distribution system operator | NA |

E_{0} | Yield of the photovoltaic plant | kWh/kWp/year |

EVs | Electrical vehicles | NA |

FE | Fuel/electricity cost | € |

FE_E | Fuel/electricity efficiency | Liter or kWh/100 km |

FE_P | Fuel/electricity price | €/liter or €/kWh |

FO&MC | Fixed operation and maintenance costs (photovoltaic plant) | % |

HC | Home-charging equipment cost | € |

i | Interest rate | % |

IC | Initial cost | € |

ICEVs | Internal combustion engine vehicles | NA |

INS | Insurance premium | € |

LCOE | Levelized cost of energy | €/kWh |

LCCOS | Annualized life cycle cost of storage | €/kWh |

LCOPR | Levelized cost of photovoltaic recharge | €/kWh |

MSRP | Manufacturer suggested retail price | € |

MAINT | Maintenance cost (vehicle) | € |

OCS | Overnight capital cost | € |

PHEV | Plug-in hybrid electrical vehicle | NA |

PR | Price recognized for the energy injected into the grid | €/kWh |

PV | Photovoltaic | NA |

PVGIS | Photovoltaic geographical information system | NA |

PV2GRID | Electricity produced by the photovoltaic plant and injected into the grid | % |

RC | Registration cost | € |

RD | Retailer discount | € |

SOC | State of charge | % |

SUB | Government subsidies | € |

TCO | Total cost of ownership | €/km |

WACC | Weighted average cost of capital | % |

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**Figure 2.**Energy source used to charge the EV and electricity discharged to the electrical grid, with varying ADT in the base-case scenario, without the solar-forecast-based strategy.

**Figure 3.**Energy source used to charge the EV and electricity discharged into the electrical grid with varying ADT in the base-case scenario with the solar-forecast-based strategy.

**Figure 4.**LCOPR, LCOS, and PV–BS electricity cost in the base-case scenario with solar forecast-based strategy.

**Figure 6.**Energy source used to charge the EV and electricity discharged into the electrical grid with varying ADT in Scenario 1.

Work Day | Day Trip | |
---|---|---|

Departure interval (h) | (7.8, 8.1) | (8, 10) |

Return interval (h) | (18, 20) | (16, 20) |

Distance traveled (km) | (20, 25) | (50, 100) |

Cold Season | Mild Season | |
---|---|---|

Departure interval (h) | (8, 9) | (7, 8) |

Return interval (h) | (17, 19) | (18, 20) |

Distance traveled (km) | (110, 145) | (150, 200) |

Sun | Car | SoC | Main Action | Conditions | Derived Actions | |
---|---|---|---|---|---|---|

A | Yes | Yes | >SoC_{min} | PV power to car | PV power > P_{charge} | SoC < 1: ΔPV power to storage |

SoC = 1: ΔPV power to LV grid | ||||||

PV power < P_{charge} | 1—Storage power to car 2—LV grid power to car | |||||

=SoC_{min} | PV power to car | PV power > P_{charge} | SoC < 1: ΔPV power to storage | |||

SoC = 1: ΔPV power to LV grid | ||||||

PV power < P_{charge} | LV grid power to car | |||||

B | Yes | No | <1 | PV power to storage | ||

=1 | PV power to LV grid | |||||

C | No | Yes | >SoC_{min} | 1—Storage power to car 2—LV grid power to car | ||

=SoC_{min} | LV grid power to car | |||||

D | No | No | - | No action takes place |

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## Share and Cite

**MDPI and ACS Style**

Scorrano, M.; Danielis, R.; Pastore, S.; Lughi, V.; Massi Pavan, A.
Modeling the Total Cost of Ownership of an Electric Car Using a Residential Photovoltaic Generator and a Battery Storage Unit—An Italian Case Study. *Energies* **2020**, *13*, 2584.
https://doi.org/10.3390/en13102584

**AMA Style**

Scorrano M, Danielis R, Pastore S, Lughi V, Massi Pavan A.
Modeling the Total Cost of Ownership of an Electric Car Using a Residential Photovoltaic Generator and a Battery Storage Unit—An Italian Case Study. *Energies*. 2020; 13(10):2584.
https://doi.org/10.3390/en13102584

**Chicago/Turabian Style**

Scorrano, Mariangela, Romeo Danielis, Stefano Pastore, Vanni Lughi, and Alessandro Massi Pavan.
2020. "Modeling the Total Cost of Ownership of an Electric Car Using a Residential Photovoltaic Generator and a Battery Storage Unit—An Italian Case Study" *Energies* 13, no. 10: 2584.
https://doi.org/10.3390/en13102584