# Comparison of the Economic and Environmental Performance of V2H and Residential Stationary Battery: Development of a Multi-Objective Optimization Method for Homes of EV Owners

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## Abstract

**:**

_{2}emissions as indices and compared the performances of V2H and SB. As a case study, a typical detached house in Japan was assumed, and we evaluated the economic and environmental aspects of solar power self-consumption using V2H or SB. The results showed that non-commuting EV owners should invest in V2H if the investment cost of a bidirectional charger is one third of the current cost as compared with inexpensive SB, in 2030. In contrast, our results showed that there were no advantages for commuting EV owners. The results of this study contribute to the rational setting of investment costs to increase the use of V2H by EV owners.

## 1. Introduction

_{2}emissions as indices. The method is formulated in a mixed integer linear programming (MILP) framework, which generalizes the model constructed by the authors [10]. The case study analyzes the sensitivity of the cost of the bidirectional charger to a low-cost SB in the future, assuming different uses of EV. The results of this study provide guidance on the future cost targets of bidirectional chargers to motivate EV owners.

## 2. Method

#### 2.1. Modeling

_{2}emissions at home. Equation (1) shows the objective function to minimize the weighted sum of the cost and CO

_{2}emissions:

_{1}and x

_{3}represent the hourly amount of energy purchased from the grid and sold back to the grid, respectively; y

_{2}and y

_{8}denote the size of PV and SB, respectively; and z

_{18}represents the binary variable, which denotes the investment for the bidirectional charger for V2H (z

_{18}= 0 when not investing in a bidirectional charger, and z

_{18}= 1 when investing in a bidirectional charger). A set of Pareto solutions related to the economy and environment can be calculated with the weight value w from 0 to 1, i.e., the minimum CO

_{2}solution is when w = 0, and the minimum cost solution is when w = 1. In Equation (1), f

_{cost}represents the total energy cost during the time horizon of the optimization problem T (hour) and is calculated using the sum of the grid purchase costs, the income from selling power to the grid, and the equipment costs as follows:

_{buy}(t) and the selling unit price p

_{sell}(t). C

_{PV}, C

_{SB}, and C

_{V2H}are cost coefficients of PV, SB, and the bidirectional charger of base size (1 kW, 1 kWh, and 1 unit, respectively), and these values include the investment and maintenance costs as follows:

_{PV}, I

_{SB}, and I

_{V2H}are investment costs; L

_{PV}, L

_{SB}, and L

_{V2H}are the product life (in years); and M

_{PV}, M

_{SB}, and M

_{V2H}are annual maintenance costs. The value 8760 in Equations (3) to (5) refers to the number of hours in a year. Notably, the investment and other costs of the EV are not included because it is assumed to be an independent investment for mobility reasons only. In Equation (1), f

_{co2}represents the total CO

_{2}emission from the grid power during the time horizon of the optimization problem T and is calculated by Equation (6).

_{2}(t) can be calculated by the normalized power production P

_{PV_unit}(t) and the size of PV y

_{2}.

_{16}(t) and x

_{19}(t) are always equivalent to the power demands D

_{EV}(t) and D

_{home}(t), respectively. P

_{PV_unit}(t), D

_{EV}(t), and D

_{home}(t) are provided as exogenous variables. In other words, they are perfectly predicted in the optimization process.

_{SB_Ch.}η

_{SB_DisCh.}< 1, η

_{EV_Ch.}η

_{EV_DisCh.}< 1).

_{8}(0) and x

_{14}(0) are given as a predetermined ratio r

_{SB_in}

_{i.}and r

_{EV_ini.}to the capacity sizes (i.e., x

_{8}(0) = y

_{8}r

_{SB_in}

_{i.}and x

_{14}(0) = Cap.

_{EV}r

_{EV_in}

_{i.}). In addition, the SoC of the batteries has a lower and upper limit, as follows:

_{EV_SOC}and ub

_{EV_SOC}are given from the specification of the EV.

_{EV_Ch.}and P

_{EV_DisCh.}are the maximum power of the EV charger and discharger, and δ

_{EV}(t) is a binary parameter that represents the absence of the EV based on its driving pattern (δ

_{EV}(t) = 0 while the EV is absent, and δ

_{EV}(t) = 1 while the EV is parked at home).

- To obtain min{f
_{cost}(x_{1}, x_{3}, y_{2}, y_{8}, z_{18})} in Equation (1), the problem takes the following form:min. objective function Equation (2)

subject to: optimization constraints Equations (7) to (28) - To obtain min{f
_{co2}(x_{1})} in Equation (1), the problem takes the following form:min. objective function Equation (3)

subject to: optimization constraints Equations (7) to (28) - Substitute min{f
_{cost}(x_{1}, x_{3}, y_{2}, y_{8}, z_{18})} and min{f_{co2}(x_{1})} calculated in the previous two steps into Equation (1) to solve the problem described as following form:min. objective function Equation (1)

subject to: optimization constraints Equations (7) to (28)

#### 2.2. Sample System

_{18}is forcibly given as 1 and an optimization calculation is performed. All the case studies are conducted using the MATLAB Optimization Toolbox [11] as a solver based on the branch and bound method.

_{EV}(t), can be calculated by their driving pattern and the vehicle efficiency shown in Table 2, and are shown in Figure 4a and b, respectively. The upper limit and lower limit of SoC are empirically set to avoid battery deterioration.

_{home}(t), estimated using previously presented information [15]. Figure 6 shows the PV power generation curve per unit capacity, P

_{PV_unit}(t), estimated from solar radiation data [16] for Nagoya city, where the capacity factor of the PV is 13.98%.

_{SB_Ch.}, r

_{SB_DisCh.}) is set to 0.333, which is the average value of residential batteries in the current Japanese market [20] (i.e., 3 h to fully charge or discharge battery). A lithium ion battery is considered for these characteristics of SB. The costs of the bidirectional charger for V2H are assumed to differ as per different scenarios, ranging from the current typical price [21] to one third of the current price. The charging and discharging maximum power of the EV (P

_{EV_Ch.}and P

_{EV_DisCh.}) are assumed to be identical to that of a normal charger in Japan.

_{buy}(t) is assumed to be the minimum unit price for domestic customers offered by the Chubu Electric Power company (0.185 €/kWh) [22]. The selling unit price, p

_{sell}(t), is assumed to be 0.04 €/kWh. The adopted CO

_{2}emission rate for grid power was assumed to be the Japanese target value for the year 2030 [23], i.e., 0.37 kg-CO

_{2}/kWh. The price and CO

_{2}efficiency of the grid are assumed to be constant values. Therefore, we ignored the economic impact of SB and V2H due to fluctuations in electricity prices. In other words, we focus on the efficiency of SB and V2H for self-consumption of PV power.

## 3. Results

_{2}emissions for the cases of non-commuter EV. Due to the limited number of calculations, these curves are approximation to the exact Pareto curves [24]. For each curve in Figure 7, the left ends were the results of cost minimization (w = 1) and the right ends show the results of CO

_{2}emission minimization (w = 0). We ensured that the Pareto curves of cases 3 and 4 did not intersect when the investment cost of the bidirectional charger was one third the current cost (i.e., I

_{V2H}is 1200 €/unit). V2H could reduce CO

_{2}emissions and energy costs as compared with SB, if the cost of the bidirectional charger was one third of the current cost. However, when the bidirectional charger cost more than two-thirds of the current cost, the economic and environmental performance of V2H is lower than that of SB. Figure 8 shows the cost structure and the optimum sizes of PV and SB, with respect to the results of cost minimization. Case 4 has 6.5 kW of PV, which is the largest as compared to other cases. According to Equation (33), if there is no excess PV generation, the levelized cost of electricity [25] of PV (LCOE

_{PV}) is calculated as 0.073 €/kWh, which is lower than the purchase unit price from the grid. In Equation (36), C

_{PV}is calculated by Equation (3), and the discount rate is not considered in this study (see Appendix A for details).

_{2}minimization, Figure 13 shows that the PV and SB sizes reached the installation upper limits to reduce the use of grid power as far as possible. The self-consumption rate, r

_{sc}, shown in Figure 9 is calculated by Equation (37).

_{2}emission in case 4 is larger than that in case 3. Under the conditions applied in this study, it is found that the SB with a capacity of 15 kWh can charge excess PV more than the EV because of the probability of the absence of EV.

_{2}emission for the cases of commuter EV. In the case of a commuter car, the tendency of cases 5, 6, and 7 is similar to the case of a non-commuter car. However, in case 8, it is clear that even if the cost of V2H is one third the current cost, it is inferior in environmental and economic performance as compared to case 7. This is because the probability of absence during the day time is high and power generation from PV cannot be charged.

## 4. Discussion

## 5. Conclusions

_{2}emissions as indices. We evaluated the economic and environmental efficiency of a typical EV owner’s detached house in Japan as a case study and compared the performance of V2H and SB. As a result, we found that V2H could be better than the low-price SB, in 2030, for non-commuting EV owners if the investment cost of a bidirectional charger is one third the current cost. In contrast, in the case of a commuting EV, V2H would not be economically and environmentally rational because the EV is absent during the daytime. The results of this study will contribute to the rational setting of investment costs for spread and the selection of EV owners to invest in V2H. In future work, we could evaluate additional future scenarios regarding diverse driving patterns using our optimization framework for fluctuations in the grid power price, the cost of PV and SB, the size of the EV battery, and the charge/discharge power of EV.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Set | |

t | index of optimization periods, t = 1, 2, ..., T (hour) |

Variables | |

x_{i}(t) (i = 1, ..., 19) | energy flow or state of charge in period t (kWh) |

y_{2} | size of PV (kW) |

y_{8} | size of SB (kWh) |

z_{18} | necessity of V2H system (binary variable) (unit) |

f_{cost} | total energy cost (€) |

f_{CO2} | total CO_{2} emission (kg-CO_{2}) |

Parameters | |

T | time horizon of the optimization problem (hour) |

p_{buy}(t)
| purchase unit price in period t (€/kWh) |

p_{sell}(t)
| selling unit price in period t (€/kWh) |

C_{PV} | cost coefficients of PV (€/kW/hour) |

C_{SB} | cost coefficients of SB (€/kWh/hour) |

C_{V2H} | cost coefficients of V2H (€/unit/hour) |

I_{PV} | investment cost of PV (€/kW) |

I_{SB} | investment cost of SB (€/kWh) |

I_{V2H} | investment cost of V2H (€/unit) |

M_{PV} | annual maintenance cost of PV (€/kW/year) |

M_{SB} | annual maintenance cost of SB (€/kWh/year) |

M_{V2H} | annual maintenance cost of V2H (€/unit/year) |

L_{PV} | product life of PV (year) |

L_{SB} | product life of SB (year) |

L_{V2H} | product life of V2H (year) |

e_{grid} | CO_{2} emission rate for grid power (kg-CO_{2}/kWh) |

P_{PV_unit}(t)
| normalized power production of PV in period t (kWh/kW) |

D_{EV}(t)
| power demand to drive EV in period t (kWh) |

D_{home}(t)
| residential power demand in period t (kWh) |

Cap._{EV} | capacity of EV battery (kWh) |

r_{EV_ini.} | ratio of initial SoC |

lb_{EV_SOC} | lower limit of SoC (kWh) |

ub_{EV_SOC} | upper limit of SoC (kWh) |

PV_{max} | maximum size of PV (kW) |

SB_{max} | maximum size of SB (kW) |

η_{SB_Ch.} | efficiency of charging for SB |

η_{SB_DisCh.} | efficiency of discharging for SB |

r_{SB_ini.} | ratio of initial SoC for SB |

r_{SB_Ch.} | ratio of charging power for SB |

r_{SB_DisCh.} | ratio of discharging power for SB |

η_{EV_Ch.} | efficiency of charging for EV |

η_{EV_DisCh.} | efficiency of discharging for EV |

P_{EV_Ch.} | charging power for EV (kW) |

P_{EV_DisCh.} | discharging power for EV (kW) |

δ_{EV} (t)
| the absence of the EV in period t |

DT | departure time (hour) |

CT | comeback time (hour) |

ST | stay time (min) |

DP | driving period (min) |

TL | trip length (km) |

V | average driving speed of EV (km/h) |

w | weight of objectives |

## Appendix A

- LCOE = the levelized cost of electricity;
- I
_{i}= investment expenditures in the year i; - M
_{i}= operations and maintenance expenditures in the year i; - F
_{i}= fuel expenditures in the year i; - E
_{i}= electricity generation in the year i;r = discount rate; and - n = life of the system.

_{PV}was formulated into Equation (36) in the main text with the following process. The variables in Equation (A1) can be rewritten using the following nomenclature in Section 2: ${I}_{i}={I}_{PV}/{L}_{PV}$, ${M}_{i}={M}_{PV}$, ${E}_{i}={\sum}_{t=1}^{8760}{P}_{PV\_unit}\left(t\right)$, and n = L

_{PV}. The PV needs no fuel, F

_{i}= 0 and the discount rate is assumed to be zero in this study, r = 0. Therefore,

_{PV}, L

_{PV}, M

_{PV}and P

_{PV_unit}(t) are independent of the year i:

_{PV}in Equation (3) into Equation (A3), Equation (A4) matches Equation (36).

## References

- Ministry of Economy, Trade and Industry. The 5th Strategic Energy Plan; METI: Tokyo, Japan, 2018. Available online: https://www.enecho.meti.go.jp/en/category/others/basic_plan/5th/pdf/strategic_energy_plan.pdf (accessed on 1 October 2019).
- Kaschub, T.; Jochem, P.; Fichtner, W. Interdependencies of Home Energy Storage between Electric and Stationary Battery. World Electr. Veh. J.
**2013**, 6, 1144–1150. [Google Scholar] [CrossRef] - Erdinc, O.; Paterakis, N.G.; Mendes, T.D.P.; Bakirtzis, A.G.; Catalao, J.P.S. Smart Household Operation Considering Bi-directional EV and ESS Utilization by Real-Time Pricing-Based DR. IEEE Trans. Smart Grid
**2015**, 6, 1281–1291. [Google Scholar] [CrossRef] - Wu, X.; Hu, X.; Moura, S.; Yin, X.; Pickert, V. Stochastic control of smart home energy management with plug-in electric vehicle battery energy storage and photovoltaic array. J. Power Sources
**2016**, 333, 203–212. [Google Scholar] [CrossRef] - Erdinc, O.; Paterakis, N.G.; Pappi, I.N.; Bakirtzis, A.G.; Catalao, J.P.S. A new perspective for sizing of distributed generation and energy storage for smart households under demand response. Appl. Energy
**2015**, 143, 26–37. [Google Scholar] [CrossRef] - Wu, X.; Hu, X.; Teng, Y.; Qian, S.; Cheng, R. Optimal integration of a hybrid solar-battery power source into smart home nanogrid with plug-in electric vehicle. J. Power Sources
**2017**, 363, 277–283. [Google Scholar] [CrossRef] - Naghibi, B.; Masoum, M.A.S.; Deilami, S. Effects of V2H Integration on Optimal Sizing of Renewable Resources in Smart Home Based on Monte Carlo Simulations. IEEE Power Energy Technol. Syst. J.
**2018**, 5, 73–84. [Google Scholar] [CrossRef] - Technology Collaboration Programme on Hybrid and Electric Vehicles (HEV TCP). Hybrid and Electric Vehicles -The Electric Drive Hauls-; International Energy Agency: Paris, France, 2019; pp. 67–73. Available online: http://www.ieahev.org/assets/1/7/Report2019_WEB_New_(1).pdf (accessed on 1 October 2019).
- Zakariazadeh, A.; Jadid, S.; Siano, P. Multi-objective scheduling of electric vehicles in smart distribution system. Energy Convers. Manag.
**2014**, 79, 43–53. [Google Scholar] [CrossRef] - Kataoka, R.; Shichi, A.; Yamada, H.; Iwafune, Y.; Ogimoto, K. Evaluation of Economic and Environmental Superiority of EV Battery in Power Systems: Development of Multi-objective Optimized Model for V2H. In Proceedings of the 32nd Electric Vehicle Symposium (EVS32), Lyon, France, 19–22 May 2019. [Google Scholar]
- MathWorks, Optimization Toolbox. Available online: https://jp.mathworks.com/help/optim/index.html?lang=en (accessed on 1 October 2019).
- Mustapha, A.; Fonseca, J.G.D.S., Jr.; Oozeki, T.; Iwafune, Y. Evaluation of Residential PV-EV System for Supply and Demand Balance of Power System. IEEJ Trans. Power Energy
**2015**, 135, 27–34. (In Japanese) [Google Scholar] [CrossRef] - Iwafune, Y.; Ogimoto, K.; Azuma, H. Integration of Electric Vehicles into the Electric Power System Based on Results of Road Traffic Census. Energies
**2019**, 12, 1849. [Google Scholar] [CrossRef] - The Energy Conservation Center, Japan. Results of the Survey of Standby Power Consumption. 2013. (In Japanese) [Google Scholar]
- Morita, K.; Manabe, Y.; Kato, T.; Funabashi, T.; Suzuoki, Y. An Evaluation of Average Electricity Demand Characteristics with Hundreds of Households. J. Jpn. Soc. Energy Resour.
**2016**, 38, 20–29. (In Japanese) [Google Scholar] [CrossRef] - New Energy and Industrial Technology Development Organization, MEteorological Test data for PhotoVoltaic System. Available online: http://www.nedo.go.jp/library/nissharyou.html (accessed on 1 October 2019).
- Power Generation Cost Analysis Working Group, Report on Analysis of Generation Costs, Etc. for Subcommittee on Long-term Energy Supply- demand Outlook. 2015. Available online: https://www.meti.go.jp/english/press/2015/pdf/0716_01b.pdf (accessed on 1 October 2019).
- Kobashi, T.; Say, K.; Wang, J.; Yarime, M. Techno-economic analyses of PV, PV + battery, PV + EV for household in Kyoto and Shenzhen towards 2030. In Proceedings of the 35th Energy Systems Economic Environment Conference, Tokyo, Japan, 30 January 2019; pp. 383–386. (In Japanese). [Google Scholar]
- Ministry of Economy, Trade and Industry. Available online: http://www.meti.go.jp/committee/kenkyukai/energy_environment/energy_resource/pdf/ 005_08_00.pdf (accessed on 1 October 2019).
- Mitsubishi Research Institute, Inc. 2017. Available online: https://www.meti.go.jp/meti_lib/report/H28FY/000479.pdf (accessed on 1 October 2019).
- Nichicon Corp., EV Power Station. Available online: https://www.nichicon.co.jp/products/v2h/about/ (accessed on 1 October 2019).
- Chubu Electric Power Co. Inc. Available online: http://www.chuden.co.jp/home/home_menu/home_basic/otoku/index.html (accessed on 1 October 2019).
- The Federation of Electric Power Companies of Japan, Expanding Use of Non-Fossil Energy Sources. Available online: https://www.fepc.or.jp/english/environment/global_warming/nuclear_lng/ (accessed on 1 October 2019).
- Hara, T. Technology Assessment based on Range Analysis of the Linear-Programming Bottom-up Energy Systems Model. J. Jpn. Soc. Energy Resour.
**2019**, 40, 202–219. (In Japanese) [Google Scholar] [CrossRef] - International Renewable Energy Agency; Data Methodology. 2015. Available online: http://dashboard.irena.org/download/Methodology.pdf (accessed on 1 October 2019).
- Landi, M. Vehicle-to-Grid developments in the UK. In Proceedings of the 32nd Electric Vehicle Symposium (EVS32), Lyon, France, 19–22 May 2019. [Google Scholar]

**Figure 7.**Pareto solution of the cost and amount of CO

_{2}emission for the cases of non-commuter EV.

**Figure 8.**Cost structure and the optimum sizes of PV and stationary battery (SB) of the minimum cost solution for the cases of non-commuter EV.

**Figure 9.**Optimized energy flow in case 3 on the day with large amount of PV power generation (

**a**) residential supply-demand balance, (

**b**) operation schedule of EV battery, and (

**c**) operation schedule of SB.

**Figure 10.**Optimized energy flow in case 4 on the day with large amount of PV power generation (

**a**) residential supply-demand balance and (

**b**) operation schedule of EV battery with vehicle-to-home (V2H).

**Figure 11.**Optimized energy flow in case 3 on the day with small amount of PV power generation (

**a**) residential supply-demand balance, (

**b**) operation schedule of EV battery, and (

**c**) operation schedule of SB.

**Figure 12.**Optimized energy flow in case 4 on the day with small amount of PV power generation (

**a**) residential supply-demand balance and (

**b**) operation schedule of EV battery with V2H.

Case | EV Driving Pattern | System Configurations | |||
---|---|---|---|---|---|

Grid | PV | SB | V2H | ||

1 | Non-commuter | ○ | - | - | - |

2 | ○ | ○ | - | - | |

3 | ○ | ○ | ○ | - | |

4 | ○ | ○ | - | ○ | |

5 | Commuter | ○ | - | - | - |

6 | ○ | ○ | - | - | |

7 | ○ | ○ | ○ | - | |

8 | ○ | ○ | - | ○ |

Vehicle efficiency | 7 | (km/kWh) | |

Capacity of EV battery | (Cap._{EV}) | 40 | (kWh) |

Ratio of initial SoC | (r_{EV_ini.}) | 0.5 | |

Lower limit of SoC | (lb_{EV_SOC}) | 8 | (kWh) |

Upper limit of SoC | (ub_{EV_SOC}) | 32 | (kWh) |

Equipment | Parameter | |||
---|---|---|---|---|

PV | Investment cost | (I_{PV}) | 2064 | (€/kW) |

Maintenance cost | (M_{PV}) | 1% of I_{PV} | (€/kW/year) | |

Product life | (L_{PV}) | 30 | (year) | |

Maximum size | (PV_{max}) | 10 | (kW) | |

SB | Investment cost | (I_{SB}) | 240 | (€/kWh) |

Maintenance cost | (M_{SB}) | 2% of I_{SB} | (€/kWh/year) | |

Product life | (L_{SB}) | 10 | (year) | |

Maximum size | (SB_{max}) | 15 | (kWh) | |

Efficiency of charging | (η_{SB_Ch.}) | 1.0 | ||

Efficiency of discharging | (η_{SB_DisCh.}) | 0.86 | ||

Ratio of initial SoC | (r_{SB_ini.}) | 0.5 | ||

Ratio of charging power | (r_{SB_Ch.}) | 0.333 | ||

Ratio of discharging power | (r_{SB_DisCh.}) | 0.333 | ||

Charger or Discharger for EV | Investment cost | (I_{V2H}) | 3600, 2400, 1200 | (€/unit) |

Maintenance cost | (M_{V2H}) | 2% of I_{V2H} | (€/unit/year) | |

Product life | (L_{V2H}) | 10 | (year) | |

Efficiency of charging | (η_{EV_Ch.}) | 0.9 | ||

Efficiency of discharging | (η_{EV_DisCh.}) | 0.9 | ||

Maximum charging power | (P_{EV_Ch.}) | 3.3 | (kW) | |

Maximum discharging power | (P_{EV_DisCh.}) | 3.3 | (kW) |

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## Share and Cite

**MDPI and ACS Style**

Kataoka, R.; Shichi, A.; Yamada, H.; Iwafune, Y.; Ogimoto, K.
Comparison of the Economic and Environmental Performance of V2H and Residential Stationary Battery: Development of a Multi-Objective Optimization Method for Homes of EV Owners. *World Electr. Veh. J.* **2019**, *10*, 78.
https://doi.org/10.3390/wevj10040078

**AMA Style**

Kataoka R, Shichi A, Yamada H, Iwafune Y, Ogimoto K.
Comparison of the Economic and Environmental Performance of V2H and Residential Stationary Battery: Development of a Multi-Objective Optimization Method for Homes of EV Owners. *World Electric Vehicle Journal*. 2019; 10(4):78.
https://doi.org/10.3390/wevj10040078

**Chicago/Turabian Style**

Kataoka, Ryosuke, Akira Shichi, Hiroyuki Yamada, Yumiko Iwafune, and Kazuhiko Ogimoto.
2019. "Comparison of the Economic and Environmental Performance of V2H and Residential Stationary Battery: Development of a Multi-Objective Optimization Method for Homes of EV Owners" *World Electric Vehicle Journal* 10, no. 4: 78.
https://doi.org/10.3390/wevj10040078