# A Robust Optimization for Designing a Charging Station Based on Solar and Wind Energy for Electric Vehicles of a Smart Home in Small Villages

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## Abstract

**:**

## 1. Introduction

## 2. Infrastructure of the Charging Station

## 3. System Modeling and Specification

- SOC: The state of charge of a battery system indicates the available capacity of the battery system as a percentage of the rated capacity. The nominal or available capacity is given by the manufacturer and represents the maximum charge of the battery that can be stored. As neither depletion nor overcharge in the battery is desirable, the SOC of the battery must be kept within proper limits—between 30% and 100%. As such, the charge/discharge time of the battery system will be determined by the limitation in the SOC for the battery, as well as the energy left in the battery.
- Depth of discharge (DOD): Cycle life is an important parameter of a battery system that decreases as the DOD increases. Many cell chemistries cannot tolerate deep discharge and may be permanently damaged after complete discharge. Thus, the DOD should be limited to an appropriate range to protect the battery from death and increase the cycle life of the battery. This range can be deduced from the limitation that SOC should not drop below a critical level.
- Battery throughput: This corresponds to the amount of energy that can be cycled in the battery system during one year.

_{b}) in series with an ideal voltage source (E

_{0}). The open circuit voltage (V

_{OC}) gives the voltage across the battery. Meanwhile, the voltage across the resistor R

_{b}and battery gives the terminal voltage of the battery V

_{b}, as shown in Figure 3. R

_{b}is a function of the SOC of the battery system (i.e., it varies depending on the SOC).

_{b}can be expressed as

_{o}is the resistor of the battery in full charge (Ω) and k is the capacity coefficient. S is the SOC factor and varies from 0, fully discharged, to 1, fully charged, given as follows:

_{10}denotes the 10 h capacity (Ah) at the reference temperature, h is the time of discharging (h), and A is the discharge current (A). From this, we can derive the relationship between the battery capacity and the discharge range as

_{lifetime,i}) of the batteries is calculated as

_{i}is the number of cycles to failure, d

_{i}is the depth of discharge (%), q

_{max}is the maximum capacity of the battery (Ah), and V

_{nom}is the nominal voltage of the battery (V). It must be noted that a fraction for “d” must be used in Equation (5).

_{T}, C

_{M}, and C

_{C}denote the total cost, the maintenance cost, and capital cost of the system, respectively.

## 4. Results and Discussion

^{2}/day. The highest value of solar radiation was recorded in May. The annual average monthly wind speed and solar radiation at the site were recorded as 4.92 m/s, and 4.48 kWh/m

^{2}/day, respectively. The annual wind speed was recorded as 4.92 m/s and the maximum wind speed as 29.70 m/s.

_{lifetime,i}) can be calculated from the lifetime curve of the battery as

_{i}is the number of cycles to failure, d

_{i}is the depth of discharge (%), q

_{max}is the maximum capacity of the battery (Ah), and V

_{nom}is the nominal voltage of the battery (v).

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Geographical layout of the proposed location, Jung-Ma-Do Island, South Korea (Google Maps, 2015).

**Figure 7.**Weibull distribution probability at the island, (scale factor: 5.53 m/s; shape factor: 1.79 extracted by the maximum likelihood method [22]).

**Figure 8.**Power–speed characteristic curve of the Osiris 10 kW wind turbine [24].

**Figure 15.**Relationship between the monthly variation in excess electricity and charging EV batteries.

**Table 1.**eTuk characteristics [23].

Items | Specification |
---|---|

Electric motor | DC motor |

Maximum speed | 50 km/h |

Passengers | 3 |

Maximum payload | 300 kg |

Outline (length × width × height) | 2980 × 1410 × 1850 (mm) |

Battery options | Lead acid or lithium-ion |

Items | Specification |
---|---|

Home charging | Level 1/2, mode ½ |

Semipublic charging | Level 2, mode 2 |

Public charging | Level 2/3, mode 2/3, DC charging (mode 4) |

Items | Specification |
---|---|

Cost of photovoltaic array ($/kW ) | 2613.45 |

Replacement cost of photovoltaic array ($/kW ) | 2287.75 |

Operation and maintenance cost of PV array ($/kW/yr) | 17.56 |

Working life of the photovoltaic modules (yr) | 20 |

Items | Specification |
---|---|

Capital cost of wind turbine ($/kW) | 6793.30 |

Replacement cost of wind turbine ($/kW) | 5248.50 |

Operation and maintenance cost ($/kW/yr) | 97.55 |

Operational life of wind turbine (yr) | 20 |

Hub height (m) | 20 |

Items | Specification |
---|---|

Capital cost of power converter ($/kW) | 2289.51 |

Replacement cost of power converter ($/kW) | 2074.87 |

Operation and maintenance cost of power converter ($/kW/yr) | 10.04 |

Lifetime of inverter (yr) | 20 |

Efficiency of inverter (%) | 95 |

Capacity relative to inverter (%) | 100 |

Efficiency of rectifier (%) | 85 |

Items | Specification |
---|---|

Nominal capacity (Ah) | 280 |

Nominal voltage for one cell (V) | 3.2 |

Number of cells in the battery module * | 92 |

Capital cost ($/kWh) | 652 |

Replacement cost ($/kWh) | 652 |

Operation and maintenance cost ($/kWh/yr) | 21.74 |

Initial state of charge (%) | 95 |

Minimum state of charge (%) | 5 |

Round trip efficiency (%) | 95 |

Float life (yr) | 10 |

Maximum charge rate (A/Ah) | 0.321429 |

Maximum charge current (A) | 140 |

Maximum discharge current (A) | 280 |

Maximum capacity (Ah) | 282.634 |

Capacity ratio c[-] | 0.822 |

Rate constant k[1/h] | 2.758 |

Depth of Discharge (%) | Cycles to Failure |
---|---|

80 | 1000 |

50 | 2000 |

30 | 4000 |

WT (kW) | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |
---|---|---|---|---|---|---|---|---|---|---|

WT fraction (%) | 5.26 | 13.33 | 23.07 | 33.33 | 41.66 | 50 | 41.17 | 47.05 | 50 | 52.63 |

PV (kW) | 180 | 130 | 100 | 80 | 70 | 60 | 100 | 90 | 90 | 90 |

PV fraction (%) | 94.73 | 86.66 | 76.92 | 66.66 | 58.33 | 50 | 58.82 | 52.94 | 50 | 47.36 |

Total power (kW) | 190 | 150 | 130 | 120 | 120 | 120 | 170 | 170 | 180 | 190 |

Inverter (kW) | 35 | 35 | 30 | 30 | 30 | 35 | 30 | 35 | 30 | 30 |

ESS (EA) | 368 | 368 | 368 | 368 | 368 | 368 | 276 | 276 | 276 | 276 |

NPC ($1,000,000) | 1.27 | 1.2 | 1.18 | 1.2 | 1.26 | 1.33 | 1.4 | 1.47 | 1.54 | 1.63 |

Cost of energy ($/kWh) | 1.14 | 1.08 | 1.06 | 1.08 | 1.13 | 1.20 | 1.26 | 1.32 | 1.39 | 1.46 |

Operating cost ($1000) | 32 | 31 | 31 | 32 | 33 | 35 | 32 | 33 | 35 | 36 |

Initial capital ($1000) | 858 | 795 | 773 | 789 | 831 | 884 | 985 | 1038 | 1095 | 1163 |

ESS Strings | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|---|---|---|

WT (kW) | 30 | 30 | 30 | 30 | 20 | 10 | 10 | 10 | 10 | 10 |

PV (kW) | 150 | 100 | 80 | 70 | 80 | 90 | 80 | 70 | 70 | 70 |

Inverter (kW) | 30 | 30 | 30 | 30 | 30 | 35 | 30 | 35 | 30 | 30 |

NPC ($1,000,000) | 1.2 | 1.18 | 1.24 | 1.34 | 1.42 | 1.51 | 1.59 | 1.71 | 1.82 | 1.95 |

Cost of energy ($/kWh) | 1.08 | 1.06 | 1.12 | 1.21 | 1.28 | 1.36 | 1.43 | 1.53 | 1.64 | 1.76 |

Operating cost ($1000) | 28 | 31 | 36 | 41 | 46 | 50 | 55 | 60 | 66 | 71 |

Initial capital ($1000) | 844 | 773 | 781 | 815 | 833 | 863 | 885 | 930 | 979 | 1039 |

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**MDPI and ACS Style**

Ahadi, A.; Sarma, S.; Moon, J.S.; Kang, S.; Lee, J.-H.
A Robust Optimization for Designing a Charging Station Based on Solar and Wind Energy for Electric Vehicles of a Smart Home in Small Villages. *Energies* **2018**, *11*, 1728.
https://doi.org/10.3390/en11071728

**AMA Style**

Ahadi A, Sarma S, Moon JS, Kang S, Lee J-H.
A Robust Optimization for Designing a Charging Station Based on Solar and Wind Energy for Electric Vehicles of a Smart Home in Small Villages. *Energies*. 2018; 11(7):1728.
https://doi.org/10.3390/en11071728

**Chicago/Turabian Style**

Ahadi, Amir, Shrutidhara Sarma, Jae Sang Moon, Sangkyun Kang, and Jang-Ho Lee.
2018. "A Robust Optimization for Designing a Charging Station Based on Solar and Wind Energy for Electric Vehicles of a Smart Home in Small Villages" *Energies* 11, no. 7: 1728.
https://doi.org/10.3390/en11071728