# Modeling and Solving Method for Supporting ‘Vehicle-to-Anything’ EV Charging Mode

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## Abstract

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## 1. Introduction

_{2}emissions. As an alternative to traditional petrol or diesel vehicles, EVs are now receiving unprecedented interest from numerous users, investors, and countries [1,2]. According to a recent report on the global electric car stock, worldwide sales of EVs have hit a new record with over 0.75 million in 2016 and the transition to electric road transport is likely to keep growing over the coming decades [3]. The fast development of EVs has also attracted researchers into power systems. EVs should rely on power grids in procuring energy for voyage support. To accommodate the charging of EVs, certain infrastructures such as charging stations, a communication link, and a control interface and system must be developed or implemented. The penetration of massive EVs will also challenge the operation of the power system, since the additional load of EV charging may potentially amplify the daily peak of power load curve and induce some adverse impacts including voltage drops, frequency oscillations, power congestion [4,5], etc.

- (1)
- Based on basic findings of V2H, V2B, V2V, and V2G, all the applications of V2A are considered and a generic model that can adapt to V2A is proposed;
- (2)
- Besides the consideration of EV charging satisfaction for EV user, battery degradation that can affect EV charging/discharging behaviors is also considered in the model through the evaluation via battery charging/discharging cycles;
- (3)
- In the proposed model, each of the EV behaviors (including the status of charging, V2H, V2B, V2V, and V2G) is assigned a single Boolean vector and the created model is then transformed into an INLP (integer nonlinear programming) problem. An intelligent module with treatment for easing the calculated variables is also designed to guide the optimization for different applications of V2A.

## 2. V2A Charging Mode

#### 2.1. V2H Charging Scenario

#### 2.2. V2B Charging Scenario

#### 2.3. V2V Charging Scenario

#### 2.4. V2G Charging Scenario

## 3. Modeling for V2A Charging Mode

_{L,t}and the V2G power price ϑ

_{V2G,t}are two different price signals; (4) the charging/discharging power is assumed to be the rated power of the EV battery.

#### 3.1. Constraints

#### 3.2. Objective Function

_{i}denotes the penalty coefficient for EV charging satisfaction quantified through the deviation of final SOC state from the desired SOC; λ

_{i}represents the penalty coefficient for EV battery degradation quantified through EV charging/discharging cycles.

#### 3.3. Problem Transformation and Solving Method

## 4. Simulation Cases

#### 4.1. Basic Parameters

_{i}and λ

_{i}are uniformly set to 1.5 and 0.15 for the test cases in Section 4.2 to Section 4.4. For the evaluation of battery degradation, Section 4.5 is given to simulate the influences of penalty coefficients ρ

_{i}and λ

_{i}on EV charging/discharging.

_{L,t}and the V2G power price ϑ

_{V2G,t}are given in Figure 8. As stated before, the two price signals are differentiated for incentive purposes of EV charging/discharging activity in response to power load profiles [17]. Meanwhile, the two price vectors are just presupposed for testing purpose, which means the prices are fixed values. As can be seen, there are two high-power price periods (11:00–13:00 and 18:00–20:00) for ϑ

_{L,t}to mitigate the morning and evening peak loads; there is one period (17:00–21:00) with high ϑ

_{V2G,t}to motivate EV discharging since the power demand in the evening can be heavy due to increased residential loads (cooking, lighting, air conditioning, etc. when people return home after work) [25]. In addition, the basic loads for the household, the building, and the charging station are presented in Figure 9.

#### 4.2. Simulation Results for the Household

#### 4.3. Simulation Results for the Building

#### 4.4. Simulation Results for the EV Charging Station

#### 4.5. Consideration for the Issue of Battery Degradation

_{i}are uniformly set for all EVs. The charging scenario of the EV charging station is analyzed with different λ

_{i}and the simulation outcome including the total load and economic profit for the operator side is presented in Figure 14. The charging/discharging behaviors of EVs are given in Figure 15. Since no EV selects discharging under the case ${\lambda}_{i}=0$, the details of EV behaviors for this scenario are therefore omitted here.

_{i}, EVs choose to perform less discharging due to the increased penalty for battery charging/discharging cycles. The users smartly choose to perform charging or discharging at adjacent time slots when λ

_{i}increases, or even give up discharging when ${\lambda}_{i}=1$. Based on Figure 14, the load profile tends to fluctuate more when λ

_{i}decreases, while the power consumption cost changes to be higher when the demand for the lifecycle of EV batteries changes is higher (i.e., with higher λ

_{i}). The battery degradation is therefore an important concern that can affect the charging/discharging behavior of EVs and the operational costs of the power consumption entity.

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Nomenclature

t | Time index |

i | EV index |

ST | Time interval set |

SE | EV set at a power consumption unit |

${Soc}_{EV,min}^{i}$ | Lower SOC limit for the ith EV |

${Soc}_{EV,max}^{i}$ | Upper SOC limit for the ith EV |

${Soc}_{EV,t}^{i}$ | SOC state of the ith EV at time t |

${Soc}_{EV,{t}_{start}}^{i}$ | SOC value at plugging-in time of ith EV |

${Soc}_{EV,{t}_{end}}^{i}$ | SOC value at plugging-out time of ith EV |

${Soc}_{EV,exp}^{i}$ | Expected SOC value of ith EV from the car owner |

${Soc}_{EV}^{i}$ | Nominal battery SOC of the ith EV |

${P}_{EV}^{i}$ | Nominal charging power of the ith EV |

${C}_{EV}^{i}$ | Battery capacity of the ith EV |

${\eta}_{c}^{i}$ | Charging efficiency of the ith EV |

${\eta}_{d}^{i}$ | Discharging efficiency of the ith EV |

${S}_{EV,t}^{i,c}$ | Charging status (0 or 1) at time t of the ith EV |

${S}_{EV,t}^{i,dV2H}$ | V2H status (0 or 1) at time t of the ith EV |

${S}_{EV,t}^{i,dV2B}$ | V2B status (0 or 1) at time t of the ith EV |

${S}_{EV,t}^{i,dV2V}$ | V2V status (0 or 1) at time t of the ith EV |

${S}_{EV,t}^{i,dV2G}$ | V2G status (0 or 1) at time t of the ith EV |

t_{start} | Charging start time |

t_{end} | Charging end time |

${T}_{EV}^{i}$ | Working period of the ith EV |

T_{B} | Time period of basic load for a power consumption unit |

${P}_{b}^{t}$ | Basic power load at time t for a power consumption unit |

ϑ_{V2G,t} | V2G power price at time t |

ϑ_{L,t} | Power load price at time t |

ρ_{i} | Penalty coefficient for energy desire of the ith EV |

λ_{i} | Penalty coefficient for charging cycles of the ith EV |

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**Figure 9.**Basic load profiles for simulation: left axis for the building and household load; right axis for the charging station load.

**Figure 10.**Outcome for the EV management of the household: (

**a**) load details with discharging; (

**b**) load details without discharging; basic household load refers to the household load without EV load profile; the optimized load profile refers to the basic household load plus the aggregated EV charging/discharging result based on the proposed model.

**Figure 12.**Outcome for EV charging of the building: basic building load refers to the building load without EV load profile; the optimized load profile refers to the basic building load plus the aggregated EV charging/discharging result based on the proposed model.

**Figure 13.**Outcome for EV charging of the charging station: basic charging station load refers to the charging station load without EV load profile; the optimized load profile refers to the basic charging station load plus the aggregated EV charging/discharging result based on the proposed model.

**Figure 14.**Simulation results of the charging station with different λ

_{i}: the load profiles in the big frame demonstrate the load curve changes to be more fluctuate with the increase of λ

_{i}; the profit of the operator in the small frame indicates the profit can be improved with the increase of λ

_{i}.

**Figure 15.**Details of the aggregated EV charging/discharging profiles for the charging station with different λ

_{i}: (

**a**–

**e**): λ

_{i}= 0, 0.1, 0.2, 0.3 and 0.5 respectively; with the increase of λ

_{i}, EVs choose to perform less discharging.

Parameter | Value | Parameter | Value |
---|---|---|---|

t_{start} range of EV | [8:00, 15:00] | ${Soc}_{EV,max}^{i}$ | 0.9 |

t_{end} range of EV | [13:00, 22:00] | ${P}_{EV}^{i}$ (kW) | 3.3 |

${Soc}_{EV,{t}_{start}}^{i}$ (range) | [0.2, 0.65] | ${C}_{EV}^{i}$ (kWh) | 24 |

${Soc}_{EV,exp}^{i}$ (range) | [0.6, 0.95] | ${\eta}_{c}^{i}$ | 0.98 |

${Soc}_{EV,min}^{i}$ | 0.2 | ${\eta}_{d}^{i}$ | 0.98 |

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**MDPI and ACS Style**

Mao, T.; Zhang, X.; Zhou, B.
Modeling and Solving Method for Supporting ‘Vehicle-to-Anything’ EV Charging Mode. *Appl. Sci.* **2018**, *8*, 1048.
https://doi.org/10.3390/app8071048

**AMA Style**

Mao T, Zhang X, Zhou B.
Modeling and Solving Method for Supporting ‘Vehicle-to-Anything’ EV Charging Mode. *Applied Sciences*. 2018; 8(7):1048.
https://doi.org/10.3390/app8071048

**Chicago/Turabian Style**

Mao, Tian, Xin Zhang, and Baorong Zhou.
2018. "Modeling and Solving Method for Supporting ‘Vehicle-to-Anything’ EV Charging Mode" *Applied Sciences* 8, no. 7: 1048.
https://doi.org/10.3390/app8071048