# V2B/V2G on Energy Cost and Battery Degradation under Different Driving Scenarios, Peak Shaving, and Frequency Regulations

^{1}

^{2}

^{*}

## Abstract

**:**

_{min}> 30% and SoC

_{max}< 90%) and subjected to very restricted charge-discharge battery cycling.

## 1. Introduction

_{1}= [10–90%], EV

_{2}= [20–90%], EV

_{3}= [30–90%], EV

_{4}= [40–90%], and EV

_{5}= [50–90%] = [SoC

_{min}–SoC

_{max}] providing the same ancillary services. The main difference of SoC usage ranges among the EV users results from the different driving profiles. The SoC limits are correlated to the driving distance to and from work for each EV user. One major observation in this study is that under these restricted scenarios, EV batteries can achieve much larger economic benefits if they jointly provide multiple services under controlled SoC limits and very restricted charge-discharge battery cycling.

## 2. Materials and Methods

#### 2.1. Electricity Bill Calculation

_{elec}= energy price in $/MWh, r(t) power consume at time t, α

_{peak}= peak demand price in $/MW. The peak demand charge r

_{peak}is based on the maximum power consumption, and it is calculated from a running average of power consumption over 15 or 30 min [8,9].

#### 2.2. Problem Formulation

- To find the optimal policy and strategies for using the energy stored in EV batteries to reduce the total energy cost H of the building owner.
- To find the SoC optimal range of EV batteries with slow battery degradation, while providing building load supply when necessary, powertrain for the EV, peak shaving and frequency regulation simultaneously.

#### 2.3. Peak Shaving

_{n}(t) the power that the n

^{th}MBESS can inject in the grid at a given time t. Note that b

_{n}(t) > 0 for discharging, b

_{n}(t) < 0 for charging. The total adjusted electricity bill H

^{a}is now given by Equation (2).

_{n}(t) is the average power injection of the n

^{th}battery, ${r}_{a}\left(t\right)=r\left(t\right)-{\displaystyle \sum}_{n=1}^{N}{b}_{n}\left(t\right)$ is the actual power meter reading when the N EVs are connected to the grid, and f(b

_{n}) is the operating cost of the nth battery.

#### 2.4. EV Battery Model and Degradation Cost

_{batt}= E − Ri.

_{0}= battery constant voltage in volts, K = polarization voltage in volts, Q = battery capacity in Ah, $\int idt$ = actual battery charge in Ah, A = exponential zone amplitude in volts, B = exponential zone time constant inverse in (Ah)

^{−1}, V

_{batt}= battery voltage in volts, R = internal resistance in Ohms, and i = battery current in (amps). The model can accurately represent the behavior of many battery types, provided the parameters are well determined. The main feature of this battery model is that the parameters can be easily deduced from a manufacturer’s discharge curve and can be set to account for temperature and aging effects [12,13,14].

_{n}is the number of cycles that the nth MBESS could be operated within.

#### 2.5. Frequency Regulations

_{n}) is the operating cost of the MBESS and s(t) is the normalized frequency regulation signal. Compared with traditional frequency regulation signals, it has a much faster ramping rate and is designed to have a zero-mean within a certain time interval, which is well aligned with the characteristics of MBESS. Note that, for providing frequency regulation service, the grid operator pays a per-MW option fee α

_{c}to a resource withstand-by power capacity C for each hour. While during the frequency regulation procurement period, the resource is subjected to a per-MWh regulation mismatch penalty (α

_{mis}) for the absolute error between the instructed dispatch and the resource’s actual response [16].

#### 2.6. Multi-objective Optimization

- -
- Minimize EV’s owner electricity bill
- -
- Such that
- ○
- The gain from selling EV energy to building owner is maximized.
- ○
- Minimize battery degradation thus minimize battery cost.
- ○
- Keep SoC within SoC
_{min}< SoC < SoC_{max}.

_{n}of each EV, battery charging/discharging power $b{}_{n}{}^{dc}\left(t\right),b{}_{n}{}^{ch}\left(t\right),$ of each EV, number of EVs connected at a given time t, and frequency regulation load baseline y(t). Participants in frequency regulation market should report a baseline y(t) to the grid operator ahead of their service time [16]. For a commercial user, the baseline y(t) is its load forecasting including the projected driving patterns of the EV owners. [T

_{0}T] = time interval considered, α

_{c}= frequency regulation revenue, and α

_{min}= frequency cost mismatch penalty.

#### 2.7. Simulation Strategy

_{1}= [10–90%], EV

_{2}= [20–90%], EV

_{3}= [30–90%], EV

_{4}= [40–90%], and EV

_{5}= [50–90%] = [SoC

_{min}–SoC

_{max}] providing the same ancillary services. The main difference of SoC usage ranges among the EV users results from the different driving profiles. The SoC limits are correlated to the driving distance to and from work for each EV user.

## 3. Results

#### 3.1. EV Owner and Household Bill

_{1}, EV

_{2}, EV

_{3}, EV

_{4}, and EV

_{5}, respectively. As shown in Figure 3, every day from 11:30 to 12:30, all the EVs have the same depth of discharge (DoD) with 20% for selling the same amount of energy to the building owner (V2B) for ancillary services on the grid side. The rest of the day, EV discharging and charging profiles are different and correspond to the EV owner’s driving and charging patterns.

_{max}= 90%) is same for each EV and its battery pack is discharged until the SoC reaches 65% (DoD of 35%), 70% (DoD of 30%), 75% (DoD of 25%), 80% (DoD of 20%), 85% (DoD of 15%), for EV

_{1}, EV

_{2}, EV

_{3}, EV

_{4}, and EV

_{5}, respectively.

_{1}, EV

_{2}, EV

_{3}, EV

_{4}, and EV

_{5}, respectively.

_{1}, EV

_{2}, EV

_{3}, EV

_{4}, and EV

_{5}, respectively.

_{min}for each EV. That is: 10% (DoD of 90%), 20% (DoD of 80%), 30% (DoD of 70%), 40% (DoD of 60%), 50% (DoD of 50%), for EV

_{1}, EV

_{2}, EV

_{3}, EV

_{4}, and EV

_{5}, respectively.

_{5}with SoC within [50–90%] shows the lowest battery degradation.

#### 3.2. Electricity Bill for Building Owner

## 4. Discussion

## 5. Conclusions

_{min}> 30% and SoC

_{max}< 90%) and subjected to very restricted charge-discharge battery cycling.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Generic Matlab/Simulink battery model with temperature and aging (equivalent full cycle) effects.

**Figure 3.**Daily 24 h profile of electric vehicles (EVs) with state of charge (SoC) limits: EV

_{1}= [10–90%], EV

_{2}= [20–90%], EV

_{3}= [30–90%], EV

_{4}= [40–90%], and EV

_{5}= [50–90%].

**Figure 4.**Battery degradation for various driving patterns and SoC limits: EV

_{1}= [10–90%], EV

_{2}= [20–90%], EV

_{3}= [30–90%], EV

_{4}= [40–90%], and EV

_{5}= [50–90%].

**Figure 5.**Comparative analysis of the original bill normalized to 1 corresponding to bill without ancillary services and others with bills after peak shaving, frequency regulation, combination of peak shaving and frequency regulation, under different SoC limits: Electricity bills to be paid by EV owners after reflecting reimbursement for ancillary services.

**Figure 7.**Comparative analysis of the original bill normalized to 1 corresponding to bill without ancillary services and others with bills after peak shaving, frequency regulation, combination of peak shaving and frequency regulation, under different SoC limits: Electricity bill for building owner.

Notations | Definitions |
---|---|

H | Daily electricity bill in $ |

H^{elect} | Daily off-peak electricity bill in $ |

H^{peak} | Daily on-peak electricity bill in $ |

H^{a} | Adjusted electricity bill after peak shaving |

α_{elec} | energy price in $/MWh |

α_{peak} | peak demand price in $/MW |

r(t) | power consume at time t |

r_{peak} | power consume during peak hours |

b_{n}(t) | Energy store in the n^{th} battery |

$\overline{b}$_{n}(t) | The average power injection of the n^{th} battery |

N | Number of EVs |

${\lambda}_{cell}^{n}$ | is the n^{th} MBESS cell price $/Wh |

K_{n} | Number of cycles that the n^{th} MBESS could be operated within |

s(t) | The normalized frequency regulation signal |

α_{c} | Frequency regulation revenue |

α_{mis} | Frequency cost mismatch penalty |

C | Power capacity |

SoC_{min} | Min State of Charge |

SoC_{t} | Current State of Charge |

SoC_{max} | Max State of Charge |

c_{n} | Frequency regulation capacity of each EV |

$b{}_{n}{}^{ch}\left(t\right)$ | Battery charging of the n^{th} EV |

$b{}_{n}{}^{dc}\left(t\right)$ | Discharging power of the n^{th} EV |

y(t) | Frequency regulation load baseline |

${P}_{max}^{n}$ | Battery capacity power of the n^{th} EV |

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**MDPI and ACS Style**

Tchagang, A.; Yoo, Y. V2B/V2G on Energy Cost and Battery Degradation under Different Driving Scenarios, Peak Shaving, and Frequency Regulations. *World Electr. Veh. J.* **2020**, *11*, 14.
https://doi.org/10.3390/wevj11010014

**AMA Style**

Tchagang A, Yoo Y. V2B/V2G on Energy Cost and Battery Degradation under Different Driving Scenarios, Peak Shaving, and Frequency Regulations. *World Electric Vehicle Journal*. 2020; 11(1):14.
https://doi.org/10.3390/wevj11010014

**Chicago/Turabian Style**

Tchagang, Alain, and Yeong Yoo. 2020. "V2B/V2G on Energy Cost and Battery Degradation under Different Driving Scenarios, Peak Shaving, and Frequency Regulations" *World Electric Vehicle Journal* 11, no. 1: 14.
https://doi.org/10.3390/wevj11010014