# Optimal Dispatch Strategy for Electric Vehicles in V2G Applications

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## Abstract

**:**

## 1. Introduction

#### 1.1. Dispatch Architectures of V2G Technology

#### 1.2. Motivation

#### 1.3. Innovation and Contribution

- A novel hourly EV battery wear model has been developed to precisely predict the hourly wear cost of EV batteries while considering all of the crucial aspects such as temperature, power level, and the SoC.
- A modified GWO method that uses a contemporary technique known as gradual reduction of the swarm size for GWO (GRSS-GWO), to reduce the convergence time and improve the accuracy of the findings.
- An accurate scheduling model for optimally charging and discharging the electricity of EVs utilizing V2G technology.
- An accurate economic model that may be used to assess the money that EV owners can earn by participating in technological projects that use V2G.

#### 1.4. Paper Outlines

## 2. Battery Wear Modelling

_{rate}), and the operating temperature. The wear mechanism of LIBs is notably influenced by these elements, but to varying degrees contingent upon the chemical composition of the cathode and the specific manufacturer of the LIBs. Battery wear is often overlooked in the economic analysis of V2G systems for EVs in various studies. Additionally, some studies in the literature have developed models to estimate battery wear, but they fail to include several crucial elements [10,32,33]. Several studies have taken into account the DoD and the operating temperature as factors in assessing the cost of EV battery wear in V2G or G2V applications [34,35]. The analysis conducted in this study did not take into account other variables, such as the C

_{rate}and operating temperature, because of the limited availability of data necessary to assess their impact [35]. This work presents a comprehensive analysis of battery wear models for lead-acid, LIB, and nickel-metal hydride (NiMH) batteries, with a specific focus on their use in the United Kingdom (UK) and China [35]. Several other methodologies considered certain elements that might impact battery wear while disregarding other ones. The technique described by references [32,33] introduces a battery wear approach that takes into account the impact of the DoD on the achievable cycle count (ACC) life cycle. This method also extracts a wear-density function (WDF) that enables the determination of discrete wear for each time period. The suggested technique failed to consider the impact of C

_{rate}and the operational temperature of the battery. Several studies have used experimental data from singular operating settings to forecast the wear mechanism of LIBs. However, it is important to note that such an approach deviates significantly from the actual wear mechanism seen in practical scenarios [34,35,36,37,38]. Furthermore, the aforementioned investigations failed to account for the potential variations in wear mechanisms, resulting from differences in the chemicals used in the cathode or the manufacturers involved. The correlation between the DoD and the ACC for reducing LIB is shown in Figure 4 [32,39].

#### 2.1. Wear Modeling Based on Achievable Cycle Count (ACC)

_{rate}, operating temperature, and the SoC of the battery [32]. The wear cost incurred within a given time in this model is determined by the power used in the charging and discharging processes, as well as the variation in SoC. One notable benefit of this particular model is its straightforwardness in determining the cost of wear. However, it is important to note that this model lacks precision and fails to account for many wear-inducing elements, such as temperature and SoC.

_{b}is the total battery cost, and E

_{br}is the rated capacity of the battery (kWh).

#### 2.2. Novel Battery Wear Model (NBWM)

_{1}, B

_{1}, C

_{1}, and D

_{1}) may be derived either from the outcomes of calendar tests or by using the results of cycle tests. The model shown in reference [32] fails to account for this particular wear, which undoubtedly has the potential to provide imprecise outcomes.

^{−1}) [42], and the activation energy parameter has been taken as a constant between E

_{a}= 30 kJ mol [43] and E

_{a}= 31.7 kJ mol [44].

_{2}, B

_{2}, C

_{2}, and D

_{2}are the cycling wear model parameters, n

_{c}is the number of cycles, and C

_{rate}is the current rate that can be obtained from Equation (11).

_{a}is the average SoC used during the cycling test, and the DoD can be obtained from Equation (14).

_{m}is the number of measurement points, ${W}_{m}^{i}$ is the measurement value of wear for point number i, and ${W}_{c}^{i}$ is the calculated value of aging obtained from Equation (13) for point number i.

_{c}number of cycles. The wear due to one ramp from SoC

^{t}

^{−1}to SoC

^{t}can be determined by dividing the cycling aging by 2n

_{c}and replacing the DoD with the actual DoD, which can be determined by Equation (16). The new wear by ramp time t

_{r}which is shown in Figure 6, can be determined from Equation (17).

_{rate}as shown in Equation (17).

_{i}is the temperature at ramp i, and the value of C

_{rate}can be obtained from Equation (11).

_{u}= 1 h), and the average SoC, SoC

_{ai}, can be determined from Equation (18).

## 3. Decentralized EV Aggregator

_{EV}is the daily driving distance, σ

_{EV}is the average daily distance of EV, and μ

_{EV}is the variance of the daily distance of EV.

_{EV}) as shown in Equation (21).

_{av}is the average speed of the EV.

_{b}is chosen to be positive for charging and negative for discharging or during the driving mode.

_{b}is the price of the new battery, and C

_{2nd}is the price of the second-life battery.

_{rate}= 0 or it can be obtained by subtracting all battery wear costs shown in Equations (29) and (30) from the total battery wear cost shown in Equation (28) as shown in Equation (31).

_{ch}is the total charging time.

_{1}is the weight value that should be used to provide the weight to the starting trip SoC ($So{C}_{{T}_{d}}^{n}$).

## 4. Optimization Algorithm

#### 4.1. Standard Grey Wolf Optimization Algorithm

- Initialization: A population of wolves is randomly initialized inside the search space, taking into account the zero value for the trip time. Each wolf symbolizes the cyclic process of charging and discharging energy over 24 h.
- Assessment of fitness: The fitness of each wolf within the population must be evaluated using the objective function as shown in Equation (35). The fitness value corresponds to the total income generated during 24 h.
- Provide a current update on the spatial distribution of wolves: The objective of this analysis is to ascertain the spatial distribution of the alpha, beta, delta, and omega wolves following their respective fitness values. The optimal solution is denoted by the symbol alpha, which is thereafter followed by beta, delta, and omega, as shown by the given equations.

_{max}is the maximum number of iterations.

- Apply boundary constraints: several boundary conditions such as the zero charging/discharging power during the driving trip, the charge/discharge power, and the SoC are within the specified limits.
- Update the fitness values: the new position is applied to the objective function, and the fitness values for each wolf is obtained.
- Update the best solution: the alpha wolf position is updated, if a better solution is found than the previous one.
- Repeat steps 2–5: the steps are repeated until a termination criterion is met (e.g., the maximum number of iterations or reaching a satisfactory solution).

#### 4.2. Novel Gradual Reduction of Swarm Size of GWO (GRSS-GWO)

## 5. Simulation Work

#### 5.1. Simulation Software

#### 5.2. Simulation Results

#### 5.3. Battery Wear Parameters Estimation

_{1}to D

_{2}, as shown in Equation (13), by comparison with the values obtained from this equation and the subsequent minimization of the RMSE, as demonstrated in Equation (15). The findings of this investigation demonstrate a notable level of accuracy in the model when considering the input data points shown in Figure 12 and Figure 13. Table 2 displays the parameters acquired by the use of the GRSS-GWO and other optimization techniques.

#### 5.4. Scheduling the Random Trip Length and Departure and Arrival Times

- The EV takes only one trip each day.
- The energy consumption per hour is constant during the trip.
- The minimum SoC during the discharging is 0.3.
- The average speed during the trip is selected as constant, equal to 15 km/h.

#### 5.5. Results of Optimal Schedule of EV Aggregator

**Case-1 (driving during the off-peak period):**The depicted scenario, as seen in Figure 15, demonstrates the effective use of an aggregator system. This system ensures that the EV battery is charged during low tariff times and discharged during high tariff periods, therefore enabling the stored energy to be efficiently contributed to the grid for V2G purposes. As seen in Figure 15, the battery undergoes charging in the first hours of the day to reach the predetermined SoC required for commencing the trip. The SoC remains constant until the time reaches T

_{d}(7:00), at which point the battery begins to deplete for the duration of the driving trip until the arrival time at t = 16:00. After the driving time, the SoC diminishes to a low level of 60%, indicating an insufficient amount of energy available for use during the high tariff period for discharging into the grid. Consequently, the battery undergoes a recharging process, reaching a SoC of 100%, during the time interval of t = 16:00 and t = 18:00. This ensures that the battery is adequately prepared for discharging during the high tariff period, which occurs from t = 19:00 to t = 21:00. Once the SoC of the battery reaches its minimum allowable value (SoC

_{min}= 0.3), the battery ceases its discharge to the grid to mitigate the potential for significant battery wear. The analysis of Figure 15 demonstrates that driving during off-peak hours in the daytime presents an advantageous chance for EVs to be charged at lower tariff rates and then discharged during high tariff times. This use of V2G ideas with EVs significantly enhances the potential income generated. The daily income generated by the operation of the EV, shown in Figure 15, amounts to USD 12.52. The revenue generated by selling energy to the grid is USD 21.92, whereas the cost of charging electricity for usage during the V2G period may be determined using Equation (33) and amounts to USD 6.21. The cost of wear resulting from V2G operations, as calculated using Equation (29), is USD 3.19. The fake charging algorithm presents an opportunity for additional money by charging the EV during low tariff times, as opposed to the expense of charging the battery after the trip. The calculation of the charging cost for both the driving duration and the self-discharge period in V2G, as seen in Figure 15, involves reducing the charging cost attributed to V2G (as defined in Equation (33)) from the overall charging cost derived from Equation (33), resulting in a value of USD 3.16. This value might be likened to the act of recharging the battery after the preceding day’s trip, amounting to a sum of USD 12.67. The observed decrease in charging expenses for the trip time of the V2G system, in comparison to the dummy charging scenario, amounts to USD 9.51. By summing the two incomes, it can be inferred that the use of V2G technology on the specific day, shown in Figure 15, would provide a total revenue of USD 22.03 for the EV owner. The substantial financial gains resulting from the implementation of V2G technologies, in contrast to the usage of fake charging, underscore its better performance and advantages for both EV owners and the grid system.

**Case-2 (driving during the low tariff period):**The scenario, shown in Figure 16, illustrates a situation where the aggregator is unable to take advantage of the low tariff times to charge the EV battery. However, it can use the high tariff period to discharge the stored energy into the grid and engage in V2G activities. If the opportunity to charge the battery during the low tariff time is missed, the aggregator will be compelled to charge at a higher tariff after the trip. This might result in increased charging costs and reduced income compared to driving during the off-peak period, as seen in case-1. As seen in Figure 16, the EV operated in driving mode from 1:00 to 8:00, resulting in a low SoC of 0.47 after the driving time. Hence, the aggregator needs to prioritize the search for the most cost-effective tariff during low tariff times to maximize the battery’s charging capacity, enabling it to supply the grid during peak hours from 18:00 to 23:00. The aggregator determined the optimal time frame for charging the EV battery to be from 9:00 to 11:00, as seen in Figure 16. Subsequently, the SoC reached its peak level and will remain at this level until 20:00, and at this point, it will begin discharging its energy into the grid during the period with the highest tariff. Once the SoC of the battery hits its minimal threshold, it is advisable to cease the discharge of the EV battery to mitigate the potential for significant wear in the LIB. This particular incident of LIB wear was observed at 22:00. Once the battery’s SoC hits its minimum allowable value (SoC

_{min}= 0.3), the battery ceases its discharge to the grid to mitigate the potential for significant battery wear. The analysis of Figure 16 indicates that driving the EV during the low tariff period does not enable the charging of the EV at reduced tariff rates. However, it does provide a chance to discharge the EV during high tariff times. The daily income generated by the operation of the EV in case-2, as seen in Figure 16, amounts to USD 10.54, in contrast to the USD 12.52 revenue observed in case-1. The price for selling energy to the grid is USD 22.15, whereas the cost of charging electricity for usage during the V2G period may be determined by referring to Equation (33) and is USD 8.19. The cost of wear resulting from V2G operations, as calculated using Equation (29), amounts to USD 3.42. The percentage decrease in income from case-1 to case-2 is calculated as (12.52–10.54)/10.54, resulting in a drop of 18.8%. This implies that failing to charge the EV battery during a time of low tariff rates might result in a decrease in income from V2G operations by 18.8%. Due to this rationale, it is advisable to arrange the travel to prevent the possibility of losing out on the time of reduced tariffs designated for charging the EV battery.

**Case-3 (driving during the high tariff period):**The scenario, shown in Figure 17, demonstrates that the aggregator will refrain from using the high tariff times to discharge the EV battery to the grid. However, it will ensure that the low tariff period is used for charging the battery. Failure to take advantage of the high tariff period for battery discharge would compel the aggregator to empty the battery during off-peak tariff periods after the trip. This might result in a decrease in the income generated from V2G operations compared to the scenario in case-1, when the EV was driven during the off-peak period. As seen in Figure 17, the EV underwent charging from 2:00 to 4:00, resulting in the SoC reaching a value of 1. The battery remained connected to the SoC until the commencement of the driving excursion at 20:00. The driving time concludes at 23:00, including all high tariff periods. Consequently, the EV will not engage in V2G activities since it lacks a high tariff period. The revenue from the third scenario shown in Figure 17 is almost negligible, indicating that it is not advisable to undertake the trip during peak hours.

## 6. Conclusions

## Funding

## Data Availability Statement

## Conflicts of Interest

## List of Symbols and Abbreviations

Symbol | Definitions | Symbol | Definitions |

V2G | vehicle-to-grid | T_{d} | departure time |

G2V | grid-to-vehicle | T_{r} | arrival time |

EV | electric vehicle | u_{av} | average EV speed |

SoC, s | state of charge | P_{EV} | the power of the battery |

SoH | state of health | E_{EVD} | energy of the driving period |

DoD, D | depth of discharge | X | dispatch matrix |

ESS | energy storage system | ${\eta}_{BC}$ | battery charging efficiency |

DSM | demand side management | ${\eta}_{BD}$ | battery discharging efficiency |

REDG | renewable energy distributed generator | σ | daily self-discharge |

GWO | grey wolf optimization | EoL | end of life |

GRSS | gradual reduction of swarm size | C_{w} | daily cost due to battery wear |

LIB | lithium-ion battery | C_{b} | price of the new battery |

C_{rate} | current rate | C_{2nd} | price of the second-life battery |

ACC | achievable cycle count | ${C}_{wV2G}^{n}$ | daily V2G battery wear cost |

WDF | wear density function | ${C}_{w\_Dr}^{n}$ | daily driving battery wear cost |

Nc | number of cycles | ${C}_{w\_Ch}^{n}$ | daily battery wear charging cost |

a and b | battery specification parameters | ${C}_{idle}^{n}$ | daily calendar battery wear cost |

AWC | average wear cost | CC | daily total charging cost |

${\eta}_{b}$ | battery efficiency | ${\lambda}^{t}$ | hourly tariff (USD/kWh) |

C_{b} | total battery price | $C{C}_{V2G}^{n}$ | charging cost for V2G |

E_{br} | battery rated capacity | T_{ch} | charging time |

TWC | total wear cost | ${R}_{V2G}^{n}$ | daily revenue due to V2G |

P_{b} | battery power | $So{C}_{{T}_{d}}^{n}$ | battery SoC at the beginning of the trip |

R | ideal gas constant | $So{C}_{0}^{n}$ | required SoC at the beginning of the trip |

E_{a} | activation energy parameter | w_{1} | weight value |

LAM | loss of active materials | PSO | particle swarm optimization |

SEI | solid electrolyte interphase | CSA | cuckoo Search Algorithm |

t_{u} | rise time | BA | bat algorithm |

W | battery wear | d | number of variables |

W_{cal} | calendar battery wear | ${\overrightarrow{V}}_{j}^{i}$ | position of ariable j at iteration i |

W_{cyc} | cycling battery wear | ${\overrightarrow{R}}_{j}^{i}$ | random vector ${\overrightarrow{R}}_{j}^{i}\in [0,1]$ |

T | temperature | a | GWO control parameter |

SoC_{min} | minimum SoC | it_{max} | maximum number of iterations |

SoC_{max} | maximum SoC | F | objective function |

SoC_{a} | average SoC | V_{best} | the position of the best wolf |

RMSE | root mean square error | F_{best} | fitness value of the best wolf |

W_{m} | measured battery wear | V_{worst} | the position of the worst wolf |

W_{c} | calculated battery wear | F_{best} | fitness value of the worst wolf |

n_{m} | number of test points | SS | swarm size |

f_{des} | distribution function | OMC | operating and maintenance cost |

L_{EV} | daily driving distance | μ_{EV} | variance of the daily distance of EV |

σ_{EV} | average daily distance | β_{EV} | specific power consumption |

E_{EV} | EV trip consumed energy |

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**Figure 3.**The architecture of the decentralized V2G aggregator [10].

**Figure 12.**The variation in the measured and calculated battery wear in capacity for different calendar aging at different temperatures and SoCs.

**Figure 13.**The variation in the measured and calculated battery wear for cycling tests at different operating conditions.

**Figure 14.**The daily driving distance, departure and arrival times, and the driving periods during the year.

Item | Value |
---|---|

No. of modules | 24 |

Module capacity | 2.4 kWh |

Battery price C_{b} | $140/kWh |

2nd life battery price | $60/kWh |

OMC | $0.1/kWh/year |

${\eta}_{BC}$$={\eta}_{BD}$ | 0.95 |

σ | 0.01% |

Items | GRSS-GWO | GWO | PSO | BA |
---|---|---|---|---|

Convergence time (s) | 0.213 441 117 | 0.821 158 456 | 0.978 254 151 | 1.149 123 715 |

RMSE (%) | 0.001 951 035 | 0.002 113 658 | 0.002 121 756 | 0.002 243 674 |

A_{1} | 472.701 163 681 | 470.414 149 675 | 470.405 579 729 | 470.398 767 233 |

B_{1} | −2.069 836 312 | −2.060 865 899 | −2.058 069 457 | −2.057 654 982 |

C_{1} | −6316.876 455 349 | −6269.356 878 725 | −6270.556 534 254 | −6270.129 739 985 |

D_{1} | 0.576 031 765 | 0.576 901 653 | 0.576 713 898 | 0.576 797 138 |

A_{2} | 26.055 099 431 | 26.163 873 352 | 25.993 877 910 | 26.106 763 973 |

B_{2} | 2.688 801 914 | 2.690 645 631 | 2.687 945 918 | 2.691 875 219 |

C_{2} | −2102.375 825 405 | −2101.912 746 436 | −2102.534 674 362 | −2102.439 726 652 |

D_{2} | 0.520 987 158 | 0.521 812 028 | 0.521 736 832 | 0.521 052 637 |

Items | Dumb Charge | V2G |
---|---|---|

Yearly wear (%) | 2.55 | 5.34 |

Battery life time (year) | 7.8431 | 3.7453 |

Yearly charging cost ($) | 904.6 | 765.4 |

Yearly wear cost ($) | 587.5 | 1230.3 |

Total yearly cost ($) | 1492.1 | 1995.7 |

Income due to V2G ($) | - | 5240.7 |

Yearly revenue ($) | - | 3245 |

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## Share and Cite

**MDPI and ACS Style**

Eltamaly, A.M.
Optimal Dispatch Strategy for Electric Vehicles in V2G Applications. *Smart Cities* **2023**, *6*, 3161-3191.
https://doi.org/10.3390/smartcities6060141

**AMA Style**

Eltamaly AM.
Optimal Dispatch Strategy for Electric Vehicles in V2G Applications. *Smart Cities*. 2023; 6(6):3161-3191.
https://doi.org/10.3390/smartcities6060141

**Chicago/Turabian Style**

Eltamaly, Ali M.
2023. "Optimal Dispatch Strategy for Electric Vehicles in V2G Applications" *Smart Cities* 6, no. 6: 3161-3191.
https://doi.org/10.3390/smartcities6060141