# A Survey Data Approach for Determining the Probability Values of Vehicle-to-Grid Service Provision

## Abstract

**:**

## 1. Introduction

_{2}) into the atmosphere is the transportation sector [3,4]. As a result, many government organizations are trying to influence the automotive sector through legislative changes in order to minimize CO

_{2}emissions into the atmosphere [5]. One of the factors that may influence such action is the promotion of electric vehicles (EVs) [6]. EVs can be divided into three main groups: battery electric vehicles (BEVs), which are vehicles that run solely on electricity from a battery pack, plug-in hybrid electric vehicles (PHEVs), which are hybrid vehicles that use electric motors and an internal combustion engine (ICE) but have the ability to charge the internal batteries from both the internal combustion engine and an electrical socket, and fuel cell electric vehicles (FCEVs), which are run by hydrogen [7]. Because electric vehicles have rechargeable batteries in their design, they can be treated as mobile electricity storage [8]. Therefore, their potential as an auxiliary source of electricity for additional demand should be exploited. These principles are the basis of vehicle-to-grid (V2G) technology or in general vehicle-to-everything (V2X) technology [9]. It involves voluntarily discharging the battery of an electric vehicle into the power grid or any other facility owned by the end-user, which can be called, in simple terms, a V2G service. It is worth mentioning here that in order to release the full potential of V2G technology, electric vehicles should be integrated with local power systems creating microgrids [10,11,12]. Through the development of renewable energy source (RES) technologies, local energy balancing solutions have become popular and there is certainly a place for electric vehicles in them [13]. It is possible to use EVs directly in covering the demand of the household (V2H—vehicle-to-home) or the commercial end user (V2L—vehicle-to-load) [9]. The idea of local energy balancing involves the efficient use of electricity produced from uncertain energy sources, such as photovoltaic plants (PVs) or wind turbines (WTs). This can be achieved by battery energy storage systems (BESS). Knowing that an EV can be treated as a mobile energy storage, its use in accumulating energy from PVs and WTs and possibly discharging it in case of a lack of electricity production due to unfavorable weather conditions seems to be appropriate. Figure 1 shows an example concept for integrating an EV into a microgrid.

## 2. Assumptions of V2G Program

#### 2.1. Definitions

**V2G service**is a defined action, which is undertaken by the V2G Program participant, aimed at the improvement of the power system operation, or ensuring sufficient capacity for the end user.**V2G Program participant (uEV)**is the owner of an electric vehicle or fleet of electric vehicles, who provides services by offering battery capacity to end users or a distribution system operator.**End user (EndUs)**is the energy consumer, who has decided to use electric vehicles for reserve power supply within the V2G Program.**V2G Program**is understood as the activity of a power company involving the use of electric vehicles to improve the operation of the power grid or/and to improve the security (assurance) of supply.**V2G service provider (V2Gsp)**is the party managing the V2G Program in a given area.**Mandatory mode**is a V2G service mode in which the V2G Program participant (uEV) receives a fixed payment in exchange for remaining on standby and unconditionally providing service on demand from the V2G service provider. If the service is not provided, the uEV will incur fines that are proportional to their participation in the V2G Program.**Optional mode**is a V2G service mode in which a V2G Program participant is paid only for the EV discharging action that is completed. The participant will not be remunerated for willingness to perform the service and remain on standby but will also not receive fines for not providing the service.

#### 2.2. Provision of V2G Service—Emergency Work for the Energy Consumer

- E
_{d}—the end user’s electricity demand from V2G Program, in kWh; - P(A)—the total probability of providing V2G service;
- e
_{V2G+,n}—the energy flow injected by n-th electric vehicle; - ${N}_{EV}^{REQ}$—the required number of electric vehicles for provision of V2G service for an end user;
- E
_{V2G+,t}—the expected energy delivered to the end user in time t.

- C—the battery capacity of the EV, in kWh;
- SOC
_{t}—the current state-of-charge (SOC) at the time of commencing V2G service provision, in %; - SOC
_{f}—the state-of-charge required for the next journey, in %; - SOC
_{0}—the minimal state-of-charge limited by technical constraints, in %; - R—a reserve, which considers the possible lengthening of the route, e.g., to avoid congestion;
- η
_{d}—the efficiency of the discharging process.

_{t}refers to the moment when the service provision commences. If the vehicle is not present at the place where the service is provided, the energy required to get it from the location where the service is accepted to the place where the service is provided must also be considered. This is denoted by Equation (3).

- SOC
_{act}—the state-of-charge at the time the service proposal is accepted by uEV, in %; - us
_{EV}—the average electricity consumption of an electric vehicle, in kWh/km; - d—the distance between the uEV and the service provision point, in km.

- ${P}_{MIN}^{EVSE}$—the minimum capacity transmitted from the V2G charging station to the power grid, in kW;
- ${P}_{MAX}^{EVSE}$—the maximum capacity transmitted from the V2G charging station to the power grid, in kW;
- ${P}_{MIN}^{CHARG}$—the minimum capacity transmitted from the EV on-board charger to the power grid, in kW;
- ${P}_{MAX}^{CHARG}$—the maximum capacity transmitted from the EV on-board charger to the power grid, in kW;
- ${P}_{V2G+}$—the discharging capacity of the EV, in kW.

- ${P}_{d}$—the maximum demand that can be covered by the V2G service, in kW;
- n
_{CS}—the number of bi-directional charging points owned by the EndUs;

- ${E}_{d}^{MAX}$—the maximum electricity demand of the EndUs in a given time frame of service provision;
- $\tau $—a single hour of V2G service provision;
- $T$—the length of the time frame, in hours.

- ${N}_{EV}^{EST}$—the estimated number of electric vehicles expected to be involved in establishing V2G service, considering the probability of service provision;
- E’
_{V2G+,t}—the expected energy delivered to the end user in time t, which covers the reserve resulting from the probability of service provision P(A) < 1.

- End user—P(EndUs);
- V2G service provider—P(V2Gsp);
- V2G Program participant—P(uEV).

- P(F
_{EVSE})—the probability of failure of a bi-directional charging point;P(D_{PL})—the probability of the availability of a V2G charging point at the place of service delivery. - P(F
_{S})—the probability of failure of a metering and billing system. - P(EC)—the probability of the user’s reaction to providing the service at a given time, e.g., receiving an economic incentive or the willingness to perform a service due to the lifestyle of the uEV;
- P(US
_{EV})—the probability of electric vehicle availability due to its lack of use; - P(INT)—the probability of service interruption.

_{EV}) was described as the probability of using the vehicle. A minor adjustment had to be made here due to the fact that service provision will only be possible when the vehicle is not in use for its own uEV’s purposes, which will be superior to service provision.

#### 2.3. Novelty

_{EV}) described in Section 2.2. Furthermore, according to [34], the probability of service provision will also depend on the participant’s decision. In order to determine these values, it was decided to use the public’s voice to design metrics that will serve as starting data in the V2Gsp business model. This approach seems to be appropriate since it will be the EV users who will ultimately use the V2G Program. The problem of a lack of social analysis in the technology area was also mentioned in [48]. As the authors note in [48], most research papers focus on the technical layer, and those that consider the social layer of the problem of implementing V2G technology are single percentages. In particular, they note that the description of user behavior was described in only 2.1% of the articles they analyzed [48]. The research survey exemplar papers use advanced statistical models, which most often illustrate the decision-making models that a V2G Program operator would need to make to ensure the viability of the service [36,38]. However, from the point of view of V2Gsp, both the statistical parameters on which the economic model will be built and, in the later real implementation stage, a tool to select the vehicles to provide these services need to be determined. In [34], such an algorithm is presented, for the operation of which the probabilities of events that make up the performance of the service should be used. These probabilities are described in detail in Section 2.2. It is therefore proposed to determine them experimentally based on results from surveys. Their purpose is to be used as starting values in the aforementioned algorithm [34]. In case of a real implementation, these indicators should be updated by the V2Gsp in real-time with current user behavior. This paper also considers the author’s approach to calculating probability values associated with the decisions made by V2G Program participants. It should be kept in mind that the fact of examining the available energy from a certain number of EVs does not mean that all this energy will be delivered to the grid or end user. By using a probabilistic approach in evaluating the provision of V2G services, EVs can be used more efficiently in their integration into the grid. Both the V2Gsp and DSO will be offered an indicator to estimate the approximate real value of the energy distributed by EVs to the grid or for end users’ own consumption. In addition to the mathematical description of the indicators determining the probability, a methodology for determining them for V2Gsp will be proposed, and example calculations based on realized surveys will be presented.

- The inclusion of the results of social surveys in the calculation process of the initial values of the V2G service provision probabilities and the calculation of the number of participants in Mandatory and optional mode (as assumed in Section 2.2).
- A proposed methodology for dealing with the calculation of the values of the probabilities of V2G service provision by V2Gsp.
- A proposed targeted methodology for calculating the probability values of the uEV reaction.
- The use of probabilistic methods to enhance the process of EV integration into the electricity grid within the scope of V2X technology.

## 3. Survey Research

## 4. Determination of the Parameters Needed to Provide the V2G Service

#### 4.1. Method Based on a Two-State Model

_{EVSE})) and the charging station availability at the service location (P(D

_{PL})). The values to calculate the first one can be found in [50]. The authors in [50] used a two-state model in their calculations. It should be noted that the transition intensities from state “0” to “1” and “1” to “0” are unique for each parameter analyzed and will be identified when discussing the individual probabilities. A “0” state may indicate a non-functioning charging station or supervisory system but may also indicate a lack of available space to discharge an EV or an interruption of V2G service. State “1” refers to events where the V2G service is provided in an uninterrupted and fault-free manner.

- ${\mathsf{\mu}}_{EVSE}\u2014\mathrm{the}\mathrm{charging}\mathrm{station}\mathrm{restoration}\mathrm{intensity}\left(\mathrm{repair}\mathrm{rate}\right);$
- ${\lambda}_{EVSE}\u2014\mathrm{the}\mathrm{charging}\mathrm{station}\mathrm{failure}\mathrm{intensity}\left(\mathrm{failure}\mathrm{rate}\right);$
- ${q}_{EVSE}\u2014\mathrm{the}\mathrm{probability}\mathrm{of}\mathrm{the}\mathrm{charging}\mathrm{station}\mathrm{being}\mathrm{out}\mathrm{of}\mathrm{service}.$

_{EVSE}. It is determined by Equation (16).

- ${\mu}_{DPL}\u2014\mathrm{the}\mathrm{intensity}\mathrm{of}V2G\mathrm{charging}\mathrm{station}\mathrm{availability}\mathrm{comeback};$
- ${\lambda}_{DPL}\u2014\mathrm{the}\mathrm{intensity}\mathrm{of}\mathrm{the}V2G\mathrm{charging}\mathrm{station}\mathrm{transition}\mathrm{into}\mathrm{an}\mathrm{occupied}\mathrm{state};$
- ${p}_{DPL}\u2014\mathrm{the}\mathrm{probability}\mathrm{of}V2G\mathrm{charging}\mathrm{station}\mathrm{availability}.$

- ${\lambda}_{S}\u2014\mathrm{the}\mathrm{intensity}\mathrm{of}\mathrm{failures}\mathrm{in}\mathrm{the}V2Gsp\mathrm{supervisory}\mathrm{control}\mathrm{system};$
- ${\mu}_{S}\u2014\mathrm{the}\mathrm{intensity}\mathrm{of}\mathrm{repairs}\mathrm{of}\mathrm{the}V2Gsp\mathrm{supervisory}\mathrm{control}\mathrm{system}$;
- ${q}_{S}\u2014\mathrm{the}\mathrm{probability}\mathrm{of}\mathrm{the}V2Gsp\mathrm{supervisory}\mathrm{control}\mathrm{system}\mathrm{failure}.$

- P(EC)—the probability of the user’s reaction to providing the service at a given time, e.g., receiving an economic incentive or the willingness to perform a service due to the lifestyle of the uEV;
- P(US
_{EV})—the probability of electric vehicle availability because of its lack of usage; - 1-P(INT)—the probability of service not being interrupted.

- ${\lambda}_{INT}\u2014\mathrm{the}\mathrm{intensity}\mathrm{of}\mathrm{transition}\mathrm{to}\mathrm{the}\mathrm{state}\mathrm{of}\mathrm{interruption}\mathrm{of}V2G\mathrm{service};$
- ${\mu}_{INT}\u2014\mathrm{the}\mathrm{intensity}\mathrm{of}\mathrm{restoration}\mathrm{from}\mathrm{interruption}\mathrm{of}V2G\mathrm{service}$;
- ${q}_{INT}\u2014\mathrm{the}\mathrm{probability}\mathrm{of}V2G\mathrm{service}\mathrm{interruption}.$

#### 4.2. Method for Determining Initial Probability Values of V2G Service Provision Based on Survey Data

- $P{\left(EC\right)}_{t}{}^{V2GL}\u2014$ the probability of V2G Program participant reaction on the provision of the V2G service at the EndUs location at time t;
- ${N}_{uEV}^{V2GL}\left(t\right)\u2014$ the number of respondents willing to provide V2G service at the EndUs location at time t;
- ${R}_{YES}^{V2GL}\u2014$ the total number of “Yes” responses in the survey question regarding the willingness to provide V2G service at the EndUs location;
- ${R}_{DK}^{V2GL}\u2014$ the total number of “Don’t know” responses in the survey question regarding the willingness to provide V2G service at the EndUs location.

_{EV}). In order to quantify this value, it is first necessary to refer to the survey data. The vehicle usage profile shown in Figure A4 will be helpful. The proposed survey examined 3-h intervals due to a willingness toward simplifying the questionnaire. However, the target version of the survey prepared by the V2Gsp should reduce the time frame to 1-h intervals. This will allow for a more accurate estimation of initial probability values of P(US

_{EV}). However, the methodology for calculating the specific probability value will also be broadened to include other components in relation to the EV usage profile. Namely, the calculation method also includes respondents who answered that they own an ICE vehicle and are considering purchasing an electric vehicle within 5 years. This procedure is intended to increase the accuracy of calculating the probability of P(US

_{EV}), assuming that current users of ICE vehicles will maintain their travel patterns, i.e., travel at similar times. The methodology for calculating P(US

_{EV}) is presented by Equations (22) and (23).

- ${N}_{US}^{EV}\left(t\right)\u2014\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{respondents}\mathrm{that}\mathrm{indicated}\mathrm{they}\mathrm{are}\mathrm{using}\mathrm{an}EV\mathrm{in}\mathrm{time}\left(t\right);$
- ${N}_{US}^{ICE}\left(t\right)\u2014\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{respondents}\mathrm{who}\mathrm{intend}\mathrm{to}\mathrm{purchase}\mathrm{an}EV\mathrm{in}5\mathrm{years}\mathrm{of}\mathrm{having}\mathrm{used}\mathrm{an}ICE\mathrm{vehicle}\mathrm{in}\mathrm{time}\left(t\right);$
- ${R}_{EV}\u2014\mathrm{the}\mathrm{total}\mathrm{number}\mathrm{of}EV\mathrm{users};$
- ${R}_{ICE}\u2014\mathrm{the}\mathrm{total}\mathrm{number}\mathrm{of}ICE\mathrm{users}\mathrm{who}\mathrm{intend}\mathrm{to}\mathrm{purchase}\mathrm{an}EV\mathrm{in}5\mathrm{years}\mathrm{of}\mathrm{having}\mathrm{used}\mathrm{an}ICE\mathrm{vehicle}\mathrm{in}\mathrm{time}\left(t\right);$
- ${P}_{1}{\left(U{S}_{EV}\right)}_{t}\u2014\mathrm{the}\mathrm{probability}\mathrm{of}\mathrm{vehicle}\mathrm{usage}\mathrm{in}\mathrm{time}\left(t\right);$
- $P{\left(U{S}_{EV}\right)}_{t}\u2014\mathrm{the}\mathrm{probability}\mathrm{of}\mathrm{electric}\mathrm{vehicle}\mathrm{availability}\mathrm{because}\mathrm{of}\mathrm{its}\mathrm{lack}\mathrm{of}\mathrm{usage}\mathrm{in}\mathrm{time}\left(t\right).$

- ${N}_{uE{V}_{V2GL}}^{MAN}\u2014\mathrm{the}\mathrm{number}\mathrm{of}V2G\mathrm{Progam}\mathrm{participants}\mathrm{in}\mathrm{mandatory}\mathrm{mode}\mathrm{for}\mathrm{a}\mathrm{given}\mathrm{type}\mathrm{of}V2G\mathrm{service};$
- ${N}_{uE{V}_{V2GL}}^{OPT}\u2014\mathrm{the}\mathrm{number}\mathrm{of}V2G\mathrm{Progam}\mathrm{participants}\mathrm{in}\mathrm{optional}\mathrm{mode}\mathrm{for}\mathrm{a}\mathrm{given}\mathrm{type}\mathrm{of}V2G\mathrm{service};$
- ${N}_{uE{V}_{V2GL}}\u2014\mathrm{the}\mathrm{total}\mathrm{number}\mathrm{of}V2G\mathrm{Program}\mathrm{participants}\mathrm{for}\mathrm{a}\mathrm{given}\mathrm{type}\mathrm{of}V2G\mathrm{service}.$

**No**” to both of the questions in Table A10 and Table A11, so that the result obtained will be the denominator of the SUR coefficient. Thus, the following methodology is proposed:

- Examine the number of respondents who declared “
**Yes**” to the question presented in Table A9 and then answered "**Yes**” and “**Yes but with additional benefits**” to the question: “In exchange for a fixed monthly remuneration, would you be willing to stand by to discharge an electric vehicle during the hours set by the V2G Program operator, being aware of potential fines for not providing the service?” and answered “**No**” in the question: “In exchange for a financial benefit for a single discharging action, would you be able to provide discharging services without incurring fines for not providing the service?”. Thus, the number of V2G Program participants for a given service provision location in mandatory only mode can be calculated. - Examine the number of respondents who declared “
**Yes**” to the question presented in Table A9 and then answered “**No**” to the question: “In exchange for a fixed monthly remuneration, would you be willing to standby to discharge an electric vehicle during the hours set by the V2G Program operator, being aware of potential fines for not providing the service?” and answered “**Yes**” to the question: “In exchange for a financial benefit for a single discharging action, would you be able to provide discharging services without incurring fines for not providing the service?”. Thus, the number of V2G Program participants for a given service location in optional mode only can be calculated. - Examine the number of participants who declared “
**Yes**” to the question presented on Table A9 and then answer “**Yes**” and “**Yes but with additional benefits**” to the question: “In exchange for a fixed monthly remuneration, would you be willing to standby to discharge an electric vehicle during the hours set by the V2G Program operator, being aware of potential fines for not providing the service?” and answered “**Yes**” to the question: “In exchange for a financial benefit for a single discharging action, would you be able to provide discharging services without incurring fines for not providing the service?”. Thus, the number of V2G Program participants for a given service location who said they were willing to participate in both modes can be calculated. Due to the aforementioned fact, these V2G Program participants are eligible for the mandatory mode first.

- $SU{R}_{MAN}^{V2GL}\u2014\mathrm{the}$ coefficient of respondents willing to participate in the V2G Program at the EndUs location in mandatory mode;
- $SU{R}_{OPT}^{V2GL}\u2014\mathrm{the}$ coefficient of respondents willing to participate in the V2G Program at the EndUs location in optional mode;
- ${N}_{MA{N}_{ONLY}}^{V2GL}\u2014\mathrm{the}$ number of respondents interested in the V2G Program at the EndUs location only in mandatory mode;
- ${N}_{OP{T}_{ONLY}}^{V2GL}\u2014\mathrm{the}$ number of respondents interested in the V2G Program at the EndUs location only in optional mode;
- ${N}_{MA{N}_{OPT}}^{V2GL}\u2014\mathrm{the}$ number of respondents interested in the V2G Program at the EndUs location in mandatory and optional mode;
- ${N}_{NOTIN{T}_{L}}\u2014\mathrm{the}$ number of respondents, who would like to discharge their vehicle at an EndUs location but are not interested in the V2G Program in mandatory and optional modes.

#### 4.3. Method for Calculating the Probability Value P(EC) after the First Month of V2G Program Settlement

_{G}and y

_{G}are the geometric coordinates of the selected point g.

_{Gmax}and y

_{Gmax}are the boundary values of the area.

_{d}. It is important to keep in mind that particular uEVs are constantly travelling, so it is necessary to average this number to indicate a single value. Therefore, it is proposed to use a solution borrowed from the analysis of electricity demand, i.e., to use an hourly averaging based on 15-min measurements. This is represented by Formula (33):

- ${N}_{{G}_{i},\tau ,{D}_{d}}^{uEV}\u2014$ the number of uEVs in a given square G
_{i}of the V2Gsp operation area on day D_{d}at hour τ; - ${N}_{{G}_{i},{t}_{15},{D}_{d}}^{uEV}\u2014$ the number of uEVs in a given square G
_{i}of the V2Gsp operation area on day D_{d}at each quarter of hour τ;

_{i}in the selected quarter of the hour τ on day D

_{d}, i.e., the vehicle monitoring system should record the x

_{g}and y

_{g}coordinates of the given uEV defined for the given square G

_{i}. Thus, the state of the number of vehicles at hour τ on day D

_{d}can be presented by the following matrix:

- i$\u2014$ the successive squares of area G;
- NG$\u2014$ the maximum number of squares in area G.

_{d}, resulting in acceptance of V2G service provision $ACP{T}_{\tau ,{D}_{d}}$ and data on all correctly received reactions on that day $N{S}_{\tau ,{D}_{d}}$, i.e., those that were delivered to the uEV and either accepted or rejected. Due to the necessity of predicting the probability value P(EC), it is then necessary to group the data by each day of the week. Thus, for a selected day of the week (e.g., Monday), this can be expressed in the form of a matrix:

- $ACP{T}_{\tau ,{D}_{d}}\u2014\mathrm{the}$ number of reactions in hour τ on day D
_{d}, ending with acceptance of V2G service provision; - τ$\u2014$ each hour of the day D
_{d}; - d$\u2014$ the same days of the week consecutively in a month (e.g., Mondays).

- $N{S}_{\tau ,{D}_{d}}\u2014$ all correctly received reactions at each hour τ of the day Dd;
- $ACP{T}_{\tau ,{D}_{d}}\u2014$ the number of reactions in hour τ on day D
_{d}, ending with acceptance of V2G service provision.

- d—the same days of the week consecutively in a month (e.g., Mondays);
- ND—the number of the same days of the week in a month (e.g., the number of all Mondays in a given month).

- ${N}_{{G}_{i},\tau ,{D}_{d}}^{avg}$—the average number of uEVs located in the area of that square in each hour τ for the same weekdays in a month;
- ${N}_{{G}_{i},\tau ,{D}_{d}}^{SUM}$—the sum of all uEVs in the area G for each hour τ for the same weekdays in a month;
- ${N}_{{G}_{i},\tau ,{D}_{d}}^{SUMavg}$—the average value of the ${N}_{{G}_{i},\tau ,{D}_{d}}^{SUM}$ in the area G for each τ hour for the same weekdays in a month;
- ND—the number of the same days of the week in a month (e.g., the number of all Mondays in a given month);
- NG—the maximum number of squares in area G;
- ${W}_{{G}_{i},\tau ,{D}_{d}}$—the ratio between ${N}_{{G}_{i},\tau ,{D}_{d}}^{avg}$ to ${N}_{{G}_{i},\tau ,{D}_{d}}^{SUMavg}$.

_{d}in the settlement month.

## 5. Results and Discussion

_{EV}). As with P(EC), the calculation will be done based on the surveys and within the defined time frames. During the surveys, 51 respondents indicated that they own a BEV or PHEV, and after a further analysis of the responses, 22 respondents indicated that they currently own an ICE vehicle and plan to purchase an EV within the next 5 years. It should be noted that the number of respondents who plan to purchase a vehicle within 5 years and are users of an ICE vehicle is from post-processing of the survey data. According to Equation (22), the sum of these indices will be the set of all users to be considered when calculating the initial probability value P

_{1}(US

_{EV}). Each respondent could select multiple responses, i.e., multiple hourly intervals. Table 3 shows the distribution of responses to the question regarding the hours of movement of users and calculates the probabilities P(US

_{EV}). It is also worth mentioning that in order to calculate the probability P(US

_{EV}), one must first calculate the value P

_{1}(US

_{EV}), i.e., the actual value indicating the share of active vehicles in traffic, according to Formula (23).

- The number of days for analysis: d = 4;
- Analysis for one-hour τ;
- The number of service acceptances and all successful reactions determined randomly;
- The operating area of a V2Gsp (G) is 6 km × 6 km;
- In each square G
_{i}, a random number of vehicles was assigned according to ${N}_{{G}_{i},\tau ,{D}_{d}}^{uEV}\in 0,3000)$

_{1}is shown. Knowing that area G consists of a 6 × 6 km grid, it can be deduced that the number of NG squares is equal to 36, i.e., there are 36 G

_{i}squares in area G. After calculating the sum of uEVs in the area for each day d according to Equation (41), the average of the sums for the four days was then obtained.

_{1}is presented in Equation (72), based on Equation (46). The matrix of probabilities ${P}^{{G}_{i}}{\left(EC\right)}_{\tau ,{D}_{d}}$ is then presented in Equation (73). It should be emphasized that the trend of changes in the values of the probabilities was not evaluated in this case study, due to its purely illustrative nature.

## 6. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Description of Survey Results

No. | Question | Total Number of Responders | Single- or Multiple-Choice | Remarks |
---|---|---|---|---|

(1) | Are you interested in electromobility and its related technologies? | 130 | Single | |

(2) | Is there an electric vehicle charging station at your place of residence? | 130 | Single | |

(3) | Is there an electric vehicle charging station at your workplace? | 130 | Single | |

(4) | Do you currently own a private internal combustion engine (ICE) passenger car? | 130 | Single | |

(5) | What hours do you use your ICE car most often? | 86 | Multiple | Only those who answered “Yes” to question (4) |

(6) | Do you currently own a battery electric vehicle (BEV) or plug-in hybrid (PHEV)? | 130 | Single | |

(7) | What hours do you use your EV car most often? | 51 | Multiple | Only those who indicated that they own an EV in question (6) |

(8) | If you own an electric vehicle, please indicate where you would be most likely to charge it. | 79 | Multiple | Only those who indicated that they do not own an EV in question (6) |

(9) | Please indicate the charging location where you are most likely to do it. | 51 | Multiple | Only those who indicated that they own an EV in question (6) |

(10) | Are you familiar with vehicle-to-grid (V2G) or vehicle-to-everything (V2X) technology? | 130 | Single | |

(11) | If you owned an electric car, would you join a V2G program, which involves plugging your car into a home charging station at the order of a third-party operator and then discharging the battery to a specified level in exchange for financial benefits? | 130 | Single | |

(12) | During what hours would you be able to provide an electric vehicle discharging service at a home charging station? | 106 | Multiple | Only those who indicated a “Yes” or “Don’t know” answer in question (11) |

(13) | If you owned an electric car, would you join a V2G program which involves traveling to a point of service (e.g., an industrial facility), plugging your car into a charging station at the order of a third-party operator, and then discharging the battery to a specified level in exchange for financial benefits? | 130 | Single | |

(14) | During what hours would you be able to provide an electric vehicle discharging service at the point of service (e.g., industrial facility)? | 56 | Multiple | Only those who indicated a “Yes” or “Don’t know” answer in question (13) |

(15) | What distance would you be able to travel to reach the point of service? | 56 | Multiple | Only those who indicated a “Yes” or “Don’t know” answer in question (13) |

(16) | What type of benefit would be your main incentive to join a V2G program? | 130 | Multiple | 8 responders did not answer |

(17) | In exchange for a fixed monthly remuneration, would you be willing to standby to discharge an electric vehicle during the hours set by the V2G Program operator, being aware of potential fines for not providing the service? | 130 | Single | 1 responder did not answer |

(18) | In exchange for a financial benefit for a single discharging action, would you be able to provide discharging services without incurring fines for not providing the service? | 130 | Single | 2 responders did not answer |

(19) | What economic incentive would make you decide to discharge your electric vehicle? | 130 | Multiple | 12 responders did not answer |

(20) | Would you be able to perform actions in a critical situation for the operation of the National Power System, i.e., the risk of a system blackout, involving arriving at an agreed location and offering the available energy stored in the battery in order to rescue the power system? | 130 | Single | |

(21) | Which of the following requirements should be met in order for you to join a V2G program? | 130 | Multiple | 7 responders did not answer |

(22) | What population range represents a place where you stay most of the year (min. 180 days per year)? | 130 | Single | |

(23) | What gross salary range represents your current monthly earnings? | 130 | Single |

Question: | Are you Interested in Electromobility and Its Related Technologies? |
---|---|

Yes | 98 |

No | 11 |

Difficult to say | 21 |

Total number of respondents | 130 |

Question: | Do you Currently Own a Private Internal Combustion Engine (ICE) Passenger Car? |
---|---|

Yes | 86 |

No | 44 |

Total number of respondents | 130 |

Question: | Do you Currently Own a Battery Electric Vehicle (BEV) or Plug-in Hybrid (PHEV)? |
---|---|

Yes—BEV | 48 |

Yes—PHEV | 3 |

Considering purchasing an electric vehicle within 5 years | 26 |

No | 53 |

Total number of respondents | 130 |

Question: | (5) What Hours Do You Use Your ICE Car Most often? | (7) What Hours Do You Use Your EV Car Most often? |
---|---|---|

00:00–06:00 | 3 | 2 |

06:01–09:00 | 51 | 30 |

09:01–12:00 | 26 | 28 |

12:01–15:00 | 23 | 29 |

15:01–18:00 | 62 | 36 |

18:01–21:00 | 35 | 22 |

21:01–23:59 | 13 | 5 |

No answer | 1 | - |

Total number of respondents | 86 | 51 |

Question: | (8) If You Own an Electric Vehicle, Please Indicate Where You Would Be Most Likely to Charge It. | (9) Please Indicate the Charging Location Where You Are Most Likely to Do It. (EV Owners) |
---|---|---|

House or parking lot in front of the building | 68 | 44 |

Workplace | 44 | 15 |

Petrol station | 14 | 3 |

Shopping mall | 14 | 6 |

Sports and recreation centers | 4 | 0 |

Total number of respondents | 79 | 51 |

Question: | Are You Familiar with Vehicle-to-Grid (V2G) or Vehicle-to-Everything (V2X) Technology? |
---|---|

Yes | 74 |

No | 33 |

I have partial knowledge | 23 |

Total number of respondents | 130 |

Question: | If you Owned an Electric Car, would you Join a V2G Program, which Involves Plugging Your Car into a Home Charging Station at the Order of a Third-Party Operator and then Discharging the Battery to a Specified Level in Exchange for Financial Benefits? |
---|---|

Yes | 72 |

No | 24 |

Don’t know | 34 |

Total number of respondents | 130 |

Question: | If You Owned an Electric Car, Would You Join a V2G Program Which Involves Traveling to a Point of Service (e.g., an Industrial Facility), Plugging Your Car into a Charging Station at the Order of a Third-Party Operator, and then Discharging the Battery to a Specified Level in Exchange for Financial Benefits? |
---|---|

Yes | 30 |

No | 74 |

Don’t know | 26 |

Total number of respondents | 130 |

Question: | In Exchange for a Fixed Monthly Remuneration, would you be Willing to Stand by to Discharge an Electric Vehicle during the Hours Set by the V2G Program Operator, being Aware of Potential Fines for not Providing the Service? |
---|---|

Yes | 29 |

No | 68 |

Yes, but with other additional benefits | 32 |

No answer | 1 |

Total number of respondents | 130 |

Question: | In Exchange for a Financial Benefit for a Single Discharging Action, Would You Be Able to Provide Discharging Services without Incurring Fines for not Providing the Service? |
---|---|

Yes | 103 |

No | 25 |

No answer | 2 |

Total number of respondents | 130 |

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**Figure 3.**Methodology for calculating the probability of V2G service provision from a V2Gsp perspective.

Duration of the Survey | 6–19 July 2021 |

Form of the Survey | Internet—MS Forms |

Number of Answers Received | 130, including 5 interviews with EV users |

**Table 2.**Distribution of responses to the question regarding the hours of potential V2G service provision location of EndUs and calculated probability $P{\left(EC\right)}_{t}{}^{V2GL}$ values.

Question: | (14) During What Hours Would You Be Able to Provide an Electric Vehicle Discharging Service at the Point of Service (e.g., Industrial Facility)? | $\mathit{P}{\left(\mathit{E}\mathit{C}\right)}_{\mathit{t}}{}^{\mathit{V}2\mathit{G}\mathit{L}}$ |
---|---|---|

00:00–06:00 | 12 | 0.21 |

06:01–09:00 | 10 | 0.18 |

09:01–12:00 | 21 | 0.38 |

12:01–15:00 | 23 | 0.41 |

15:01–18:00 | 9 | 0.16 |

18:01–21:00 | 17 | 0.30 |

21:01–23:59 | 23 | 0.41 |

Question: | What Hours Do You Use Your Car Most Often? | Probability of Using Vehicle P_{1}(US_{EV}) | Probability of Electric Vehicle Availability Related to the Lack of Use P(US_{EV}) | |
---|---|---|---|---|

Hours: | BEV and PHEV Owners | ICE Owners, Who Intend to Buy an EV within 5 Years | ||

00:00–06:00 | 2 | 1 | 0.04 | 0.96 |

06:01–09:00 | 30 | 12 | 0.58 | 0.42 |

09:01–12:00 | 28 | 4 | 0.44 | 0.56 |

12:01–15:00 | 29 | 4 | 0.45 | 0.55 |

15:01–18:00 | 36 | 15 | 0.70 | 0.30 |

18:01–21:00 | 22 | 6 | 0.38 | 0.62 |

21:01–23:59 | 5 | 4 | 0.12 | 0.88 |

Hours: | Probability of Service Not being Interrupted 1-P(INT) | Probability of Electric Vehicle Availability Related to the Lack of Use P(US_{EV}) | Probability of uEV Reaction on the Provision of the V2G Service at the EndUs Location $\mathit{P}{\left(\mathit{E}\mathit{C}\right)}_{\mathit{t}}{}^{\mathit{V}2\mathit{G}\mathit{L}}$ | Probability Relates to the V2G Service Provision at an EndUs Location from a uEV Perspective P(uEV)_{V2GL} |
---|---|---|---|---|

00:00–06:00 | 0.95 | 0.96 | 0.21 | 0.20 |

06:01–09:00 | 0.42 | 0.18 | 0.07 | |

09:01–12:00 | 0.56 | 0.38 | 0.20 | |

12:01–15:00 | 0.55 | 0.41 | 0.21 | |

15:01–18:00 | 0.30 | 0.16 | 0.05 | |

18:01–21:00 | 0.62 | 0.30 | 0.18 | |

21:01–23:59 | 0.88 | 0.41 | 0.34 |

Hours: | Probability Relates to the V2G Service Provision at an EndUs Location from a uEV Perspective P(uEV)_{V2GL} | Probability Relates to the V2G Service Provision from a V2Gsp Perspective P(V2Gsp) | Probability Relates to the V2G Service Provision from an EndUs ^{1} Perspective P(EndUs) | Total Probability of V2G Service Provision at an EndUs Location P(A) _{V2GL} |
---|---|---|---|---|

00:00–06:00 | 0.20 | 0.99 | 0.9518 | 0.18 |

06:01–09:00 | 0.07 | 0.07 | ||

09:01–12:00 | 0.20 | 0.19 | ||

12:01–15:00 | 0.21 | 0.20 | ||

15:01–18:00 | 0.05 | 0.04 | ||

18:01–21:00 | 0.18 | 0.17 | ||

21:01–23:59 | 0.34 | 0.32 |

^{1.}In this case, EndUs is the secured customer of the V2G Program. This could be a household or other industrial facility.

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

${N}_{uEV}^{V2GL}$ | 30 |

${N}_{MA{N}_{ONLY}}^{V2GL}$ | 1 |

${N}_{MA{N}_{OPT}}^{V2GL}$ | 21 |

${N}_{OP{T}_{ONLY}}^{V2GL}$ | 7 |

${N}_{NOTINT}{}_{L}$ | 1 |

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Zagrajek, K.
A Survey Data Approach for Determining the Probability Values of Vehicle-to-Grid Service Provision. *Energies* **2021**, *14*, 7270.
https://doi.org/10.3390/en14217270

**AMA Style**

Zagrajek K.
A Survey Data Approach for Determining the Probability Values of Vehicle-to-Grid Service Provision. *Energies*. 2021; 14(21):7270.
https://doi.org/10.3390/en14217270

**Chicago/Turabian Style**

Zagrajek, Krzysztof.
2021. "A Survey Data Approach for Determining the Probability Values of Vehicle-to-Grid Service Provision" *Energies* 14, no. 21: 7270.
https://doi.org/10.3390/en14217270