*4.1. Considerations*

Table 3 contains the information regarding how the variables that have been introduced in the previously detailed equations have been given numeric values according to the existing related work. Some of those variables do not change in the three scenarios but many other do so, as they are closely linked to the case study involving the vehicle (fuel, distance driven, etc.). In this manuscript, the price of a V2G solution has been estimated to be \$7500 higher than an ICE-powered counterpart; as far as the United States are concerned, financial aid of up to that quantity is o ffered to the buyers of a full EV solution in some regions [3,46], so it has been included as an EV overprice in the model.

As for the battery replacement, it has been regarded as an average value of the figures found in [47] and [48]. The result has been depicted in Table 2, which considers four vehicle models. Several car models are considered in this chart, according to the information provided in [47]. It has been considered that the data in [47] can be divided into a best case scenario with a 40 kWh battery, where the Nissan Leaf owner does not require to pay any extra other than the battery replacement, and a worst case scenario where the Nissan Leaf owner must pay both for the special adapter kit (\$225) and labor costs of \$1000 when the old battery is exchanged with the new one (also with a 40 kWh battery). These results demonstrate alignment with other studies that show battery cost to have been declining during the last decades, such as the one shown in [49].


**Table 2.** Average battery cost per kilowatt/hour.

Considering that a vehicle battery of 40 kWh has been used for this manuscript, the cost of its replacement used in the numerical assessment results in **175.14 \$**/**kWh** × **40 kWh** = **\$7005.6**.

It must be noted that the figures corresponding to professional, frequent, and occasional drivers are strongly related to the information that has been inferred from several sources present in this manuscript, such as [50] and [58]. It is said in [50] that taxi cabs can be driven up to 70,000 miles, whereas it is claimed in [58] that average miles travelled by a vehicle are 11,370. This is the mileage that has been defined for frequent drivers (people who drive a car often enough to require it during a significant amount of days of the year but do not make a living out of using automobiles). In order to strengthen the criteria used to have an accurate view of the mileage that defines each case study (professional, frequent, and occasional drivers) two more references have been studied. On the one hand, it is said in [66] that 2813 gallons per car and per year are consumed by taxi drivers, who represent the archetypical professional driver use case. On the other hand, it is claimed in [67]

that 524 gas gallons are used yearly per vehicle. Despite these figures are prone to change as time goes by or depending on boom or bust economic cycles, they can be used as representative values of mileage and gas consumption. Consequently, and considering the ratio of gas usage existing between professional and frequent drivers (2813/524 = 5.368) it has estimated that a) since frequent drivers drive 11,370 miles per year and b) mileage figures for professional drivers are unlikely to go beyond 70,000 miles per year, professional driver mileage can be estimated as 11,370 × 5.368 = 61,033 miles per year. As it will be described in use case C, due to the data presented in [68], it has been estimated that occasional drivers make use of automobiles a quarter of time (which has been correlated to mileage) than frequent drivers. Another aspect to consider is the relationship between the mileage for each use case and the energy being used in every one of them. It has been estimated that, according to the figures that can be obtained from [50] and [58] and the ratio of gas usage explained in the previous paragraph, yearly mileage will be of 61,033 miles for a professional driver, 11,370 miles for a frequent driver and 2842.5 miles for an occasional driver. Additionally, if the average figures that can be extracted from [61] are considered as well, battery consumption would be of 20,301.67 kWh for professional drivers, 3781 kWh for frequent ones and 945 kWh for occasional ones. Furthermore, there is a certain battery degradation coming from using the V2G functionalities of the enhanced EV which is far more significant than usual wear o ff in an EV battery. Consequently, the energy that can be traded every year depends on (a) the amount of energy available for trade (the more frequent a person drives, the higher amount of energy is used for driving; hence, V2G energy costs will be overall higher as lower profits can be made from trading) and (b) battery degradation (as time goes by, capacity of the battery will shrink). These considerations are especially important for Tables A5–A7, where profitability of the solution is described in relation to whether battery degradation is present or not.

#### *4.2. Case Study A: Professional Drivers*

This case study involves people whose main job implies driving or taking passengers in a private-like means of transport (taxi drivers are the most typical example). This kind of job implies that there will be high costs in consumed fuel and maintenance for ICE-based vehicles. As represented in Table 3 and mentioned earlier, the costs and usage for professional drivers have been calculated considering those according to [53], namely, the yearly average consumption of gas is 2813 [63]/524 [67] = 5.368 times the one made by the frequent drivers even if, as mentioned before, there are cases where taxi cabs are driven up to 70,000 miles per year [45]. The following figures, adjusted to inflation, have been obtained:

$$Ex\_{ICE} = \\$68,843.39 \, Ma\_{ICE} = \\$404,203.13\, ^\circ F\_{ICE} = \\$90,926.12$$

It can be inferred that the total costs for a professional driver using an ICE automobile for twelve years are the following ones:

$$C\_{totICE} = \\$35,285 + \\$563,972.65 = \\$599,257.65$$

If a V2G solution is used instead of an ICE-based vehicle, the results obtained when adjusted to inflation are di fferent and overall lower:

$$Ex\_{V2G} = \ $12,278.20$ 
$$Ma\_{V2G} = \$$
90,887.29 \text{ total (with a 40 kWh battery)}$$

$$Fc\_{V2G} = \ $19,602.71$ 
$$V2G \text{ conversion + Cost of the installation = \$$
1936}$$

From these figures, it is calculated that the total costs for a professional driver using a V2G automobile are:

*CtotV*2*G*= \$42, 785 + \$1936 + \$7005.60 + \$12, 278.20 + \$19, 602.71 + \$90, 887.29 = \$174, 494.79


**Table 3.** Variables included in the mathematical model.


**Table 3.** *Cont.*

\* Professional drivers, \*\* Frequent drivers, \*\*\* Occasional drivers \*\*\*\* 120% represents that a charge cycle and a fifth of another one are lost \*\*\*\*\* Chosen as a plausible hypothesis.

As it can be inferred from the previous calculations, it can be seen that the V2G solution is far more economically efficient for a professional driver in the long term than an ICE vehicle. The graphical representation of the cumulative result that has been calculated for each of the years is displayed in Figure 2. At the same time, Table A1 is showing in the Appendix A how numerical calculations vary on a yearly basis as well.

**Figure 2.** Graphical representation of the calculation results for professional drivers.

If the results that have been obtained are separated so that operational costs can be considered more accurately, it can be seen how despite a) a higher Capex if an EV is purchased; b) the required infrastructure to make the EV work as a V2G solution; and c) a battery renewal, the operational costs of the ICE vehicle are far higher in this scenario starting from year 1, mostly but not only, due to the maintenance costs required to have the ICE working satisfactory. This is the key advantage that the V2G solution has, which makes it economically far more advisable under these circumstances if compared to the ICE alternative. The graphical comparison of Opex costs has been displayed in Figure 3. Note that the battery replacement has been included as an Opex-related expenditure, so it is present in the cumulative figures. Moreover, it is considered that the first year of usage (year 0 in the previous graphs) there are not operational costs, which start being added at year 1. That is why this and the other equivalent graphs show year 0, whereas Opex-related ones do not.

Note that the previous results have been obtained under conditions deemed as "suboptimal" in terms of cost of energy purchase and sell. That is, all the energy has been bought during valley hours and sold during peak hours in a proportion of 80/20. This implies that according to the parameters that have been included in (8), (9), (10), and (11), it has been considered that 80% of the energy purchased was done so during valley hours and the other their during peak hours (so that *fbb* = 0.8 and *fsb* = 0.2), whereas 80% of the energy was sold during peak hours and the other 20% during valley ones (and thus, *fss* =0.8 and *fbs* =0.2). Furthermore, small losses when charging and discharging the vehicle may result in a loss of electricity during these procedures (hence, *ef* = 0.95, as described in Table 3. Lastly, the degradation of the battery has also been considered when doing the calculations according to the mathematical model. Hence, the energy that has been estimated to be sold every year decreases over time in the rate established in (14).

Overall, the proportion that is sold during each of the time periods will depend on the available power to operate in the market and the availability of the user of the V2G solution. There are two important aspects that can be inferred by all these calculations: under a time period of longer length than the one used here (12 years) the advantages of the V2G solution over the ICE one will be even more notorious as the ones portrayed in this time span, as cost differences between both of them are always unfavorable for the ICE vehicle. Additionally, a suboptimal scenario has little to no influence in the calculations done for both battery rental and acquisition, as the former one will become unfavorable in the long term, according to the figures obtained for battery rental that have been introduced in Section 4.5.

**Figure 3.** Yearly and cumulative OPEX expenses between an ICE vehicle and a V2G, professional drivers.

#### *4.3. Case Study B: Frequent Drivers*

The most representative situation that can be conceived for this use case is a freelance worker with a specific job that make them travel a significant distance every day (self-employed positions, etc.), but do not use driving as their business core. Frequent drivers are regarded in this numerical assessment as the average group of people, so they have been assigned the default figures that have been found in literature.

If the same calculations that were done previously are repeated for this use case, the next results are obtained adjusted to inflation:

$$Ex\_{ICE} = \\$12,824.83 \, Ma\_{ICE} = \\$88,770.04$$

$$F\_{ICE} = \\$16,937.54$$

Thus, the following costs will have to be assumed by the owners of an ICE vehicle during its lifetime will be

$$C\_{totICE} = \\$35,285 + \\$118,532.40 = \\$153,817.40$$

Should a V2G solution be used, the results would be

$$\text{Ex}\_{V2G} = \ $2486.41$ 
$$\text{Ma}\_{V2G} = \$$
30,401.65 \text{ (with a 40 kWh battery)}$$

$$\text{Fc}\_{V2G} = \ $-9233.58$ 
$$\text{V2G conversion + Cost of the installation} = \$$
1936$$

Note that the fuel (electricity) cost for the V2G vehicle is negative for this case study, due to the fact that selling the energy surplus is creating a profit for the end users of the vehicle, to the point that energy trading results economically advantageous for the end user in terms of energy costs. This is due to the fact that energy is being bought and sold in a proportion that makes the sold energy more economically significant in absolute values than the one that is being bought. Therefore, the engagemen<sup>t</sup> in energy trading for clients using the V2G solution becomes profitable, as the usage of vehicle-to-grid technology makes possible decreasing the costs of using an electric vehicle when the unused power is sold back. Thus, the total costs for a frequent driver that owns a V2G automobile would be:

*CtotV*2*G* = \$42, 785 + \$1936 + \$7005.60 + \$30, 401.65 − \$9233.58 + \$2486.41 = \$75, 381.09

Figure 4 depicts the graphical representation of the obtained results whereas the calculations that have been carried out are presented in Table A2 of the Appendix A. Note that Figures containing graphs show a sudden non-linearity for the costs of the V2G solution event between years 8 and 9. This is due to the fact that it has been estimated that it will be the moment when battery from the V2G solution will have to be eventually replaced, so expenses rise accordingly to the \$7005.60 that have to be spent. Moreover, benefits towards the V2G solution do not start right away but after year 2, thus showing that this scenario is less advantageous due to the lower costs for the ICE vehicle.

**Figure 4.** Graphical representation of the calculation results for frequent drivers.

As mentioned previously, Figure 5 depicts the di fferences in operational costs between the V2G and the ICE vehicle. Albeit with a smaller gap resulting from the lesser usage of the automobiles, the results are essentially replicated for this case study: yearly expenses, and cumulative ones when the battery replacement costs are included, are lower for the V2G than the ICE vehicle.

**Figure 5.** Comparison between yearly and cumulative OPEX expenses between an ICE vehicle and a V2G, frequent drivers.

As stated previously, purchasing and ICE vehicle results in a worse economy cost for the prosumer if compared to acquiring a full V2G solution (as the former implies higher costs of fuel, maintenance and externalities during the vehicle lifetime). Fuel consumption falls considerably for the V2G in this scenario, as more energy is used for trading operations. The suboptimal scenario is also used for this use case with the same set of variable values that was employed before (*fbb* =0.8, *fsb* =0.2, *fss* =0.8, *fbs* =0.2, and *ef* = 0.95). As in the previous case, despite obtaining a worse result with a suboptimal scenario where energy is neither bought nor sold under the best possible circumstances, it is still better than the one that would be obtained with the ICE solution.

#### *4.4. Case Study C: Occasional Drivers*

An occasional driver has been defined with the same criteria that was done in [68] and [69], that is to say, "A driver who operates a vehicle less than 25 percent of the total miles put on the car during a year". Consequently, it can be assumed that, when compared to frequent drivers, an occasional driver will use the vehicle one fourth of the time a frequent driver would, so all the expenses have

been considered to be one fourth of the ones calculated in the previous case study. As far as the ICE automobile is concerned, results adjusted to inflation are as follows:

$$Ex\_{ICE} = \\$3206.21 \, Ma\_{ICE} = \\$34,607.92$$

$$F\_{ICE} = \\$4234.38$$

Therefore, the resulting budget for an ICE vehicle owned by an infrequent driver would be

$$C\_{totICE} = \\$35,285 + \\$42.048,52 = \\$77,333.52$$

Thus, operational costs have become lower than the purchase of the vehicle itself. If a V2G solution is used, results obtained are

$$Ex\_{V2G} = \ $805.70$ 
$$Ma\_{V2G} = \$$
20,015.83 \text{ (with a 40kWh battery)}$$

$$F\_{V2G} = -\ $14,128.02$ 
$$V2G \text{ conversion } + \text{ Cost of the installation} = \$$
1936$$

As it happened before, the fuel costs for electricity in this case are negative. What is more, since there is more electricity available to be sold (as it is used to a lesser extent by the vehicle), saving costs become even more prominent than in the previous case study. The final costs would be as follows:

$$C\_{\text{tot}\,V2G} = \ $42,785 \,+ \,\$ 1936 \,+ \,\ $7005.60 \,+ \,\$ 805.7 \,+ \,\ $20,015.83 \,- \,\$ 14,128.02 \,= \ $\$ 5,419.48 \,\text{Hz}$$

As it was done in the previous cases, the suboptimal scenario has been used with the same set of variables (*fbb* = 0.8, *fsb* = 0.2, *fss* = 0.8, *fbs* = 0.2, and *ef* = 0.95) energy costs are higher than in the optimal scenario. Unlike previous case studies, the EV-V2G is not as in clear advantage over the ICE vehicle in terms of expenses as it was before. What is more, it would not be until the fourth year of ownership that the V2G solution shows a better performance when compared to the ICE automobile. The main reason for this is that, although the V2G solution decreases its costs as long as the battery is kept the same, as soon as the latter is replaced, costs rise above the ICE level, thus closing the gap between the two kinds of vehicles. The graphical representation of this fact is shown in Figure 6.

**Figure 6.** Graphical representation of the calculation results for occasional drivers.

Additionally, Figure 7 shows a comparison between operational costs between the V2G and the ICE options for occasional drivers. As in previous cases, yearly and cumulative expenses for operational costs are lower when the EVV2G is used instead of the ICE. However, the differences are less significant this time, to the point that the higher purchase cost of the EVV2G and its frequent battery replacement make it harder to justify using it. Interestingly enough, if the battery replacement is not taken into account, OPEX for the V2G shows almost stagnant figures. This is due to the fact that the V2G is used so little that it is highly available to trade energy in favorable terms with the overall grid system, and it results in a profit for the end user who owns it.

Table 4 shows a numerical summary of the cost of these three use cases.

**Figure 7.** Yearly and cumulative OPEX expenses between an ICE vehicle and a V2G, frequent rivers.


**Table 4.** Costs summary of ICE and V2G.

#### *4.5. Comparison between Battery Rental and Battery Ownership*

If it is chosen to purchase an EV where the battery is rented rather than acquired with the same vehicle, the average costs obtained after twelve years (adjusted to inflation) with one battery replacement according to the mathematical model are as follows:

> *CAPEXV*2*G* = \$51, 726.60 (with a 40 kWh battery purchase) *CAPEXV*2*G* = \$56, 586.66 (with 40 kWh battery rental)

The yearly comparison of each option has been depicted in Figure 8, whereas the calculations themselves have been placed in the Appendix A, Table A4.

**Figure 8.** Graphical representation of battery rental costs versus battery purchase ones.

If these results are compared thoroughly, it can be seen that the battery purchase option becomes more advisable to use in the long term when the EV has been enabled to make use of V2G technology, whereas it is the opposite for shorter term ownership (5 or less years). This is due to the fact that the battery installed in the vehicle becomes depleted at a faster rate than a conventional EV which makes no use of V2G, thus being more likely to have its battery replaced once during its usage timespan. Should the battery not require to be replaced, then battery ownership option would result more competitive. However, it must be taken into account that usually, no manufacturer that o ffers battery rental as an option expects its customers to use it as part of the equipment of V2G technology. Probably, manufacturers would put restrictions to their usage if end users were openly planning to use their vehicles with this kind of technology.

It must be noted that, with the battery rental option, all the considerations done previously regarding battery degradation are still valid. Battery will degrade at a similar rate regardless of how the owner pays for its usage, as the components and chemical reactions that make it work remain the same in both cases. That is why battery replacements are considered under the purchase option, as any V2G solution will make use the car battery intensively (due to the very nature of V2G, which demands more frequent energy discharges and recharges than a EV battery used one-way only) and will have to be replaced after a relatively short amount of time, whereas a rented battery will degrade with the same parameters but the cost of its replacement will not have to be assumed by the end user.

Nevertheless, the scenario where the rented battery of the EVV2G is replaced every year could be put forward as another part of this study. In this case, yearly degradation could be considered as zero (as the battery would be replaced every year) and greater amounts of energy could be purchased and sold, due to the battery capacity being maintained during the lifetime of the V2G solution. In this case, more energy would be available for trading operations, thus resulting in an increase of the profitability of the rented battery V2G solution. Yearly surplus in energy availability would progressively increase compared to a purchased battery, as shown in Table 5. Should it be assumed that only yearly degradation is taking place with the battery rental option, results would vary in favor of the latter, but the overall tendency would be the same: for long periods of time, battery purchase would be more e fficient than battery rental.


**Table 5.** Profit difference between battery degradation and non-battery degradation. Assuming a yearly replacement of the battery, it would be the di fference of battery renting vs. battery ownership.

The yearly figures that would be obtained would be as portrayed in Tables A5–A7 for professional, frequent and occasional drivers. Note that regardless of the kind of driver that makes use of the

solution the di fference is the same in every case, as the increase in energy available is due to the same reason (the same improvement in energy used for trade operations).

#### **5. Impact on Grid Utilities**

The previously described model has been conceived for its usage in V2G solutions that become part of the entities able to provide power to sell and purchase at the electricity markets. For example, in [70] it is stated that despite the dominant trend in charging V2G is using o ff-peak hours, coincident user patterns can pose a threat for power system components both when charging vehicles and injecting power to the grid. The authors claim that it would be possible to overcome that problem by assessing the suitable V2G penetration level for optimal operation and precisely planning the V2G behavior on the distribution system. Furthermore, [71] describes how the addition of V2G parking lot facilities creates additional energy losses in the feeders of the electric utility owners derived from the behavior of reactive power injection and the load patterns of the users. A way to minimize this issue would be locating optimally a parking lot along the aforementioned feeder.

Additionally, V2G technology can be used to make power consumption more regular and avoid the peaks and valleys that create issues for the power grid: because of the tendency of end users to charge their vehicles in o ff-peak hours and not to demand that energy during the peak ones, V2G e ffectively becomes a way to enhance peak shaving and valley filling curves of energy demand. It is stated in [72] that combining V2G solutions with energy storage and photovoltaic electricity generation could result in a reduction of up to 37% during peak periods. Furthermore, in [73] it is claimed that by following a strategy based on comparing a forecasted load curve with another one based on forecasting available charge and discharge power peak shaving can be controllable and real, thus proving that V2G can be used as a way to create a more balanced demand of electricity. What is more, it is said in [74] that a high penetration of EVs is very likely to demand a stronger and more reliable power network; according to the authors of that manuscript, transformer replacement costs reach 72% of the total deployed transformers value with an EV penetration of 50%. However, this manuscript does not consider that the added power for that V2G can be brought to the power grid. Moreover, it is stated in [75] that distribution transformer may experience a measurable loss of life resulting of the increased strain that power demanded by plug-in hybrid electric vehicles (PHEVs) may produce. In this case, this study deals mostly with how PHEVs interact with the grid, describing the possibility of using V2G technology as part of the applications of PHEVs. The results shown in this manuscript demonstrate that V2G can be a viable solution for end users to obtain an economical benefit with their vehicles. However, they also show that the status of development in batteries makes profitability di fficult, as the rapid degradation and their relative expensive cost depletes most of the benefits that could be obtained. Arguably, other options implying reducing the costs of purchasing an EV and converting it into an EVV2G could be satisfactory, but such a solution looks unlikely to happen in the short term. Overall, it is assumed that the existence of V2G solutions will strain the power grid in the short term, but there are advantageous solutions that can be integrated in the resulting smart grid. A typical solution that could come to this system advantage would be the integration of V2G technology with the other components of the power grid via middleware architectures [76] so they can be seamlessly included in such heterogeneous deployments.
