Energy and Demand Forecasting Based on Logistic Growth Method for Electric Vehicle Fast Charging Station Planning with PV Solar System

Abstract

Electric vehicle (EV) charging may impose a substantial power demand on existing low voltage (LV) and medium voltage (MV) networks, which are usually not prepared for high power demands in short time intervals. The influx of E-mobility may require an increase in grid reinforcements, but these can be reduced and optimized by a combination of new technologies, tools, and strategies, such as the deployment of solar PV generation integrated with aggregated energy storage systems. One of the challenges in the implementation of charging infrastructures in public stations is coupling the projected sizes of energy demand and power requirements in each location for each charger. This paper describes a method to estimate projected values for energy consumption and power demand in EV fast charging stations (CS). The proposed ideas were applied in a concept facility located in Campinas, Brazil, in a structure equipped with two 50 kW DC Fast Chargers, local 12.5 kW/13.2 kWp PV generation (to reduce energy impacts to the grid), and a 100 kW/200 kWh storage system, using electrochemical batteries (to minimize peak power requirements).

1. Introduction

The rapid growth of distributed energy resources (DER) in recent years has subjected distribution systems to new challenges in accommodating new technologies while maintaining acceptable levels of reliability. Among the DER, electric vehicles (EV) are considered strategic assets, as they can behave as a load or generator (from vehicle to grid; V2G), demanding high power in a short time interval during the charging process and also having unpredictable insertion characteristics, typical of disruptive technologies on the market. Mainstream EVs have the potential to transform the automotive industry through the electrification of transportation and can contribute to decarbonization of the planet [1].

In order to mitigate the effects of connecting EV chargers to the grid, charging structures equipped with local generators and energy storage systems (ESS) can be used to reduce energy consumption and decrease power demand from the grid. This would mitigate the impact at the point of coupling and would also contribute to improvements in the short-term profitability of the deployment of fast charging stations (CS) [2].

For the future of electric vehicles and potential number of users of EV charging services, studies of EV fleet growth are essential. Previous studies have used exponential and logarithmic models based on consumer choice and behavior, such as discrete consumption or agent-based models, to consider the diffusion of innovations, as well as logistic growth models [3,4,5].

Due to it being the early stages of EV insertion, charging patterns and consumer preferences are not yet entirely known, so it has been common to make assumptions based on surveys (opinion polls) [6]. Considering user data available in NHTS, the National Household Travel Survey (an inventory of the U.S. residents’ travel behavior), [7] presented a methodology that built electric vehicle adoption scenarios and simulated charging behavior in the long term under a mature BEV market, considering factors such as high BEV penetration, long range, and adequate charging infrastructure with fast chargers. By aggregating an individual’s charging decisions, the collective effects of nationwide BEV charging under a mass-market scenario could be examined. [8] presented a strategy to forecast the electricity demand of electric vehicles by analyzing consumer charging patterns. The authors conducted a survey with discrete choice experiments where consumer preferences were estimated through a mixed logit model, simulating the effect of choices related to EVs adoption scenarios. The work estimated the number of EVs in Korea, compared the electricity consumption of EV charging with total electricity consumption in Korea, and predicted overall impact on power load. Similar approaches were presented in [9] (Italy) and [10] (Austria).

In developing countries where there are no widely established charging networks and no subsidies for infrastructure development, impact assessments in terms of energy and demand must be observed for each specific region, at a microregional level. This study presents an analysis that uses a localized approach, as opposed to an approach at the country or macroregional level, and the projections and estimates aim to evaluate the impacts of energy and demand allocated to each charging station.

Once the intra-urban fleet associated with vehicles registered in a specific location is known, planning a solution that integrates generation and storage requires one critical piece of information: the forecast of consumption and demand associated with the EV fast charging stations (FCS). In this context, this paper describes a strategy to predict the energy consumption and power demand for a FCS installed in Campinas, Brazil. Initially, the logistic growth method is used to carry out vehicle fleet projections (number of vehicles). Based on fleet data, we propose a method to evaluate the region of influence for each charging station, and assess the energy requirements for each EV charger, considering the presence of other stations nearby. The results are then applied to design a Public EV Fast Charging Station Project (PFCSP), equipped with a photovoltaic (PV) solar generation and energy storage system with lead-carbon battery cells, that is implemented under a research and development initiative.

For the reader, this paper is organized as follows. Section 2 presents the proposed systems for the research and development project. Section 3 describes the methodology used to estimate projections of the number of electrical vehicles in the city of Campinas, Brazil. Section 4 presents the methodology used to estimate the required number of charging stations to meet power demand projections. Section 5 presents the proposed EV system. Finally, some conclusions are drawn in Section 6.

2. Project Description-Public EV Fast Charging Stations

We applied a method to estimate the energy and demand requirements to subsidize the development of a research and development project (R&D). This R&D focused on expanding charging infrastructure with reduced impact on the distribution network, integrating charging stations, energy storage system based on lead-carbon battery cells, and grid-tie photovoltaic systems through an energy management system (EMS). The objective was to develop a modular system able to be inserted into urban and suburban environments, considering the connection constraints of the electrical grid, and allowing multiple vehicles to be recharged at feeder branches with low available power capacity. The batteries are key components to reduce the impact of high-power recharges in the distribution network and to maximize the use of photovoltaic energy generated on site; thus, increasing the self-consumption factor of the connection point.

The R&D project PD-00063-3059/2019 entitled “Solutions to Support the Expansion of Electric Vehicle Recharge Infrastructure: EV Charging Stations Integrated with the Battery Technology (Lead-Carbon, PbC) and Photovoltaic Systems (PV)” was approved under the National Electric Energy Agency (ANEEL) Research and Development (R&D) Program, in the strategic initiative 022/2018. It started in 2019, with proponent CPFL Energy and executing entities the Federal University of Pernambuco (UFPE), Edson Mororó Moura Institute of Technology (ITEMM), and Accumulators Moura and the Advanced Institute of Technology and Innovation (IATI).

A simplified electrical connection diagram of the PFCSP is shown in Figure 1. The photovoltaic system is composed of a 12.5 kW/13.2 kW_peak inverter. Two EV fast charging stations (50 kW DC + 22 kW AC Rated Power, equipped with CCS2, CHAdeMO, and AC Type 2 terminal plugs) are supplied by a 100 kW/200 kWh battery storage system (grid-tie).

The design of the solution is illustrated in Figure 2. The energy storage system is allocated to a container-type structure. The generation of energy to reduce the consumption associated with recharges is produced by 30 PV modules mounted on a metallic structure (which functions by fixing PV modules and providing protection against the heat and sunshine for parked vehicles during the charging process). The charging stations are public and can be accessed by users without restrictions upon payment for EV recharging. The next topic describes the studies used to estimate electric vehicle charging station (EVCS) energy consumption requirements.

3. Electric Vehicle Fleet Growth Forecast

3.1. General View

To couple the sizing and specifications of the components to the market reality, keeping in mind the expected lifetime of the equipment, power demand estimations must be made. To do this, we must know the number of electric vehicles using the EVCS. This information is essential, but difficult to measure because public charging points can be accessed by different types of users with different profiles.

To estimate the energy consumption of the EV stations, the first step is to model the electric vehicle fleet in the city. To do this, we implemented a survey of the history of vehicles, and used this as a database to project the adoption of electric vehicles. Then, a mathematical model was applied to make projections and scenarios of the adoption of electric vehicles. Finally, based on the projections of electric vehicles, we estimated the recharging demand and expected average energy consumption for the FCS.

The following section describes the mathematical model used to forecast scenarios for the EV fleet in the city of implantation.

3.2. Modeling the EV Intra-Urban Fleet-Mathematical Model Based on the Logistic Growth Method

Diffusion models (e.g., the Logistic, Bass model, and Gompertz model) describe the development of product market acceptance over time and are particularly useful if historic data are available [11,12]. These models also have some drawbacks, such as the need to endogenously estimate the market potential. However, diffusion models are relatively straightforward to implement and can be based on historical data of the innovation or a similar product [3]. Logistic models have been particularly useful in applications with limited information, to project the adoption rate of new technologies. For instance, in [13], a comparison of the application of different diffusion methods for the telecommunications market is presented. A number of previous studies indicate that Logistic models are the most appropriate method in explaining the telecommunications market. [14] shows that the Logistic model has better performance compared with the Gompertz model in the case of the mobile phone market in Colombia. [15] uses four predictive functions including Logistic, Gompertz, Bass, and Bass discrete models to evaluate the number of new adopters in the mobile telephone market of Taiwan. Additionally, [16] shows that the Logistic model tops the Bass model in sale forecasting with limited information. The relevance of logistic models for EV predictions has been demonstrated in prior studies (e.g., [17,18]). In [3], the logistic growth method is used to forecast the trajectory of electric vehicle sales in several countries. In summary, the logistic growth model has presented consistent results in applications involving the projection of the number of EVs, particularly in assessments with limited information (i.e., absence of an extensive database associated with the number of vehicles in the region under study).

Electric vehicles are considered a technology with adoption of disruptive market behavior, which is characterized by rapid growth. Logistic growth models (LGM), such as those proposed by Nele Rietmann, Beatrice Hügler, and Theo Liven, described in [3], can be used to make projections of disruptive resources (DR), considering aspects such as the saturation of resources in the market.

The LGM is inspired by the growth of new populations of organisms in nature. Therefore, contrary to exponential and logarithmic methods of diffusion of innovations, there is an assumption of limited resources in the environment that prevents the unlimited growth of any new group of individuals in wild populations. These modelling assumptions results in an S-shaped curve, with accelerated growth of the innovative technology at the beginning, stabilization, and deceleration as a function of saturation at the end of the curve, as illustrated in Figure 3 [3].

Although the model was initially used to project populations in nature, it was observed that historically, the rate of adoption (rate of Technology Adoption—TA) of new technologies in society has had the same S-curve profile. For illustrative purposes, Figure 4 shows historical values of the rates of adoption of new technologies in the United States, where it is verified that, despite some displacement deviations in the vertical axis (jumps or abrupt drops in adoption rates), the historical behavior of S-shaped growth. Additionally, the rates of diffusion and adoption of new technologies have increased over the years (faster disruptive growth) [19], as can be observed in Figure 4.

Studies based on the S-shaped logistic growth curve presented in recent years have indicated that the LGM model is one of the most accurate for forecasting EV fleet growth and assessment of adoption [3]. It is worth noting that balancing considerations must be made when applying this model, so that previously known real conditions are not extrapolated. In this work, the procedure described in [3] was adapted to estimate the electric vehicle fleet in the city of Campinas (intra-urban fleet), as presented in [20]. The steps for applying the model are described in the following section.

3.3. Methodology Implementation Steps

Considering the LGM formulation, the electric vehicle fleet can be estimated using the logistic growth general equation:

$$I\left(t\right)=\frac{L}{1+\left(\frac{L}{I\left(0\right)}-1\right)\times e^{-kLt}}$$

(1)

where I(t) is the estimate of the vehicle fleet over time t (years), L is the saturation limit of the logistic growth curve, I(0) is the initial fleet in the reference year for the projections, and k is the growth factor (a parameter of the LGM based method). Curve parameters must be adjusted to historical data. However, in applications aimed at specific locations, one difficulty is finding the historical record of the number of electric, hybrid, or ICE (internal combustion engine) vehicles. The flowchart in Figure 5 presents a step-by-step method to estimate the EV fleet, describing the procedures adopted to forecast the growth projection for the local EV fleet (considering different available databases).

Steps 1 and 2 estimated the total light/passenger vehicle fleet, including combustion ICE vehicles. Equation (1) could be applied. Historical records indicated that the city’s registered fleet was around 600,000 vehicles. The parameters of the equation that adjusted the behavior of the S-curve to the real behavior of this fleet are 747,800 for L and 1.18 × 10⁻⁸ for k.

Steps 3 and 4 estimated the fleet but only considered vehicles equipped with electric propulsion that could be externally charged (i.e., BEV and PHEV electric vehicles). The general form of the logistic growth equation for EVs in Campinas is presented in Equation (2). Based on steps 2 to 4, the value k_VE is 7.14 × 10⁻⁸ and L_VT = L_VE = 747,800.

$$I_{EV}\left(t\right)=\frac{L_{EV}}{1+\left(\frac{L_{EV}}{I_{EV}\left(0\right)}-1\right)e^{-k_{EV}\times L_{EV}\times t}}$$

(2)

Figure 6a presents the growth curve adjusted to historical data, defined in Equation (2), for the EV fleet in the city (comparison of registered data to the model)—the model adequately fits the data. After fitting the curve to historical data, the model can be used to obtain future projections. In the long term, one of the uncertainties is the growth rate or the technology adoption ramp. Considering variations in growth factors, it is possible to derive different growth scenarios. Figure 6b illustrates the EV fleet projections for three distinct scenarios.

In all scenarios the fleet reaches the saturation threshold, but occurs in a different period for each scenario. In scenario 1, the growth factor of the EV fleet is equal to the historical growth of the TVF. In this case, $k_{I }=1.0\times k_{VT}=1.180\times {10}^{-8}$. In scenario 2, the EV fleet growth factor is 80% of the historical TVF growth ($k_{II }=0.8\times k_{VT}=9.44\times {10}^{-9}$). Finally, in scenario 3, which is more pessimistic in terms of adoption, a growth factor for the EV fleet of 60% of the historical growth of the fleet is considered ($k_{III}=0.6\times k_{VT}=7.08\times {10}^{-9}$).

Considering the developed model, Figure 7 presents curves representing the replacing of internal combustion vehicles with electric vehicles. Projections indicate that, by the end of the 21st century (between 2089 and 2138), up to 99% of vehicles registered in the city could be electric.

Table 1. Number of Electric Vehicles in Campinas: Projection Scenarios.

Year	2022	2023	2024	2025	2026	2027	2028	2029	2030
Scenario 1	1924	2520	4769	9002	16,895	27,646	39,367	52,103	65,891
Scenario 2	1924	2520	4769	9002	15,277	22,057	29,347	37,173	45,559
Scenario 3	1924	2520	4769	8323	12,154	16,210	20,501	25,039	29,833

and Figure 8 show the growth projections for the number of EVs in the city of Campinas, for the scenarios described previously. It is estimated that, by 2030, a fleet between 29,833 to 65,891 EVs will be registered in the city.

4. Demand Forecast for Energy Charging—Campinas City

Although projections indicate that, by 2030, the Campinas fleet will reach 65,891 EVs, the energy consumption related to charging this number of vehicles is not entirely absorbed by public charging stations, because charging events can also be carried out at home or at work (on private/proprietary chargers). Considering the apportionment of recharging events in different situations, this topic presents a survey of the estimated consumption [kWh] and demand [kW] for the EV Public Fast Charging Stations Project (PFCSP) planned for Campinas.

Due to the low level of maturity of the recharge market, the behavior and usage profiles of EV owners, including general preferences of how and where charging is carried out are still not widely known. Some surveys indicates that up to 80% of charging events occur at home charging stations and between 15 and 25% of recharges in chargers installed in workplaces [6]. Public fast charging stations are the type of infrastructure with the lowest percentage of use, with only about 5% of recharge occurrences (also known as opportunity recharge). These surveys must be only interpreted in their specific contexts, as these percentages may vary depending on the local characteristics of the region.

The work proposed by Barech and Moser in [10], based on a case in Austria, evaluated the distribution of future recharge allocation across different types of charging stations, in order to evaluate the need for EV infrastructure in the country. The results of the model indicate that, for Austrian users, the majority of recharges (approximately 88%) occur at the user’s residence (Category 1—Residential recharge when the user is at home). Approximately 8.8% of recharges are carried out at the workplace (Category 2—Recharge at work). About 1.7% of recharges are carried out at public charging stations (Category 3—Recharging at public stations) and, finally, about 1.5% of recharges take place at fast stations (Category 4—Recharge at fast). These percentages, however, can be highly correlated to the availability of each type of charger. In Brazil, the recharge rate on the public network can be between 10% (for users with residential recharge availability) and 24.4% (for all types of recharges), according to a study carried out within the Promobe project [23]. In summary, these values are imprecise and based on the experience of other countries and should be reassessed when more data on the Brazilian profile become available.

As there remains a high degree of uncertainty related to the use of public charging stations in Campinas, three scenarios of recharge rates in the public network will be considered: Scenario A—5% of recharges occur at public stations, Scenario B—10% of recharges at public stations, and Scenario C—15% of recharges at public stations. In this way, each projection scenario (Scenarios 1, 2, and 3) will correspond to a recharge rate scenario in public stations. In Figure 9, the expansion of all scenarios of projection of electric vehicles and the rate of use of public appliances is presented (Scenario 1, 2, and 3 of projection of fleet combined with scenarios A, B, and C of frequency of recharging in public chargers).

Once the scenarios of EV charging at public stations have been defined, the average consumption [kWh] can be estimated (as will be described in the next section), to later plan the necessary infrastructure to meet electricity requirements.

4.1. Energy Consumption and Demand Estimates

Based on the EV fleet projection data, we obtained the average energy consumption associated with Campinas (intra-urban fleet) in charging events carried out at public charging stations. The consumption, in kWh, depends on the usage profile, which varies depending on the vehicle usage mode.

For the macroregion of interest (state of São Paulo, Brazil), the average daily commute is approximately 54.1 km/day [23] (average value). The expected value of consumption as a function of recharges $C_{avg}\left(s,t\right)$, for the number of vehicles in the scenarios presented previously, can be estimated using Equation (3).

$$C_{avg}\left(s,t\right) \left[\frac{\mathrm{kWh}}{\mathrm{day}}\right]=N_{EVs}\left(s,t\right)\times D_{avg}\left(t\right)\left[\mathrm{km}/\mathrm{day}\right]\times {\gamma }_c\left(s,t\right)\times C_e,$$

(3)

where $D_{avg}$ is the average daily commute or intensity of use, in km/day, for which we adopted values from the Pro study; $N_{EVs}$ is the number of electric vehicles, based on the previously presented EV projection scenarios (s) in the year t; ${\gamma }_c$(s,t) is the rate of use of fast public fast charging stations (PFS), for which scenarios were also previously presented, and $C_e$ is the average value of energy consumed by the battery system per km, in kWh/km, as presented in the following section.

4.2. Evaluation of the Energy Consumption Parameter—Ce

The $C_e$ parameter represents the energy consumption of each category of vehicles, and can be estimated as a function of the energy E in kWh consumed by each vehicle and its average autonomy $A_{VE}$ (km), as presented in Equation (4):

$$C_e=E \left[\mathrm{kWh}\right]/A_{VE}\left[\mathrm{km}\right]$$

(4)

The $C_e$ value used in the simulations was based on the efficiency data based on tests carried out by Inmetro [24], which includes the average energy consumption of the most used EV models in Brazil, with a reference value of 0.16 kWh/km (an average value for the group). This value may vary depending on the vehicle fleet, driver behavior, and technologies used by manufacturers, among other factors. Figure 10 illustrates the patterns of different categories of vehicles [25]; it is observed that most electric vehicles have values between 0.13 and 0.20 kWh/km.

Table 2. EVs Energy Consumption: Based on Inmetro data [24].

Category	Brand	Model	Energy Consumption (kWh/km)
Sub Compact	Renault	Twizy	0.11
Medium	BMW	i3	0.16
Medium	Renault	Zoe	0.18
Big	Nissan	Leaf	0.16
Extra Large	Jaguar	I-Pace	0.20
Compact	JAC	IEV 40	0.16
Average value			0.16

shows some EV models analyzed with their respective energy consumption (EV models available in the region under study).

As can be seen, one of the input parameters in Equation (3) is the number of electric vehicles. This value defines the target fleet of the EV Public Fast Charging Stations Project (PFCSP). Using the parameters described above and the EV projection scenarios for Campinas as a reference, it is possible to estimate the energy demand associated with the city’s fleet. However, not all vehicles in the city will be regularly accessing the local chargers. The value of consumption can vary significantly depending on the target fleet. The term target fleet is used as the number of EVs that the PFCSP must be able to serve continuously without any restriction of access to stations for simultaneous use. In the next section, the strategies used to estimate the target fleet will be discussed.

4.3. Target Fleet for Charging Station Estimates Based on Consumer Rational Choices

The planning of corridors for electric mobility, as well as allocation strategies for EVCS, usually consider parameters such as [26]: (1) Vehicle characteristics: usually represented by battery storage capacity [kWh] and average range [km]; (2) Characteristics of the road/route: represented by the average flow of vehicles; (3) Structure of the charging system: quantity and power of charging stations, as well as the number of sockets/plugs in each station; (4) Characteristics associated with user profile, age group, and range anxiety, and; (6) Availability of remaining capacity at the connection point [27].

As some data are not available at specific locations (or are imprecise, such as the flow of vehicles on the road at the installation site), methodologies based on the potential use of the CS can be employed, noting the objective of the evaluation, such as equipment sizing (construction of scenarios to propose conceptual projects coupled with the reality of the place/local).

Some characteristics associated with user profiles must be considered in the planning and allocation of charging stations, as described in [6]: (i) users tend to recharge near their homes or work; (ii) the existence of other charging stations in the vicinity may represent possible competition (causing a market share effect between nearby stations). One of the strategies adopted to estimate the CS target fleet was to delimit a region of influence and a region of competition.

4.4. FCSP’s Region of Influence

The region of influence is defined as the area that potential users are more likely to choose for charging [20]. The area of the region of influence can be estimated through Equation (5).

$$S_{Inf}=\pi {\left[\frac{1}{2}{A}_{EV}\left(t\right)\times \left(1-{\rho }_a\left(t\right)\right)\right]}^2,$$

(5)

where ${\rho }_a$ is the “range anxiety” parameter, typically 0.8 (0.8 in 2020, reaching 0.9 in 2030) [9], $A_{EV}$ is the average annual autonomy of the group of EVs, considered between 200 and 400 km (2020 to 2030), and the factor of ½ in the equation represents that the user is looking for a charging station and plans to reach it with at least half the autonomy of when he started the journey (this assumption is based on the idea that the rational user will avoid deep battery discharges).

It is expected that the region of influence will vary over the years, depending on the knowledge of users, maturity in EV use (with possible reductions in range anxiety), and an increase in the autonomy of vehicles (higher energy density of batteries, higher engine efficiency, etc.). The graph in Figure 11 illustrates the projection of the radius and area of the electric station’s region of influence, year by year, considering the composition of these two factors (${\rho }_a$ and $A_{EV}$). Considering the assessed horizon (2030), the average value of the radius of the region of influence is 21.5 km. Therefore, the area of influence is delimited by a region with an average diameter of 43.0 km, centered on the place where the charging stations are installed.

The fit of the region of influence was validated based on user survey data, as described in the study [28] and catalogued in the paper, “A review of consumer preferences of and interactions with electric vehicle charging infrastructure” [6]. As described, EV users usually recharge at stations up to 50 miles (≅80 km) away from their homes. In Figure 12, we observe that almost 100% of the recharges are carried out at stations up to 50 miles away. It is also observed that more than 80% of recharge events occur at about 40 km from the users’ homes. This is an indication that users from the region surrounding the charging stations tend to use them preferentially (there is a correlation between the number of vehicles in the region and the potential demand for charging services at nearby EVCS).

The number of EVs in the CS region of influence ($N_{EV-Sinf})$, assuming uniform distribution throughout the territory (this initial approximation has been used in [23]), can be determined as a function of the area of influence and total area of the municipality ($A_{City})$, using Equation (6).

$$N_{EV-Sinf}=N_{EVs-City}\frac{\pi {\left[\frac{1}{2}{A}_{EV}\left(1-{\rho }_a\right)\right]}^2}{A_{City}}$$

(6)

Figure 13 illustrates the circular region that defines the area of influence of the charging stations delimited by the radius of the inner circle (the effective radius varies along the horizon of the study). Figure 14 shows the EV projection scenarios but considers only the fleet in the region of competition.

The outermost circular ring in Figure 13 illustrates a second region, called the region of competition, defined as having a radius equal to twice the region of influence. The competition region is used to estimate the number of CS that compete for the demand of EV charging in the region of interest. The main idea is that the distance from the center of the competition region to the limit is defined as the distance that completely discharges the residual capacity of the vehicle’s battery. For example, a user with ${\rho }_a=0.8$, in an EV with a range of 200 km, will seek to recharge when the SoC of the EV battery is at most close to 20%. From the moment the user decides to recharge until the residual capacity is fully discharged, the residual autonomy is about 40 km. Therefore, if there is no preference for station type, any station within the radius of the competition region can be selected to recharge.

There are about 20 charging stations (public or accessible to users in the region) in the vicinity of our charging station [29], as shown in Figure 15.

Thus, in an initial estimate, adopting the premise that the demand for recharge is distributed among the CSs in the competition region, the portion of EVs allocated to the project’s EVCS can be estimated through Equation (7),

$$N_{EV-\mathrm{LCS}}\left(t\right)=\frac{N_{\mathrm{EV}-\mathrm{S}Inf}\times {\gamma }_c\left(t\right)}{N_{CS}\left(S_{Comp},t\right)},$$

(7)

where $N_{EV-\mathrm{LCS}}$is the number of EVs associated with the local charging station; $N_{\mathrm{EV}-\mathrm{S}Inf}$was previously defined through Equation (6); ${\gamma }_c\left(t\right)$was defined through scenarios A, B, and C; and $N_{CS}\left(S_{Comp},t\right)$ is the number of charging stations in the competition region ($S_{Comp}$). An average linear growth of 5% per year of the number of charging stations in the competition region was also considered (assumption based on the empirical observation of the historical growth in the number of stations), as shown in Figure 16.

Figure 17 shows the projection of the number of potential electric vehicles potentially serviced exclusively by the charging stations of the project (this figure can be interpreted as a projection of the potential of EVs served exclusively by the charging stations of Campinas). Despite the high number of EVs estimated for the city presented in the projections, due to demand sharing, the number of EVs (or charging events at public stations) served by the station is significantly lower.

4.5. Expected Value of Average Consumption [kWh] at Charging Stations

Considering the number of electric vehicles at the charging stations of the project, $N_{EV-\mathrm{LCS}}$, the expected average energy consumption can be estimated using Equation (8):

$$C_{avg}\left(s,t\right)=N_{EV-\mathrm{LCS}}\left(s,t\right)\times D_{avg}\times {\gamma }_c\left(s,t\right)\times C_e\left(f\right).$$

(8)

In Equation (8), the variable $N_{EV-LCS}$is the number of EVs after defining the target fleet or market share (depending on the region of influence) and the division according to the sharing of demand for recharge between stations in the region of competition. $C_e\left(f\right)$ represents the average energy consumption of the fleet, considering the category of vehicles registered in the city databases. Figure 18 shows all the average daily consumption scenarios for the CS (which has Campinas as a reference for the installation site).

4.6. Power Demand [kW] at the Campinas EVCS

Considering the typical load curves for fast charging stations and using the previously obtained average consumption estimates, we can extrapolate the results to estimate average expected peak demand [in kW]. Reference [30] presents a load profile considering public fast chargers located in Italy. Considering the typical load profile for fast electric stations and the profile proposed for Campinas in [31], the peak hour power demand and the number of CS needed to meet the expected demand requirements can be estimated. For example, as illustrated in Figure 19, in a hypothetical scenario of an average daily consumption of 1000 kWh/day, peak hour demand would be around 180 kW. Figure 20 illustrates the expected peak demand value, depending on the EV adoption scenarios, consumer projections associated with the local EV charging station fleet, and the expected load profile.

4.7. Number of Charging Stations in the Facility to Meet Demand Scenarios of Campinas

The number of stations to meet expected peak demand scenarios can be estimated as a function of the peak rated power provided by each charging station. The peak demand value can be determined by applying a conversion factor from average daily consumption to demand, as presented in Equation (9).

$$N_{CS}=\frac{D_{peak} \left[\mathrm{kW}\right]}{P_{DC-CS}\left[\mathrm{kW}\right]}=\frac{C_{avg} \left[\frac{\mathrm{kWh}}{\mathrm{day}}\right]\times C{F}_{E\to D}}{P_{DC-CS}},$$

(9)

where $N_{CS}$ is the number of charging stations required to meet the expected value for peak demand; $D_{peak}$ is the peak hour demand, according to the load curve; $P_{DC-CS}$ is the rated peak power that is continuously available from the DC charging station; and $C{F}_{E\to D}$ is the conversion factor from average daily consumption to peak demand. The number of stations to meet the peak demand, along the analysis horizon, is illustrated in Figure 21. For this evaluation, we assumed that each station could be used simultaneously by up to three users, with an availability of up to 60 kW of power in the DC plug and up to 22 kW in the AC plug, with AC supply current limitation of up to 125 A at 380 V.

As can be seen in Figure 21, two fast charging stations are necessary to meet the expected demand scenarios over the horizon. The use of two stations makes it possible to carry out two simultaneous DC recharges for each charger; four EVs can be DC charged simultaneously.

5. Photovoltaic Solar Generation to Meet the Energy Requirements

To meet the energy consumption associated with EV charging stations, a 12.5 kW/13.2 kW_peak solar photovoltaic generation system was connected (composed of 30 monocrystalline photovoltaic modules connected in two strings with independent MPPT management). Figure 22 illustrates the positioning of the photovoltaic modules in the project. Considering climate data factors such as solar irradiation, temperature, wind speed, orientation, and inclination, the monthly PV production was illustrated for the initial year of operation (see Figure 23). The annual generation is 20,045 kWh/year (sum of production for the 12 months).

A comparison between the accumulated energy associated with expected consumption of EV charging events and accumulated PV generation is presented in Figure 24, considering a performance ratio of 88.3% and annual module degradation rate of 3.2% per year. It is possible to observe an energy surplus until 2025. Therefore, given the consumption scenarios, in the initial years of operation, PV solar generation will be sufficient to meet expected consumption. With the growth in the number of EVs over the years, there will be a need to expand the photovoltaic system. Regarding the consumption curve, the value of accumulated E[C] is obtained by summing the expected value of energy consumption from all previous years. In each year, the expected value of consumption is obtained through the average of consumption in all scenarios (all scenarios are used to obtain the E(C) in each year).

6. Conclusions

One of the challenges in the large-scale adoption of electric vehicles in Brazil has been the unavailability of public charging infrastructure. Due to high investment costs, new EV charging stations enterprise and projects must be rationally dimensioned, to achieve short-term economic viability. One of the obstacles to adequate planning is the lack of information and strategies, such as knowledge of the fleet of electric vehicles in a certain location, which is essential information for the structuring of station models. Our study presented the application of an electric vehicle fleet forecasting method, considering a specific region (Campinas, Brazil).

The first step of the study projected the growth of the electric vehicle fleet, implementing a logistical growth curve, adjusted to the historical data of the fleet registered in each microregion. The projections, presented in the form of scenarios, indicated that the fleet could reach between 29,000 and 65,000 vehicles by 2030.

Based on the fleet projections for each city, we estimated year-by-year expected average consumption for the new EV fast public charging stations in the city of Campinas. These estimates considered factors such as the expected behavior of users and the possibility of sharing demand with other stations in the vicinity (effect of competition between enterprises). The results indicate that, despite the uncertainty associated with the data, two fast charging stations (with simultaneous AC and DC recharge) could meet the peak demand scenarios of the Campinas Project, in the ten-year horizon until 2030. Given our consumption scenarios, PV solar generation would be sufficient to meet the expected EV charging energy consumption during the initial years of operation.

The method presented in this paper was applied to the planning of an enterprise developed for R&D project PD-00063-3059/2019. The values and estimates presented in this work are intrinsically related to the assumptions adopted and the available databases that were consulted.