The storage power can be both positive (discharging) and negative (charging) based on the battery charging or discharging. In the same way, the DC chargers could be capable of supplying power from the EVs’ battery to the grid and loads. This mode of operation is generally called V2G and vehicle-to-X (V2X) [
29], and it considers the bi-directional power flows of the charger. However, the AC charger, which can only absorb power from the grid and internal power sources, might be capable of modulating absorption to help the grid and the district for power balancing and other services. This mode of operation, which considers the unidirectional power flow of the charger, concerns both the V1G [
31,
32] and the SC mode [
26]. The CMS could manage the EVs’ power flows for achieving optimization goals such as:
The CMS’s logics for smart charging mode is better described in
Section 3. CMS control for being implemented needs both load and production power measurements. Furthermore, to implement grid power-sharing, the data of the power that the ED exchange with the grid are required as well. The load and the generation of daily power flows are extracted from annual data measurements. A similar procedure is done for the point of common coupling (PCC) power profile. On the other hand, EVs’ daily power flows are more challenging to be extrapolated because of the difficulties in finding data and the statistically weak number of electric vehicles. However, EV penetration is quickly growing [
4], and the current data are expected to strongly increase in the next years. For these reasons, current measurement data are not sufficient to extrapolate the EV charging power profile. As shown in Equation (2), instant by instant, the EV charging power is given by the aggregation of
N charging power of each
within the ED (
):
where
N is the total number of EVs within the ED, and
EVi is a generic electric vehicle belonging to the district. To evaluate the
for each vehicle, it is necessary to analyze all the factors that affect the EV’s charging power. The daily charging power profile of an electric vehicle may depend on the following variables [
37]:
All these variables could be different for each vehicle, resulting in a multitude of various charging events. Aiming to fetch variables from an aggregate population of EVs, this paper proposes different analyses on the basis of the Italian EV fleet, drivers’ behavior, charging infrastructure, and on the parking and charging times.
2.2. Electric Car Fleet Analysis
In order to evaluate the charging power, the batteries’ capacity and the daily consumption for each vehicle belonging to a wide EV population, the Italian electric fleet has been considered and analyzed.
Table 1 shows the EV data, referring to the vehicles registered in 2019 [
38]. The table shows the battery capacity, the estimated consumption (referred to the world harmonized light-duty vehicles test procedure—WLTP) declared by manufacturers [
39], and the max AC and DC charging power for each vehicle model. Some of these models have different options for battery capacity and engine size (such as Zoe ZE40 and Zoe ZE50, which have batteries of 44 kWh and 55 kWh). To simplify the analysis in this paper, the characteristics of the most popular models for each brand are only considered.
Figure 3 shows an elaboration of the table’s data. From the data in
Table 1, the weighted average capacity of the EV batteries is 40.31 kWh.
Figure 3a shows that the majority of EVs (63.2%) have a battery capacity between 40 kWh and 50 kWh. Only 7.1% of EVs have a capacity greater than 90 kWh. However, a good part of EVs have a capacity of about 20 kWh, which refers to the high number of Smart cars (29.6%) registered in Italy in 2019.
Figure 3b shows the EVs specific consumptions in the WLTP driving cycle compared to the percentage of registered models.
Table 1 shows the maximum AC charging power
of each EV model, which depends on the onboard converter. The weighted average of the maximum AC charging power is 11.13 kW. The charging power depends on both the onboard charger and the AC charging stations, and it is equal to the minimum power between the
and
(e.g., because of the onboard converter’s size limit, the max AC charging power of the Nissan Leaf is 6.6 kW even if it charges through a 22 kW station). By analyzing the data, only 21.73% of EVs (Renault ZOE) can exploit all the maximum available power from the 22 kW AC stations, 55.62% of EVs for the 11 kW AC stations and 57.72% for the 7 kW stations. However, almost all EVs (70.34%) can exploit all the available power from the 5 kW AC stations.
The daily charging power’s profile of each
depends, as well as on the onboard converter and charging stations, on the CC–CV charging algorithms, then on the SOC’s value during charging:
The standard charging protocol consists of two phases. During the CC phase, the battery is charged by a constant current and a quasi-constant power. As a result, the SOC linearly increases, and the power assumes a constant profile in the plot “charging power [kW]” versus “SOC (%)”, whose value depends on both
and
. When the battery voltage reaches the cut-off value, the voltage is kept constant and the current consequently decreases (CV phase). As a result, the power decreases following the current profile, and the SOC increases slowly. Considering the same battery, the SOC’s value that coincides with the start of the CV phase depends on the charging rate, and therefore on the charging power. Different charging powers provide different profiles as a function of the SOC.
Figure 4 shows the characteristics of a 40 kWh battery during charging through three levels of power: 50, 22 and 7 kW that correspond to a C-rate of about 1.25 C, 0.55 C, and 0.18 C, respectively. The data were extrapolated by battery characteristics and the charging behavior of the Nissan Leaf [
39].
Figure 4a shows that the charging of 7 kW (<0.2 C) is less affected by the CV phase limitation. However, as the charging power increases, the CV phase is more pronounced. This paper analyzes this kind of dependence for each EV models’ battery.
2.3. Analysis of Drivers’ Behavior and Consumptions
For evaluating the charging time for each EV, it is necessary to know the vehicle’s SOC value at the beginning of the charging process (
). For this reason, this Section analyzes the daily energy consumption of the aggregated EV population. The energy consumed during the
k-th day (
) by the
i-th vehicle
is called
.
depends on the specific consumption
and on the daily travailed distance
:
The specific consumption of each EV (in WLTP rating) is shown in
Table 1.
Figure 3b shows the
for each EV model compared to the percentage of the registered model. The weighted average
for the EV population under investigation is 16.67 kWh/100 km. To extract the data of the daily distance traveled, it is necessary to investigate the driver’s behavior.
From the statistics in the report [
40], the average distance traveled by a vehicle in a year is 12,240 km. Therefore, the average distance traveled per day is about 33 km. The statistics in the document [
41] report an overview of the mobility and drivers’ behavior in terms of the number and length of daily travels. From the extrapolation of the report’s data,
Table 2 shows, with good approximation, the percentage of daily distance traveled, categorized by length groups: close distance, short distance, medium distance, and long distance.
Through analyzing
Table 1, and according to [
42], the probabilistic distribution that better estimates the daily distance travel of vehicles is the Weibull function.
Figure 5a shows the Weibull distribution with
λ = 37.5 and
k = 1.7. This distribution provides a reasonable estimation of the drivers’ behavior, especially for close and short distances, which represent 70% of total travel. It can be seen in the cumulative curve (at the bottom of
Figure 5a) that 10% of vehicles travel below 8 km per day, 60% of them between 8 and 40 km, and the remaining 30% travels more than 40 km per day.
Figure 5b shows the daily distance
traveled by each driver belonging to a population of 100 vehicles, during the
k-th day. The data were obtained by applying the Weibull function. It can be seen in
Figure 5b that the average traveled distance is about 33 km per day.
Knowing the specific consumption and the daily distance traveled by each vehicle, using Equation (5) it is possible to calculate the energy consumed by the
i-th vehicle in the
k-th day. To calculate the
) (%), which is the initial SOC of the
i-th EV at the
k-th day, this paper proposes the following hypotheses:
is the day the
has the last total charging, in which
=
, then the
is given by Equation (6):
where
is the energy consumption referred to the days before the day
. For example, the
considers the consumption of the previous three days,
,
, and
), starting from the initial SOC’s value of the last full charging day (
). For each vehicle, the energy consumed in
depends on the distance
. This distance could be or not the same each day. For instance, the distances traveled by
during three days could be
) = 20 km
= 24 km and
= 8 km. However, every day, the average value (33 km per day) and distribution (Weibull) of the traveled distances must be the same for the total vehicles’ population, according to
Table 2 and
Figure 5. These concepts will be better explained in
Section 4 using data from a real vehicle population’s scenario.
2.4. Parking Time Analysis
To evaluate the charging time, it is necessary to know the time that each vehicle spends plugged to the charging station absorbing power. For each vehicle
, this paper considers the daily charging time (referred to the day
) as the period between the initial time of charging
) that is the instant in which
is plugged in, and the final time of charging
where
is the charging time of
referring to
. The
is the instant where
ceases to absorb power from the CS and it may depend on two conditions:
The vehicle is plugged, but the SOC reaches the maximum value, the charging stops, and =;
The vehicle is unplugged because the users left the parking lot even if the charging is incomplete, <.
The hypothesis introduced is that the instant of arrival in the parking lot coincides with the beginning of the charging, as shown in Equation (8). On the other hand, the final charging instant could coincide or not with the departure time of the vehicle from the parking lot, as in Equation (9):
The arrival and departure times of each vehicle and all of them together with the parking time were obtained by monitoring the users’ access to the parking lots. The data were collected considering private and public parking lots. Data refer to several typologies of parking scenarios: mall, station, airport, city center, municipal parking, office building, working place, and companies’ parking lots. The distribution and numbers of data can be very different for each scenario, as well as the parking times. By analyzing each vehicle’s access (in and out), it is possible to extrapolate the users’ behavior and the parking time distribution for each different scenario. This paper focuses on the working place parking scenario (companies, office building, etc.), as extensively shown below.
The scenario under consideration concerns a population of 160 vehicles, and the input data are
and
The arrival and departure times were subsequently sampled every 15 min.
Figure 6a shows the input data; for each vehicle (y axis), the arrival and departure times (x axis) are registered. By processing these input data, it is possible to extrapolate
Figure 6b, which shows the number of arrivals (top-frame) and departures (bottom-frame) within each 15 min interval of the day. It can be seen in the figure that the vehicle arrivals can be divided into two major sub-groups: first arrivals, which are the events within the time interval [00:00–12:00] and concern about 80% of users; and the second arrivals, that refer to the time interval [12:00–24:00] covering the remaining 20% of vehicles. In the same way, departure events can be divided into two sub-groups: first departures that cover 30% of users and are registered before 14:00; and second departures, which belong to the interval [14:00–24:00] and concern 70% of vehicles. For each group, the probabilistic distribution that better simulates the users’ behavior is extrapolated. In this way, it will be possible to extend this kind of behavior as well for a population of a larger or smaller number of vehicles.
Table 3 shows in detail the probabilistic distribution obtained for each sub-group of events. The total distribution of arrivals and departures is given by the sum of its two respective sub-groups. As shown in
Figure 6b and
Table 3, the distribution of the total arrival is provided by the sum of two normal functions (NFs). On the other hand, the overall departures distribution consists of two Weibull functions (WFs) with different parameters. By using these data, the number of vehicles that are present in the parking lot in each 15 min interval is calculated.
Figure 6c shows the number of presences in the parking lot. It can be seen that the probabilistic function of presences (blue line), which is obtained by using the parameters in
Table 3, matches well with the real data curve (red line).
Figure 6d shows the parking times of each vehicle, which are calculated by Equation (3). The average parking time, referring to real data, is about 5 h (4 h and 57 min); on the other hand, the average parking time obtained by the probabilistic distribution is 5 h and 3 min. Besides, the figure shows the parking time error for each vehicle, which is obtained by the difference between the probabilistic and actual data. The average error is 7 min which corresponds to less than 3% of the average value of the real data, while the root mean square error (RMSE) is 7%. As can be seen in the figure, since the actual and probabilistic data are sampled in 15 min intervals, the error has been quantized every 15 min as well. The maximum error value is 45 min, which corresponds to a 15% error and concerns only 8% of the population. Most of the population has an error that is less than 15 min (5% error referred to the average), and 30% of the population has 0% error. These parameters further confirm the good overlay between the real and the stochastic behavior.
2.5. EVs’ Power Flow Calculation Algorithms
This Section explains the logic and methods that allow calculating the daily EV power flows for different scenarios and populations. Once the population’s number of vehicles, their characteristics, and the parking lot scenario are all identified, this algorithm is capable of forecasting and calculating the power that each EV requires for charging in each time interval of the day. Furthermore, it can forecast the total EVs’ charging power, which could be related to the aggregate group of vehicles that belongs to the single parking lot or the entire energy district. According to
Section 2.4, the sample time of the algorithm is set to 15 min, then the generic day
consists of 96 intervals of 15 min each. The algorithm’s input data are obtained by the previous analyses done in
Section 2.1,
Section 2.2,
Section 2.3, and
Section 2.4.
As mentioned above, the scenario under investigation is the working place parking lot, where
N is the number of total EVs that used the parking during the day. Through the
Section 2.2 analysis, it is possible to define an
N-sized array, named
. The
array contains information about the EVs’ model and is made using the percentages of registered EVs that are reported in
Table 1. For example, if
N = 100, the
vector would consist of 100 elements of which 22 correspond to Renault ZOE, 19 to Tesla Model 3, 13 to Nissan Leaf, and so on. In the same way, from
Table 1 it is possible to define the N-size array of the batteries’ capacities (
[kWh]), of the max on-board charger powers (
[kW]), and the specific consumptions (
[kWh/100km]). By the 0analysis in
Section 2.3, the N-size array of the distances traveled in
is defined and named
(km). Finally, the array of the maximum powers that are available on the charging stations (
[kW]) is defined. The elements of each vectors’ row refer to the vehicle which is present in the corresponding row of the
ID array. For example, Equation (10) shows that the i-th vehicle (
) is a Tesla Model 3 that traveled 70 km during
(
= 70). The i-row of all other vectors refers to the Tesla Mod. 3’s parameters. The
array depends on the charging infrastructure, however, the i-row of
refers to the charging station plugged into the i-th vehicle (in this case, by Tesla M.3).
By
Section 2.4 analysis, it is possible to define the matrix of the vehicle presences in the parking lot (
PK), which contains information about the arrivals, departures, and parking times of each EV in the day
. The matrix is shown in Equation (11) and is calculated using the arrival (blue) and departure (red) times for each vehicle. The time range within
and
represents the parking time (
).
PK is calculated at each time interval
, and since
= 15 min, considering a population of N vehicles and a period of 24 h,
PK results in an
matrix. Generally, if the time step resolution is higher (
< 15 min), the number of the matrix’s columns is higher than 96. Following the order of the
ID array, each row corresponds to a vehicle, while each column corresponds to a time interval of
. As shown in Equation (11), the value of the matrix elements is 1 only if the vehicle is parked; otherwise, it is 0. For each interval
(which refers to time
to time
) and each
, the following conditions apply:
where
j is the
PK column, and
i is the
PK row. By Equation (12), for each
PK row, the first non-zero element corresponds to the arrival times. On the other hand, the last non-zero element corresponds to the time interval preceding the departure time, and all the elements within this time-range are equal to one. If
= 160, the sum of the row-elements for each column (
) provides the plot in
Figure 6c, as well as the sum of the elements only relating to
and
, which provides the plots in
Figure 6b.
For describing the forecasting algorithm, this Section focuses on calculating the daily power flow referring to a single
,
The algorithm’s output must be an
matrix which contains the charging power value [kW] of each vehicle for each time interval, this output matrix is called
and
. Then, from Equation (2), the total parking charging power, for each time interval
is a row-vector (96-sized) named
and is given by
The forecasting logics are shown in the flow chart in
Figure 7. The model starts calculating at the beginning of
, considering the first-time interval (j = 1, which time belongs to [00:00–00:15]). As long as
remains equal to zero, the output
is zero because the vehicle is not in the parking lot and cannot be plugged on the charging station. As soon as the vehicle arrives in the parking lot,
switches to one and keeps this value while the vehicle is parked. By Equation (8), the charging starts at the arrival times, and the initial charging power
is set to the minimum value between
and
. After that, the initial value of the power is multiplied by a scale-factor
. The scale factor considers the variation of power during charging which depends on the CC–CV phases. Therefore, as shown by Equation (4) and
Figure 4a, the power could decrease during the charging process depending on the SOC value. Using a lookup table, which depends on each vehicle’s battery capacity,
is calculated as a function of the SOC and the initial charging power value for each time interval
. In fact,
represents the value of the charging power in per-units (p.u.), which is reported to the rated power in the CC phase. Therefore, the scale factor is about
=1 during the CC phase and decreases during the CV phase to reach zero as soon as the charging ends,
= 0.
From
Figure 7, the algorithm’s input (black input arrows) and output data (green output arrow) can be observed. On the other hand, the red signals consider the logics of start and stop charging. As previously explained in Equations (8) and (9), the charging can end (
if the vehicle leaves the parking (
PK switches from 1 to 0) or if the battery reaches the maximum SOC value (
reaches zero). Therefore, the scale factor (blue signal) is used for both calculating the end charging instant, and to calculate the EV charging power in each time interval through Equation (14):
Finally, according to the objective of calculating the daily charging power of the single-day , the forecasting process ends when j = 96 (time step [23:45–24:00]). Once the matrix is determined, Equation (13) calculates the total daily power profile of the parking lot (PEVs).