Estimating the charging profile of individual charge sessions of Electric Vehicles in the Netherlands

The mass adoption of Electric Vehicles (EVs) might raise pressure on the power system, especially during peak hours. Therefore, there is a need for delayed charging. However, to optimize the charging system, the progression of charging from an empty battery to a full battery of the EVs, based on real-world data, needs to be analyzed. Currently, many researchers view this charging profile as a static load and ignore the actual charging behavior during the charging session. However, this study investigates how different factors influence the charging profile of individual EVs based on real-world data of charging sessions in The Netherlands, and thereby enable optimization analysis of EV smart charging schemes.


Introduction
Although the mass adoption of Electric Vehicles (EVs) is often seen as beneficial in reducing greenhouse gas emissions, it will put an additional load on the electric power system, with potential adverse effects on its operation. Currently, the charging activity of EV users is highest during evening peak periods around 18.00, when EV users arrive at home [1]. The charging infrastructure indeed has the potential to significantly impact the local electrical grids [1]. Due to the possibility for demand peak shaving in the afternoon, and the current lack of according management of charging behavior, many researchers emphasize a need for delayed charging [1,2,3,4]; this can result in "many benefits, such as cheaper electricity rates for consumers, peak demand load shaving, and night time demand valley filling" [1, p. 268].
However, to actually improve time management of charging, the variables influencing the charging time need to be known and the effects of these variables need to be analyzed. This enables understanding of the actual charging profile of the EVs. This charging profile entails the progress of charging of a battery over time, and this leads to the considered question: What effect do external variables have on charging from an empty battery until a full battery?
In this research the charging profiles of EVs are analyzed with real world data. "In many designs and studies related to EV battery chargers, the EV battery loads are considered as a static load, and the realistic system behavior of the batteries during the charging process has been ignored" [2, p 483]. Research that is done on these charging profiles have not yet been validated with real world data. They have only been obtained with data from laboratory experiments [2,4], or with the use of transportation data combined with predictive or stochastic approaches [3]. More importantly, Jain and Jain [3] emphasize that the "accurate modeling of the charging profile of EVs is fundamental for [...] the impacts of increased EV load and their charging mechanism on [the] distribution system, [namely] overloading of transformers and cables, circuit losses, and power quality" and the effect on market price in the electricity market [3, p. 74].
This research aims to fill this research gap by analyzing the charging profiles of Electric Vehicles (EVs), and studying the public AC charging points with real world data. The state of literature is presented after which a theoretical model, entailing both variables based on literature and exploratory variables influencing the charging profile, is presented. With a regression analysis on data of charging sessions of EVs these variables are analyzed and the results are presented. Subsequently, conclusions on the predictive value of these variables are made. Based on these conclusions, knowledge of the effects of the variables lead to more accurate charging profiles.
2 State of the art

Battery characteristics
The speed of energy transfer is dependent on two factors: the Voltage (V) and the current, which is expressed in Ampere (A). Because power transfer is based on the Voltage multiplied by the current, with the same Voltage, a lower current will make energy transfer go slower and thus results in a lower charging speed of batteries. This charging of a Li-ion battery consists of 3 sequential phases. When the battery is completely depleted, the first phase occurs, and during this 'pre-charge' phase, the current is kept low, and the Voltage is increasing. However, most of battery charging of EVs take place in the second and third phase, which is illustrated in figure 1 [5]. The second phase starts when the EV is 10% charged, meaning the car has a State-of-Charge (SOC) of 10%. During this constant current (CC) phase, the current is kept constant at a high level, until the Voltage of the lithium cell reaches a specified Voltage level. The third phase starts at that point, in which the Voltage is kept constant, with a exponentially decaying current. During this phase the battery is charged with a trickle current and therefore the charging of the battery is slower [2].

Environmental effects 2.2.1 Peak
Many researchers have used data on the charging infrastructure to investigate the charging behavior of EV users, looking at the peak demand, and predicting the pressure on the energy aggregators, used for local distribution of power [1,3,6]. The large demand of electrical power for charging EVs can lead to undesired peaks, potentially overloading transformers and cables, leading to circuit losses and reduced power quality -such as a decrease in Voltage level [3]. These extra large peaks in electrical consumption coincide with peaks in household consumption [7], since people tend to charge their cars immediately when they get home [1]. In [7] it is mentioned that they used household power consumption profiles, which are typical for Belgium, which can be seen in figure 2.
For this research the peak times as defined in [7] and [8] are considered. Both studied peak consumption, and examined power losses and Voltage deviation for different Plug-in EV (PEV) penetration levels. This penetration level implies the percentage of households charging a PEV; in a residential power network of 20 houses and 4 PEVs the penetration level is 20%. They consider PEV penetration levels between EVS30 International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium  0 and 30%, since 20% penetration "is representative of early low PEV adoption case in the near future as PEV prices remain too high for most families to afford PEVs initially" [8, p. 4]. As shown in table 1, during peak time, power losses can reach 5% in summer during peak time (18.00 -21.00), and 6% in winter, which theoretically leads to a decrease in charging speed with the same factor.
In addition to the power losses, the Voltage level deviates -with a maximum of 10.3%, in winter and 8.7% in summer -from the situation in which no EVs are charging, as shown in figure 3 and table 2, which are retrieved from [7]. These Voltage deviations "cause reliability problems which must be avoided to assure good operation of electric appliances" [7, p. 371], and could potentially lead to a lower charging speed.

Day/evening
Another implication of their findings is the existence of difference between charging during the night and during the day or the evening. On the one hand, the rate of power losses with EVs charging is higher during the day (10.00-16.00) than during the night (21.00-06.00) and this can result in higher charging speeds during the night. This is because charging during the day and the evening is more demanding for the distribution grid, since the households' electricity demand -as was shown in figure 2 -is also higher.
On the other hand, during the night the low Voltage level is expected to have a negative relationship with the charging speed. Because the household electricity demand is low, and many EVs are charging, there is a higher ratio of electricity demand for EV charging to household demand. This relative surplus of EVs during the night potentially decreases the Voltage level as shown in figure 3. "Between 23h00 and 04h00, most of the vehicles are charging and the Voltage drop during these hours is the largest and deviates the most from the 0% PHEV [penetration] Voltage profile" [7, p. 373]. In contrast, as mentioned in [5], the network Voltage drops are within acceptable levels, since the Voltage deviations stay below 1%.

Temperature
The temperature of the battery also influences the charging profile: the battery has to be heated to transfer energy. Subsequently, EVs are able to absorb power to charge the battery, unless extensive heating of the EVS30 International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium battery forces the charging to pause; the battery can cool down to manage possible overheating of the battery [9]. Moreover, battery cells are suggested to operate most effectively between 20 -25 degrees of Celsius, and when the battery temperature diverges from this ideal, the Battery Management System (BMS) of the car reduces the requested current, making sure the health of the battery cells is protected [10].
This BMS can be equipped with a temperature management system to control the cell temperature, reducing the effect of the outside temperature. Additionally, the battery temperature is not only influenced by the outside temperature, but charging and driving will generally increase battery temperature as well [13].

Battery degradation
A study by [11] researched the lithium-ion batteries by conducting the capacity loss over time and over charging cycles. They found that the time influences the capacity of the battery, so that it the capacity loss "progresses linearly with the square root of the time" [p. 2]. This decrease in battery capacity was due to several variables: for higher temperatures this decay in capacity was larger as can be seen in Fig.  4a and when the State-of-Charge was lower, the decay was lower as well -as shown in Fig. 4b. This illustration shows that after about 200 charge cycles -at 15 degrees and 50% of the total capacity charged -the battery loss is around 3.5%.

Theoretical model
Charging profiles are dependent on a large number of variables, that can be categorized in (i) environmental, (ii) charge point, (iii) car characteristics and (iv) external factors. Due to the scope of this paper a limited amount of variables is presented.

Environmental effects
As mentioned in section 2.2.1, power losses and Voltage deviations can lead to lower charging speeds during peak time and therefore the binary variable peak is considered in this research. Although it is uncertain if this holds for the power grid in the Netherlands as well, peak is expected to be negatively related to charging speed. Due to the lower power losses and higher Voltage deviations, which are mentioned in section 2.2.2, the effect of the binary variable day is uncertain. The effect of the variable temperature on the charging speed is explored and is expected to have a positive relationship with charging speed because temperatures lower than 20 degrees are suggested to negatively impact the charging speed.

Charge point
In the electrical power distribution system it is expected that if more cars are charging at the same time, the Voltage in the system decreases, and power loss increases. Since most charge points have two sockets, possibly facilitating two cars at the same time, this research will explore potential power loss on the micro-scale of the charge point itself; if on both the sockets of a charging point cars are charging, does this affect the charging profile? Furthermore, this research will consider the effect on the maximum charging speed if the car at the other socket is not charging but only connected. In consequence, the effects of the binary variables double charge -with the possibility of the other car taking up power -and double connection on the charging speed are analyzed.
EVS30 International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium The effect of double charging and double connection is evaluated with the Voltage of the car at the other socket as well. Because both the level of penetration in an electrical power system and the charging method -e.g. 400V -affect the maximum charging speed [7], this can result in a difference in effect between a three-phase car (400V), using the other socket, and a single-phase car (230V).

Car characteristics 3.3.1 Voltage
Besides the current, the Voltage defines the charging speed. There are two methods of alternating current (AC) charging: single-phase charging (230V) and three-phase charging (400V). Three-phase charging facilitates charging speeds three times as fast as with single-phase charging; it only uses √ 3 times the Voltage of single-phase charging to enable this charge speed difference. Because of this difference in speed of charging, this research takes the binary variable voltage -either single-phase (0) or three-phase (1) -into account and has examined the difference of the two methods of energy transfer.

Battery degradation
As [11] showed that batteries lose capacity over time and over charging cycles, this likely impacts the charging profile of the EVs. If due to this capacity loss the last phase of charging -the Constant Voltage phase -is affected, the charging speed of the battery might be altered. This last phase of charging is the CV phase, in which the amount of Ampere is lowered and thus also the speed is lowered. Due to the capacity loss, an effect on overall charging speed can occur, hence the continuous battery degradation variable is examined.

Conclusive model
All these variables might have an effect on the charging profile, and the complete model is illustrated in figure 5. The variables are presented in the categories: environmental effects (time, temperature), charge point effects (connection/charging at sockets), car/battery characteristics, and other variables. This is a multiple linear regression model, which intends to predict the charging profile. This profile is described as the average charging speed until full SOC. Each individual charging session is considered and the variables with changing values over time are averaged over the time the car has not reached full SOC. The results of this model are presented in the next chapter.

Methods
This section first describes the dataset with its parameters. From these parameters the variables discussed in the previous section are calculated; this chapter describes how these variables are transformed in a regression model.

Dataset
The dataset used in this research is provided by the Municipality of Amsterdam and the energy providers responsible for the delivery of the energy. This dataset consists of two parts: EVS30 International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium  Errors were recognized and filtered as mentioned in [12,13]. Furthermore some changes were made in order to get the same representation of data for both providers. Moreover, the charge points with more than two sockets were filtered, in order to get a good measure for the variables double connection and double charge. After filtering out above errors, the database consisted of 4.8 million records of meter values and 128.000 records of charging sessions..

Regression
This research explains the charging profile with the help of a linear regression. The linear regression is used as means to see the influence of the variables on the charging speed. The linear charging profile is obtained by averaging the charging speed until full SOC. The variables from the theoretical model are analyzed with regard to this average charging speed. Figure 6 suggests that the aggregate charging can be regarded as a linear profile. Because a charging session can last from 14.00 to 17.00 -and charges from 14.00 to 16.00 -the hourly temperatures of 14.00 and 15.00 are taken into account and averaged over the charge session until full SOC -the hourly temperatures of 14.00 and 15.00 are averaged. The SOC is on the x-axis, while total amount charged is on the y-axis. At the right top corner, the car is fully charged. At the left bottom corner, the battery is completely empty.

Dependent variable: ∆charging speed
To obtain the linear charging profile, which is described as the average charging speed until full SOC, the total amount charged is divided by the time it takes to charge to full SOC. This average charging speed is called the delta of the charging session. Batteries can remain a long time in the 99% State-of-Charge before reaching 100%, which is for the purpose of preventing overcharging, by charging with low current. Therefore, in this research full SOC is reached when the car is not charging more than 100 W in the next hour, which entails that even with 99% SOC, they can be considered as fully charged. In

Independent variables
The variables day and peak were measured by looking at the time of charging and the timespan used for the variable day is 8.00-23.00 and for peak is 17.00-21.00. The variable temperature is measured by looking at both the historical hourly and daily temperatures distributed by the KNMI of the weather station in Schiphol over 2015 and 2016 [14]. Also for this variable, the mean is calculated for the charging session when the car has not reached full SOC. For these binary variables this implies that if for EVS30 International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium example during the charging session 2 out of 3 hours it is day time, the value of the variable day will be 0.67. Battery degradation is measured by ranking all the sessions over RFIDs and examining the average charging speed of the charging sessions over the amount of charging cycles.
To measure Voltage, the individual cars were categorized based on the RFID. The RFIDs can be categorized in two groups, depending on their maximum charging speed: single-phase or three-phase. Only 400V EV chargers can have charging speeds over 7.4 kW, and therefore maximum charging speeds over 7.6 kW (to correct for a margin of error), categorizes the EV as a 400V car.
To filter out errors and outliers surrounding the maximum charging speed, also the second maximum speed is calculated. In case the second maximum speed differs widely from the maximum speed , the charging session with the maximum charging speed is filtered out and the maximum speed is recalculated. This step is repeated until the maximum charging speed is close to the second maximum charging speed. For the data with provider EVNET, which has meter values in Wh, the limit of difference between maximum charging speed and the second maximum speed is at 200 W. For the NUON data, since the meter values are in kWh, the maximum difference is 1 kW between the maximum and second maximum charging speed. By doing so, large outliers are filtered, but this also means that charging stations with only a handful charging sessions might be filtered out, which also holds for charging stations with only one record of a 400V car.

Regression model
The results section first describes an the regression model, after which the results of the individual variables is elaborated upon. The total model gives the regression output as in table 6, in which the dependent variable ∆ of charge session -the average charging speed of a charging session -is expressed in W. All variables except for battery degradation are rounded to two decimals in the regression model.

Environmental effects
The hypothesis that during peak time the charging of EVs would be slower is falsified as the effect is significantly positive. Following the research of [7] as suggested in section 2.2.1, a negative effect was expected for charging during peak time, but the results indicate that the charging speed is higher when the car is charging during peak time, with an estimated positive effect of 65 W (2.4%) in case the car is completely charged until full SOC between 17.00 -21.00.
The variable day was one the one hand expected to have a negative effect due to more power loss during the day, while on the other hand the higher Voltage levels during the day and the evening suggested a EVS30 International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium positive effect on charging speed. The results from the model suggest an overall negative effect of 5.7% on the average charging speed of the EVs by charging during daytime. However, taking a closer look at figure 7, it shows that 230V cars charge around 10% slower around 05.00 than during daytime, while 400V have valley hours around 08.00 in the morning. In this figure the slow pre-charge phase and trickle current phase (start and end of charging) are filtered, which could have impacted this result.
The effect of temperature on the charging time is positive, and since this is a continuous variable, for every degree of Celsius increase, the charging speed increases with 3.7 W. So for a difference of 20 degrees, the average charging speed difference is expected to be 2.7%. This result means that overall charging is slower when it is colder and as can be seen in figure 8, this is especially true for 230V cars below zero degrees. This may suggest that this is because 230V cars have slower charge speeds, and thus it is more difficult to heat the battery for maximum charging speed. The higher charge speeds of 400V cars restrain maximizing charge speed with higher temperatures, while taking care of the battery health.

Charge point
The results of the variables double connection, double charge and voltage other socket are illustrated in 7. Interestingly, there is a large contrast between 230V and 400V cars. In situations 1-4 the results are shown for when at the measured socket (socket 1) a 230V is charging. When at the other socket another 230V car is connected, there is a small positive result (situation 1). However, if at the other socket a 230V car is charging (situation 2), the average charging speed goes down with 1.5 %; if the car at the other socket is a 400V car instead, the charging speed actually goes up with around 1.5% when it is only connected and when it is also charging (situations 3 and 4). Therefore it makes a difference for a 230V car if at the other socket a 400V car is connected, and also when it is charging.
Situations 5-8 show the effect on charging speed for when a 400V car is connected at socket 1. If a 230V car is charging at the other socket (situation 5) this results in a 6% decrease, while when the 230V car at the other socket is charging (situation 6), there is an increase of 3%. In situation 7 at both sockets 400V cars are connected, which has an insignificant result. When these 400V cars are both charging (situation 8), however, the average charging speed drops 7%.
These results show that there is a large contrast between the charging of 230V cars and 400V cars, and also that there is a large effect of the interaction between the cars at the same charging station. The charging speed is dependent on the Voltage level of the car at the other socket, and if it is charging or only connected. This study can not explain this contrast and

Car characteristics
The variable that explores the difference between single-phase (230V) and three-phase (400V) cars was expected to be three times as high. This is true as can be seen in multiple figures, and the regression table 6 shows that the effect is at least three times as high,Therefore, the hypothesis that three phase charging speeds can be predicted by approximately multiplying the charging speed with three can be confirmed.   figure 9. In the figure, the effects are normalized compared to the first charge session.

Discussion
In this section the limitations of this research will be discussed.
The linearity of the variables can be discussed, since some of the variables show a clear non-linear pattern. The regression model that is used, therefore does not give the full image, hence why the figures give a better representation of the actual influence of the variables. Furthermore, since the battery degradation can only be calculated on the sessions that were in the dataset and thus a car that is charging for the 150 th time can be marked as the first charge session. Therefore it is hard to draw final conclusions about the specific battery degradation of cars and its effect on charging speed. There might be other endogenous variables playing a role in the impact of the amount of charge cycles on the average charging speed. To have a better view of the influence of battery degradation, a longer time period can be chosen. By making sure the first charging sessions of a car are tracked the influence of battery degradation can be checked. Furthermore, by comparing the amount of charge sessions between cars, the direct influence of battery degradation can be examined.
From the literature, the effect during peak time, was expected to be negative [7,8], but this variable EVS30 International Battery, Hybrid and Fuel Cell Electric Vehicle Symposium has not had a significant impact on the average charging speed in this study. The lack of negative effect could be due to a strong power grid with large capacity. However, more research can be done to explain the difference in positive peak time relationship, since this effect is different than expected. What is more, the regression model suggested a negative effect of charging during the day, but figure 7 shows a positive result, meaning that there are endogenous variables influencing the regression output. Including more variables would give a better image of the actual effects of the variables, which is not possible in this research due to the scope.
In this research data was used from two energy providers: EVNET and NUON. Because the data provided by NUON was different in precision -a factor of thousand -the precision in the variables can also have been affected, certainly since trickle charging at the end of a charge session was mostly filtered because of this lack of precision. However, the precision of the EVNET data also implied difficulty in determining a cutting-off point at which a car was described as fully charged. Due to this arbitrarily chosen point, the effects of -and during -trickle current are hard to compare for both providers.

Conclusion
This research aims to provide a more extensive analysis of the charging profile of EVs, through studying variables influencing the charging profile at the public alternating current charging points. Until now, the charging time has only been based on the maximum charging speed, which is calculated by dividing the session time by the total amount charged, as mentioned in [13]. Various variables influence charging speed and total charging time and their effect is analyzed. This research demonstrates, based on real world data that indeed many variables influence charging time. The most important findings show that the Voltage level of a car has a large impact, especially in combination with the result that amount of cars being connected or charging at a single charging station influence the charging speed, as illustrated in table 7. Moreover, the charge speed decays due to battery degradation and during daytime and peak hours as illustrated in figure 7 suggest a positive relationship with charging speed.
The results of this study are used to further develop a model that includes most important influencing factors on charging profiles of EVs and can be used to predict these charging profiles. With the predictors of the complete model, the actual charging time can be estimated with more accuracy based on the available data, which makes it possible to further optimize charging behaviour.