# Flexibility of Electric Vehicle Demand: Analysis of Measured Charging Data and Simulation for the Future

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## Abstract

**:**

## 1. Introduction

_{req}) into the EV battery. In previous studies on smart charging, the maximum available EV demand flexibility was often assessed in a simplified way, not investigating the diversity in connection durations and charging durations for the different transactions. Lopes et al. [11] used three types of EVs, with charging powers of 1.5, 3, and 6 kW, respectively, and an average value of 4 h for $\mathsf{\Delta}{T}_{\mathrm{charge}}$. The study assumed that all existing vehicles plugged in at 21:00 in the evening. Clement-Nyns et al. [12] divided the day into different time slots and assumed that all EVs had a maximum charging power of 4 kW. The EVs plugged in during a certain time slot and had to be fully charged by the end of the time slot, thereby underestimating the flexibility of EV demand, as in reality, the connection durations are expected to exceed the durations of the time slots used. Claessen et al. [9] used a normal distribution of charging start and end times around a fixed mean, a maximum power flow of 3.7 kW, and discrete values for E

_{req}per transaction (3, 6, or 12 kWh). Wu et al. [7] used a plug-in time between 07:00 and 08:00 and a plug-out time between 18:00 and 19:00, the (dis)charging power was flexible between −10 and 10 kW, and E

_{req}was assumed to be 12 kWh for each transaction. Jian et al. [13] used a chi-squared distribution for arrival times and a normal distribution for the simulation of $\mathsf{\Delta}{T}_{\mathrm{connect}}$, with a fixed mean of 10 h and a fixed standard deviation of 3 h, and a maximum charging power of 4 kW for all EVs. In the study by Van der Kam & Van Sark, a uniform distribution between 3 and 6 h was used for trip durations, and it was assumed that the EV was always connected when it was not on a trip, thereby overestimating the available flexibility [8]. The maximum charging power was set at 6.6 kW or 22 kW in that study, depending of the type of EV that was simulated. Scharrenberg et al. [14] used hourly frequency distributions of arrival and departure times from the Dutch national mobility study [15] for defining the availability of EVs for smart charging. This is more realistic than using predefined distributions, yet the study did not consider connection durations of individual transactions nor the diversity of charging durations for different transactions. Further, a charging power of 3.7 kW was used for all EVs. Liu et al. [16] used National Travel Surveys in the Nordic region to assess the availability of EVs for smart charging, but did not link this availability with charging durations. So far, only a few studies have been found that assessed the available EV demand flexibility by combining $\mathsf{\Delta}{T}_{\mathrm{connect}}$ and $\mathsf{\Delta}{T}_{\mathrm{charge}}$. By taking into account the plug-in time (${t}_{\text{plug-in}}$) as well, the changes of available flexibility over time can be investigated. A study by D’Hulst et al. (2015) investigates time-dependent flexibility of several appliances, among which are EVs. The EV flexibility was based on a pilot in which seven EVs were monitored over a period of 10 weeks [17]. The charging power of the EVs in the study was limited to 2.3 kW. To achieve a realistic assessment of the maximum potential flexibility of EV demand and the time dependency of the available flexibility, it is necessary to investigate the differences between $\mathsf{\Delta}{T}_{\mathrm{connect}}$ and $\mathsf{\Delta}{T}_{\mathrm{charge}}$ for a large number of transactions. The earliest study found in which this was done was published in 2017 and examines a Dutch and a Flamish dataset [18]. The authors present a time-varying response potential in kW for different charging locations. A more recent study by Flammini et al. provides an extensive statistical analysis of EV behavior based on Dutch charging station data, including idle times [19]. However, the authors give no clear results on how idle time, and thus the flexibility, varies over the time of the day. Another recent study analysed one year of Dutch present-day public charging station data, including the flexibility and its time-dependency [20].

## 2. Methods

- ${t}_{\text{plug-in}}^{i}$: the plug-in time for transaction i.
- ${t}_{\text{plug-out}}^{i}$: the plug-out time for transaction i.
- ${P}_{\mathrm{charge}}^{i}\left(t\right)\left[\mathrm{kW}\right]$: power charged at each time t during transaction i, with a sufficiently high time resolution ($\Delta t$ ≤ 15 min). In this study, this data is referred to as the ‘measured charging profile’.
- Possibly also ${E}_{\mathrm{req}}^{i}$ [kWh], which is the total charged energy during each transaction. However, this metric can also be derived from ${P}_{\mathrm{charge}}^{i}\left(t\right)\left[\mathrm{kW}\right]$ if $\Delta t$ is sufficiently small.
- A unique anonymous identity for each EV j that occurs in the dataset. For each transaction i in the dataset, the identity of the charging EV j must be known.

#### 2.1. Analysis of Time-Dependent Flexibility of EV Demand

**Fixed constant charging power**, ${P}_{\mathrm{fixed}}$ [kW], which can be chosen depending on the type of car or the type of charging station. The charging duration for this fixed constant charging power profile is $\mathsf{\Delta}{T}_{\mathrm{charge},\mathrm{Pfixed}}^{i}$, which is calculated using Equation (4).$$\mathsf{\Delta}{T}_{\mathrm{charge},\mathrm{Pfixed}}^{i}={E}_{\mathrm{req}}^{i}/{P}_{\mathrm{fixed}}^{i}$$**Transaction-specific maximum constant charging power**$,{P}_{\mathrm{max}}^{i}$ [kW], is the maximum value of charging power ${P}_{\mathrm{charge}}^{i}\left(t\right)\left[\mathrm{kW}\right]$ that occurs during transaction i. The charging duration $\mathsf{\Delta}{T}_{\mathrm{charge},\mathrm{Pmax}}^{i}$ is calculated using Equation (5).$$\mathsf{\Delta}{T}_{\mathrm{charge},\mathrm{Pmax}}^{i}={E}_{\mathrm{req}}^{i}/{P}_{\mathrm{max}}^{i}$$**Transaction-specific average constant charging power**, ${P}_{\mathrm{av}}^{i}$ [kW], is the average power of transaction i, which is calculated using Equation (6).$${P}_{\mathrm{av}}^{i}={E}_{\mathrm{req}}^{i}/\mathsf{\Delta}{T}_{\mathrm{charge}}^{i}$$

#### 2.2. EV Categories

^{−1}·day

^{−1}]), averaged over the year, exceeds a certain threshold. The demarcation is set at 3.45 kWh·day

^{−1}, which is 50% of the average daily energy demand of a Dutch electric passenger car, based on an average daily distance of 34.6 km [30,31] and a driving efficiency of 5 km·kWh

^{−1}[32]. This assumption was found to yield meaningful results (see Section 4.1). For PHEVs, ${E}_{\mathrm{daily}\text{}\mathrm{av}.}^{j}$ is less informative as the share of electricity demand in their total energy demand is unknown. Therefore, for PHEVs, the frequency of long transactions (${f}_{\mathrm{long}}^{j}$ [week

^{−1}]) is used as a decision parameter, in which a long transaction was defined as a transaction with a connection duration of over 6 h. The division of EVs is illustrated in Figure 2. Using this division, the available flexibility can also be expressed per EV category by selecting only transactions by EVs from a certain category.

#### 2.3. Scenarios EV Fleet Size

- The car possession rate (CPR [HH
^{−1}]), which is the number of passenger cars per household (both EV and non-electric), is the same in all scenarios. - In the ‘High’ scenario, all passenger cars will be BEVs, based on the Dutch governmental target of 100% of the passenger cars sold in 2030 being emission free [1].
- In the ‘High’ scenario, the maximum number of unique visiting BEVs per month is limited to 50 times the current number of charging stations in the area.
- The difference in number of EVs between the ‘Current’ and the ‘Medium’ scenario is half the difference between the ‘Current’ and the ‘High’ scenario for each EV category.
- The lifetime (LT) of an EV is assumed to be 15 years [33].

^{−1}] is the car possession rate, LT [year] is the lifetime of an EV, and ${N}_{\mathrm{days},\mathrm{data}}$ is the number of days in the measured dataset. By combining this with the current number of EVs occurring in the dataset, the size of the different EV categories can be derived for each scenario. The scenarios are not associated with specific years, as it is uncertain when a 100% EV market share will be reached in the Netherlands [34].

#### 2.4. Simulation: Preparation Input Data

#### 2.5. Simulation Steps

- From the available data, for each EV j in the dataset the number of transactions is normalized to the simulation period using Equation (9).$${N}_{\mathrm{tr},\mathrm{sim}}^{j}={N}_{\mathrm{tr},\mathrm{data}}^{j}\xb7{N}_{\mathrm{days},\mathrm{sim}}/{N}_{\mathrm{days},\mathrm{data}}$$In Equation (9), ${N}_{\mathrm{tr},\mathrm{sim}}^{j}$ is the average number of transactions that EV j has during a period with the same length as the simulation period. ${N}_{\mathrm{tr},\mathrm{data}}^{j}$ is the number of transactions within the measured dataset for a certain EV j, ${N}_{\mathrm{days},\mathrm{sim}}$ is the number of days in the simulation period, and ${N}_{\mathrm{days},\mathrm{data}}$ is the number of days in the measured dataset.
- A number of simulated transactions ${N}_{\mathrm{tr},\mathrm{sim}}^{m}$ was assigned to each simulated EV m in a certain category using the measured number of transactions by a randomly chosen EV j from that category, as expressed by Equation (10).$${N}_{\mathrm{tr},\mathrm{sim}}^{m}={N}_{\mathrm{tr},\mathrm{sim}}^{j}$$
- Next, all ${N}_{\mathrm{tr},\mathrm{sim}}^{m}$ transactions for this EV m are simulated. To each separate simulated transaction q of this EV m, a day within the simulation period is assigned, taking into account the ratio between the number of transactions on weekdays and on weekend days as it is in the measured data, using Equations (11) and (12):$${p}_{\mathrm{week},\mathrm{cat}}={N}_{\mathrm{tr},\mathrm{data},\mathrm{cat},\mathrm{week}}/{N}_{\mathrm{tr},\mathrm{data},\mathrm{cat}},$$$${p}_{\mathrm{weekend},\mathrm{cat}}=1-{p}_{\mathrm{week},\mathrm{cat}}.$$In these equations, ${p}_{\mathrm{week}}$ and ${p}_{\mathrm{weekend}}$ are the probabilities that the simulated transaction q takes place on a week or weekend day, respectively; ${N}_{\mathrm{tr},\mathrm{data},\mathrm{cat},\mathrm{week}}$ is the number of weekday transactions by EVs in a certain EV category in the measured dataset; and ${N}_{\mathrm{tr},\mathrm{data},\mathrm{cat}}$ is the total number of transactions by EVs in this category in the measured dataset.
- The starting hour (${h}_{\text{plug-in}}^{q}$) of the simulated transaction q is stochastically chosen based on the number of transactions in each set with size ${N}_{\mathrm{tr},\mathrm{data},\mathrm{cat},\mathrm{period},h\text{plug-in}\mathrm{in}=k}$ (bottom row Figure 3). The probability that a simulated transaction q starts within a certain hour for transactions starting at week days, for example, is calculated using Equation (13). For weekend days, the method is analogous.$${p}_{{h}_{\text{plug-in}}=\text{}k}=\frac{{N}_{\mathrm{tr},\mathrm{data},\mathrm{cat},\mathrm{week},{h}_{\text{plug-in}}=k\text{}}}{{N}_{\mathrm{tr},\mathrm{data},\mathrm{cat},\mathrm{week}}}\text{}\mathrm{for}\text{}\{k\in \mathbb{N}|0\text{}\le k\le 23\}$$In Equation (13), ${\mathrm{p}}_{{h}_{\text{plug-in}}=k}$ is the probability that the simulated transaction q starts within hour k. Using the probability distribution resulting from Equation (13), ${h}_{\text{plug-in}}^{q}$ is stochastically simulated for each transaction q. After assigning ${h}_{\text{plug-in}}^{q}$, the exact simulated plug in time ${t}_{\text{plug-in}}^{q}$ for each transaction q is derived by assigning a number of minutes within ${h}_{\text{plug-in}}^{q}$. This number of minutes is a randomly chosen multiple of $\Delta t$.
- One measured transaction i is chosen randomly from the union of the set of transactions for which ${h}_{\text{plug-in}}={h}_{\text{plug-in}}^{q}$ and the associated similar sets (see Section 2.4). Both ${E}_{\mathrm{req}}^{i}$ and $\mathsf{\Delta}{T}_{\mathrm{connect}}^{i}$ from this transaction were assigned to the simulated transaction q, as expressed in Equations (14) and (15). This way both the dependency of ${E}_{\mathrm{req}}^{q}$ and $\mathsf{\Delta}{T}_{\mathrm{connect}}^{q}$ to ${h}_{\text{plug-in}}^{q}$ and the dependency of ${E}_{\mathrm{req}}^{q}$ and $\mathsf{\Delta}{T}_{\mathrm{connect}}^{q}$ are respected.$${E}_{\mathrm{req}}^{q}={E}_{\mathrm{req}}^{i}$$$$\mathsf{\Delta}{T}_{\mathrm{connect}}^{q}=\mathsf{\Delta}{T}_{\mathrm{connect}}^{i}$$
- All EVs in the simulation charge uncontrolled at constant power, starting at ${t}_{\text{plug-in}}^{q}$ and ending when ${E}_{\mathrm{req}}^{q}$ is reached for each simulated transaction q. To determine the constant charging power ${P}^{q}$ [kW] that the simulated EV m uses during simulated transaction q, the three different constant charging powers (see Section 2.1 and Figure 1) are used in the simulation and compared:
**1.****Fixed constant charging power**: ${P}^{q}$ is set equal to ${P}_{\mathrm{fixed}}$. If the simulated EV m is a BEV, ${P}_{\mathrm{fixed}}$ is assigned to each simulated transaction q as expressed in Equation (16).$${P}^{q}={P}_{\mathrm{fixed}}=\{\begin{array}{c}{P}_{\mathrm{max},\mathrm{CP}}\mathrm{if}\mathrm{EV}m\mathrm{is}\mathrm{a}\mathrm{BEV}\\ {P}_{\mathrm{max},\mathrm{EV}}\mathrm{if}\mathrm{EV}m\mathrm{is}\mathrm{a}\mathrm{PHEV}\end{array}$$**2.****Transaction-specific maximum constant charging power:**${P}^{q}$ is set equal to ${P}_{\mathrm{max}}^{i}$ [kW], as expressed in Equation (17). By using this method, it is assumed that EVs charge constantly at ${P}_{\mathrm{max}}^{i}$.$${P}^{q}={P}_{\mathrm{max}}^{i}$$**3.****Transaction-specific average constant charging power**: ${P}^{q}$ is set equal to ${P}_{\mathrm{av}}^{i}$ [kW], which is defined using Equation (6). The assignment is expressed in Equation (18).$${P}^{q}={P}_{\mathrm{av}}^{i}$$These three charging power methods result in three different simulated charging power profiles for each simulated transaction q. Using transaction-specific average constant charging power, the simulation is expected to yield most realistic results, as the simulated charging duration is equal to the measured charging duration (see Figure 1).

- As the plug-in times are chosen independent from each other, a constraint has to be set in order to ensure that, for a single EV, the interval between plugging out and then plugging in again for the next transaction is large enough. The constraint ensures that the EV theoretically has enough time to use the charged amount of energy during the period that the EV was not connected to the charging station. If all transactions of a simulated EV m are put in chronological order, the constraint used in this study is given by Equation (19).$$0<\frac{{E}_{\mathrm{req}}^{q}}{{t}_{\text{plug-in}}^{q}\text{}-{t}_{\text{plug-out}}^{q-1}}\text{}{P}_{\mathrm{dis},\mathrm{max}}\text{}\mathrm{for}\text{}\{q\in \mathbb{N}|1q\le {N}_{\mathrm{tr}}^{m}\}$$
- The maximum EV discharge power during a trip, ${P}_{\mathrm{dis},\mathrm{max}}\left[\mathrm{kW}\right]$, is assumed to be 20 kW for all EVs, based on an average speed during the trip of 100 km·h
^{−1}and a driving efficiency of 5 km·kWh^{−1}[32,37]. After the simulation of every transaction, it is checked whether this constraint is met. If violated, the last simulated transaction is removed and re-simulated.

## 3. Case Study Description

^{−1}[39].

_{max,CP}is 22 kW. This value of 22 kW is used as ${P}_{\mathrm{fixed}}$ for BEVs in the simulation. For PHEVs, in the simulation, ${P}_{\mathrm{fixed}}$ is set equal to 3.7 kW, which is the maximum charging power for the top five best sold PHEVs in the Netherlands, as mentioned in Section 2.2. For each transaction i, the following data are available:

- ${t}_{\text{plug-in}}^{i}$: the plug-in time
- ${t}_{\text{plug-out}}^{i}$: the plug-out time
- ${P}_{\mathrm{charge}}^{i}\left(t\right)\left[\mathrm{kW}\right])$: power charged at each time t during transaction i, with $\Delta t$ = 5 min
- ${E}_{\mathrm{req}}^{i}$ [kWh]: the total charged energy
- An identity-key of each unique charging EV

## 4. Results

#### 4.1. Measured Data: EV Fleet and Transaction Parameters

^{−1}·day

^{−1}. The number of visiting BEVs in the dataset is 21 times higher than the number of local BEVs, but the average daily charging frequency for visiting BEVs is only 0.01 transactions EV

^{−1}·day

^{−1}. This difference is also reflected in the average daily volume charged per EV, ${E}_{\mathrm{daily}\text{}\mathrm{av}.}$, which is 8.41 kWh·EV

^{−1}·day

^{−1}for local BEVs and 0.17 kWh·EV

^{−1}·day

^{−1}for visiting BEVs. The number of different local PHEVs in the dataset is 20, while 617 unique visiting PHEV IDs were charging during the measurement period. The transaction frequencies differ by a factor 1.3 for BEVs and PHEVs. ${E}_{\mathrm{daily}\text{}\mathrm{av}.}$ is around a factor 3.5 lower for local PHEVs compared with local BEVs. For visiting EVs, this difference is around a factor 3.

#### 4.2. Measured Data: Time-Dependent Flexibility

#### 4.3. Simulation: Scenarios EV Fleet Size

^{−1}, it will be 0.4 HH

^{−1}in the ‘High’ scenario as well. Using a LT of 15 years and taking into account that ${N}_{\mathrm{days},\mathrm{data}}$ is 365, and applying Equation (7), ${N}_{\mathrm{BEV},\text{}\mathrm{local},\mathrm{High}}$ is calculated to be 145. The future EV fleet size scenarios are given in Table 2.

#### 4.4. Simulation: Scenario Results

^{−1}, 643 kWh·day

^{−1}, and 1227 kWh·day

^{−1}for the ‘Present-day’, ‘Medium’, and ‘High’ scenarios, respectively (left graph in Figure 7). Given that in the simulated area, the average daily baseload was 4013 kWh·day

^{−1}in December 2017 and 3254 kWh·day

^{−1}in June 2017, the EV demand in the ‘High’ scenario would cause roughly an increase in electricity demand of one-third compared with present-day household demand. The maximum peaks in aggregated EV demand occurring in the simulated month are shown in the right graph in Figure 7. In the ‘High’ scenario, maximum peaks range from 286 kW to 393 kW when ${P}_{\mathrm{fixed}}$ is used, while this range is from 214 kW to 301 kW for ${P}_{\mathrm{max}}^{i}$ and 194 kW to 284 kW for ${P}_{\mathrm{av}}^{i}$. Relatively speaking, the simulated highest peak using ${P}_{\mathrm{fixed}}$ is on average 33% higher than the simulated highest peak using ${P}_{\mathrm{av}}^{i}$. This difference is lower than the average relative difference between ${P}_{\mathrm{av}}^{i}$ and ${P}_{\mathrm{fixed}}$ for the separate transactions in the original data, which is 67% ± 18% for BEVs, as mentioned in Section 4.1. This is explained by the fact that $\mathsf{\Delta}{T}_{\mathrm{charge}}^{i}$ is shorter when the simulated charging power is higher (see Figure 1), and thus the different transactions are less likely to overlap each other in the simulation, that is, the transactions show a lower simultaneity.

## 5. Discussion

^{−1}during the trip and a driving efficiency of 5 km·kWh

^{−1}[32,37]. These numbers are uncertain as they depend on multiple variables such as the characteristics of the driving cycle and the battery technology. Yet, the exact value of the constraint is not expected to have a major impact on the results, as the constraint is not binding for most of the simulated transactions.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Indices | Description | |

i | index of transaction in measured dataset | |

j | index of EV in measured dataset | |

q | index of transaction in simulated dataset | |

m | index of EV in simulated dataset | |

k | hour of the day $\{k\in \mathbb{N}|0\text{}\le k24\}$ | |

Symbols | Description | Units |

${h}_{\text{plug-in}}^{i}$ | plug-in hour of transaction i | [-] |

${E}_{\mathrm{daily}\text{}\mathrm{av}.}^{j}$ | average daily energy charged by EV j | [kWh·EV^{−1}·day^{−1}] |

${E}_{\mathrm{req}}^{i}$ | energy required during transaction i | [kWh] |

${N}_{\mathrm{CS},\mathrm{sim}}$ | number of charging stations in simulation area | [-] |

${N}_{\mathrm{CS},\mathrm{total}}$ | number of charging stations in total area | [-] |

${N}_{\mathrm{days},\mathrm{data}}$ | number of days in measurement period | [-] |

${N}_{\mathrm{days},\mathrm{sim}}$ | number of days in simulation period | [-] |

${N}_{\mathrm{EV},\text{}\mathrm{sim},\mathrm{cat},\mathrm{scen}}$ | number of simulated unique EV IDs in category ‘cat’ and scenario ‘scen’ | [-] |

${N}_{\mathrm{EV},\mathrm{data},\text{}\mathrm{cat}}$ | number of unique EV IDs in category ‘cat’ in measured dataset | [-] |

${N}_{\mathrm{EV},\mathrm{data}}$ | number of unique EV IDs in measured dataset | [-] |

${N}_{\mathrm{HH}}$ | number of households | [-] |

${N}_{\mathrm{tr},\mathrm{data},\mathrm{cat},\mathrm{period},h\text{plug-in}=k}$ | number of transactions in measured dataset by EVs in category ‘cat’ during period ‘period’ for which the plug-in hour is k | [-] |

${N}_{\mathrm{tr},\mathrm{data},\mathrm{cat},\mathrm{period}}$ | number of transactions in measured dataset by EVs in category ‘cat’ during ‘period’ (week or weekend) | [-] |

${N}_{\mathrm{tr},\mathrm{data},\mathrm{cat}}$ | number of transactions in measured dataset by EVs in category ‘cat’ | [-] |

${N}_{\mathrm{tr},\mathrm{data}}$ | total number of transactions in measured dataset | [-] |

${N}_{\mathrm{tr},\mathrm{sim}}^{j}$ | number of transactions by EV j during simulation period | [-] |

${P}_{\mathrm{av}}^{i}$ | average charging power during transaction i | [kW] |

${P}_{\mathrm{charge}}^{i}\left(t\right)$ | power charged at each time t during transaction i | [kW] |

${P}_{\mathrm{dis},\mathrm{max}}^{m}$ | maximum discharge power during a trip of simulated EV m | [kW] |

${P}_{\mathrm{fixed}}$ | fixed charging power | [kW] |

${P}_{\mathrm{max}}^{i}$ | maximum charging power during transaction i | [kW] |

${P}_{\mathrm{max},\mathrm{EV}}$ | maximum power charged by the EV | [kW] |

${P}_{\mathrm{max},\mathrm{CP}}$ | maximum power delivered by the charging point | [kW] |

${P}_{\mathrm{max}}^{j}$ | maximum charging power occurring over all transactions by EV j in measured dataset | [kW] |

${P}_{\mathrm{max}}^{m}$ | maximum charging power for simulated EV m | [kW] |

${P}^{q}$ | charging power for simulated transaction q | [kW] |

${f}_{\mathrm{long}}^{j}$ | frequency of transactions with a duration > 6h for EV j | [week^{−1}] |

${f}_{\mathrm{daily}\text{}\mathrm{av}.}^{j}$ | average daily transaction frequency of EV j | [EV^{−1}·day^{−1}] |

${p}_{{h}_{\text{plug-in}}=\text{}k}$ | probability that ${h}_{\text{plug-in}}$= k | [-] |

${p}_{\mathrm{period},\mathrm{cat}}$ | probability that a simulated transaction of simulated EV m in category ‘cat’ falls in ‘period’ (week or weekend) | [-] |

${t}_{\text{plug-in}}^{i}$ | plug-in moment of transaction i | [-] |

${t}_{\text{plug-out}}^{i}$ | plug-out moment of transaction i | [-] |

$\Delta t$ | time step in measured charging profiles | [h] |

CPR | car possession rate | [HH^{−1}] |

LT | lifetime of an EV | [year] |

$\mathsf{\Delta}{T}_{\mathrm{charge},\mathrm{Pfixed}}^{i}$ | charging duration during transaction i based on ${P}_{\mathrm{fixed}}^{i}$ | [h] |

$\mathsf{\Delta}{T}_{\mathrm{charge},\mathrm{Pmax}}^{i}$ | charging duration during transaction i based on ${P}_{\mathrm{max}}^{i}$ | [h] |

$\mathsf{\Delta}{T}_{\mathrm{charge}}^{i}$ | measured charging duration during transaction i | [h] |

$\mathsf{\Delta}{T}_{\mathrm{connect}}^{i}$ | connection duration of transaction i | [h] |

$\mathsf{\Delta}{T}_{\mathrm{flex}}^{i}$ | available flexibility during transaction i | [h] |

Acronyms | Description | |

BEV | battery electric vehicle | |

EV | electric vehicle | |

ID | identity | |

LV | low voltage | |

MV | medium voltage | |

PHEV | plug-in hybrid electric vehicle |

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**Figure 1.**Example of measured and constant charging power profiles using a typical transaction i by a battery electric vehicle (BEV). The measured charging power profile of this example transaction i, which is ${P}_{\mathrm{charge}}^{i}\left(t\right)\left[\mathrm{kW}\right],$ is shown in black. Like any realistic charging profile, this profile is not constant. The black arrows on top illustrate the definitions of $\mathsf{\Delta}{T}_{\mathrm{connect}}^{i}$, $\mathsf{\Delta}{T}_{\mathrm{charge}}^{i}$, and $\mathsf{\Delta}{T}_{\mathrm{flex}}^{i}$ for the measured transaction i. Further, the three corresponding constant charging power profiles (green, blue, and red) are depicted for this transaction i, using three different constant charging powers: ${P}_{\mathrm{fixed}}$, ${P}_{\mathrm{max}}^{i}$, and ${P}_{\mathrm{av}}^{i}$. For all profiles, the energy charged during the transaction is kept equal to the measured value (${E}_{\mathrm{req}}^{i}$).

**Figure 2.**Categorization of electric vehicles (EVs), in which ${P}_{\mathrm{max}}^{j}$ is the maximum charging power of EV j, ${E}_{\mathrm{daily}\text{}\mathrm{av}.}^{j}$ is the average amount of energy charged for EV j per day, and ${f}_{\mathrm{long}}^{j}$ is its frequency of transactions with a duration >6 h.

**Figure 3.**Division of transactions. The dots indicate parts of the division tree that are not shown. The corresponding number of transactions in each set is given at the right of the figure.

**Figure 4.**From top to bottom, the histograms for ${h}_{\text{plug-in}}$, ${h}_{\text{plug-out}}$, $\mathsf{\Delta}{T}_{\mathrm{connect}}$, ${E}_{\mathrm{req}}$, and the average transaction power ${P}_{\mathrm{av}}$ are given for all transactions in the measured data, per EV category.

**Figure 5.**Analysis of the measured charging power profiles per transaction for BEVs (

**top**) and PHEVs (

**bottom**). For each transaction i, two points are plotted: a red one depicting ${P}_{\mathrm{av}}^{\mathrm{i}}$, and a blue one depicting ${P}_{\mathrm{max}}^{\mathrm{i}}$. The transactions are sorted in order of increasing ${P}_{\mathrm{max}}^{\mathrm{i}}$. The green line shows the value of ${P}_{\mathrm{fixed}}$ (see Section 2.1).

**Figure 6.**(

**a**) Available flexibility of aggregated EV demand in measured data, average values for each time of the day (5 min resolution). The demand profile shows a peak in the evening that is highly flexible, while the flexibility of the EV demand during the day is limited. (

**b**) Aggregated demand profiles and available flexibility per EV category in measured data; average values for each time of the day (5 min resolution).

**Figure 7.**Boxplots of average daily aggregated EV demand (

**left**) and highest peak in EV demand (

**right**) on the medium voltage (MV)/low voltage (LV)-transformer under study are given. The highest peaks in EV demand are given for the three different charging powers used, showing that peaks are largely overestimated when ${P}_{\mathrm{fixed}}$ is used as EV charging power.

**Figure 8.**(

**a**) Presentation of the simulated time-dependent flexibility, averaged over the day over all 50 simulation runs, for ‘Medium’ (

**left**) and ‘High’ (

**right**) scenarios, using ${P}_{\mathrm{fixed}}$ (22 kW for BEVs and 3.7 kW for PHEVs). (

**b**) Presentation of the simulated time-dependent flexibility, averaged over the day over all 50 simulation runs, for ‘Medium’ and ‘High’ scenarios, using ${P}_{\mathrm{av}}^{i}$ (see Equation (18)).

**Table 1.**Key figures of electric vehicle (EV) charging station measured data analysis over the measurement period 1 August 2017 to 31 July 2018, covering 21 charging stations within the Lombok district in the city of Utrecht.

Category | ${\mathit{N}}_{\mathbf{E}\mathbf{V},\mathbf{d}\mathbf{a}\mathbf{t}\mathbf{a},\mathbf{c}\mathbf{a}\mathbf{t}}$ [#] | ${\mathit{f}}_{\mathbf{d}\mathbf{a}\mathbf{i}\mathbf{l}\mathbf{y}\mathbf{a}\mathbf{v}.}$ [EV^{−1}·day^{−1}] | ${\mathit{E}}_{\mathbf{d}\mathbf{a}\mathbf{i}\mathbf{l}\mathbf{y}\mathbf{a}\mathbf{v}.}$ [kWh·EV^{−1}·day^{−1}] |
---|---|---|---|

Local BEV | 13 | 0.47 | 8.41 |

Visiting BEV | 273 | 0.01 | 0.17 |

Local PHEV | 20 | 0.35 | 2.37 |

Visiting PHEV | 617 | 0.01 | 0.06 |

All EVs | 923 | 0.02 | 0.26 |

**Table 2.**Number of unique EV identities (IDs) occurring in the simulation for the different EV categories and scenarios for EV fleet size, per EV category.

Category | N_{EV,sim,cat,Present-day} | N_{EV,sim,cat,Medium} | N_{EV,sim,cat,High} |
---|---|---|---|

Local BEV | 5 | 75 | 145 |

Visiting BEV | 72 | 186 | 300 |

Local PHEV | 5 | 2 | 0 |

Visiting PHEV | 168 | 84 | 0 |

All EVs | 250 | 347 | 445 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Gerritsma, M.K.; AlSkaif, T.A.; Fidder, H.A.; van Sark, W.G.J.H.M.
Flexibility of Electric Vehicle Demand: Analysis of Measured Charging Data and Simulation for the Future. *World Electr. Veh. J.* **2019**, *10*, 14.
https://doi.org/10.3390/wevj10010014

**AMA Style**

Gerritsma MK, AlSkaif TA, Fidder HA, van Sark WGJHM.
Flexibility of Electric Vehicle Demand: Analysis of Measured Charging Data and Simulation for the Future. *World Electric Vehicle Journal*. 2019; 10(1):14.
https://doi.org/10.3390/wevj10010014

**Chicago/Turabian Style**

Gerritsma, Marte K., Tarek A. AlSkaif, Henk A. Fidder, and Wilfried G. J. H. M. van Sark.
2019. "Flexibility of Electric Vehicle Demand: Analysis of Measured Charging Data and Simulation for the Future" *World Electric Vehicle Journal* 10, no. 1: 14.
https://doi.org/10.3390/wevj10010014