Flexibility of Electric Vehicle Demand: Analysis of Measured Charging Data and Simulation for the Future
"> Figure 1
<p>Example of measured and constant charging power profiles using a typical transaction <span class="html-italic">i</span> by a battery electric vehicle (BEV). The measured charging power profile of this example transaction <span class="html-italic">i</span>, which is <math display="inline"><semantics> <mrow> <msubsup> <mi>P</mi> <mrow> <mi>charge</mi> </mrow> <mi>i</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo> </mo> <mrow> <mo>[</mo> <mrow> <mi>kW</mi> </mrow> <mo>]</mo> </mrow> <mo>,</mo> </mrow> </semantics></math> is shown in black. Like any realistic charging profile, this profile is not constant. The black arrows on top illustrate the definitions of <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msubsup> <mi>T</mi> <mrow> <mi>connect</mi> </mrow> <mi>i</mi> </msubsup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msubsup> <mi>T</mi> <mrow> <mi>charge</mi> </mrow> <mi>i</mi> </msubsup> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msubsup> <mi>T</mi> <mrow> <mi>flex</mi> </mrow> <mi>i</mi> </msubsup> </mrow> </semantics></math> for the measured transaction <span class="html-italic">i</span>. Further, the three corresponding constant charging power profiles (green, blue, and red) are depicted for this transaction <span class="html-italic">i</span>, using three different constant charging powers: <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mrow> <mi>fixed</mi> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msubsup> <mi>P</mi> <mrow> <mi>max</mi> </mrow> <mi>i</mi> </msubsup> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msubsup> <mi>P</mi> <mrow> <mi>av</mi> </mrow> <mi>i</mi> </msubsup> </mrow> </semantics></math>. For all profiles, the energy charged during the transaction is kept equal to the measured value (<math display="inline"><semantics> <mrow> <msubsup> <mi>E</mi> <mrow> <mi>req</mi> </mrow> <mi>i</mi> </msubsup> </mrow> </semantics></math>).</p> "> Figure 2
<p>Categorization of electric vehicles (EVs), in which <math display="inline"><semantics> <mrow> <msubsup> <mi>P</mi> <mrow> <mi>max</mi> </mrow> <mi>j</mi> </msubsup> </mrow> </semantics></math> is the maximum charging power of EV <span class="html-italic">j,</span> <math display="inline"><semantics> <mrow> <msubsup> <mi>E</mi> <mrow> <mrow> <mi>daily</mi> <mtext> </mtext> <mi>av</mi> </mrow> <mo>.</mo> </mrow> <mi>j</mi> </msubsup> </mrow> </semantics></math> is the average amount of energy charged for EV <span class="html-italic">j</span> per day, and <math display="inline"><semantics> <mrow> <msubsup> <mi>f</mi> <mrow> <mi>long</mi> </mrow> <mi>j</mi> </msubsup> </mrow> </semantics></math> is its frequency of transactions with a duration >6 h.</p> "> Figure 3
<p>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.</p> "> Figure 4
<p>From top to bottom, the histograms for <math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mrow> <mtext>plug-in</mtext> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mrow> <mtext>plug-out</mtext> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mi>T</mi> <mrow> <mi>connect</mi> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>E</mi> <mrow> <mi>req</mi> </mrow> </msub> </mrow> </semantics></math>, and the average transaction power <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mrow> <mrow> <mi>av</mi> </mrow> </mrow> </msub> </mrow> </semantics></math> are given for all transactions in the measured data, per EV category.</p> "> Figure 5
<p>Analysis of the measured charging power profiles per transaction for BEVs (<b>top</b>) and PHEVs (<b>bottom</b>). For each transaction <span class="html-italic">i</span>, two points are plotted: a red one depicting <math display="inline"><semantics> <mrow> <msubsup> <mi>P</mi> <mrow> <mi>av</mi> </mrow> <mi mathvariant="normal">i</mi> </msubsup> </mrow> </semantics></math>, and a blue one depicting <math display="inline"><semantics> <mrow> <msubsup> <mi>P</mi> <mrow> <mi>max</mi> </mrow> <mi mathvariant="normal">i</mi> </msubsup> </mrow> </semantics></math>. The transactions are sorted in order of increasing <math display="inline"><semantics> <mrow> <msubsup> <mi>P</mi> <mrow> <mi>max</mi> </mrow> <mi mathvariant="normal">i</mi> </msubsup> </mrow> </semantics></math>. The green line shows the value of <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mrow> <mi>fixed</mi> </mrow> </msub> </mrow> </semantics></math> (see <a href="#sec2dot1-wevj-10-00014" class="html-sec">Section 2.1</a>).</p> "> Figure 6
<p>(<b>a</b>) 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>b</b>) Aggregated demand profiles and available flexibility per EV category in measured data; average values for each time of the day (5 min resolution).</p> "> Figure 6 Cont.
<p>(<b>a</b>) 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>b</b>) Aggregated demand profiles and available flexibility per EV category in measured data; average values for each time of the day (5 min resolution).</p> "> Figure 7
<p>Boxplots of average daily aggregated EV demand (<b>left</b>) and highest peak in EV demand (<b>right</b>) 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 <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mrow> <mi>fixed</mi> </mrow> </msub> </mrow> </semantics></math> is used as EV charging power.</p> "> Figure 8
<p>(<b>a</b>) Presentation of the simulated time-dependent flexibility, averaged over the day over all 50 simulation runs, for ‘Medium’ (<b>left</b>) and ‘High’ (<b>right</b>) scenarios, using <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mrow> <mi>fixed</mi> </mrow> </msub> </mrow> </semantics></math> (22 kW for BEVs and 3.7 kW for PHEVs). (<b>b</b>) Presentation of the simulated time-dependent flexibility, averaged over the day over all 50 simulation runs, for ‘Medium’ and ‘High’ scenarios, using <math display="inline"><semantics> <mrow> <msubsup> <mi>P</mi> <mrow> <mi>av</mi> </mrow> <mi>i</mi> </msubsup> </mrow> </semantics></math> (see Equation (18)).</p> ">
Abstract
:1. Introduction
2. Methods
- : the plug-in time for transaction i.
- : the plug-out time for transaction i.
- : power charged at each time t during transaction i, with a sufficiently high time resolution ( ≤ 15 min). In this study, this data is referred to as the ‘measured charging profile’.
- Possibly also [kWh], which is the total charged energy during each transaction. However, this metric can also be derived from if 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, [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 , which is calculated using Equation (4).
- Transaction-specific maximum constant charging power [kW], is the maximum value of charging power that occurs during transaction i. The charging duration is calculated using Equation (5).
- Transaction-specific average constant charging power, [kW], is the average power of transaction i, which is calculated using Equation (6).
2.2. EV Categories
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].
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).In Equation (9), is the average number of transactions that EV j has during a period with the same length as the simulation period. is the number of transactions within the measured dataset for a certain EV j, is the number of days in the simulation period, and is the number of days in the measured dataset.
- A number of simulated transactions 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).
- Next, all 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):In these equations, and are the probabilities that the simulated transaction q takes place on a week or weekend day, respectively; is the number of weekday transactions by EVs in a certain EV category in the measured dataset; and is the total number of transactions by EVs in this category in the measured dataset.
- The starting hour () of the simulated transaction q is stochastically chosen based on the number of transactions in each set with size (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.In Equation (13), is the probability that the simulated transaction q starts within hour k. Using the probability distribution resulting from Equation (13), is stochastically simulated for each transaction q. After assigning , the exact simulated plug in time for each transaction q is derived by assigning a number of minutes within . This number of minutes is a randomly chosen multiple of .
- One measured transaction i is chosen randomly from the union of the set of transactions for which and the associated similar sets (see Section 2.4). Both and from this transaction were assigned to the simulated transaction q, as expressed in Equations (14) and (15). This way both the dependency of and to and the dependency of and are respected.
- All EVs in the simulation charge uncontrolled at constant power, starting at and ending when is reached for each simulated transaction q. To determine the constant charging power [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: is set equal to . If the simulated EV m is a BEV, is assigned to each simulated transaction q as expressed in Equation (16).
- 2.
- Transaction-specific maximum constant charging power: is set equal to [kW], as expressed in Equation (17). By using this method, it is assumed that EVs charge constantly at .
- 3.
- Transaction-specific average constant charging power: is set equal to [kW], which is defined using Equation (6). The assignment is expressed in Equation (18).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).
- The maximum EV discharge power during a trip, , 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
- : the plug-in time
- : the plug-out time
- : power charged at each time t during transaction i, with = 5 min
- [kWh]: the total charged energy
- An identity-key of each unique charging EV
4. Results
4.1. Measured Data: EV Fleet and Transaction Parameters
4.2. Measured Data: Time-Dependent Flexibility
4.3. Simulation: Scenarios EV Fleet Size
4.4. Simulation: Scenario Results
5. Discussion
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 | |
Symbols | Description | Units |
plug-in hour of transaction i | [-] | |
average daily energy charged by EV j | [kWh·EV−1·day−1] | |
energy required during transaction i | [kWh] | |
number of charging stations in simulation area | [-] | |
number of charging stations in total area | [-] | |
number of days in measurement period | [-] | |
number of days in simulation period | [-] | |
number of simulated unique EV IDs in category ‘cat’ and scenario ‘scen’ | [-] | |
number of unique EV IDs in category ‘cat’ in measured dataset | [-] | |
number of unique EV IDs in measured dataset | [-] | |
number of households | [-] | |
number of transactions in measured dataset by EVs in category ‘cat’ during period ‘period’ for which the plug-in hour is k | [-] | |
number of transactions in measured dataset by EVs in category ‘cat’ during ‘period’ (week or weekend) | [-] | |
number of transactions in measured dataset by EVs in category ‘cat’ | [-] | |
total number of transactions in measured dataset | [-] | |
number of transactions by EV j during simulation period | [-] | |
average charging power during transaction i | [kW] | |
power charged at each time t during transaction i | [kW] | |
maximum discharge power during a trip of simulated EV m | [kW] | |
fixed charging power | [kW] | |
maximum charging power during transaction i | [kW] | |
maximum power charged by the EV | [kW] | |
maximum power delivered by the charging point | [kW] | |
maximum charging power occurring over all transactions by EV j in measured dataset | [kW] | |
maximum charging power for simulated EV m | [kW] | |
charging power for simulated transaction q | [kW] | |
frequency of transactions with a duration > 6h for EV j | [week−1] | |
average daily transaction frequency of EV j | [EV−1·day−1] | |
probability that = k | [-] | |
probability that a simulated transaction of simulated EV m in category ‘cat’ falls in ‘period’ (week or weekend) | [-] | |
plug-in moment of transaction i | [-] | |
plug-out moment of transaction i | [-] | |
time step in measured charging profiles | [h] | |
CPR | car possession rate | [HH−1] |
LT | lifetime of an EV | [year] |
charging duration during transaction i based on | [h] | |
charging duration during transaction i based on | [h] | |
measured charging duration during transaction i | [h] | |
connection duration of transaction i | [h] | |
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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Category | [#] | [EV−1·day−1] | [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 |
Category | NEV,sim,cat,Present-day | NEV,sim,cat,Medium | NEV,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 |
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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
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 StyleGerritsma, 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