Developing a statistical electric vehicle charging model and its application in the performance assessment of a sustainable urban charging hub

Figures & data

Table 1. Data headers from Transport Scotland EV charging dataset.

Entry	Data Item	Entry	Data Item
1	Charging event	10	Charge Cost £
2	User ID	11	Charger Location
3	Charger ID	12	Charger Group
4	Charger Point Connector ID	13	Charger Model Type
5	Charger Start Date	14	Host ID
6	Charge Start Time	15	Card Status
7	Charge End Date	16	Tag Serial
8	Charge End Time	17	Vehicle Type
9	Total Charge Taken kWh

Table 2. Data headers from the City of Glasgow EV charging dataset.

Entry	Data Item	Entry	Data Item
1	SDR ID (–)	7	Cost £
2	Site Name (–)	8	Consumption kWh
3	Card Number (–)	9	Duration hh:mm:ss
4	Charger ID (–)	10	Charge Start (Date)
5	Connector Number (–)	11	Charge End (Date)
6	Currency (–)

Figure 1. Probability and cumulative probability of weekly vehicle charging frequency, ${\mathit{c}}_{chf}$, derived from the transport Scotland dataset.

Table 3. Daily charging probability modifiers.

Day Type	Modifier
Weekday	1.02
Saturday	1.13
Sunday	0.78

Figure 2. Probability distribution, $p_{chs}$ and cumulative probability distributions, ${\mathit{c}}_{chs}$ of EV charging event starting for weekdays and weekends derived from the Transport Scotland dataset.

Figure 3. The probability $p_{chE}$ and cumulative probability ${\mathit{c}}_{chE}$ and off a particular charge being taken (kWh).

Figure 4. Flow chart illustrating a vehicle-centric probability-based algorithm to calculate an aggregate charging profile.

Figure 5. Example of demand profile for a fleet of 80 electric vehicles.

Figure 6. Simulated and monitored time-dependent charging probabilities.

Figure 7. Simulated and monitored cumulative probabilities of charge taken during a charge event.

Figure 8. Mean charge taken and std. dev. of charge taken from dataset and simulation.

Figure 9. Duke St car park (Image: Google street view) and rendered image of the ESP-r Duke St Car Park model with roof-mounted PV arrays and shading from surrounding buildings.

Table 4. Characteristics of the PV panels used in the analysis (Longi 2020).

Open circuit voltage ($V_{OC}$)	49.5 V
Short circuit current. ($I_{SC}$)	11.66 A
Voltage at maximum power point ($V_{MP}$)	41.7 V
Current at maximum power point ($I_{MP}$)	10.92 A
Reference insolation (${\dot{Q}}_{ref}$)	1000 W/m^2
Reference temperature ($T_{ref}$)	298 K
Number series connected cells in a branch ($n$)	144
Number of parallel connected branches ($m$)	6
Number of panels ($q$)	24
Temperature sensitivity of $I_G$ ($\beta$)	1.072

Figure 10. PV array annual energy yield vs slope.

Figure 11. Simulated car park half-hourly PV output.

Figure 12. Car park charging hub electrical load flow model.

Table 5. Battery parameters used with the model (GCC 2018).

battery capacity ($C_{MAX}$)	0–500 kWh
minimum state of charge ($SO{C}_{MIN}$)	0.2
charging efficiency (${\eta }_C$)	0.960
discharge efficiency (${\eta }_D$)	0.972
battery standing loss ($\epsilon$)	6.25 × 10^−5 of $C_B(t)$ per time step
converter efficiency (${\eta }_X$)	0.9

Table 6. Charger ‘fleet’ used with the model (ChargePlace Scotland 2023).

Charger information		Connector information
Charger Type	Number of connectors	Maximum Power (kW)	Type	Maximum Power (kW)	Type	Maximum Power (kW)	Type
OC4S 1	2	22	Fast 22	22	Fast 22
OC4S 2	2	22	Fast 22	22	Fast 22
OC4S 3	2	22	Fast 22	22	Fast 22
OC4S 4	2	22	Fast 22	22	Fast 22
Rapid 1	3	51	RDC^a	51	RAC^2	43	RAC
Rapid 2	3	51	RDC	51	RAC	22	Fast 22
Rapid 2	3	51	RDC	51	RAC	22	Fast 22

^a RDC – rapid DC; RAC – RAPID AC.

Figure 13. Example of time series output from the simulation, for the case with 50 vehicles and 100 kWh battery.

Table 7. Annual simulated electrical demand with different numbers of vehicles using the hub^a.

Vehicles	10	20	50	100	200	500
EV Demand (MWh)	17.5	29.3	71.9	156.8	302.6	732.0
Total Car Park Demand (MWh)	95.9	107.7	150.3	235.2	381.1	810.4

^a As the EV charging profiles are generated using a probabilistic model, the increases in energy demand will not be exact multiples of the number of vehicles.

Figure 14. REC and RUF (expressed as a %) for different supporting battery sizes and vehicle fleets.

Figure 15. Imported electrical energy against battery size for different vehicle fleets.

Figure 16. Peak imported power against battery size for different vehicle fleets.

Figure 17. Exported electrical energy against battery size for different vehicle fleets.

Figure 18. Peak exported electrical power against battery size for different vehicle fleets.

Figure 19. Simulated variation in PV output, vehicle demand, battery SOC, power export and import on 20/21 June for the case with 500 vehicles and 500 kWh battery.

Figure 20. Simulated variation in PV output, vehicle demand, battery SOC, power export and import on 20/21 June for the case with 50 vehicles and 50 kWh battery.

Figure 21. Average battery state of charge (expressed as a %) against battery size for different vehicle fleets.

Figure 22. Net carbon emissions due to use of PV and battery against battery size for different vehicle fleets.

Table

$c$	specific heat	J/kgK
$\mathit{c}$	cumulative probability	0–1 or 0–100%
$C$	capacity	kWh
$Ce$	net carbon emissions	kg
$Ci$	EV charging carbon emissions	kg
$Cx$	carbon offset from PV exports	kg
$d$	modifier	(–)
$e$	charge on an electron (1.602177 × 10^−19)	C
$E$	Energy	kWh
$f$	fraction	0–1
$F$	generator fraction	0–1
$I$	current	A
$k$	Boltzmann constant (1.380649×10^−23)	J/K
$m$	number of parallel connected branches in a panel	–
$M$	mass	kg
$n$	number of series connected cells in a branch	–
$p$	probability	0–1 or 0–100%
$P$	power	W
$q$	number of panels	–
$\dot{Q}$	solar insolation	W/m^2
$REC$	renewable energy contribution	0–100%
$RUF$	renewable utilisation factor	0–100%
$SOC$	state of charge	0–100%
$T$	temperature	K
$t$	time	S
$\mathrm{\Delta }t$	time increment	s
$V$	voltage	V
$X$	random variable	0–1 or 0–100%
Greek Symbols
$\beta$	temperature sensitivity coefficient	–
$\delta$	generator carbon intensity	kg/kWh
$\gamma$	time dependent grid carbon intensity	kg/kWh
$\epsilon$	battery standing loss	0–1
$\lambda$	diode factor	–
$\eta$	efficiency	0–1
Subscripts
$B$	battery
$C$	charge
$chd$	daily charge
$ch{d}^{\mathrm{\prime }}$	modified daily charge
$chE$	charge energy
$chs$	charge start
$chx$	charge in period $x$
$cp$	charge point
$D$	discharge
$E$	energy
$EV$	electric vehicle
$G$	generation current
$i$	event, layer or number of charges per week
$j$	PV material layer or charging time interval
$k$	charge energy taken
$L$	light generated current
$LV$	low voltage
$m$	modifier
$MIN$	minimum
$MAX$	maximum
$OL$	other electrical loads
$OC$	open circuit
$MP$	maximum power point
$PV$	photovoltaic
$ref$	reference value
$s$	start time
$SOL$	solar
$SC$	short circuit
$t$	time
$TD$	total demand
$v$	vehicle
$x$	variable, period
$X$	converter

Longi Solar Ltd. 2020. Datasheet, LR4-72 HPH 455 M G2.

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GCC (Glasgow City Council). 2018. “Specifications for the Duke St Car Park PV Canopy.” Glasgow City Council Project Report.

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ChargePlace Scotland. 2023. “ChargePlace Scotland Live Map, App.” ChargePlace Scotland live map – Charge Place Scotland. Accessed March 1, 2023.

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Data availability statement

The data and modelling tools that support the findings of this study are available from DOI: 10.15129/21b5782d-a229-42f9-8f17-1f9a60f91197.