Page 46 - DP-2-2

Design+ EV charging capacity through queuing model

ρ <ρ<1 (XIII) gross national product expressed in monetary terms; T is
t
G
(B) Waiting time limit the work hours of the laborer; N is the number of workers;
P
and T =D×T /5, where D is the number of working days in
w
G
We need to consider not only the return on investment the year; and T is the average weekly working hours.
for the investor and the equipment utilization but also the w
reasonability of the queuing time. Thus, the efficiency of The gross domestic product and other data of Hohhot
CSs and user satisfaction needs to reach a good balance. City in 2022, as shown in Table 2, were obtained from the
Through queuing theory, we can calculate the average Hohhot City 2023 Statistical Yearbook.
queuing time and charging time under different numbers Substituting the data in Table 2 into Equation XVI, the
of charging terminals, directly reflecting the efficiency of average user time cost in Hohhot in 2022 can be obtained
users waiting for charging. For users, a long waiting time as 86.85 yuan by the production method.
will seriously affect their experience and satisfaction. To The parameters of the public fast-charging capacity
ensure that the queuing time of users is not too long, we optimization model are set as follows. The operating life
need to introduce a limit. The waiting time should be set to of the station r is set to 10 years. The discount rate d is set
less than the maximum queuing time, as in Equation XIV. at 5%. The charging facilities of the public fast-CS adopt
This maximum queuing time can be determined based on split charging equipment, including high and low voltage
the user’s needs, behavioral habits, and expectations of the integrated charging box transformer and charging terminal.
charging service.
The price of 800 kVA charging box-type transformer c
xb
W ≤W (XIV) is 520,000 yuan. The unit price of the charging terminal
s t
Taking into account the above analysis of the objective c is 6,000 yuan. The land cost of the public fast CS c is
zd
td
function and constraints, the public fast-CS capacity 2 million yuan. The construction cost of the station c is
js
optimization model can be expressed as Equation XV. 100,000 yuan. The annual inspection and maintenance
cost of each terminal c is 1,000 yuan. The distribution
wh
F
min k = γ F 1 ik + γ F 2 tk cost per unit capacity α is 5000 yuan/kVA, and the load

 ratio of the transformer is set to 80%. The distribution cost
 st ρ  . . t ρ < < 1, s ≤ W W t (XV) of the charging box transformer c can be calculated to
pd
be 5 million yuan. The battery capacity of the EV q is set
2.5. Case analysis to 60 kWh and the maximum queuing time that EV users
We collected data about the operation of a public fast-CS can tolerate is set to 10 min. The time cost for EV users is
in Hohhot. The time distribution of the arrival process and 86.85 yuan/h. Since there is a land cost for this station, the
service process of the charging service system of this fast-CS weighting factor is set to γ = 0.6, γ = 0.4.
2
1
has been analyzed as described in Section 2.2. It is known The facility utilization rate of a public CS is calculated
that the arrival interval time obeys a negative exponential as ρ = λ/μs. For the charging service system not to form
distribution with parameter 9.47, so the number of vehicles an infinite queue, ρ should be ≤1. Substituting the values
arriving at the CS per unit time is λ = 0.106. The charging of λ and μ, s = 5.06, the minimum number of charging
duration obeys a normal distribution with parameter terminals in the public fast-CS is determined as 6. The
47.25; then the number of vehicles that can be served per facility utilization rate of the public fast-CS ρ should be
unit time is μ = 0.021. greater than a certain minimum value ρ to ensure the
t
The production method is a method of determining the sustainable operation of the CS. By setting ρ = 0.3, the
t
cost of time based on the value that the traveler can create. maximum number of charging terminals in the public fast
The production method assumes that travelers are engaged CS is determined as 16.
in productive activities if they are not waiting. They can When the number of charging terminals is >13, the
create national income or gross national product. In the charging power allocated to a single charging terminal will
queuing theory model, when considering the time cost of be <60 kW, which means that the charging time for EVs will
EV users, it is a common method to use the production
method, which is calculated as in Equation XVI. Table 2. Statistical data of Hohhot in 2022
P Year Employment Gross domestic Weekly Number
W p = T G ×N P (XVI) number product working hours of working
G
days
In the formula, W is the cost per unit of time to the user 2022 1.574 million 332910.46 48.9 h 249 days
p
calculated according to the production method; P is the people million yuan
G
Volume 2 Issue 2 (2025) 9 doi: 10.36922/dp.4225