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Design+ EV charging capacity through queuing model

of the box-type transformer; c is the land cost of the station; utilization of charging equipment, waiting time of users,
td
c is the construction cost; c is the unit price of the charging and cost-benefit analysis. Multiple constraints need to
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js
terminals; c is the cost of inspection and maintenance of the considered in optimizing problem. By comprehensively
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individual terminals; and s is the number of charging parking considering the needs of investors and users, we can
spaces in the station. P denotes the power of the integrated formulate a public CS facility optimization plan that
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box-type transformer; α is the distribution cost (yuan/kVA); can both ensure return on investment and enhance
and β is the optimal load factor. user experience. This enables formulating a public CS
User time cost, including the queuing time for users optimization plan that ensures return on investment while
waiting for vacant charging spaces and the waiting time enhancing user experience through improved service
for EV charging, as in Equations XI and XII. CS operation quality and operational efficiency.
hours are divided into peak and off-peak periods. The (A) Facility utilization constraints
number of CS terminals in off-peak period is larger than
the number of EVs, and EVs can be charged without From the investor’s perspective, facility utilization
queuing and can receive a larger charging power. In the should exceed a certain value. Facility utilization is critical
peak period, the CS will be swarmed with charging vehicles to return on investment. Investors put money into a public
queuing up for charging. This paper focuses on the study of CS project with the expectation that they will recover their
the user’s time cost during the peak charging period. investment and realize a profit within a reasonable period
of time. If the facility utilization rate is too low, it means
H
F tk = c t (W q G +W ct ) 24 (XI) that the payback period will be extended and the return
on investment will be affected. Therefore, it is essential
W ct = /qP (XII) for investors to set an appropriate lower limit for facility
utilization. Determining the facility utilization needs to
In the formula, c is the average time cost of EV users, take into account not only the size and cost structure of
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and W is the charging time, and it is related to the power the investment but also market demand and competitive
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of the charging terminal. P=P /s denotes the power conditions to ensure the sustainability of the project.
xb
allocated to the charging terminal; H denotes the number From the user’s perspective, the utilization rate of the
of charging vehicles per day; q denotes the battery capacity facility should not be >1. The utilization rate of the charging
of the EV; and s is the number of charging terminals. equipment is directly related to the user’s experience and
There are usually two modes of construction of public satisfaction. Users often choose to use public CSs for
fast CSs: Investment construction and joint construction. convenience and urgency, meaning they expect the CS is
Investment construction generally means that the immediately available when they need it, rather than having
investor-operator of the CS bears the cost of the land and to wait for it. A facility utilization rate of 1 means that the
builds the CS by itself. Co-construction means that the facility is always in use, which can significantly reduce user
investor-operator and the landowner build the CS together satisfaction. Therefore, to improve the user experience, it is
in a cooperative mode, and the land is expropriated free important to ensure that the utilization rate of the charging
of charge. When the CS is constructed based on the facilities is <1. This means that corresponding measures
investment construction mode, the investing operator need to be taken in the planning and management of
often bears the larger portion of the land rent. In such a equipment. Thus, the number of devices available and the
situation, more attention should be paid to the investment layout design need to be reasonably optimized, and the
cost of the investor. The value of the weight coefficient is users should be guided to effectively plan the charging
suggested to be γ > γ , so that the optimization model will time. Under the ideal circumstances, the users would be
1
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pay more attention to reduce the investment cost. Under able to use the charging equipment quickly and easily
the co-construction model, since there is no land cost, when they need it, thus enhancing their satisfaction.
the investment cost only includes the equipment cost and
construction, operation, and maintenance cost. Using this Facility utilization rate, as a key indicator, directly affects
model, how to reduce the user time cost is key. The value of the payback period and the profitability of the project as
the weighting coefficient is suggested to be γ > γ , so as to well as the charging experience of users. The planning and
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ensure that the comprehensive social cost is lower. design of public CSs should ensure that the project can
recover the investment cost in a reasonable period of time
2.4.2. Constraint condition and avoid prolonged waiting time for charging; therefore,
Facility optimization of public CSs is a complex decision the facility utilization rate should be constrained, as in
problem that involves multiple factors, including the Equation XIII.

Volume 2 Issue 2 (2025) 8 doi: 10.36922/dp.4225