Simultaneous Charging at all the Parking Spaces in a Car Park
MATHEMATIC MODEL OF SIMULTANEOUS CHARGING
*Binomial Distribution finds many applications in many scientific and engineering fields which is a Probability Distribution with the Mean (µ) and Variance (s) of which is represented by the following formulas:
µ = np
s = (npq)^0.5
where,
n - no. of repeated trials
p - probability of success
q - probability of unsuccess = (1 – p)
Remark:
a) Mean of a Probability Distribution is the mathematical expectation or the expected value of a random variable
b) Variance of a Probability Distribution is deviation of an observation from its mean
*Ronald E. Walpole & Raymond H. Myers – Probability and Statistics for Engineers and Scientists
By using Binomial Distribution, the Mean No. of Car Charging (C-Mean) at all the parking spaces in the car park can be taken as the Mean (µ) of Binomial Distribution
C-Mean = N x P (1)
where,
N - no. of parking spaces
P - probability of a car in charging = (t / T)
t - average time required for a car charge to its FULL
T - average time that a car required charging
Taking into consideration of the Variance of a Probability Distribution, it is conservative to add 2s to the Mean (C-Mean) to give the Simultaneous Charging (C-Sim) at all the parking spaces in the car park:
C-Sim = C-Mean + 2s
= N x P + 2 x (N x P x Q)^0.5 (2)
where,
Q - probability of a car not in charging = (1 – P)
Remark:
2 Times of Variance is added to cater for both “Charging” and “Not Charging” cases.
In Hong Kong, residential parking spaces in the car park each car will take a charge of every 2-3 days and average time required a car charge to its FULL takes ***3hrs. Take an average of car take a charge of every 2.5 days
**Item 4.3a) of Design Guidelines for Electric Vehicle Charging-Enabling Infrastructure under the EV-Charging at Home Subsidy Scheme issued by Environmental Protection Department.
***Summary Table of Different Charging Arrangements in Annex D of Technical Guidelines on Charging Facilities for Electric Vehicles issued by Electrical and Mechanical Services Department
Taking into consideration that the driving style in Hong Kong Residential Development, it is conservative to assume half of the car parked in a car park of a residential development having daily departure from the car park. It means that a Utilization Factor (UF) of 0.5 can be applied to the Simultaneous Charging of all parking spaces in a car park for design the Electrical Vehicle Charging-Enabled Infrastructure (EVCEI). In addition, a worst case assumption should be made for car departed in a car park of a residential development return to the car park within a period of 3 Hours that a Peaking Factor (P.F.) of 8 should be applied for sizing the EVCEI. Therefore, Design Simultaneous Charging (C-D-Sim) will be taken as
C-D-Sim = C-Sim x UF x P.F. = 4 C-Sim