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4. Prediction of EVs charging 
This section shows the application of the predictive function defined by the equation (1) for predicting the 
charging rates of a set of EVs. The basic parameters and the evolution of 𝜆𝜆 are shown in Fig. 1. 
Fig. 1. Predictive function and its parameters 
In order to determine the parameters of the predictive function, first we consider an arrival frequency of recharge 
requests. According to inter-arrivals of charging requests, it is possible to determine the maximum quantity of the 
energy for serving each EV. By applying this charging policy, the queue of EVs within charging stations can be 
controlled and the long waiting of EV can be avoided. By fixing a given charging time for each EV and by knowing 
the number of charging points, the equation (1) expressing the variation of the average charging rate leads to the 
results depicted in Fig. 2. The three curves of this figure correspond to different numbers of charging points. In this 
case, we consider a charging station with 5 (blue line in the figure), 6 (brown line), and 7 (grey line) charging points 
to evaluate the evolution of the predictive function. The number of EV requests varies for 1 until 15 requests. As 
also shown in this figure, the accepted charging minimum rate is fixed to 𝑃𝑃
!"#
= 50 %. Also, we limit the charging 
rate to 𝑃𝑃
!"#
= 80% corresponding to the fast charging (20 min to 30 min). It is worth noting that certain batteries, 
such as Li-Ion technologies, can be charged until 80% in less than 30min, and the last 20% (from 80% to 100%) are 
charged very slowly according to the battery characteristics (usually about 5 hours are required for reaching the full 
charging (100%) [20]. 
The predictive approach using the equation 1 allows informing the EV drivers about the needed quantity of 
energy and required charging time according to the characteristics and needs of driving. Fig2. Charging rate vs the 
number of EVs. Fig.3 shows the average charging time for the two cases: the fully charging of each EV, and while 
considering only the needed energy according to the driver needs and inter-arrival of charging requests. From these 
results, we remark that using only required energy for EVs, the charging stations are less occupied and the EVs 
waiting are less important. 
 
NaitSidiMoh et al./ Procedia Computer Science 00 (2018) 000–000 
 5 
Fig. 2. Charging rate vs the number of EVs Fig. 3. Comparison of the average charging times for the two cases 
According to these results, a charging algorithm based on the predictive function is proposed for predicting 
charging rates and times. By applying this algorithm, the required energy amount for EVs according to the state of 
charge (SoC) of the battery could be predicted. More precisely, the SoC of the battery is one of the most major 
parameters in the charging process. The proposed algorithm is mainly based on this parameter in order to avoid the 
long waiting and spend more time in the charging process. This algorithm is depicted by the flowchart of Fig. 4, 
where 𝐶𝐶𝐶𝐶
!"#
is the corresponding charging time to 𝑃𝑃
!"#
, and 𝐶𝐶𝐶𝐶
!"#
is the corresponding charging time to 𝑃𝑃
!"#
. The 
algorithm allows determining the exact value of charging rate and charging time for multiple charging demands. 
Furthermore, the two parameters 𝑛𝑛
!"
and 𝑛𝑛
!"
play a major role to find the exact values of charging rate and charging 
time for each EVs. In fact, the average charging rate (𝜆𝜆) varies between 𝑃𝑃
!"#
(when 𝑛𝑛
!"
=𝑛𝑛
!"
)and 𝑃𝑃
!"#
(for 𝑛𝑛
!"
=
𝑛𝑛
!"
). Thus, the algorithm checks the number of received charging requests𝑛𝑛
!"
, the arrival dates of these requests, 
and then calculate the charging rate and the charging time for each request individually according to these input 
parameters. 
Fig. 4. Predicting the charging time and rate for each EV 
In the flowchart depicted in Fig. 4, three subroutines are used to compute the charging rates (𝜆𝜆
!
j ) and times 
(𝑡𝑡
!
j ) for each member of EVs set according to the available charging point numbers (𝑛𝑛
!"
) and the number of EV 
𝜆𝜆
!
(j) = 𝑃𝑃
!"#
; 
𝑡𝑡
!
(j) = 𝑡𝑡
!
. 
𝜆𝜆
!
(j) = 𝜆𝜆(𝑗𝑗); 
𝑡𝑡
!
(j) =
!(!)∙!"
!"#
!""
. 
𝜆𝜆
!
(j) = 𝑃𝑃
!"#
;
𝑡𝑡
!
(j) = 𝐶𝐶𝐶𝐶
!"#
. 
Yes 
Yes 
No 
No 
𝑃𝑃
!"#
: Maximum proposed charging time; 
𝑃𝑃
!"#
: Minimum proposed charging time; 
𝑖𝑖 = 1, 𝑁𝑁
!!!!!, 𝑗𝑗 = 1, 𝑀𝑀
!!!!!!, 
𝑡𝑡
!
(j) - charging time of j𝑡𝑡ℎ EV within 𝑖𝑖𝑖𝑖ℎ received 
demands; 
𝜆𝜆
!
(j) - charging rate of j𝑡𝑡ℎ EV within 𝑖𝑖𝑖𝑖ℎ received 
demands; 
𝑛𝑛
!"
(𝑖𝑖) ≤ 𝑛𝑛
!"
𝑛𝑛
!"
(𝑖𝑖) ≥ 𝑛𝑛
!"
𝑖𝑖 = 𝑖𝑖 + 1 
1 
2 
3 

---

132 
A. Nait-Sidi-Moh et al. / Procedia Computer Science 141 (2018) 127–134
6 
NaitSidiMoh et al./ Procedia Computer Science 00 (2018) 000–000 
requests (𝑛𝑛
!"
), which are received at a given time. Furthermore, the found average charging rates (𝜆𝜆(𝑗𝑗)) and the 
average charging times (𝑡𝑡
!
) based on accordingly the equations (2), and (3), (4), (5) will be main parameters to 
determine the charging rates and times of EVs set individually. 
The two considered scenarios: with and without considering required energy for EVs are used to show the 
differences between the proposed charging policies. The Gantt chart of Fig. 5 (a) shows the charging time and 
waiting time for each EV without considering the needed energy for charging requests. Without considering this 
energy, each EV is planned to be fully charged, consequently certain EVs have to wait for long time. Thus the 
accumulation of waiting times becomes more and more raised with the arrival of other charging requests. However, 
by considering the required energy of each demand and the inter-arrival of all charging requests, the predictive 
charging time varies from minimum charging time 𝐶𝐶𝐶𝐶
!"#
, corresponding in our case to the minimum accepted 
charging rate 𝑃𝑃
!"#
, to the arrival time of the next accepted charging request, which is limited by 𝐶𝐶𝐶𝐶
!"#
. If the next 
charging demand arrives after 𝐶𝐶𝐶𝐶
!"#
, the charging point is free and can be used at any time. In this case, the EVs 
will be charged with at least an accepted amount of energy and the accumulated waiting of EVs can be considerably 
reduced. The Gantt chart depicted in Fig. 5 (b) illustrates the results of this second case. Here, we consider that the 
needed battery energy varies between 20 and 80 %. We keep our first charging condition that charges each battery at 
least 50%, when the next EV charging demand arrives before the desired time and the battery can be charged for 
more than 50%. 
(a) (b)
Fig. 5. Waiting time and charging time (a) without needed energy, (b) with considering needed energy 
Furthermore, Fig. 6 (a) presents the difference between desired charging rates (according to the needed energy of 
each EV) and proposed charging rates. The needed energy is considered in this case for showing the comparison 
between the two approaches. We can see the difference of the desired charging rate and the proposed charging rate. 
The proposed charging rate is less than the desired charging rate because it depends on the requested time interval. 
In Figure 6 (b), distinguishable differences of the waiting times for the two studied cases are presented. The large 
scale reducing of the waiting times is compared to the battery SoC and charging without this information. Battery 
energy information, such as the SoC and related charging technology (slow or fast charging) can be helpful for the 
companies of energy distribution and smart grids in order to schedule daily loading costs. When the decision of 
charging EVs with 100% of energy is not kept, the accumulation of EVs waiting times can be reduced till 49.8%. 
 
NaitSidiMoh et al./ Procedia Computer Science 00 (2018) 000–000 
 7 
(a) (b) 
Fig. 6. (a) the difference between the desired and proposed charging rate, (b) the waiting time evolution