20th Iranian Conference on Electrical Engineering, (ICEE2012), May 15-17, Tehran, Iran
Charging of plug-in electric vehicles: Stochastic modelling of load demand within domestic grids Ehsan Pashajavid
Masoud Aliakbar Golkar
K. N. Toosi University of Technology
K. N. Toosi University of Technology
Tehran, Iran
Tehran, Iran
[email protected]
[email protected]
Abstract-This paper proposes a stochastic approach based on
•
D eriving the hourly load demand of PEVs in order to determine the penetration level of the vehicles by evaluating the impacts on the grid.
•
Quantifying the load delivered through a transformer which can be useful for various distribution system applications such as network planning, load
Monte Carlo simulation to derive the load demand of a fleet of domestic commuter plug-in electric vehicles. At first, appropriate non-Gaussian probability density functions are fitted to the employed datasets to generate random samples required in the Monte Carlo simulation. The datasets include home arrival time, daily travelled distance and home departure time of randomly
management and probabilistic load flow as well as sitting and sizing issues [6].
selected private ICE vehicles. In each iteration, extraction of the charging profile is carried out for the individual PEVs in order to derive the hourly aggregated load profile of the fleet. Then,
The most effective factors on the load demand of PEVs are home arrival time, daily travelled distance, home departure time, driving habits and road traffic conditions [7]. Besides, battery capacity of PEVs and efficiency of the battery chargers can be noted as well. Some of the mentioned factors, due to the related uncertainties, are not deterministic. Thus, it is essential to employ stochastic and probabilistic modeling approaches [8].
probability density function of the aggregated load of the PEVs within each hour is estimated. Eventually, the expected value of the hourly load demand can be calculated regarding the achieved power distributions.
The PEVs are assumed to be charged
through a distribution transformer. Thus, profile of the power delivered through the transformer to the PEVs is attained which can be useful for various distribution system applications such as network planning, load management and probabilistic load flow as well as sitting and sizing issues.
This paper proposes a stochastic method based on Monte Carlo simulation to achieve two abovementioned goals, namely extracting the hourly aggregated load demand of PEVs and quantifying the power delivered to a fleet of PEVs through a domestic transformer. Home arrival time, daily travelled distance and home departure time of a set of commuter ICE
Keywords-Electric vehicles; stochastic modeling; smart grid; distribution network; load modeling.
I.
INTRODUCTION
Recently, a great attention has been paid to plug-in electric vehicles (PEVs) as one of the hopeful and effective means in order to tackle the energy crisis and to alleviate the environmental problems [1,2]. A considerably extensive amount of regulatory and technical efforts have been making to provide affordable PEVs. Therefore, a numerous number of PEVs will be undoubtedly on the road all around the world [3].
vehicles in Tehran is used as the input datasets. [n order to generate the required random samples, the aforesaid random variables (RVs) are modeled by probability density functions (pdfs) fitted to them. Unlike most of the earlier researches that used the Normal pdf for the sake of simplicity [9, I 0], this paper suggests appropriate non-Gaussian pdfs to fit to the RVs. In addition, the effectiveness of the modeled pdfs in comparison
PEVs can be generally divided into two categories, namely
with the Normal pdf is illustrated. Afterwards, the devised stochastic modeling algorithm with two scenarios to extract the initial state-of-charge (SOCinit) of PEV batteries is thoroughly explained. By applying the approach, the hourly load distribution functions of the PEVs is derived. Eventually, the
battery electric vehicles (BEV) which are pure electric vehicles and plug-in hybrid electric vehicles (PREV) that include both electric motors and internal combustion engines (ICEs) [4]. The possibility of bidirectional power transfer with the grid is one of the salient characteristics of PEVs. Actually, PEVs can absorb power from the grid when the state-of-charge (SOC) of the battery is low. On the other hand, it is possible for PEVs to inject power into the grid (V2G), especially, during the peak load hours [5]. However, V2G requires a longer time to be practical [1].
distributions are employed to extract the demand profile of the fleet. The remainder of this paper is organized as follows. The employed datasets are reviewed and modeled by fitting appropriate pdfs to them in section [I. Section III elaborates the proposed stochastic methodology. Afterwards, the simulation results are discussed in section [v. Eventually, the paper is summarized in section V.
Estimating the power consumption of the PEVs may be considered as one of the critical challenges. This issue can be addressed in two ways:
978-1-4673-1148-9112/$3l.00 ©2012 IEEE
535
II.
generated applying the extracted pdfs in section II. The available charging time (t.vi) for each of the PEVs is calculated by subtracting the departure time of the next day (dn+l) from
DATASETS OF THE ICE VEHICLES
The employed datasets in the modeling algorithm have been gathered using questionnaires filled-out by the randomly selected owners of the commuter light duty ICE vehicles in Tehran. The owners were asked to give merely the data. The datasets include home arrival time travelled distance (trd) and home departure time vehicles during weekdays. The datasets can be seen
the arrival time of today (a,J The battery capacity (Capbat), SOCinib power rating (Prat) and efficiency (Cchr) of the battery chargers determine the necessary time (tful1) to fully charge the battery. In case tfull would be less than t.vi, the complete charging of the battery can be accomplished. In any other way, it would be impossible to fully charge the battery. The bigger the battery capacity and the lesser the power ating of the
commuting (at), daily (dt) of the in Fig.l.
To generate random samples required in the Monte Carlo simulation, it is essential to fit pdfs to the datasets. Most of the earlier researches have used the Gaussian (Normal) pdf as a straightforward distribution that did not match with the datasets
charger, the longer time is necessary to fully charge the battery. Accordingly, the hourly power consumption of the PEVs can
and this led to inaccurate results. It is suggested in this paper to
of the load profile of the individual PEVs (DPIPn) is fulfilled in
fit appropriate non-Gaussian pdfs to the three mentioned RVs. In fact, a number of pdfs are tested on them and then, the best is selected. As may be seen in Fig. I (a), the Weibull pdf Ctdt(t)) is suggested as the most appropriate function to be fitted to the departure time RV as below:
order to estimate the demand profile of the fleet (DPFm).
be estimated after arriving at home. In each iteration, extraction
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.
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o
1
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(I)
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To model the daily travelled distance a type III Generalized expected value (Gev) pdf (2) is derived. The result is illustrated in Fig.l(b).
8.5 7.5 ) pa=rt u re'-' ti=me D e= '-i(=ho=u r'= O.06i---r___,---___r-' - -----,-��:====;_r �
.;;;
� � �
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r.tid (d)
.
1 = -
(J,,;,
(1 + k tr,/
(d
(d-fitrd)� 1 -j1 ) -(1+-) -(l+k"d--) d 0"" tod) k", e ,
'"
(2)
c::::::J Data - - - Normal pdf
0.05 0.04
--
Gevpdf
0.03 0.02
Ii. e: 0.01
(JII;,
o
As it is shown in Fig. I (c), a type III Generalized expected value (Gev) pdf (3) is fitted to the home arrival time RV as well.
-
10
20
40
30
50
Trawlled distance (km)
0.6i-----,-----,-------,----'---�--,------;:;��===il
(3) Arrival time (hour)
Figure I.
Moreover, the extracted distribution of each RV is compared
The data and pdfs of (a) home departure time d" (b) daily travelled distance trd and (c) home arrival time a,.
with the Normal pdf fitted to the same dataset in order to verify the mentioned claim (Fig. I). It is seen that fitted non-Gaussian pdfs provide a better approximation of the original datasets. The parameters of the fitted pdfs are given in TABLE I.
TABLE 1.
In the next section, the extracted pdfs are utilized to generate the random samples.
III. A.
Datasets
MODELING METHODOLOGY
THE PARAMETERS OF THE FITTED PDFS The Normal pdf
a=7.67454
(T.vd, = 0.43178
jJ=21.3812
fly", = 21.4150 (TN'" = 8.58711
The proposed algorithm
The main objective of this paper is to extract the hourly load demand of the PEVs with uncoordinated charging. It is assumed that only the home charging is available and the PEVs are plugging into the grid as soon as their arrival. Figure 2 illustrates the overall procedure of the proposed approach. First of all, the random samples of at (�), trd (tr,,) and dt (d,,) are
at
536
The suggested pdf
flVd, = 7.48436
fly" = 17.7170 (TN" = 1.01385
k" = -0.052368 , fl", = 17.6568 (T", = 7.1222
k" = -0.060798 fl" = 17.2700 (T", = 0.84832
[t is notable that the PEVs are supposed to be charged through a distribution transformer. Therefore, profile of the power delivered to the PEVs through the transformer is attained as well. Considering [N as the iteration number of the Monte Carlo
DPF
simulation, the explained procedure is carried out for IN times in order to derive the distribution of the aggregated power consumption of the fleet within each hour (D APFh). Afterwards, the expected values of the hourly load demand of the PEVs can be calculated regarding the D APF". Eventually,
EN = Total number of PEVs IN = Iteration number m=1
demand profile of the fleet (DPF) is estimated by employing the extracted hourly expected values. B.
The battery initial SOC
Extraction of the battery SOC of the PEV s at the charging start time (SOCinit) is done with two following scenario cases:
Random generation (an, trdn, dn)
•
tavi = dn - an tfulln=(1 OO-SOCinitn)xCapbat/(1 OOxPratXCchr)
Case 1: As the worst case, the battery initial SOC of the PEVs (SOCinit) can be assumed to be a constant. This constant is determined according to the depth-of discharge (D OD ) of the PHEVs as follows:
SOC;n;,n =100-DOD
(4)
However, the mentioned assumption is not feasible in reality. Therefore, it is suggested to alter (4) by using randomly generated positive numbers through employing an exponential pdf as below:
{
\
SOCinim = 00
��OD
fexp (x ) = -- e f.1exp •
+ Rand (fexp (x
)) (5)
POXI'
Case 2: The SOCinit is determined based on the daily travelled distances. Regarding the fact that tavi in home charging is usually bigger than tfulb it is rational to assume that the battery SOC are 100% at the departure time of the PEVs. Hence, the SOCinit of the PEV can be derived as follows:
SOCmlln , =100
lrdn Ceif X Caphm
xlOO
(6)
where Ceff is the efficiency coefficient of the PEVs during driving which is dependent on the driving patterns and traffic conditions as well as driver efficiency of the electric motors.
IV.
Figure 2,
SIMULATIONS AND DISCUSSIONS
D ue to the assumption that the fleet is delivered power through a distribution transformer, it seems rational to perform the simulation for 20 PEVs. The above-explained procedure is repeated 10000 times to deal with the related uncertainties. The simulation parameters can be found in TABLE 11.
Flowchart of the proposed approach,
537
TABLE II.
THE SIMULATION PARAMETERS
10000 random samples. Then, the SOCinit is determined accordingly which can be considered as the worst case. The synthetic results can be seen in Fig. 4(a). As it is obvious, a number of the PEVs have fully charged batteries (SOCinitn=100%) correspondent to the untraveled vehicles.
10000
IN
EN
20
DOD
70% 3kW 20kWh 2km/kWh
Cchr
0.9
j.1cv..p
8
A.
Synthetic datasets
Figure 3 presents distribution of the randomly generated samples (the synthetic data) for PEVs by using the three suggested pdfs in section n. Each generated set includes 10000 samples. As it is obvious from Fig. 3(a), the generated samples of dt is distributed between 4:30 a.m. and 8:30 a.m. with the
C.
transformer. According to Fig. 2, the procedure is repeated for 10000 times in order to derive the distribution of the aggregated power consumption of the fleet within each hour (D APFh). The estimated D APFh at h=16 olclock, h=19 olclock and h=22 o'clock regarding two scenarios of the battery initial SOC explained in section IV.B is shown in Fig. 5(a), Fig. 5( b) and
The battery initial SOC of the PEVs
To derive the battery initial SOC of the PEVs the mentioned scenarios are employed: Case 1: Regarding to (5),
•
fexp(x)
Fig. 5(c) respectively. Moreover, the demand profile of the fleet (DPF) consisted by the expected values of the D APFh is presented in TABLE 111.
used to generate
IS
As may be expected, the DPF values calculated by adopting the first scenario (case1) are generally greater in comparison with the estimated results employing the second scenario (case 2).
PEVS
20 4000
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3000
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2000
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4000
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" me (hour) __,__----,---,------ --' i- _ '-__,__-___,_--,---- --,
.---_
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Travelled distance (km)
4000
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The aggregated power consumption
The demand profile of the fleet (DPFm) is achieved by estimating the demand profile of the individual PEVs (DPIPn) in each iteration of the devised procedure. As it is mentioned in section lll, the estimated profile can be adopted as the profile of the power delivered to the PEVs through the distribution
highest num ber of occurrence between 7:30 a.m. and 8 a.m.. Fig. 3( b) presents the generated samples of trd distributed between 0 km and 76 km. 0 km means the PEV departure is not happened. Fig. 3(c) shows the generated samples of at distributed between 15 p.m. and 24 p.m.. The highest num ber of occurrence appears between 17 p.m. and 17:30 p.m..
B.
Case 2: The SOCinit is determined based on the daily travelled distances. According to (6), the SOCinitn is dependent on the travelled distance (trdn), the battery capacity (Capbat) and the efficiency coefficient of PEVs during driving (Ceff). The distribution of the synthetic initial SOCs of the PEVs is shown in Fig. 4( b).
•
14
o -- · ---- --40 30
�----.- ·---- ..�----'-50 80 70 80
12
-- ' --
90
100
SOCinil
3000��---,---�--�-�- -___,_--�-__.
80
2500
3000
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1000
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0 15
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----- ---- ' ---17
·--------"--...... 22 21 lime (hour)
�
o 30
24
40
50
60
70
80
90
100
sOeinit
Figure 4. Battery initial SOC generated by using (a) scenario No. 1, (b) scenario No. 2.
Figure 3. The randomly generated samples of (a) home departure time db (b) daily travelled distance trd and (c) home arrival time al.
538
10
2000 � 1500
domestic commuter plug-in electric vehicles has been devised. A series of datasets, including home arrival time, daily travelled distance and home departure time of randomly selected private ICE vehicles have been employed. To avoid any mismatching between the original dataset and their probabilistic models, appropriate non-Gaussian probability density functions has been fitted to them. Extraction of the charging profile has been performed in each iteration for the individual PEVs in order to estimate the hourly aggregated load profile of the fleet. Afterwards, probability density function of the aggregated load of the PEVs within each hour has been derived by applying the Monte Carlo simulation. The expected value of the hourly load demand has finally been
_Case 1 c::::::JCase 2
c
i"
8
8
1000
� 500 0 0
15
10
20
25 (kW)
Load demand
30
35
40
45
" 4000 g � 3000 "
82000 :£ 1000 0 40
calculated regarding the achieved power distributions. 42
44
46
48
Load demand
60
(kW)
REFERENCES
Load demand
(kW)
Figure 5. The distribution of the aggregated power consumption of the PEVs (DAPFh) regarding two scenarios of the battery initial SOC at (a) h=16 o'clock (b) h=19 o'clock, (c) h=22 o'clock.
TABLE III.
DEMAND PROFILE OF THE FLEET (DPF) DELIVERED THROUGH A DISTRIBUTION TRANSFORMER (W)
Hours
Case 1
Case 2
Hours
Case 1
Case 2
2 3 4 5 6 7 8 9 10 II 12
4806.55 ll22.78 212.01 32.38 3.66 0 0 0 0 0 0 0
3106.79 709.22 121.69 15.92 2.70 0 0 0 0 0 0 0
13 14 15 16 17 18 19 20 21 22 23 24
0 0 205.88 22623.76 52557.08 57000.38 56678.69 54044.72 48384.19 37408.21 26518.46 14151.84
0 0 199.01 22022.61 51048.34 54728.31 52702.32 48386.52 42582.69 3384l.04 22466.78 10270.33
V.
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CONCLUSION
Tn this contribution, a stochastic approach based on Monte Carlo simulation to derive the load demand of a fleet of
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