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1. Study of Economic System at Compensation for
Voltage Drop Utilizing Charging Power Adjustment of
Electric Vehicles
Yuta Nakamura,Yuki Mitsukuri, Masaru Iguchi,
Yuji Mishima
National Institute of Technology, Hakodate College, Japan
Ryoichi Hara, Hiroyuki Kita,
Hokkaido University,
Sapporo, Japan
Abstract— A surge of needs for the low carbon society promotes
a spread of electric vehicle (EV). EVs could be charged at night
simultaneously, as a result, severe voltage drop may happen.
The authors have proposed the method which can compensate
the voltage drop caused by EV charging by means of adjusting
charging schedules and controlling reactive power. However,
though the method can avoid the voltage violation, the method
includes the inequality between EVs in other words, the only EV
which is in terminal node in distribution system where voltage
violation is likely to occur has to decrease charging power
because the method is autonomous distributed control which is
based on only self-voltage information. In this paper, we
formulate a convenience loss of EV owner due to adjust reactive
power and charging power. We propose a method to calculate
the benefit of the EV owner and the cost needed by the voltage
control using the EVs.
Index Terms-- Electric vehicles, Voltage control, Costs,
distribution system
I. INTRODUCTION
Electric vehicles (EV) have been attracting great attentions
and expectations since they can run at good fuel efficiency
without exhaust gases. Therefore, it is expected that the EVs
will become more and more popular. Generally, the usage of
EV strongly depends on our lifestyle; most EVs run in the
daytime and are parked and charged at night[1-2]. The current
time-of-use tariff program offered by the utility company will
enlarges the EV charging in nighttime. If most of EVs are
charged from the distribution systems through electricity plug
at home, emergence of EVs would enlarge the peak load at
night in residential areas. Added to the problem of voltage
drop in distribution system due to an overload, it is considered
that installing a SVR (Step Voltage Regulator) is the
conventional measures to the voltage compensation in the
distribution system side. However, a method to compensate
for the voltage by the EV charger itself which causes a voltage
drop is also considered. [3]
If EV consists of inverter, it can control both active and
reactive powers in principle. We have focused that point and
proposed basic algorithm to keep voltage by avoiding voltage
violation due to simultaneous EV charging at nighttime[4]-[7].
In [4]-[7], the adjustment of active and reactive power is
executed within not losing convenience of EV owner. These
voltage control methods base on the premise that all EVs
always execute the method. However, in practice, by reducing
the charging power in order to avoid voltage deviations, if it
cannot charge the amount of power required for the driving, a
large convenience loss of EV owner is generated.
On the other hand, the voltage control by EV charging has
a potential to reduce cost of keeping voltage which DSO
(Distribution system operator) must pay. If DSO is able to be
distributed a part of the costs reduced by voltage control of EV
as an incentive to EV owners, there is a possibility that the
disadvantage of the EV owner to cooperate in keeping system
voltage can be solved. If DSO is able to design appropriate
such economic institutions, it is possible to solve disadvantage
of EV owner and keeping the system voltage at a lower cost
than the conventional yet.
In this paper, we propose method to calculate the
economic loss of EV owner generated by adjusting the active
and reactive power at the time of charging .Furthermore using
an economic loss, we propose method to calculate the
incentive for EV owner and cost of voltage control by EV.
II. VOLTAGE CONTROL IN DISTRIBUTION SYSTEM
A. Voltage Control in Two Node System
In a simple two-node distribution system shown in Fig.1,
the voltage drop along the feeder can be approximated as
r
rs
V
QXPR
VV
+
=- (1)
where, sV , rV are the voltages at sending and receiving
The south Hokkaido Science Promotion Foundation and
Sakurai funds of the Institute of Electrical Engineers of Japan
978-1-4799-7537-2/14/$31.00 ©2014 IEEE
Figure 1. Two nodes distribution system model

2. nodes, P and Q are the active power and the reactive power
consumed at receiving node, R , X are the resistance and
reactance of feeder. This equation implies that the voltage at
receiving node can be controlled by P and Q .
B. Modeling of EV
In this paper, it is supposed that EV has inverter. In
principle, the inverter can control active and reactive powers
simultaneously. Therefore, an EV is modelled as a load which
can control active and reactive power consumption freely
within its capacity. Here, the discharge from the EV’s battery
is not considered in this paper.
C. PQ control
Fig.2 expresses the relationship between active power (P)
that EV battery charges and reactive power (Q) that EV
battery consumes. EV can control P and Q independently
within inverter capacity. If typical EVs prevailing nowadays
are connected to a distribution system for charging through
their inverter, EVs charge their battery by maximum inverter
capacity because EVs finish charging in the shortest possible
time. This charge method is called “normal charging”
hereafter. If EVs are penetrated massively, voltage drop in the
system by increase of charging power would be large.
On the other hand, in order to avoid voltage violation, PQ
control method proposed in previous studies reduce the
charging power and consume lead reactive power. By the
inverter equipped with the EV, PQ control adjusts the active
and reactive power while checking the voltage of EV’s node.
In general, since the voltage at the terminal of the system is
lower than other voltage, opportunities for PQ control at the
terminal increase. Therefore, instead of contributing to
voltage keeping more than other EVs, EVs in terminal of the
system take a long time to charge. As a result, EV in terminal
of system has insufficient amount of SOC, and the probability
of generating a convenience loss that mileage is limited is
higher than other EVs.
Thus, it is necessary to minimize the suppression of the
charging power for the reason why it leads to the convenience
loss. The detailed control method is described in [4]. As
shown in Fig.2, in this study, the amount of decrease of
charging power and reactive power by the PQ control are
defined P and Q .
III. ECONOMIC SYSTEM AT VOLTAGE CONTROL BY EVS
A. Economic System
If many EVs are installed in the distribution systems and
charged in nighttime when electricity prices cheaper than
other time, there is a possibility that voltage violation of the
lower limit occurs by increasing active power. In this study,
problem of voltage violation due to charging of EVs and the
counter measures against are discussed. Fig.3 is an image of
the comparison of the method proposed in this study with the
method taken by the conventional control voltage. Further, in
this paper, it is intended to propose a method for calculating
the incentive needed by PQ control. A cost taken in a
conventional voltage control and the comparison of two
voltage control methods would like to be a future work.
B. Expected Convenience Loss of EV owner
Since charging power is reduced by PQ control, the
charging time is longer than that by normal charge. As a
result, there is a possibility that EV owner sustain a
convenience loss such that the driving distance is limited
shorter. In this study, the cost to which is converted the
convenience loss is called as "economic loss" here after. As
for this it would be an important point to consider on the
economic loss whether SOC of EV can charge more than
the SOC level needed next day until the time to start using
EV. In this paper, the economic loss caused by the SOC level
at the time to start using EV is formulated. The relationship
between the economic loss and SOC level at the time to start
using EV is shown in Fig.4. Here, economic loss is
formulated by dividing three areas of SOC shown in Fig.4.
Figure 3. Comparison of voltage keeping method
EV DSO
Distribution
system
charging voltage control
conventional method
DSODistribution
system
voltage control
occurrence
of loss
EV
Compare
charging
incentive
cost
PQ control
Figure 2. The image of PQ control
P
leadQ
o
normal charge
adjust P and Q
Lower voltage
Higher
voltage
PQ control
⊿P
⊿Q
Figure 4. The loss at time to start using EV
SOC E[kWh]
economiclossLE[JPY]
EAi EBi
LAi
LBi
（１） （２） （３）
EFi
LCi

3. i : The i th EV [kWh]
AiE : SOC by which EV can drive to a the rapid charger [kWh]
BiE : SOC required for driving through one day [kWh]
FiE : SOC of full level [kWh]
AiL : Economic losses for that EV cannot be used through one
day [JPY]
BiL : Economic losses for using a rapid charger [JPY]
CiL : Economic loss associated with convenience loss by
limiting unscheduled driving [JPY]
Area (1) shown in Fig.3 means that SOC is not enough to
drive through one day. In this area, since EV owner cannot
use the EV and must use the other transportation, large
economic loss is generated. Area (2) means that since there is
a rapid charger within range of distance to the destination, EV
can drive to the rapid charge. In this area economic loss is
generated, such as rapid charging fee and waiting time for
charging. However, In order to use EV through a day, the
economic loss is lower than area (1) because EV can be used
through one day. Area (3) means that SOC is enough to drive
through a day but SOC is not full. In this area, the distance
which EV can drive related unscheduled driving is longer
than area (2), but shorter than full SOC. So the economic loss
in the area is generated. Here, area (1) and (2) are supposed to
be linear and area (3) is supposed to be a quadratic curve
based on the concept of utility in economics. Thus, formula
of economic loss is represented as equation (2). If SOC is
enough to drive one day's distance, economic loss become
smaller significantly.
(2)
The economic loss at the time to start using EV by the PQ
control is supposed to be as equation (3).The economic losses
by PQ control is obtained from the difference between
economic losses NCiL by SOC NCiE when normal charge is
executed and economic losses PQiL by SOC PQiE when PQ
control is executed. That is shown in Fig.5.
NCiPQii LLL ‐= (3)
C. Distribution Method of Incentive by PQ Control
In this study, it is assumed to receive an incentive from
DSO as value for the contribution of keeping voltage when
PQ control is executing. In general, the voltage of node which
is far from the power source is lowered by increasing in the
reactance and resistance of distribution line. As a result, the
amount of PQ control of EV at the terminal node is more than
other EVs. Therefore, the incentive which matches to the
amount of control has to be distributed. In this study, it is
assumed that DSO distributes a part of the costs reduced by
PQ control at a rate of each voltage contribution as an
incentive. The voltage contribution is the degree of voltage
improvement by PQ control of EV.
The voltage contribution )(tCi at a certain time is defined as
following equation (4), referring to equation (1)
)()()( tQXtPRtC iiiii  (4)
Thus, the larger resistance iR and reactance iX of
distribution line are, the bigger voltage contribution )(tCi is.
If the amount of PQ control is same, the voltage contribution
by EV at a terminal node is large, and the incentive also
increases. In addition, amount of PQ control also varies
depending on the state of the system changing from time to
time. Therefore, after calculating the incentive each per unit
time, a total incentive in the charging period is calculated as
the sum of the incentive in the each time. The incentive iI is
calculated by the following equation (5).
∑
0
)(
T
t
tCFI ii

 (5)
F :Incentive unit price [JPY /min]
T :Charging finish time ( 0t :Charging start time）
In this study, as a unit time supposed to be 1 minute, the
incentive is obtained by multiplying a sum of the contribution
by the incentive unit price at each minute. The benefit iG of
EV owner in one charging period is the difference between
economic losses iL by PQ control and incentive iI . iG is
calculated by equation (6).
iii LIG ‐= (6)
D. Determination of Incentive Unit Price
In the case when the incentive by PQ control is less
( 0iG ) and an economic loss of EV owner is generated and,
the possibility that EV owner does not execute PQ control is
high. As a result, the voltage cannot be kept. On the other
hand, if incentive unit price is set to be very high, DSO needs
the higher cost than conventional voltage keeping measures.
Therefore, it is necessary for DSO to determine the
appropriate incentive unit price F . By setting an appropriate
incentive unit, it is possible that the proposed voltage keeping
method by PQ control costs less than conventional voltage
control method.
AiL  Aii EE 
EiL )( Aii
AiBi
CiBi
Bi EE
EE
LL
L 


  BiiAi EEE 
Ci
BiBi
iFi
L
EE
EE
2








 FiiBi EEE 
Figure 5. The loss by PQ control at time to start using EV
SOC E[kWh]
economicloss[JPY]
EPQi ENCi
LPQi
LNCi
Li

4. In this study, if the profit is generated by the PQ control,
EV owner is assumed to execute PQ control. In addition, it is
assumed that the cost needed by PQ control is the sum of
incentive paid to the EV owner. In order to gain a profit by
PQ control, EV owner needs the incentive iI which is the
same amount as the economic loss iL at least. The minimum
required incentive unit iF of EV owner i is calculated as
follows by equation (5) and equation (6).
∑
0=
)(
=
T
t
tC
L
F
i
i
i (7)
Since economic losses iL and amount of PQ control ( P
and Q ) are different depending on each EV, the minimum
required incentive unit iF is different in each EV. Therefore,
the DSO is supposed to determine the incentive unit F as the
maximum value of iF so that all EV owners obtain benefit by
PQ control.
)max( iFF  (8)
IV. SIMULATION
A. Simulation Conditions
In order to calculate the cost needed by PQ control,
simulation is executed with distribution system model
consisted of 12 residential load and three EVs shown in Fig.6.
Three EVs are EV1, EV2 and EV3 respectively, as shown in
Fig 6. The impedance and resistance values are shown in
table 1.These values are per unit values which are from power
source to the residential load, which based on impedance of
the primary feeder.
All EVs introduced are assumed to have the
characteristics of Table 2. The economic loss due to SOC at
time to start using EV has the characteristics like Fig.7. In
this simulation, the time to start using EV is 3:00.
In this paper, we executed following two simulations.
First simulation is to calculating the incentive unit needed to
execute PQ control in the case assumed the load of one day.
Thus, proposed method of calculating incentive and changing
of charging power and reactive power by PQ control are
shown by this simulation. This is called as simulation 1.
In the system in which voltage violation is generated
every day by charging EV, the possibility that the cost needed
for PQ control become higher than that needed by
conventional method is high. Conversely, if the frequency of
voltage violation is few, the method by PQ control would be
more economic advantage than conventional method.
Therefore, in addition to calculation of cost through one day,
it is necessary to calculate the cost in a longer period.
Considering this, as another simulation, we calculate the cost
needed by PQ control in the case where the annual load is
assumed. This is called as simulation 2.
Lest the voltage violation is generated by only residential
load, the sending voltage from distribution substation is set to
be 6.6kV from 8AM to 10PM (heavy load period) and
6.35kV from 10PM to 8AM (light load period). Specific
conditions in each simulation are shown below.
1) Simulation 1
Assumed load curve of each residential load is shown in
Fig.8 (inductive reactive power is defined as positive and
active and reactive power of EV is not included).Fig.9
illustrates the time-sequential voltage profile in residential
which is farthest from the pole transformer.
TABLE I. RESISTANCE AND INDUCTANCE OF EACH RESIDENTIAL
residential
load No.
resistance
Ri [pu]
reactance
Xi [pu]
1, 7 17.8 6.5
2, 8 5.6 6.0
3, 9 16.2 4.4
4, 10 4.1 3.9
5, 11 14.7 2.3
6, 12 2.5 1.8
TABLE II. PARAMETER OF EVS
Value
Time to start charging st 23
Time of departure et 3
Capacity of inverter for EV S 3kVA
SOC of full level EF 15kWh
SOC by which EV can drive to a the rapid charger EA 2kWh
SOC required for driving through one day EB 4kWh
Economic losses for that EV cannot be used
through one day
LA 9600JPY
Economic losses for using a rapid charger LB 1300JPY
Economic loss associated with convenience loss by
limiting unscheduled driving
LC 1100JPY
Parameters
Figure 7. The economic loss at time to start using EV
0
2000
4000
6000
8000
10000
0 5 10 15
economicloss[JPY]
SOC [kWh]
Figure 6. Simulation system
service wire
(DV3.2)
service wire
(DV3.2)
residential load
residential load7
6 5 4 3 2 1EV1EV2EV3
9101112 8
secondary feeder(SV60)
5m 40m5m 40m 5m 40m
5m 40m5m 40m 5m 40m
pole
transformer
50m
secondary feeder(SV60)
50m
Figure 8. Daily Load curve of one residential load without EV
0.0
0.5
1.0
1.5
2.0
2.5
12:00 15:00 18:00 21:00 0:00 3:00 6:00 9:00 12:00
ActiveamdReactive
power[kW,kvar]
Hour
active power reactive power

5. 2) Simulation 2
In [8], hourly residential average load data in every month
have been published as the maximum value of 1. In addition,
the annual average sum value of the residential power
consumption is shown in [9]. In this study, we assume a
yearly residential load as shown in Fig.10 on basis of [8]-[9].
Further, in order to calculate the number of days that the
voltage violation is occurred, it is assumed that the lead curve
of each month shown in Fig.10 is regarded as the load curve
of 15th
day. And load curves from 15th
day of a month to the
15th
day of next month changes at constant rate.
In this simulation, in order to compare annual cost with
EV spread level and the number of days in which voltage
violation occurs are calculated in three cases. Three cases are
that 3 EVs are connected shown in Fig.6, the residences from
No.1 to No.6 in Fig.6 have EVs and all 12 residences have
EVs. However, the number of voltage violation days is
obtained by counting the date in which the PQ control is
executed to keep voltage. That means voltage violation is
generated by only normal charge.
B. Calculation of Incentive Unit (Simulation 1)
Table 3 is the results of simulation based on the
conditions described in the previous section. Voltage
violation in EV3 is not occured by normal charge. However,
since voltage violation is occurred at the nodes that EV1 and
EV2 connect, EV1 and EV2 avoid voltage violation by
executing the PQ control. As a result, the economic losses by
PQ control are generated. However if incentive unit F is
equal to 0.036 [JPY/min] or more, owners of EV1 and EV2
obtain benefit positive iG . At this time, since the sum of
incentive distributed to each EV is 141 [JPY], the cost that
the DSO needs in order to avoid voltage violation is 141
[JPY]. The cost needed for PQ control and incentive unit
price F are obtained by executing such as this calculation.
On the other hand, in EV1, the relationship between the
charge and reactive power and charging time is illustrated in
Fig.11. Since residential load is relatively large at 23:00 as
shown in Fig.8, the amount of reactive power and reduced
charging power of the EV1 which is located on a terminal
node is large. However, because the residential load becomes
small after 1:00, the voltage of the node connected by EV1
and EV2 can be kept even with normal charge. Therefore, PQ
control is executed until 1:00 and economic losses by PQ
control is compensated by incentive from 23:00 to 1:00.
Fig.12 shows the relationship between incentive money
and time. Since P and Q are changed by the time, the
amount of incentive increase varies by each time. After 1:00,
because P and Q of equation (5) are zero, the amount of
incentive in each EV is not changed.
C. Yearly Cost Needed for PQ Control (Simulation 2)
In three case that the number of EV are 3,6 and 12
respectively shown in Ⅳ-A 2) ,the result of the number of
voltage violation days and annual cost needed to execute PQ
control is shown as table 4. When three EVs are connected,
although voltage violation is occured in 36 days, the amount
of PQ control is small. In this case, the needed cost is only
Figure 10. Yearly load curve of one residential load without
EV
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0:00 4:00 8:00 12:00 16:00 20:00 0:00
averageload[kW]
hour
Jan
Apr,Oct
Jul
Figure 11. Active and reactive power of EV1
P
leadQ
23:00
2.1
2.1
3
0
2.5
1.6 0:00
1:00
charging start
Figure 12. Incentive of PQ control
0
20
40
60
80
100
120
23:00 0:00 1:00 2:00 3:00 4:00 5:00
IncentiveIi[JPY]
hour
EV1
EV2
TABLE III. RESULTS OF SIMULATION 1
Incentive unit
Fi [JPY/V2
]
Max(Fi)
Incentive
Ii [JPY]
Total cost
[JPY]
Charging
finish time
EV1 0.032 105 4:28
EV2 0.036 36 4:12
EV3 - 0 4:00
0.036 141
Figure 9. Voltage at each node without EV
94
95
96
97
98
99
100
12:00 15:00 18:00 21:00 0:00 3:00 6:00 9:00 12:00
Voltage[V]
Hour
Minimum voltage level

6. 150 [JPY] per year. However, when the number of EV is six,
voltage violation is occured every day in the normal charge.
As the result, the needed annual cost is 6,903[JPY]. When
twelve EVs are connected, the needed annual cost exceeds
160,000 [JPY].
On the other hand, the cost needed to execute PQ control
per day with each number of EV is shown in Fig.13. In case
of three EVs, the cost is 0 [JPY] in most of days and since
voltage violation is occured in only January and February, the
annual cost is few. In case of six EVs, although the cost of
approximately 80 [JPY] per day is needed in January and July,
the voltage can be kept by a few cost in other season.
However, in case of 12 EVs, the cost which is exceeded 350-
650 [JPY] per day takes throughout the year. The reason why
the cost increase is two point. One is larger voltage drop by
increasing EVs. Another is that the EV owners needing
incentive increase.
Therefore, in the case of fewer EVs, the cost that the DSO
has to pay could be reduced more by PQ control than the cost
for conventional method to keep voltage. However, if EVs
are used in many residences, the possibility that the
conventional voltage method, such as installing SVR, is more
effective than PQ control would be high. However, this
simulation set up severe condition that SOC of all EVs is zero
before charging through yearly. Usually, it is rare to happen
like this severe condition. If SOC before charging start time is
set up more realistic, it is possible to keep the voltage with
less cost.
V. CONCLUSION
In this paper, the economic loss of the owner of the EV by
PQ control is formulated and the method to evaluate the PQ
control from the viewpoint of cost is proposed. Then, the
needed costs of executing PQ control through one day or year
are calculated by implementing simulation in the distribution
system model. As a result, since the needed cost increases
with the number of EV, PQ control is considered particularly
effective in the diffusion stage of EV.
In future, comparing the cost of conventional method
and cost of the PQ control is an important subject.
Furthermore, considering whether PQ control is executed or
not based on EV owner's benefit and SOC of EV before
charging, we would like to propose a voltage control method
that benefit of DSO and EV owners are maximized.
ACKNOWLEDGMENT
This work is supported by the south Hokkaido Science
Promotion Foundation and Sakurai funds of the Institute of
Electrical Engineers of Japan.
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TABLE IV. RESULTS OF SIMULATION 2
3 36 150
6 365 6903
12 365 161500
number
of EV
number of voltage
deviation days
annual cost
[JPY]
Figure 13. Total cost of PQ control
0
100
200
300
400
500
600
1 4 7 10 12
needcost[JPY/day]
month
3EV
6EV
12EV