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Yan Xu, Member, IEEE Leon M. Tolbert, Senior Member, IEEE
John D. Kueck, Senior Member, IEEE D. Tom Rizy,Senior Member, IEEE
Fig. 1. System configuration of a parallel active filter.
Voltage and Current Unbalance Compensation
Using a Parallel Active Filter
Abstract—A three-phase insulated gate bipolar transistor
(IGBT)-based parallel active filter is used for current and/or
voltage unbalance compensation. An instantaneous power
theory is adopted for real-time calculation and control. Three
control schemes, current control, voltage control, and integrated
control are proposed to compensate the unbalance of current,
voltage, or both. The compensation results of the different
control schemes in unbalance cases (load unbalance or voltage
source unbalance) are compared and analyzed. The simulation
and experimental results show that the control schemes can
compensate the unbalance in load current or in the voltage
source. Different compensation objectives can be achieved, i.e.,
balanced and unity power factor source current, balanced and
regulated voltage, or both, by choosing appropriate control
schemes.
Index Terms—current unbalance, voltage unbalance,
nonactive power, current control, voltage control
I. INTRODUCTION
Power quality, especially current unbalance, current
harmonics, and voltage unbalance, has drawn much attention,
and much research work has been performed in this area. One
means of correcting these power quality problems is to
provide nonactive power compensation. However, there are
still no standard definitions of instantaneous nonactive power
and instantaneous nonactive current [1-4]. A parallel active
filter is an effective way to eliminate or mitigate the
harmonics and unbalance in current [5-6].
Voltage unbalance is generally not as severe as current
unbalance; however, it may have a more severe impact on
both loads and power system equipment. The negative impact
of voltage unbalance on induction motor has been studied in
depth [7-8]. Series connected converter-based compensator
have been proposed for voltage unbalance compensation,
voltage sag compensation, and voltage regulation [9-13]. For
both the compensation of voltage unbalance and load current
harmonics, an active filter for voltage regulation together
with passive filters (5th and 7th) for current harmonics
compensation is proposed in [14]. While in [15], a series
active filter and a parallel active filter are connected to
perform both voltage and current compensation tasks at the
same time. A method of voltage unbalance mitigation using a
parallel active filter is also presented in [16].
The instantaneous power theory presented in [4] is used for
the active filter presented in this paper because the definitions
of instantaneous power and instantaneous nonactive power
are suitable for real-time nonactive power compensation
purpose. This instantaneous power theory will be elaborated
in Section III.
A feedback controller is presented in this paper to perform
both voltage unbalance and current unbalance compensation
in a parallel active filter. The system can compensate the
nonactive power component and/or the unbalance in the load
current, and/or regulate and balance the system voltage.
Either one or both of the tasks can be performed at the same
time, depending on the compensation objectives. The
compensator can provide the nonactive component in the
load current if a balanced and unity power factor source
current is desired; or regulate the system voltage to a certain
level by injecting nonactive power to the system. Thus, it can
compensate the unbalance from the utility or from the load.
Y. Xu, L. M. Tolbert, J. D. Kueck and D. T. Rizy are with Oak Ridge
N
ational Laboratory, Oak Ridge, TN 37831 (e-mail: xuy3@ornl.gov,
tolbertlm@ornl.gov, kueckjd@ornl.gov, rizydt@ornl.gov).
L. M. Tolbert is with The University of Tennessee, Knoxville, TN 37996-
2100 (e-mail: tolbert@utk.edu).
Prepared by the Oak Ridge National Laboratory, Oak Ridge, Tennessee
37831, managed by UT-Battelle for the U.S. Department of Energy under
contract DE-AC05-00OR22725.
The submitted manuscript has been authored by a contractor of the U.S.
Government under Contract No. DE-AC05-00OR22725. Accordingly, the
U.S. Government retains a non-exclusive, royalty-free license to publish
from the contribution, or allow others to do so, for U.S. Government
p
urposes.
29191-4244-0655-2/07/$20.00©2007 IEEE
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Fig. 2. Current control diagram.
II. SYSTEM CONFIGURATION
The system configuration of a parallel nonactive power
compensator is shown in Fig. 1. The compensator is
connected in parallel with the load, and the rest of the system
is simplified as an infinite utility voltage source with a
system impedance of Rs+jȦLs. The parallel compensator is
connected through the coupling inductor Lc at the point of
common coupling (PCC), and the PCC voltage is denoted as
vt. The filtering capacitor Cf is used to mitigate the ripple in
the compensator current ic. The compensator only provides
(generates or consumes) nonactive power, and there is no
energy source connected to the DC link. The DC link voltage
vdc is regulated by the compensator at a given level.
By providing a certain amount of nonactive power, the
compensator can eliminate or mitigate the unwanted
components, such as nonactive power, harmonics, and
unbalance in the load current; it also can regulate the voltage
vt at a certain level. The compensator can perform these two
tasks individually or as an integrated control of the voltage
and the current together.
III. INSTANTANEOUS POWER THEORY
An instantaneous nonactive power theory [4] is adopted to
calculate the instantaneous variables based on the
measurements (vt,il,ic, and vdc), and to implement control,
depending on the compensation objectives and control
schemes. In a three-phase system with a voltage vector v(t)
and a current vector i(t) (vectors for voltage and current will
be denoted in bold),
1 2 3
( ) [ ( ), ( ), ( )]T
t v t v t v t v, (1)
1 2 3
( ) [ ( ), ( ), ( ) ]T
t i t i t i t i. (2)
The instantaneous power p(t) and the average power P(t)
over the averaging interval [t-Tc,t] are defined by (3) and (4):
3
1
( ) ( ) ( ) ( ) ( )
T
k k
k
p t t t v t i t
¦
v i , (3)
1
( ) ( )
c
t
ct T
P
t p d
T
W W
³. (4)
The averaging interval Tc can be chosen arbitrarily from
zero to infinity, and for different Tc values, the resulting
active current and nonactive current will have different
characteristics [17]. In a periodic system with period T,Tc is
normally chosen as integral multiples of T/2 to eliminate
current harmonics.
The instantaneous active current ia(t) and instantaneous
nonactive current in(t) are defined by, respectively,
2
( )
( ) ( )
( )
p
P t
t t
V t
a p
i v , (5)
( ) ( ) ( )t t t
n a
i i i . (6)
The voltage vp(t) is the reference voltage, which is chosen
based on the characteristics of the system and the desired
compensation results. Vp(t) is the rms value of the reference
voltage vp(t), i.e.,
1
( ) ( ) ( )
c
t
p
ct T
V t d
T
W W W
³T
p p
v v . (7)
The rms values of the voltage v(t) and the current i(t) are,
respectively,
1
( ) ( ) ( )
c
t
ct T
V t d
T
W W W
³T
v v , (8)
1
( ) ( ) ( )
c
t
ct T
I
t d
T
W W W
³T
i i . (9)
The definitions in this instantaneous nonactive power
theory are all consistent with the standard definitions for
three-phase fundamental sinusoidal systems. They are also
valid in other various cases, such as single-phase systems,
non-sinusoidal systems, and non-periodic systems as well, by
changing the averaging interval Tc and the reference voltage
vp(t). In this theory, all the definitions are instantaneous
values. Therefore, they are suitable for real-time control, and
provide advantages for the design of control schemes, which
will be discussed in the next section.
IV. CONTROL SCHEMES OF THE UNBALANCE COMPENSATION
In a three-phase power system, voltages or currents are
balanced if the amplitudes of the three-phase voltages or
currents are equal and the phase-angles between consecutive
phases are also equal, and in a three-phase case, the phase
angle is 2ʌ/3. From the standpoint of the compensator
connected in parallel with a load, there are two kinds of
unbalance; one is an unbalanced load, and the other one is an
unbalanced voltage source (could be caused by other loads,
or by the generators in the system). In the first case, the load
current il is not balanced, which results in unbalance in the
voltage vt. If the unbalanced load is compensated so that a
balanced current is drawn from the utility, then the voltage vt
will also be balanced, that is, the unbalance is compensated in
the load current compensation. While in the second case, the
load draws unbalanced current because of the unbalanced
voltage vt. This unbalance can only be compensated with
voltage regulation.
In this section, a current unbalance compensation control
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Fig. 3. Voltage control diagram.
Fig. 4. Control diagram of the integrated current and voltage control.
scheme and a voltage unbalance compensation control
scheme are presented and compared, and an integrated
control which combines the two control schemes together is
also presented.
A. Current Unbalance Compensation
The control diagram of current control is shown in Fig. 2.
The nonactive component in the load current is calculated by
the instantaneous power theory in section III (equations (5)
and (6)), and this nonactive component is provided by the
compensator; therefore a balanced, unity power factor source
current is drawn from the utility. The compensator output
voltage is controlled so that the compensator current tracks
the reference ic
*, as shown in (10).
1 1
0
( ) ( )
t
P I
K K dt
³
* * *
c t c c c c
v v i i i i (10)
* * *
c c1 c2
i i + i (11)
The reference compensator current ic
*has two components,
ic1
*and ic2
*. The first component, ic1
* is the nonactive
component in the load current calculated by the instantaneous
power theory. The system is assumed to be ideal in the
instantaneous power theory; however, there are losses in the
real compensator. Therefore if no active power is provided to
the compensator, the DC link capacitor voltage vdc will vary.
Vdc is the average value of the DC link voltage vdc over one
cycle. To regulate the DC link voltage, some active power is
drawn from the utility to meet the losses. This active current
is referred to as ic2
*, which is in phase with the PCC voltage
vt. Therefore, a control loop is designed as shown in (12).
2 2
0
[ ( ) ( ) ]
t
* *
P dc dc I dc dc
K V V K V V dt
³
*
c2 t
i v (12)
The sum of ic1
* and ic2
* is the current that the compensator
needs to provide.
B. Voltage Unbalance Compensation
In power systems, most voltage unbalance conditions are
due to magnitude inequalities while the phase-angles are
equal (2ʌ/3) or nearly equal. Therefore, in this paper,
unbalanced voltages with unequal magnitudes are considered,
and this kind of voltage unbalance can be compensated by a
parallel compensator by providing nonactive power. The
control principle is to control the compensator so that its
output is only nonactive power (if losses are neglected.),
which is accomplished by keeping the compensator output
voltage vc in phase with the voltage vt, and controlling the
three phase magnitudes of vc. In each phase, when the
magnitude of vc is larger than that of vt, the compensator
generates nonactive power; if the magnitude of vc is smaller
than that of vt, the compensator consumes nonactive power.
By controlling the three phase magnitudes of the
compensator voltage vc individually, the rms values of the
three phase voltages of vt are controlled at a given level Vt
*.
To meet the losses, the reference compensator voltage is
shifted a small phase angle ș* so that a small amount of
active power is drawn by the compensator. The phase angle
ș* is controlled so that the DC link voltage vdc is maintained
at a given value. The control diagram is illustrated in Fig. 3.
*
1 1
0
[1 ( ) ( ) ] ( )
t
* *
P t t I t t
K V V K V V dt t
Z T
³
*
c t
v v (13)
*
2 2
0
( ) ( )
t
* *
P dc dc I dc dc
K V V K V V dt
T
³ (14)
In Fig. 3, the first input of the phase angle shift block is the
compensator reference voltage calculated by the voltage
regulation requirement. This compensator reference voltage
is phase-shifted in the phase angle shift block, and the phase
shift angle ș* is decided by the DC link voltage control loop,
which is the second input of the phase angle shift block.
C. Integrated Compensation
Can the compensator regulate the voltage and compensate
the load nonactive power at the same time? An integrated
compensation is proposed which approaches this goal. The
control diagram is shown in Fig. 4, which is essentially a
current control loop integrated with the voltage regulation.
The reference current contains three components, the load
nonactive component ic1
*, the voltage regulation component
ic3
*, and the DC link control component ic2
*, where ic1
* and
ic2
* are the same as in subsection IV.A, and the voltage
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TABLE I. VOLTAGE AND CURRENT UNBALANCE CONTROL
Control
schemes
Compensation
results
Load
unbalance Voltage source unbalance
Source current Balanced, pf 1 Unbalanced, pf 1
Voltage
control
PCC voltage
Balanced,
regulated
magnitude
Balanced, regulated
magnitude
Source current Balanced, pf = 1 Balanced, pf = 1
Current
control
PCC voltage
Balanced,
unregulated
magnitude
Unbalanced, unregulated
magnitude
Source current Balanced, pf 1 Balanced, pf
1
Unbalanced,
pf 1
Integrated
control
PCC voltage
Balanced,
regulated
magnitude
Unbalanced,
regulated
magnitude
Balanced,
regulated
magnitude
(a)Load current (A) (b) PCC rms voltage (V)
(c) Source current (current control) (d) Source current (integrated control)
(e) Source current rms (A) (f) Compensator current rms (A)
Fig. 5. Load unbalance compensation (simulation).
regulation component ic3
* is
3 3
0
[ ( ) ( ) ] ( )
2
t
* *
P t t I t t
K V V K V V dt t
S
Z
³
*
c3 t
i v (15)
The integrated control combines the current loop and the
voltage control loop together. The two control loops can
work individually by shutting down the other control loop
(turning the control gains to zero), or work together. This
provides the flexibility for the parallel active filter to do both
current and voltage control without any hardware
reconfiguration.
V. SIMULATION AND EXPERIMENTAL RESULTS
Considering there are two kinds of unbalance: load
unbalance and voltage source unbalance, and there are three
control schemes: current control, voltage control, and
integrated control, all the combinations of compensation and
their results are listed in Table I. The compensation results of
the source current and the PCC voltage are compared.
The simulation results of load unbalance compensation and
voltage source unbalance compensation are shown below.
Experimental results of load unbalance compensation are
presented at the end of the section.
A. Load Unbalance (Simulation)
The three-phase load current together with phase a voltage
is shown in Fig. 5a. The current is unbalanced and lagging
the voltage. There is no compensation from t = 0 s to t =
0.4 s, and the rms values of the voltage vt, the source current
is, and the compensator current ic are shown in Figs. 5b, 5e,
and 5f, respectively. Current compensation is performed from
t = 0.4 s to t = 0.8 s to achieve balanced source currents and
unity power factor (in phase with the voltage). The voltage is
balanced since the load now draws balanced current from the
utility, and the magnitude is increased.
From t = 0.8 s to t = 1.2 s, the integrated compensation is
performed with the reference line-to-neutral rms voltage set
to 277 V. The voltage is regulated at 277 V and balanced.
The source current is leading the voltage because there is
some nonactive power provided by the compensator to the
utility, and the magnitude of the source current is increased
some as shown in Fig. 5e. At both the current compensation
and the integrated compensation, the compensator current is
unbalanced and more nonactive current is flowing to the
system at the integrated compensation condition.
As listed in Table I, both the voltage and the source current
balance can be achieved using either current control or
voltage control. In current control, the voltage magnitude is
not regulated, but the source current is controlled to unity
power factor, while in voltage control, the voltage magnitude
is regulated, but the source current is not controlled to unity
power factor (usually a leading power factor because
nonactive power is provided to the utility to boost the
voltage).
B. Voltage Source Unbalance (Simulation)
If the voltage source is unbalanced, the current
compensation can make the source current balanced and
unity power factor, while the voltage compensation can make
the voltage balanced and magnitude regulated, as shown in
Table I. If the integrated control is used, either a balanced
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(a)Load current (A) (b) PCC rms voltage (V)
(c) Source current (current control) (d) Source current (integrated control)
(e) Source current rms (A) (f) Compensator current rms (A)
Fig. 6. Simulation of voltage source unbalance compensation (balanced
voltage is desired).
(a)Load current (A) (b) PCC rms voltage (V)
(c) Source current (integrated control) (d) Source current rms (A)
Fig. 7. Simulation of voltage source unbalance compensation (balanced
source current is desired).
source current or a balanced voltage can be achieved,
depending on the compensation objective.
Fig. 6 shows the simulation results of the current control
and the integrated control with balanced voltage as
compensation objective. The load current is shown in Fig. 6a
with phase a voltage. The load current is lagging the voltage
and is slightly unbalanced because of the unbalanced voltage.
There is no compensation from t = 0 s to t = 0.4 s, and the
rms values of the voltage, the source current, and the
compensator current are shown in Figs. 6b, 6e, and 6f,
respectively.
Current compensation is performed from t = 0.4 s to
t = 0.8 s, and the source current is balanced and unity power
factor (in phase with the voltage). The voltage is still
unbalanced since the compensator only provides the
compensation of the load unbalance and nonactive power,
and the unbalance in the voltage remains. The magnitude of
the voltage is increased. The load now draws balanced
current from the utility despite the unbalanced voltage. This
is done by choosing the positive sequence of the voltage as
the reference voltage vp(t) in (5). From t = 0.8 s to t = 1.2 s,
the integrated compensation is performed with the reference
line-to-neutral rms voltage set to 277 V. The voltage is
regulated at 277 V and balanced. The source current is
leading the voltage because there is some nonactive power
provided by the compensator to the utility, and the source
current is not balanced as shown in Fig. 5e. At both the
current compensation and the integrated compensation, the
compensator current is unbalanced and more nonactive
current is flowing to the system at the integrated
compensation condition.
Fig. 7 shows the simulation results of the integrated control
with balanced source current as the compensation objective.
There is no compensation from t = 0 s to t = 0.2 s, and
integrated control from t = 0.2 s to t = 0.8 s. The average
value of the three-phase rms voltages are regulated at 277 V,
therefore the nonactive power provided from the
compensator is equal in each phase. Fig. 7c shows the source
current, which is leading the voltage. In Fig. 7d, it shows that
the source current is nearly balanced when the integrated
control is performed.
C. Load Unbalance (Experiment)
An unbalanced resistive and inductive (RL) load is tested
in this experiment. The inductors of the RL load are not equal
in each phase; therefore, the three-phase load currents are not
balanced, as shown in Figure 8b. The system line-to-neutral
rms voltage is 120 V. The load resistor is 10.8 ȍ in each
phase, and the load inductors are 30 mH, 10 mH, and 10 mH,
respectively. The coupling inductor is 10 mH in each phase,
the DC link voltage is 450 V. The three-phase system
voltages are balanced, which is shown in Fig. 8a. The source
current after compensation together with the phase a voltage
is shown in Fig. 8c. The source current is nearly balanced
compared to the load current, and in phase with the voltage.
The compensation current is shown in Fig. 8d, which is
unbalanced and 90º out of phase with the voltage. Current
control is used in the experiment, i.e., the compensation
objective is to provide the unbalance component and the
nonactive component in the load current so that the source
current is balanced and unity power factor.
Current control is used in the experiment, i.e., the
compensation objective is to provide the unbalance
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(a) System voltage vs(t) (b) Load current il(t)
(c) Source current is(t) (d) Compensation current ic(t)
Fig. 9. Single-phase load in a three-phase system (experiment).
TABLE III. RMS VALUES OF THE SINGLE-PHASE LOAD COMPENSATION.
Il (A) Is (A)
Phase a 7.20 4.44
Phase b 7.22 4.97
Phase c 0.43 3.97
Iunbalance 137.17% 22.42%
(a) System voltage vs(t) (b) Load current il(t)
(c) Source current (d) Compensation current ic(t)
Fig. 8. Three-phase unbalanced RL load compensation (experiment).
TABLE II. RMS VALUES OF THE CURRENT UNBALANCE COMPENSATION.
Il (A) Is (A)
Phase a 8.06 8.11
Phase b 9.00 7.95
Phase c 11.81 8.35
Iunbalance 38.97% 4.92%
component and the reactive component in the load current so
that the source current is balanced and unity power factor.
The unbalance of the three-phase currents is calculated as
max{ | |, | |, | |}
( , , )
a b b c c a
unb alan ce
abc
I I I I I I
IAv g I I I
, (16)
where
( , , ) ( ) / 3
a b c a b c
Avg I I I I I I . (17)
The rms values of the three phase load currents and the
source currents after compensation are listed in Table II. The
unbalance of the load currents and the source currents is also
listed in the table. The unbalance of the load current is
38.97%, and the unbalance of the source current is improved
to 4.92% after compensation.
Fig. 9 shows a single-phase load in a three-phase system.
Fig. 9a is the three-phase system voltage, which is
fundamental sinusoidal and balanced. An RL load is
connected between phase a and phase b, and the three-phase
load currents are shown in Fig. 9b. The phase a current and
the phase b current are equal in magnitude and opposite in
phase, and the phase c current is zero. The rms values of the
load currents are listed in the second column in Table III. The
rms value of phase c current is not zero because of the
measurement error and noise. This single-phase load in a
three-phase system can be viewed as an extreme case of load
current unbalance. The unbalance of the three-phase load
currents is listed in Table III, which is 137.17%.
The source current after compensation is shown in Fig. 9c.
The magnitudes of phase a and phase b source currents are
reduced, and there is a current in phase c. The rms values of
the three phase source currents are shown in the third column
of Table III, and the unbalance of the source current is
improved to 22.42%. The values of phase a and phase b are
reduced and the three phases are more balanced after
compensation.
VI. CONCLUSIONS
A three-phase IGBT-based parallel connected nonactive
power compensator is presented for current and/or voltage
unbalance compensation. An instantaneous power theory is
used for real-time calculation and control. Three control
schemes, current control, voltage control, and integrated
control are proposed to compensate unbalanced current,
unbalanced voltage, or both.
The instantaneous power theory is suitable for parallel
active filter application, because it can provide real-time
calculation and control for the compensator. The definitions
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of instantaneous active current and instantaneous nonactive
current are feasible for current and voltage unbalance
compensation because the definitions of the three-phase
currents and voltages are independent of each other.
Three control schemes are proposed. Either current
unbalance (caused by the load) or voltage unbalance (caused
by other loads or generators in the system) can be
compensated using the parallel active filter. Different
compensation objectives can be achieved, i.e., balanced and
unity power factor source current, balanced and regulated
voltage, or both, by choosing appropriate control schemes.
The integrated control has the flexibility to implement current
control and voltage control separately or together. Thus, a
parallel active filter can perform both current unbalance
compensation and/or voltage unbalance compensation
without any hardware reconfiguration, which brings
flexibility to the compensation system and reduces capital
costs.
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