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Electric Power Systems Research 78 (2008) 58–73
Control of a 3-phase 4-leg active power filter under
non-ideal mains voltage condition
Mehmet Ucar, Engin Ozdemir ∗
Kocaeli University, Technical Education Faculty, Electrical Education Department, 41380 Umuttepe, Turkey
Received 29 August 2005; received in revised form 2 October 2006; accepted 13 December 2006
Available online 25 January 2007
Abstract
In this paper, instantaneous reactive power theory (IRP), also known as p–q theory based a new control algorithm is proposed for 3-phase
4-wire and 4-leg shunt active power filter (APF) to suppress harmonic currents, compensate reactive power and neutral line current and balance the
load currents under unbalanced non-linear load and non-ideal mains voltage conditions. The APF is composed from 4-leg voltage source inverter
(VSI) with a common DC-link capacitor and hysteresis–band PWM current controller. In order to show validity of the proposed control algorithm,
compared conventional p–q and p–q–r theory, four different cases such as ideal and unbalanced and balanced-distorted and unbalanced-distorted
mains voltage conditions are considered and then simulated. All simulations are performed by using Matlab-Simulink Power System Blockset.
The performance of the 4-leg APF with the proposed control algorithm is found considerably effective and adequate to compensate harmonics,
reactive power and neutral current and balance load currents under all non-ideal mains voltage scenarios.
© 2006 Elsevier B.V. All rights reserved.
Keywords: 4-Leg shunt active power filter; Instantaneous power theory; Non-ideal mains voltage; Unbalanced load
1. Introduction
The widespread increase of non-linear loads nowadays, significant amounts of harmonic currents are being injected into
power systems. Harmonic currents flow through the power
system impedance, causing voltage distortion at the harmonic
currents’ frequencies. The distorted voltage waveform causes
harmonic currents to be drawn by other loads connected at
the point of common coupling (PCC). The existence of current
and voltage harmonics in power systems increases losses in the
lines, decreases the power factor and can cause timing errors in
sensitive electronic equipments.
The harmonic currents and voltages produced by balanced
3-phase non-linear loads such as motor drivers, silicon controlled rectifiers (SCR), large uninterruptible power supplies
(UPS) are positive-sequence harmonics (7th, 13th, etc.) and
negative-sequence harmonics (5th, 11th, etc.). However, harmonic currents and voltages produced by single phase non-linear
loads such as switch-mode power supplies in computer equip-
∗
Corresponding author. Tel.: +90 262 3032248; fax: +90 262 3032203.
E-mail address: [email protected] (E. Ozdemir).
0378-7796/$ – see front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.epsr.2006.12.008
ment which are connected phase to neutral in a 3-phase
4-wire system are third order zero-sequence harmonics (triplen
harmonics—3rd, 9th, 15th, 21st, etc.). These triplen harmonic
currents unlike positive and negative-sequence harmonic currents do not cancel but add up arithmetically at the neutral bus.
This can result in neutral current that can reach magnitudes as
high as 1.73 times the phase current. In addition to the hazard
of cables and transformers overheating the third harmonic can
reduce energy efficiency.
The traditional method of current harmonics reduction
involves passive LC filters, which are its simplicity and low
cost. However, passive filters have several drawbacks such as
large size, tuning and risk of resonance problems. On the contrary, the 4-leg APF can solve problems of current harmonics,
reactive power, load current balancing and excessive neutral
current simultaneously, and can be a much better solution than
conventional approach.
The IRP theory introduced by Akagi et al. [1,2] has been
used very successfully to design and control of the APF for
3-phase systems. This theory was extended by Aredes et al.
[3], for applications in 3-phase 4-wire systems. The IRP theory was mostly applied to calculate the compensating currents
assuming ideal mains voltages. However, mains voltage may be
M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (2008) 58–73
59
Fig. 1. The basic compensation principle of the shunt APF.
unbalanced and/or distorted in industrial systems. Under such
conditions, control of the 4-leg APF using the p–q theory does
not provide good performance. For improving the APF performance under non-ideal mains voltage conditions, new control
methods are proposed by Komatsu and Kawabata [4], Huang
et al. [5], Chen and Hsu [6], Haque et al. [7], Lin and Lee [8],
Chang and Yeh [9] and Kim et al. [10]. This paper presents a new
control algorithm for the shunt 4-leg APF even for all non-ideal
mains voltage and unbalanced non-linear load condition. Performance of the proposed scheme has been found feasible and
excellent to that of the p–q theory under unbalanced non-linear
load and various non-ideal mains voltage test cases.
2. The 4-leg shunt active power filter
Fig. 1 shows the basic compensation principle of the shunt
APF. A shunt APF is designed to be connected in parallel with
the load, to detect its harmonic current and to inject into the
system a compensating current, identical with the load harmonic
current. Therefore, the current draw from the power system at
the coupling point of the filter will result sinusoidal as shown in
Fig. 2 and Eq. (1). Fig. 2 shows load current (iL ), compensating
current reference (iC ) and desired sinusoidal source current (iS )
waveform, respectively.
iS = iL + iC
(1)
Fig. 2. Load, APF and source current waveforms.
In 3-phase 4-wire systems, two kinds of VSI topologies such
as 4-leg inverter and 3-leg (split capacitor) inverter are used.
The 4-leg inverter uses 1-leg specially to compensate zerosequence (neutral) current. The 3-leg inverter is preferred for
due to its lower number of switching devices, while the construction of control circuit is complex, huge DC-link capacitors
are needed and balancing the voltage of two capacitors is a
key problem. The 4-leg inverter has advantage to compensation
for neutral current by providing 4th-leg and to need for much
less DC-link capacitance and has full utilization of DC-link
voltage.
Fig. 3 shows the power circuit of a 4-leg shunt APF connected
in parallel with the 1-phase and 3-phase loads as an unbalanced
and non-linear load on 3-phase 4-wire electrical distribution system. The middle point of each branch is connected to the power
system through a filter inductor.
The APF consists of 4-leg VSI, 3-legs are needed to compensate the 3-phase currents and 1-leg compensates the neutral
current [11]. The 4-leg VSI has 8 IGBT switches and an energy
storage capacitor on hysteresis–band current controllers is used
to obtain the VSI control pulses for each inverter branch. High
order harmonic currents generated by the switching of the power
Fig. 3. Power circuit of the 4-leg shunt APF.
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M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (2008) 58–73
semiconductor devices of the PWM inverter is filtered by using
a small RC high-pass filter, as shown in Fig. 3.
3. The p–q theory based control strategy
The p–q theory based control algorithm block diagram for
the 4-leg APF is shown in Fig. 4.
Form the Eqs. (2) and (3), the p–q theory consist of an algebraic transformation (clarke transformation) of the measured
3-phase source voltages (vSa , vSb , vSc ) and load currents (iLa ,
iLb , iLc ) in the a–b–c coordinates to the α–β–0 coordinates, followed by the calculation of the instantaneous power components
(p, q, p0 ) [2,3].
⎤
⎡
1
1
1
√
√
√
⎡ ⎤
⎤
⎡
2
2 ⎥
⎢
v0
⎥ vSa
⎢ 2
2⎢
1
1 ⎥⎢
⎢ ⎥
⎥
⎢ 1
(2)
−
− ⎥
⎣ vα ⎦ =
⎥ ⎣ vSb ⎦
⎢
3⎢
2
2
⎥
√
√
vβ
v
⎣
3
3 ⎦ Sc
0
−
2
2
⎡
⎤
1
1
1
√
√
√
⎡ ⎤
⎡
⎤
2
2 ⎥
⎢
i0
⎢ 2
⎥ iLa
2⎢
1
1 ⎥⎢
⎢ ⎥
⎥
⎢ 1
(3)
−
− ⎥
⎣ iα ⎦ =
⎢
⎥ ⎣ iLb ⎦
3⎢
2
2
⎥
√
√
iβ
i
⎣
3
3 ⎦ Lc
0
−
2
2
Instantaneous real power (p), imaginary power (q) and zerosequence power (p0 ) are calculated as Eq. (4).
⎤⎡ ⎤
⎡ ⎤
⎡
i0
p0
0
0
v0
2⎢
⎥⎢ ⎥
⎢ ⎥
v α v β ⎦ ⎣ iα ⎦
(4)
⎣ p ⎦=
⎣0
3
q
0 −vβ vα
iβ
The total instantaneous power (p3 ) in 3-phase 4-wire system
is calculated as sum of instantaneous real and zero-sequence
power.
p3 = p + p0 = v0 i0 + vα iα + vβ iβ = va ia + vb ib + vc ic
(5)
The instantaneous real and imaginary powers include AC and
DC values and can be expressed as follows:
p = p̄ + p̃ = p̄ + p2ω + ph
q = q̄ + q̃ = q̄ + q2ω + qh
(6)
DC values (p̄, q̄) of the p and q are the average active and
reactive power originating from the positive-sequence component of the load current. AC values (p̃, q̃) of the p and q are
the ripple active and reactive power originating from harmonic
(ph , qh ) and negative sequence component (p2ω , q2ω ) of the load
current [12,13].
For harmonic, reactive power compensation and balancing
of unbalanced 3-phase load currents, all of the imaginary power
(q̄ and q̃ components) and harmonic component (q̃) of the real
power is selected as compensation power references and compensation current reference is calculated as Eq. (7).
i∗Cα
vα −vβ
−p̃ + p̄
1
= 2
(7)
i∗Cβ
−q
vα + v2β vβ vα
Since the zero-sequence current must be compensated, the
reference compensation current in the 0 coordinate is i0 itself:
i∗C0 = −i0
(8)
The additional average real power (p̄) is equal to the sum of
p̄loss , to cover the VSI losses and p0 , to provide energy balance
inside the active filter.
p̄ = p̄0 + p̄loss
(9)
The signal p̄loss is used as an average real power and is
obtained from the voltage regulator. DC-link voltage regulator is
designed to give both good compensation and an excellent transient response. The actual DC-link capacitor voltage is compared
by a reference value and the error is processed in a PI controller,
which is employed for the voltage control loop since it acts in
order to zero the steady-state error of the DC-link voltage [3].
Eqs. (7) and (8) represent the required compensating current references (i∗C0 , i∗Ca , i∗Cβ ) in α–β–0 coordinates to match the
demanded powers of the load. Eq. (10) is valid to obtain the
compensating phase currents (i∗Ca , i∗Cb , i∗Cc ) in the a–b–c axis in
terms of the compensating currents in the α–β–0 coordinates:
⎡
⎤
1
√
1
0
⎢ 2
⎥⎡ ∗ ⎤
⎡ ∗ ⎤
⎥ iC0
⎢
√
iCa
⎢
1
3 ⎥
2⎢ 1
⎢ ∗ ⎥
⎥ ⎢ i∗ ⎥
−
(10)
⎢√
⎥ ⎣ Ca ⎦
⎣ iCb ⎦ =
⎢
⎥
2
2
3
⎢ 2
√ ⎥ i∗Cβ
i∗Cc
⎣ 1
3⎦
1
√
−
−
2
2
2
Finally, neutral reference current is calculated as follows:
i∗Cn = i∗Ca + i∗Cb + i∗Cc
(11)
4. The p–q–r theory based control scheme
Fig. 4. The p–q theory based control algorithm block diagram for the 4-leg APF.
The p–q–r theory proposed by Kim et al. [10] with reference
current control method, which can control the system currents
balanced and sinusoidal even when mains voltages are unbalanced or distorted. But, the calculation steps become rather high
as can be defined following equations.
After a transformation of 3-phase source voltages (vSa , vSb ,
vSc ) and load currents (iLa , iLb , iLc ) from a–b–c coordinates to
M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (2008) 58–73
α–β–0 coordinates, according to Eqs. (2) and (3), the currents
are transformed from α–β–0 coordinates to p–q–r coordinates
(ip , iq , ir ) as follows:
⎡
⎤
v0
vα
vβ
⎡ ⎤
⎡ ⎤
ip
⎢
v0αβ vβ v0αβ vα ⎥ i0
⎥⎢ ⎥
1 ⎢
⎢ ⎥
⎢ 0 − vαβ
(12)
vαβ ⎥
⎣ iq ⎦ =
⎢
⎥ ⎣ iα ⎦
v0αβ ⎣
⎦
v
v
v
v
0
α
0
β
ir
iβ
vαβ −
−
vαβ
vαβ
where v0αβ = v20 + v2α + v2β , vαβ = v2α + v2β .
Therefore, to get the source currents balanced and sinusoidal,
the reference compensation currents (i∗Cp , i∗Cq , i∗Cr ) are selected
as Eq. (13).
i∗Cp = ĩp
i∗Cq = iq
i∗Cr = ir +
i p v0
vαβ
(13)
The compensation currents in p–q–r coordinates are inversely
transformed to α–β–0 coordinates (i∗C0 , i∗Cα , i∗Cβ ) as Eq. (14) and
then to a–b–c coordinates (i∗Ca , i∗Cb , i∗Cc ) as Eq. (10).
⎡
⎤
v0
0
vαβ
⎡ ∗ ⎤
⎡ ∗ ⎤
iC0
⎢
v0αβ vβ
v0 vα ⎥ iCp
⎢
⎥
1 ⎢ vα −
−
⎢ i∗ ⎥
⎢ ∗ ⎥
(14)
vαβ
vαβ ⎥
⎣ Cα ⎦ =
⎢
⎥ ⎣ iCq ⎦
v
0αβ ⎣
v0αβ vα
v 0 vβ ⎦ i ∗
i∗Cβ
vβ
−
Cr
vαβ
vαβ
The neutral reference current is determined as Eq. (11).
5. The proposed control algorithm
The p–q theory is suitable for ideal 3-phase systems but is
inadequate under non-ideal mains voltage cases. In fact, under
non-ideal mains voltage conditions, the sum of components
(v2α + v2β ) will not be constant and alternating values of the
instantaneous real and imaginer power have current harmonics
and voltage harmonics. Consequently, the APF does not generate compensation current equal to current harmonics and gives
to mains more than load harmonics than required. To overcome
these limitations, the p–q theory based a new control algorithm to
decrease total harmonic distortion for desired level is proposed;
the instantaneous reactive and active powers have to calculate
after filtering of mains voltages. The proposed theory is designed
for 3-phase 3-leg inverter system under non-ideal cases by Kale
and Ozdemir [14]. In this paper the control theory is evaluated
for 3-phase 4-wire 4-leg inverter system. The proposed method
has a simple algorithm, which allows compensating harmonics, reactive power, neutral current and imbalance load currents
under unbalanced non-linear load and non-ideal mains voltage
cases. The proposed p–q theory based method block diagram
for the 4-leg APF is shown in Fig. 5.
Since the mains voltages, applied to control algorithm of the
4-leg APF is to be balanced and sinusoidal, proposed voltage
harmonics filter block diagram is shown in Fig. 6.
61
Fig. 5. The proposed p–q theory based method block diagram for the 4-leg APF.
In the proposed method, instantaneous voltages are first converted to synchronous d–q coordinates (Park transformation) as
Eq. (15).
vd
2 sin(ωt) sin(ωt − 120◦ ) sin(ωt + 120◦ )
=
3 cos(ωt) cos(ωt − 120◦ ) cos(ωt + 120◦ )
vq
⎡ ⎤
va
⎢ ⎥
(15)
× ⎣ vb ⎦
vc
The produced d–q components of voltages are filtered by
using the 5th order low-pass filters (LPF) with a cut-off frequency at 50 Hz. These filtered d–q components of voltages
are reverse converted α–β coordinates as expressed in Eq. (16).
These α–β components of voltages are used in conventional
IRP theory. Hence, the non-ideal mains voltages are converted
to ideal sinusoidal shape by using LPF in d–q coordinate.
vα
sin(ωt) cos(ωt)
v̄d
=
(16)
sin(ωt) − cos(ωt)
vβ
v̄q
So, the mains voltages are assumed to be an ideal source in
the calculation process. Since the APF input voltages have no
zero-sequence components, zero-sequence power is (p0 ) to be
always zero.
These reference currents calculated by the control algorithm
equations should be supplied to the power system by switching
of the IGBT of the inverter. The method for generation of
the switching pattern is achieved by the instantaneous current
control of the 4-leg APF line currents. The actual 4-leg APF
line currents are monitored instantaneously, and then compared
to the reference currents generated by the control algorithm. A
hysteresis–band PWM current control is implemented to generate the switching pattern of the VSI. The hysteresis–band PWM
current control is the fastest control method with minimum hard-
Fig. 6. Voltage harmonics filtering block diagram.
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M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (2008) 58–73
Fig. 7. Matlab-Simulink simulation block diagram of the 4-leg APF.
ware and software but variable switching frequency is its main
drawback [15]. Matlab-Simulink simulation block diagram of
the proposed method controlled the 4-leg APF is shown in Fig. 7.
6. Simulation results
Harmonic current filtering, reactive power compensation,
load current balancing and neutral current elimination performance of the 4-leg APF with the proposed method, the p–q
and p–q–r theory have been examined under four mains voltage
cases, including ideal mains voltage, unbalanced mains voltage, balanced-distorted mains voltage and unbalanced-distorted
mains voltage cases. The purpose of the designed case studies
is to show the validity and performance of the proposed APF
control strategy, even if the mains voltages are highly distorted
and unbalanced. The presented simulation results were obtained
by using Matlab-Simulink Power System Toolbox for a 3-phase
4-wire power distribution system with a 4-leg shunt APF.
3-Phase thyristor rectifier and 1-phase diode rectifier nonlinear loads are connected to the power system, in order to
produce an unbalance, harmonic and reactive current in the
phase currents and zero-sequence harmonics in the neutral current. The 4-leg APF is switched on 0.15 s later. After 0.2 s, a
single-phase diode bridge rectifier load is connected to phase
“c” to evaluate the dynamic performance of the 4-leg APF. Firing angle of 3-phase thyristor rectifier is α = 30◦ and RL load is
connected on the DC side. DC side of 1-phase diode rectifiers
is connected RC filtered ohmic load. Since reactive power compensation performance of the 4-leg APF is showed clearly, load
and source current are enlarged to two times in phase “c”. The
comprehensive simulation results are discussed below.
6.1. Ideal mains voltage case
Fig. 8 shows the harmonic current filtering and load current balancing simulation results with the p–q, the p–q–r theory
and proposed method for the 4-leg APF under ideal mains voltages. 3-Phase source currents are balanced and sinusoidal after
compensation in three control methods for this case. The neutral current is successfully cancelled with three control methods
as shown in Fig. 9. The reactive power compensation simulation results with the p–q, the p–q–r theory and proposed
method are shown in Fig. 10. Compensated source currents
are in phase with 3-phase mains voltages. Harmonic spectra
of iLc load and iSc source current under ideal mains voltage
case is shown in Fig. 11. Detailed summary of load currents,
source currents and their total harmonic distortion (THD) levels are shown in Table 1. The proposed method, the p–q
and the p–q–r theory are feasible under ideal mains voltages
case.
6.2. Unbalanced mains voltage case
Unbalanced loads or 1-phase loads that are not evenly distributed between the phases of a 3-phase system will cause
voltage unbalance. Excessive voltage unbalance can cause motor
overheating and failure of power conversion components and
increases the stresses of power electronics. When 3-phase power
system is not balanced, effective values of phase voltages is not
equal and there will be fundamental negative-sequence voltage
component in the mains voltage.
Voltage unbalance can be quantified using the following definition according to IEEE Std. 100-1992 as shown below Eq.
M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (2008) 58–73
Fig. 8. (a–e) Harmonic currents filtering under ideal mains voltage case.
Fig. 9. (a–d) Neutral current elimination under ideal mains voltage case.
63
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M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (2008) 58–73
Fig. 10. (a–d) Reactive power compensation under ideal mains voltage case.
Fig. 11. Harmonic spectra of (a) iLc load current and (b) iSc source current under ideal mains voltage case.
Table 1
Detailed summary of load currents, source currents and their THD levels under ideal mains voltage case
3-Phase and neutral
Load currents
t < 0.2 (s)
Source currents
t > 0.2 (s)
p–q theory
0.15 < t < 0.2 (s)
p–q–r theory
t > 0.2 (s)
0.15 < t < 0.2 (s)
Proposed method
t > 0.2 (s)
0.15 < t < 0.2 (s)
t > 0.2 (s)
THD (%)
A-phase
B-phase
C-phase
Neutral
26.18
26.27
45.77
77.30
25.97
26.01
56.69
77.26
3.41
3.40
3.29
–
3.72
3.48
3.42
–
3.40
3.25
3.34
–
2.94
2.87
3.02
–
3.59
3.51
3.37
–
4.05
3.68
3.91
–
RMS (A)
A-phase
B-phase
C-phase
Neutral
27.28
27.23
51.13
30.02
27.39
27.37
79.01
60.01
28.78
28.63
28.97
0.93
37.12
36.44
37.56
1.05
30.87
30.73
31.12
1.13
39.60
39.32
40.00
1.37
29.37
29.20
29.54
0.97
38.12
37.41
38.54
1.14
M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (2008) 58–73
65
Fig. 12. (a–e) Harmonic currents filtering under unbalanced mains voltage case.
(17) [16].
voltage unbalance (%)
=
maximum deviation from average
× 100
average of three phase − phase voltages
(17)
An alternative way of calculating voltage unbalance is defined
as the ratio of negative to positive-sequence voltage.
voltage unbalance (%) =
|V1− |
× 100
|V1+ |
(18)
3-Phase unbalanced mains voltage is given in Eq. (19) [5].
⎤ ⎡
⎤ ⎡
⎤
v1a+
v1a−
vda
⎥ ⎢
⎥ ⎢
⎥
⎢
(19)
⎣ vdb ⎦ = ⎣ v1b+ ⎦ + ⎣ v1b− ⎦
vdc
v1c+
v1c−
⎡
For this case, the unbalanced 3-phase mains voltages are
shown Eq. (20). The power system has not zero-sequence voltage
component.
vda = 311 sin(ωt) + 31 sin(ωt)
vdb = 311 sin(ωt − 120◦ ) + 31 sin(ωt + 120◦ )
vdc = 311 sin(ωt + 120◦ ) + 31 sin(ωt − 120◦ )
method for the 4-leg APF under unbalanced mains voltages are
shown in Fig. 12. While the load current THD level is 45.49%
before 0.2 s, 56.54% after 0.2 s in phase “c”. Since compensation current references of the 4-leg APF have negative-sequence
component, the 3-phase compensated source currents are not
sinusoidal with the p–q theory is shown in Fig. 12(c). The THD
value of source current after compensation is 10.20% during
0.15 < t < 0.2 s and 10.23% after 0.2 s in phase “c” with the p–q
theory. Since negative-sequence component of mains voltage
with the proposed method is eliminated, after compensation 3phase source currents are balanced and sinusoidal as shown in
Fig. 12(e). After compensation, THD level of source current
is 3.49% during 0.15 < t < 0.2 s and 3.63% after 0.2 s in phase
“c” with the proposed method. The neutral current elimination and reactive power compensation is successfully done with
three control methods as shown in Figs. 13 and 14, respectively.
Harmonic spectra of iLc load and iSc source current under unbalanced mains voltage case is shown in Fig. 15. Detailed summary
of load currents, source currents and their THD levels are shown
in Table 2. The unbalanced mains voltage in a 3-phase 4-wire
power system will not affect the 4-leg APF performance with
proposed algorithm.
(20)
Harmonic current suppression and load current balancing
simulation results with the p–q, the p–q–r theory and proposed
6.3. Balanced-distorted mains voltage case
When 3-phase mains voltages are balanced-distorted,
mains voltages contain harmonic voltage components except
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M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (2008) 58–73
Fig. 13. (a–d) Neutral current elimination under unbalanced mains voltage case.
fundamental component. 3-Phase balanced-distorted mains
voltage is expressed as Eq. (21) [5].
⎡
vba
⎤
⎡
v1a+
⎤
⎡
vah
⎤
⎢
⎥ ⎢
⎥ ⎢
⎥
⎣ vbb ⎦ = ⎣ v1b+ ⎦ + ⎣ vbh ⎦
vbc
v1c+
vch
(21)
The 3-phase 4-wire distribution system with unbalanced 3phase and 1-phase loads, the voltage disturbances (especially
unbalanced and even harmonics) are very common especially
in Turkey [17]. In order to simulate a real case distortion level,
mains voltages are measured with a power harmonic analyzer.
The measured real mains voltage waveform, THD level and its
harmonic spectrum is shown in Fig. 16. The mains voltage have
Fig. 14. (a–d) Reactive power compensation under unbalanced mains voltage case.
M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (2008) 58–73
67
Fig. 15. Harmonic spectra of (a) iLc load current and (b) iSc source current under unbalanced mains voltage case.
Table 2
Detailed summary of load currents, source currents and their THD levels under unbalanced mains voltage case
3-Phase and neutral
Load currents
t < 0.2 (s)
Source currents
t > 0.2 (s)
p–q theory
p–q–r theory
0.15 < t < 0.2 (s)
t > 0.2 (s)
0.15 < t < 0.2 (s)
Proposed method
t > 0.2 (s)
0.15 < t < 0.2 (s)
t > 0.2 (s)
THD (%)
A-phase
B-phase
C-phase
Neutral
22.01
27.99
45.49
77.27
22.00
28.08
56.54
77.28
10.04
10.05
10.20
–
10.16
10.37
10.23
–
5.78
6.17
5.73
–
5.61
5.49
5.68
–
3.24
3.74
3.49
–
3.59
3.31
3.63
–
RMS (A)
A-phase
B-phase
C-phase
Neutral
29.44
26.55
47.88
28.60
29.45
26.52
74.61
57.15
28.25
28.00
28.13
0.92
35.75
34.82
35.82
1.01
31.82
29.31
29.59
1.17
39.98
36.75
37.33
1.37
28.68
28.55
28.65
0.96
36.99
35.99
37.02
1.03
dominant 5th harmonic component and also have 3rd, 7th, 11th
harmonic component. For this case, the distorted 3-phase mains
voltages are expressed as below Eq. (22).
THD level of source current after compensation is 7.61% during 0.15 < t < 0.2 s and 6.79% after 0.2 s in phase “c” with the
p–q theory. The performance of the p–q theory for this case is
vba = 311 sin(ωt) + 3.7 sin(3ωt) + 18.6 sin(5ωt − 120◦ ) + 4.5 sin(7ωt) + 3.1 sin(11ωt − 120◦ )
vbb = 311 sin(ωt − 120◦ ) + 3.7 sin(3ωt) + 18.6 sin(5ωt) + 4.5 sin(7ωt − 120◦ ) + 3.1 sin(11ωt)
vbc = 311 sin(ωt + 120◦ ) + 3.7 sin(3ωt) + 18.6 sin(5ωt + 120◦ ) + 4.5 sin(7ωt + 120◦ ) + 3.1 sin(11ωt + 120◦ )
Fig. 17 shows that the harmonic current filtering and load
current balancing simulation results with the p–q, the p–q–r
theory and proposed method for the 4-leg APF under balanceddistorted mains voltages. While the load current THD level
is 40.41% before 0.2 s, 50.29% after 0.2 s in phase “c”. The
(22)
shown not qualified. 3-Phase source currents are balanced and
sinusoidal after compensation with the proposed method and
THD level of source current after compensation is 3.64%
during 0.15 < t < 0.2 s and 3.39% after 0.2 s in phase “c”.
Figs. 18 and 19 show the neutral current elimination and
Fig. 16. The measured real mains voltage waveform, THD level and its harmonic spectrum.
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M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (2008) 58–73
Fig. 17. (a–e) Harmonic currents filtering under balanced-distorted mains voltage case.
reactive power compensation performance with three control
methods for the 4-leg APF, respectively. At the same time,
the 4-leg APF compensates reactive current of the load and
improves power factor and eliminates zero-sequence current
components. Harmonic spectra of iLc load and iSc source current under balanced-distorted mains voltage case is shown in
Fig. 20. Detailed summary of load currents, source currents and
their THD levels are shown in Table 3. There is a significant
Fig. 18. (a–d) Neutral current elimination under balanced-distorted mains voltage case.
M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (2008) 58–73
69
Fig. 19. (a–d) Reactive power compensation under balanced-distorted mains voltage case.
Fig. 20. Harmonic spectra of (a) iLc load current and (b) iSc source current under balanced-distorted mains voltage case.
Table 3
Detailed summary of load currents, source currents and their THD levels under balanced-distorted mains voltage case
3-Phase and neutral
Load currents
t < 0.2 (s)
Source currents
t > 0.2 (s)
p–q theory
0.15 < t < 0.2 (s)
p–q–r theory
t > 0.2 (s)
0.15 < t < 0.2 (s)
Proposed method
t > 0.2 (s)
0.15 < t < 0.2 (s)
t > 0.2 (s)
THD (%)
A-phase
B-phase
C-phase
Neutral
25.15
25.15
40.41
71.01
25.38
25.12
50.29
70.22
7.64
7.37
7.61
–
7.35
7.60
6.79
–
5.28
5.04
4.84
–
5.04
4.47
4.63
–
3.73
3.70
3.64
–
3.55
3.36
3.39
–
RMS (A)
A-phase
B-phase
C-phase
Neutral
27.48
27.47
48.89
27.91
27.36
27.50
74.48
55.57
29.63
29.44
29.86
1.06
38.05
37.23
38.33
1.15
30.87
30.69
31.10
1.22
38.55
38.11
39.03
1.50
29.70
29.49
29.87
0.97
37.71
36.93
38.01
1.05
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M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (2008) 58–73
Fig. 21. (a–e) Harmonic currents filtering under unbalanced-distorted mains voltage case.
reduction in harmonic distortion level with the proposed technique. Therefore, the performance of the proposed method is
better than that of the conventional p–q theory. The balanceddistorted mains voltage in a 3-phase 4-wire power system will
not affect the 4-leg APF performance by using the propose
method.
6.4. Unbalanced-distorted mains voltage case
When 3-phase mains voltage are unbalanced and distorted,
mains voltage contains negative-sequence component and
harmonic voltage components. In this case, 3-phase balanceddistorted mains voltage is expressed as Eq. (23).
⎡
⎤ ⎡
⎤ ⎡
⎤ ⎡
⎤
vdba
v1a+
v1a−
vah
⎢
⎥ ⎢
⎥ ⎢
⎥ ⎢
⎥
(23)
⎣ vdbb ⎦ = ⎣ v1b+ ⎦ + ⎣ v1b− ⎦ + ⎣ vbh ⎦
vdbc
v1c+
v1c−
vch
For this case, the unbalanced 3-phase mains voltages are
shown Eq. (24).
and proposed method for the 4-leg APF under unbalanceddistorted mains voltages. While the load current THD level
is 42.31% before 0.2 s, 54.8% after 0.2 s in phase “c”. The
THD level of source current after compensation is 11.99% during 0.15 < t < 0.2 s and 10.75% after 0.2 s in phase “c” with
the p–q theory. The performance of the p–q theory for this
case is shown not qualified. After compensation the source currents become sinusoidal and balanced with the proposed method
and THD level of source current after compensation is 3.86%
during 0.15 < t < 0.2 s and 3.57% after 0.2 s in phase “c”. The
neutral current elimination and reactive power compensation
is successfully done with three control methods as shown in
Figs. 22 and 23, respectively. Harmonic spectra of iLc load and
iSc source current under unbalanced-distorted mains voltage
case is shown in Fig. 24. Detailed summary of load currents,
source currents and their THD levels are shown in Table 4. The
unsymmetrical distorted voltage system is the most severe condition. However, good results can be obtained by the proposed
theory.
vdba = 311 sin(ωt) + 31 sin(ωt) + 3.7 sin(3ωt) + 18.6 sin(5ωt − 120◦ ) + 4.5 sin(7ωt) + 3.1 sin(11ωt − 120◦ )
vdbb = 311 sin(ωt − 120◦ ) + 31 sin(ωt + 120◦ ) + 3.7 sin(3ωt) + 18.6 sin(5ωt) + 4.5 sin(7ωt − 120◦ ) + 3.1 sin(11ωt)
vdbc = 311 sin(ωt + 120◦ ) + 31 sin(ωt − 120◦ ) + 3.7 sin(3ωt) + 18.6 sin(5ωt + 120◦ ) + 4.5 sin(7ωt + 120◦ )
(24)
+ 3.1 sin(11ωt + 120◦ )
Fig. 21 shows the harmonic current filtering and load current balancing simulation results with the p–q, the p–q–r theory
The design specifications and the main parameters of the system used in the simulation study are indicated in Table 5. From
M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (2008) 58–73
71
Fig. 22. (a–d) Neutral current elimination under unbalanced-distorted mains voltage case.
the 4-leg APF control block diagram in simulation study, it can
be seen that the hardware of the proposed algorithm is simpler
than that of the conventional p–q theory and earlier the proposed algorithms [4–10] and that in addition its compensation
performance is better.
All figures show that the actual currents are almost agrees
with the reference currents. The waveforms indicate that after
compensation the mains currents are still sinusoidal even when
the mains voltages are distorted and/or unbalanced. In an unsymmetrical or distorted voltage system, the results obtained by the
p–q theory are not good. However, the proposed theory gives
good results for both non-ideal and distorted voltage system. The
results obtained by simulations with Matlab-Simulink Power
System Blockset show that the proposed approach is more flex-
Fig. 23. (a–d) Reactive power compensation under unbalanced-distorted mains voltage case.
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M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (2008) 58–73
Fig. 24. Harmonic spectra of (a) iLc load current and (b) iSc source current under unbalanced-distorted mains voltage case.
Table 4
Detailed summary of load currents, source currents and their THD levels under unbalanced-distorted mains voltage case
3-Phase and neutral
Load currents
t < 0.2 (s)
Source currents
t > 0.2 (s)
p–q theory
p–q–r theory
0.15 < t < 0.2 (s)
t > 0.2 (s)
0.15 < t < 0.2 (s)
Proposed method
t > 0.2 (s)
0.15 < t < 0.2 (s)
t > 0.2 (s)
THD (%)
A-phase
B-phase
C-phase
Neutral
21.35
26.77
42.31
78.81
21.45
26.68
54.8
78.81
12.11
11.70
11.99
–
11.83
11.63
10.75
–
7.06
6.96
7.13
–
6.66
6.65
6.82
–
3.80
3.75
3.86
–
3.74
3.60
3.57
–
RMS (A)
A-phase
B-phase
C-phase
Neutral
29.85
26.79
46.05
27.63
29.74
26.8
71.08
55.12
29.47
29.08
29.29
1.05
36.77
35.62
36.66
1.10
31.75
29.08
29.52
1.28
39.19
35.80
36.63
1.49
28.91
28.69
28.79
1.00
36.74
35.61
36.39
1.07
ible than conventional approaches for compensating reactive
power and harmonic, neutral current of the load, even if the
mains voltages are severely distortion and/or unbalanced. In the
proposed method, the distorted mains voltages do not affect the
compensated mains current.
Table 5
System parameters used in simulation
Parameter
Value
Source
Voltage (VSabc )
Frequency (f)
Impedance (RS , LS )
220 Vrms /phase-neutral
50 Hz
10 m, 50 ␮H
4-Leg shunt APF
DC-link voltage (VC )
DC capacitor (CDC )
Switching frequency (fS )
AC side filter (RC , LC ), (RF , CF )
800 V
1500 ␮F
12 kHz/average
(0.1 , 1 mH), (2 , 20 ␮F)
Load
3-Phase thyristor rectifier
(RL1 , LL1 ), (RDC1 , LDC1 )
Firing angle
(0.1 , 3 mH), (12 , 20 mH)
30◦
1-Phase diode rectifier
(RL2 , LL2 ), (RDC2 , LDC2 , CDC1 )
(RL3 , LL3 ), (RDC3 , LDC3 , CDC2 )
(0.1 , 1 mH), (15 , 1 mH, 470 ␮F)
(0.1 , 1 mH), (15 , 1 mH, 470 ␮F)
7. Conclusion
In this paper, a new 3-phase 4-wire and 4-leg shunt APF control algorithm has been proposed to improve the performance of
the 4-leg APF under unbalanced non-linear loads and non-ideal
mains voltage cases. The new control theory has been presented,
which is suitable for 4-wire shunt APF design under unbalanced
and distorted mains voltage cases. The computer simulation
has verified the effectiveness of the proposed control scheme.
The simulation results prove that the following objectives have
been successfully achieved even if under unbalanced load and
non-ideal mains voltage conditions.
(I)
(II)
(III)
(IV)
(V)
Current harmonics filtering.
Reactive power compensation.
Load current balancing.
Elimination of excessive neutral current.
High performance under both dynamic and steady state
operations.
The 4-leg inverter based shunt APF is found effective to meet
IEEE Std. 519-1992 standard recommendations on harmonic
levels in all of the non-ideal voltage conditions [18]. The
studied control approach compensates neutral current, reactive
power and harmonics as well as unbalanced and reactive
M. Ucar, E. Ozdemir / Electric Power Systems Research 78 (2008) 58–73
current components, and this will be really appreciated by the
distribution system.
73
This research is supported by TUBITAK Research Fund (No.:
103E034-AY-57).
instantaneous mains voltages
vSabc
vα , vβ , v0 instantaneous mains voltages in the α–β–0 coordinates
v1a+ , v1b+ , v1c+ fundamental positive-sequence part of mains
voltage
v1a− , v1b− , v1c− fundamental negative-sequence part of mains
voltage
Appendix A. List of symbols
References
Acknowledgement
CDC
DC capacitor
CF
switching harmonics filter capacitor capacitance
iCabc
instantaneous compensation currents
i∗Ca , i∗Cb , i∗Cc instantaneous compensation current references in
the a–b–c coordinates
i∗C0 , i∗Cα , i∗Cβ instantaneous compensation current references in
the α–β–0 coordinates
i∗Cp , i∗Cq , i∗Cr instantaneous compensation current references in
the p–q–r coordinates
iLabc
instantaneous load currents
instantaneous source currents
iSabc
iα , iβ , i0 instantaneous currents in the α–β–0 coordinates
ip , iq , ir instantaneous currents in the p–q–r coordinates
LC
APF filter inductance
LS
source inductance
load filter inductance
LL
n
neutral
p
instantaneous real power
p̄
average real power
p̃
oscillating part of real power
p̄loss
average real power loss
p0
instantaneous zero-sequence power
p2ω
negative sequence part of real power
3-phase total instantaneous real power
p3
ph
harmonic part of real power
p̄
average real power
q
instantaneous imaginary power
q̄
average imaginary power
q̃
oscillating part of imaginary power
q2ω
negative-sequence part of imaginary power
harmonic part of imaginary power
qh
RC
APF filter resistance
switching harmonics filter resistance
RF
RS
source internal resistance
RL
load filter resistance
vah , vbh , vch harmonic parts of mains voltage
vba , vbb , vbc balanced-distorted instantaneous mains voltages
vd , vq instantaneous mains voltages in the d–q coordinates
vda , vdb , vdc unbalanced instantaneous mains voltages
vdba , vdbb , vdbc unbalanced-distorted instantaneous mains
voltages
[1] H. Akagi, Y. Kanazawa, A. Nabae, Instantaneous reactive power compensators comprising switching devices without energy storage elements, IEEE
Trans. Ind. Appl. 1A-20 (1984) 625–630.
[2] J. Afonso, C. Couto, J. Martins, Active filters with control based on the p–q
theory, IEEE Ind. Electron. Soc. Newslett. 47 (3) (2000) 5–11.
[3] M. Aredes, J. Hafner, K. Heumann, Three-phase four-wire shunt active filter
control strategies, IEEE Trans. Power Electron. 12 (2) (1997) 311–318.
[4] Y. Komatsu, T. Kawabata, A control method for the active power filter in unsymmetrical voltage systems, Int. J. Electron. 86 (10) (1999)
1249–1260.
[5] S.J. Huang, et al., A study of three-phase active power filters under non-ideal
mains voltages, Electr. Power Syst. Res. 49 (1999) 125–137.
[6] C.C. Chen, Y.Y. Hsu, A novel approach to the design of a shunt active
filter for an unbalanced three-phase four-wire system under nonsinusoidal
conditions, IEEE Trans. Power Delivery 15 (4) (2000) 1258–1264.
[7] M.T. Haque, T. Ise, S.H. ve Hosseini, A novel control strategy for active
filters usable in harmonic polluted and/or imbalanced utility voltage case of
3-phase 4-wire distribution systems, in: Proceedings of Ninth International
Conference on Harmonics and Quality of Power, 2000, pp. 239–244.
[8] B.R. Lin, Y.C. Lee, Three-phase power quality compensator under the
unbalanced sources and nonlinear loads, IEEE Trans. Ind. Electron. 51
(5) (2004) 1009–1017.
[9] G.W. Chang, C.M. Yeh, Optimisation-based strategy for shunt active power
filter control under non-ideal supply voltages, IEE Proc. Electr. Power Appl.
152 (2) (2005) 182–190.
[10] H. Kim, F. Blaabjerg, B. Bak-Jensen, J. Choi, Instantaneous power compensation in three-phase systems by using p–q–r theory, IEEE Trans. Power
Electron. 17 (5) (2002) 701–710.
[11] A.N. Segura, G.M. Aguilar, Four branches inverter based active filter for
unbalanced 3-phase 4-wires electrical distribution systems, in: Proceedings
of the IEEE-IAS 2000 Annual Meeting, Rome, Italy, 2000, pp. 2503–2508.
[12] F.Z. Peng, G.W. Ott, D.J. Adams, Harmonic and reactive power compensation based on the generalized instantaneous reactive power theory
for 3-phase 4-wire systems, IEEE Trans. Power Electron. 13 (6) (1998)
1174–1181.
[13] E.H. Watanabe, R.M. Stephan, M. Aredes, New concepts of instantaneous
active and reactive powers in electrical systems with generic loads, IEEE
Trans. Power Delivery 8 (2) (1993) 697–703.
[14] M. Kale, E. Ozdemir, Harmonic and reactive power compensation with
shunt active power filter under non-ideal mains voltage, Electric Power
Syst. Res. 77 (2005) 363–370.
[15] L. Malesani, P. Mattavelli, P. ve Tomasin, High-performance hysteresis
modulation technique for active filters, IEEE Trans. Power Electron. 12 (5)
(1997) 876–884.
[16] The New IEEE Standard Dictionary of Electrical and Electronics Terms,
IEEE Std. 100-1992.
[17] Uçar, M., Design and implementation of 3-phase 4-wire shunt active power
filter, Master Thesis, Kocaeli University, Turkey, 2005.
[18] IEEE Recommended Practice and Requirements for Harmonic Control in
Electrical Power Systems, IEEE Std. 519-1992.