M. Sarra*,
J-P. Gaubert1
J. Electrical Systems 10-4 (2014): 445-455
Regular paper
Advanced Control Strategy of a
Transformerless Three Phase Shunt
Hybrid Power Filter
JES
Journal of
Electrical
Systems
This paper describes an advanced control algorithm applied to a three phase shunt hybrid active
power filter (SHAPF) for power-quality improvement and reactive power compensation required
by a nonlinear load. The proposed control uses a robust PLL based on Multi-Variable Filters
(MFV) to determine the reference current for the SHAPF. The SHAPF is formed by a single
7th tuned LC filter per phase and a small-rated three-phase active filter, which are directly
connected in series without any matching transformer. The required rating of the active filter is
much smaller than that of a conventional standalone active filter be. All simulations are
performed by using Matlab-Simulink Power System Blockset and validated with an experimental
test bench developed in the LIAS laboratory, University of Poitiers. Various simulation and
experimental results of the proposed control algorithm are presented under steady state and
transient conditions to confirm his validity and effectiveness.
Keywords: Shunt Hybrid Active Power filter, Harmonics, Phase Looked Loop (PLL), Multi-Variable
Filter (MVF), Voltage Source Inverters (VSI), Power quality.
Article history: Received 27 February 2014, Received in revised form 21 Mars 2014, Accepted 15 September 2014
1.
Introduction
Many loads installed in power systems are classified as non-linear devices. Increasing
use of non-linear loads, such as diode or thyristor rectifiers, cycloconverters, switch mode
power supply (SMPS) in computers, rectifier devices in TVs, ovens, telecommunication
power supplies and others, causes excessive neutral currents, harmonic current injection,
reactive power burden in the power system, and draw non-sinusoidal currents from utility
grids, thus contributing to the degradation of power quality in energy distributed generation
or industrial power systems. They result in poor power factor, lower efficiency and
interference to adjacent communication systems. Traditionally power passive filters (PPFs)
have been used to eliminate the current harmonics and to improve the power factor. However,
these PPFs present many disadvantages such as:
• The requirement to implement one filter per frequency harmonics that needs to be
eliminated;
• Sensitive to frequency variation of the utility;
• The risk of series/parallel resonance;
• The filter frequency is fixed, and not easy to adjust;
In order to overcome the above mentioned disadvantages inherent in PPFs, various kind of
pure active power filters (APF) configuration have been researched and developed, however
they also have some disadvantages such as:
• It is difficult to construct a large-rated current source.
• The cost of active filters in industrial applications could be very high because of
the large power rating of the used power converter.
• These cost considerations limit the applications of active filters in power systems
[1]-[7].
* Corresponding author: University of Bordj Bou Arreridj & Science and Technology Faculty ;
sarramust1@yahoo.fr
1
Université de Poitiers jean.paul.gaubert@univ-poitiers.fr
Copyright © JES 2014 on-line : journal/esrgroups.org/jes
M. Sarra, J-P. Gaubert: Advanced Control Strategy of a Transformerless 3ph Shunt Hybrid Power Filter
As an alternative to mitigate the problems and to inherit advantages of PPFs and pure
APFs, different topologies of hybrid active filters by connecting APFs and PPFs in series or
parallel with various control strategies, have been proposed in recent years as lower cost
alternatives to pure APFs used alone. This paper describes a Transformerless SHAPF
formed by a single LC filter per phase tuned to the seventh-harmonic frequency and a smallrated three-phase active filter based on a three-phase voltage-source PWM converter. The
passive and active filters are directly connected in series. The dc voltage of the active filter is
much lower than the supply line-to-line RMS voltage because no supply voltage is applied
across the active filter. The supply voltage is applied across the capacitor of the passive filter.
Moreover, no additional switching-ripple filter is required for the SHAPF because the LC
filter operates not only as a harmonic filter but also as a switching-ripple. This SHAPF is
based on advanced control algorithm consisting of synchronous reference frame (SRF)
rotating at fundamental angular speed using a Multi-Variable Filters (MFV) based robust
PLL to determine the reference current for the algorithm control [8]-[11].
2.
System configuration and basic compensation principle
Figure1 presents the power scheme of the SHAPF proposed in this paper and designed
to reduce the total harmonic distortion (THD) of is below 5%. It consists of a three-phase
three wire supply voltage, three phase six pulse rectifier, and the active filter which is
directly connected to the system through the LC filter. In this paper, the passive filter,
through which iF flows, is not tuned to most dominant 5th harmonic frequency but the
second most dominant 7th harmonic frequency for the following reasons:
•
The passive filter tuned to the 7th harmonic frequency is less bulky and less
expensive than that tuned to 5th frequency as long as both filters have the same
inductor LF.
• The passive filter tuned to the 7th harmonic frequency offers less impedance to the
11th and 13th harmonic components, compared to that tuned to the 5th harmonic
frequency.
Rs
Supply
Voltage
Ls
Is
Rd
Ld
IF
7th tuned
passive filter
Robust
PLL
Control
Algorithm
Non Linear
Load
LF7
CF7
Cdc
Isabc
Vsabc
RL LL
IL
6
PWM
Vdc
DC- Bus
Regulator
Fig.1. Structure of the proposed SHAPF
The active filter consists of a three-phase voltage-source PWM converter using six
IGBTs, and a DC capacitor Cdc. This hybrid topology allows the inverter to have a very
weak DC-side voltage. The passive filter sinks the 7th harmonic current, while the active
filter compensates for the other harmonic currents produced by the diode rectifier (non
linear load). The SHAPF compensate non linear load current harmonics by injecting equal
446
J. Electrical Systems 10-4 (2014) 445-455
but opposite harmonic compensating current, so it operates as a current source injecting the
harmonic components but phase-shifted by 180°.
Figure 1 can be simplified for one phase as shown in Fig. 2a, where Zs is the source
impedance and Zf is the total impedance of the passive filter. The active filter is considered
as a voltage source VAF, the load is assumed to be an ideal current source IL, and ZS is the
impedance of the LC filter. When no active filter is connected (VAF =0), assuming that the
supply voltage is balanced and sinusoidal gives the supply harmonic current ISh as follows:
I Sh =
ZF
S . LS + Z F
(1)
I Lh
If the supply impedance ωhLS is much smaller than Zf, desirable filtering characteristics
could not be obtained. Moreover, harmonic resonance between LS and ZF may occur at a
specific frequency, thus causing the so-called harmonic-amplifying phenomena.
When the active filter is connected, it helps the passive filter to absorb the load harmonic
current ILh, so that a small amount of harmonic current can flow to the supply. In addition,
the active filter can damp out the harmonic resonance. The supply harmonic current ISh, the
terminal harmonic voltage VTh, and the output voltage of the active filter VAF are given as
follows:
I Sh =
ZF
R + S . LS + Z F
I Lh
(2)
.
(3)
S .L Z
VTh = − R + S . LSS +FZ F I Lh
.
VAF =
ZF
R + S . LS + Z F
(4)
I Lh
Equation (2) tells us that Fig. 2(a) is equivalent in ISh to Fig. 2(b). This means that a pure
resistor K(Ω) is connected in series with LS as shown in Fig. 2(b). If K
ZF all the
harmonic currents injected from the load would sink into the LC filter. If
ωhLS, K
would dominate the filtering characteristics. In addition K acts as a resistor to damp out
parallel harmonic resonance between LS and ZF. Shortly, the principle is to increase ZS and
decrease ZF simultaneously. [8]-[10]
VT
Ls
VTh
IF
Ls
IS
ZF
ISh
IFh
K
ZF
IL
Vs
ILh
VAF
VAF
(a)
(b)
Fig.2 Single Phase equivalent circuit
447
M. Sarra, J-P. Gaubert: Advanced Control Strategy of a Transformerless 3ph Shunt Hybrid Power Filter
Figure 3 shows the filtering characteristics (relationship between ISh and ILh) of the
hybrid filter for different values of K. When the active filter is not connected in series with
the LC filter, harmonic-amplifying phenomenon appears in a frequency range of 200–700
Hz. When the active filter is combined, no harmonic-amplifying phenomenon occurs.
However, the filtering characteristic of the hybrid filter is satisfactory only at the seventh
harmonic frequency.
30
K=0
K=10
20
K=30
10
K=60
G a in (d B )
0
-10
-20
-30
-40
-50
0
10
1
10
2
3
10
10
4
10
5
10
Frequency (Hz)
Fig.3 filtering characteristics
3.
Hybrid active filter control
Figure 4 shows the proposed control circuit of SHAPF, which detects the three-phase
supply currents Isabc , three-phase voltage supply Vsabc and the DC-bus voltage Vdc and then
builds the reference voltages Vsabc* for the PWM voltage source inverter. First, the
three-phase supply currents (Isa, Isb, and Isc) are measured and transformed
into the instantaneous active (Id) reactive (Iq) components using
synchronous reference frame (SRF) rotating at fundamental angular speed
with the positive sequence of the system voltage (5).
$

 $ 2π 
 $ 2π   i 
cos
cos
−
cos
θ
θ
sa


θ +

id  2 
3
3   



 is 
i  = 
$
$
$

3
2π    b 
 2π 

 q
 – sin θ – sin  θ −
 − sin  θ +
 i
3 
3    sc 



(5)
Where is the phase of the positive sequence of the system voltage which is provided by
the robust PLL proposed in this paper. The system under study is a three-wire system where
the zero sequence may be neglected, so only id and iq are considered. The active and
reactive currents can also be decomposed in their DC and AC components.
id  id DC + id AC 

i  = 
i
+
i
q
   qDC qDC 
448
(6)
J. Electrical Systems 10-4 (2014) 445-455
Where (idDC, iqDC) are respectively the d-axis and q-axis direct components which
correspond respectively to the fundamental active and reactive components, and (idAC, iqAC)
are respectively the d-axis and q-axis alternating components which correspond
respectively to the harmonic active and reactive components.
It is hoped that the network supplies the DC values of the active current, while its AC
components, as well as the reactive current, is supplied by the SHAPF. Concerning the
reactive current, its DC value is provided by the passive filter, while the inverter provides
an AC voltage to damp the harmonics. A second-order low-pass filter (LPF) with a cutoff
frequency of 12 Hz extracts ac components from id. The obtained and iq* are then fed
into the proportional plus integral (PI) regulators to generate the required voltage command
for the inverter. A dq to abc transformation is applied to convert the inverter voltage
command back to three-phase quantities. The sine/triangle modulation generates square
wave switching commands to achieve harmonic isolation and dc-bus power balancing of
the active filter inverter.
Vsa Vsb Vsc
Robust PLL
θ̂
Isa
Id
abc
LPF
%Ι d
Vd*
PI
dq
Va*
Vb *
Isb
Isc
Iq *
Iq
Vq*
PI
dq
DC-bus Voltage Control
Vdc
*
Voltage
abc
Vc*
∆ Iq
Regulator
Vdc
Fig. 4 Control diagram of the SHAPF
3.1
DC-bus voltage control
The active filter can build up and regulate the dc capacitor voltage by itself without
any external power supply. Fig. 5 shows the block diagram of the dc-voltage control with a
proportional-plus-integral (PI) regulator. When the active filter is controlled to produce a
fundamental voltage being in phase with the fundamental leading current of the passive
filter, an active power formed by the leading current and the fundamental voltage is
delivered to the dc capacitor. Therefore, the electrical quantity to be controlled in a dc
voltage feedback loop is not ∆Id but ∆Iq [8].
In the knowledge that the current control loop (inner loop) must be much faster than
the DC voltage loop (external loop) at high operating switching frequency, which means
that the bandwidth of the external loop is much lower than that of the inner one, then it can
be assumed that the poles of its transfer function is not involved in the stability of the
external loop. Consequently, in steady state the current closed loop gain has a unity value
(Is (s)/Is*(s) =1). Then, the global control loop scheme in Fig. 5a can be simplified.
Therefore, the choice of PI regulator parameters (Ki, Kp) is based on the step response of
449
M. Sarra, J-P. Gaubert: Advanced Control Strategy of a Transformerless 3ph Shunt Hybrid Power Filter
this simplified closed loop.
On the other hand, to limit and smooth mains current at started and dumping transient
time, an anti-windup loop has been introduced to the PI controller (Voltage regulator) as
shown in Fig.5b.
Then, the expression of voltage control loop is:
*
Vdc
Vdc
Kp
Ki
.S +
Cdc
= Cdc
Kp
Ki
S2 +
.S +
Cdc
Cdc
(7)
From (5) the relation between Vdc and Vdc* is a second order transfer function in the form
of:
Vdc *
2.ξω n.S + ω n 2
=
Vdc S 2 + 2.ξω n.S + ω n 2
(8)
Where ωn is natural frequency and ξ is damping coefficient. The T.F contains two poles and
one zero, this proves that the proposed voltage controller based on an antiwindup PI,
insures a fast response and good stability for transient states. By equaling (5) and (6), Ki
and Kp can be deduced. [14], [15].Hence, Kp= 2. ξ. ωn.Cdc and Ki= Cdc.ωn2
However, the Bode diagram of the closed loop transfer function shown in Fig.5c represents
a good stability with a margin phase PM=127° and a bandwidth BW =62 rad /s.
PLL
Sin
Vdc*
Vdc
Voltage
Regulator
Is
*
X
is *
ߝ
GVSi
1
If
R+L.S+1/C.S
f f
f
Vf
Inverter T.F
Antiwindup
PI Controller
Passive Filter T.F
Vs
Inner current control loop
Outer voltage control loop
(a)
450
1
Cdc.S
Is
Capacitor T.F
Ic
Ic1
Vdc
J. Electrical Systems 10-4 (2014) 445-455
Kp
VDC*
Vc
ε
Vr Ismax
1
S
Ki
VDC
1
Ta
(b)
(c)
Fig.5 Bloc diagram of the DC-bus voltage control
3.2
Proposed robust PLL
The proposed control strategy’s main objective proposed in this paper is to improve
the performance of the SHAPF by using a robust PLL based on a Multi-Variable Filter
(MVF) which can extract directly the fundamental voltage in the α-β axis with high
performance that allows making insensible the PLL to the disturbances specifically to the
harmonic and unbalanced voltage. [16],[17].
Vα
K
Vsa
Vsb
Vsc
abc
1
S
Vsd*= 0
V̂α
X
ωc
ω̂
PI
ωc
αβ
Vβ
K
1
S
1
S
θ̂
V̂β
X
Multi-Variable Filter (MVF)
Sin
Cos
Fig. 6 Robust PLL principle scheme
Figure 6 illustrates the principle scheme of the proposed robust PLL. The most
important part of this structure is the MVF expressed in (7), permits filtering the stationary
reference frame components of the main voltages at the network frequency (50 Hz),
without introducing either a phase shift or a voltage change amplitude.(H(s) = 0 db)
(Fig.7).Where,(ωc, k) are the cut-off frequency and the dynamic gain respectively.
k (s + k )
k.ωc
.
V
α ( s) −
.V β (s)
(s + k )2 + ωc2
(s + k )2 + ωc2
k (s + k )
k.ωc
Vˆ β (s) =
.V β (s) +
.V α (s)
2
2
(s + k ) + ωc
(s + k )2 + ωc 2
Vˆα (s) =
(9)
451
M. Sarra, J-P. Gaubert: Advanced Control Strategy of a Transformerless 3ph Shunt Hybrid Power Filter
The bode diagram of the Multi-Variable Filter in 3D results in the following figures:
0
2
1
-20
P ha s e (ra d)
Mag (dB)
-10
-30
0
-1
0
100
20
100
40
80
50
-2
0
60
f(Hz)
40
20
0
60
80
50
K
100
f( Hz)
(a)
K
100
(b)
Fig. 7 Bode diagram of Multi-Variable Filter a) magnitude and b) phase versus f and K
The Fig. 7 indicates that, at 50Hz, the phase angle of bode diagram is null, which
means that the two input and output signals are in phase. Fig.8 presents the robust
PLL simulation results done in the worst cases. Fig.8a illustrates the
polluted supply voltage containing harmonics and random noise, and in
Fig.8d is presented the perfect sinusoidal and balanced voltage generated
by the proposed robust PLL, that proves the good results in filtering of
the voltage harmonics without generating any phase-shifting and eliminate
the unbalance which can appear in the electric network.
2
S in – c o s (ra d )
V sa _ d isto rte d (V )
(ra d )
200
100
0
-100
-200
0
0.04
0.08
0.12
0.16
1
0
-1
-2
0
0.2
0.04
0.08
0.12
0.16
0.2
0.12
0.16
0.2
t(s)
t(s)
(a)
(b)
2
6
V s_ ab c (V )
θ (ra d )
1
4
2
0
0
0
-1
0.04
0.08
0.12
0.16
0.2
-2
0
0.04
t(s)
0.08
t(s)
(c)
(d)
Fig.8 Robust PLL simulation results
4.
System modeling and simulation
To simulate the proposed control strategy of the SHAPF, a model is developed in
Matlab/Simulink® environment using SimPower Systems Blockset.
The complete active filter system is composed mainly of a three-phase source, a nonlinear
load which is a three phase rectifier feeding an inductive load, a PWM voltage source
inverter, and a control bloc. It should be noted that the simulation parameters are identical
to those used for experimentation and are summarized in Table1.
452
J. Electrical Systems 10-4 (2014) 445-455
Table 1.
SYSTEM COMPONENTS AND PARAMETERS VALUES
Supply Voltage
Line frequency
Supply line
impedance
VSabc = 50V (rms)
f =50 Hz
RS =0.1 Ω ,
LS =0.05 mH
RL =0.1 Ω ,
LL =0.05 mH
RD1 =16.1 Ω ,
RD2 =30 Ω
LD =1 mH
LF7 =1.9 mH,
LC7 =110µF
Nonlinear load
components
7th tuned passive
filter
Quality Factor Q
APF DC-capacitor
42
Cdc = 1100 µF
APF DC-bus voltage
Vdc* = 15 V
Voltage regulator
Parameters
Current regulator
Parameters
Resonant frequency
Kpv=0.156, Kiv=11.1
Kpc=0.156, Kic=11.1
350 Hz
LPF Cut-off frequency
fLPF = 12 Hz
Computer simulation verifies the viability and effectiveness of the proposed hybrid
filter. At first, the results of simulation before connecting the filter to the network polluted
by the nonlinear load are presented in Fig. 9. It can be noticed in Fig.9d that, without
passive ore active filters in the system, the source current is presents a high harmonic
distortion (THDi=27,38%) caused by the presence of the nonlinear load. Otherwise, it can
also be noted that the significant current generated by this nonlinear load, are 5th, 7th, 9th and
11th order, among them the biggest is the 5th.
M a g ( % o f F u n d a m e n ta l
80
60
40
Vsa (V)
20
0
-20
-40
-60
100
THDv= 0.29 %
80
60
40
20
0
0
2
4
6
8
10
12
14
16
18
20
-80
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Harmonic Order
t (s)
(a)
(b)
M a g (% o f F u n d a m e n ta l)
8
6
4
Isa (A)
2
0
-2
-4
-6
100
THDi= 27.38 %
80
60
40
20
0
0
2
4
6
8
10
12
14
16
18
20
-8
0
0.02
0.04
0.06
0.08
0.1
t (s)
(c)
0.12
0.14
0.16
0.18
0.2
Harmonic Order
(d)
Fig. 9 Simulation waveforms before connecting the SHAPF
In the next section, the simulation results of the system are presented in steady and
transient states. Fig. 10 presents the waveform of supply voltage Vsa (V), load current Ica
(A), supply current Isa (A), the DC-bus voltage Vdc (V), the active power P (W) and the
reactive power Q (VAR).
453
M. Sarra, J-P. Gaubert: Advanced Control Strategy of a Transformerless 3ph Shunt Hybrid Power Filter
80
Vsa (V)
60
40
V
s
a(
V
)
20
0
-20
-40
-60
-80
0
0.05
0.1
0.15
0.2
t
0.25
0.3
0.35
0.4
(s)
15
Ica (A)
10
I
c
a(
A
)
5
0
-5
Start Load variation
-10
-15
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
t (s)
15
THDi = 2.71 %
Isa (A)
10
Is
a(
A
)
5
0
-5
-10
-15
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
t (s)
ifa (A)
8
SHAPF Switch ON
If
a
(
A
)
4
0
-4
-8
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
t (s)
50
V
d
c(
V
)
Vdc (V)
40
Vdc
*
30
15
10
0
0.1
0.2
0.3
0.4
t (s)
Fig.10 Simulation waveforms after connecting the SHAPF in transient state
When the SHAPF is applied to the system (switched on) at time t=0.08s, it can reduce
the supply current THDi from 27.38% to 2.71% so, it becomes almost sinusoidal waveform,
which proves that the proposed SHAPF control strategy has the capability of compensating
for current harmonics successfully. On the other hand, it can be observed how the SHAPF
behaved under a first step change in the nonlinear load DC side at t=0.2s from RD2 to RD1
and from RD1 to RD2 at t=0.3s.
Q S (Var )
P S (W )
After the nonlinear load changes occurred, the supply current was distorted for about one
cycle (about 20ms), which would not produce any bad effect on external circuits and
equipment, because the proposed SHAPF with its robust control strategy recovered from
the transient state in one cycle. The DC-bus voltage Vdc was well regulated, even in the
transient state, because of the use of the DC-voltage control with its anti-windup loop.
SHAPF Switch ON
Start Load variation
1000
500
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
500
0
-500
t (s)
Fig. 11 Active power P and reactive power Q in transient state
454
J. Electrical Systems 10-4 (2014) 445-455
5.
Conclusion
A shunt hybrid active power filter (SHAPF) based on a advanced control algorithm
consisting of synchronous reference frame (SRF) rotating at fundamental angular speed
using a Multi-Variable Filters (MFV) based robust PLL has been studied in this paper to
determine the reference current for the SHAPF in order to improve the power quality and
compensate reactive power required by nonlinear load. The SHAPF is formed by a single
7th tuned LC filter per phase and a small-rated three-phase active filter, which are directly
connected in series without any matching transformer. The required rating of the active
filter is much smaller than that of a conventional standalone active filter. With the advanced
control system designed in this paper the proposed SHAPF can attenuate harmonics well
and has a good dynamic performance. Finally, various simulation and experimental results
of the proposed control algorithm are presented under steady state and transient conditions
to confirm his validity and effectiveness.
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