2004 11th International Conference on Harmonics and Quality of Power
VAr Compensation and Elimination of Harmonics
in Three-phase Four-Wire System Based on Unified
Constant-frequency Integration Control
Sachin Hirve, Kishore Chatterjee, and B. G. Femandes
Department of Electrical Engineering, IIT Bombay, Mumhai 400076, India
email: [email protected]
Abstmcl-In this paper, an attempt has been made to design a
shunt active power tilter based on Unified Constant-frequency Integration (UCI) Control, for a three-phase four-wire system with
unbalanced loads. The active power filter provides compensation
currents in such a way that the utility supplies only the balanced
fundamental frequency current at unity power factor, even if
the load draws reactive and harmonic currents. The proposed
scheme does not need to sense utility voltages, thereby reducing
the complexity. In this paper, UCI control is applied to both
four-leg and three-leg inverter topologies. The effectiveness of
the proposed scheme is demonstrated by simulation results.
I. INTRODUCTION
The proliferation of power electronics devices have resulted
in distortion of the steady state ac current and voltage waveforms. Equipments realized through these devices pose as
non-linear loads and draw reactive and harmonic currents in
addition to the active load current. The reactive and harmonic
currents lead to poor power factor, low efficiency, electromagnetic interference with neighboring electronic appliances and
overheating of transformers [l]. In addition to the undesirable harmonic currents flowing through the phase conductors,
single phase non-linear loads cause a very large current to
flow through the neutral wire. In most of the distribution
systems, power is distributed through three-phase four-wire
network. The non-linear loads, present in the system, result in
excessive neutral current due to triplen harmonics, which are
potentially damaging to both neutral conductor and distribution
transformer [l].
Static VAr Compensators (SVCs) have been used for reactive power compensation of non-linear loads. But the size of
energy storing capacitor and inductor used in the compensator
is generally large. They also inject considerable amount of
harmonics in the system. All these limitations of SVCs can
be solved by Static Synchronous Compensators. These static
converter based var generators, are known as Active Power
Filters (APF).
APF is a viable solution for the compensation of reactive
power and harmonic currents drawn by non-linear loads.
Various control strategies have been proposed for the control
of APF for compensation of three-phase non-linear loads.
Active power filters for three-phase systems without neutral
conductor have been successfully developed [l]. But the issue
0-7803-8746-5/04/$20.00 02004 IEEE.
of elimination of harmonics in three-phase four-wire systems
is
not addressed extensively,
In [l], the compensation of harmonic currents in threephase four-wire system has been achieved using hysterisis
hand controller for both split-capacitor and Four-leg inverter
topologies. But hysterisis hand controller results in continuously varying switching frequency and make high frequency
filtering difficult. Whereas in constant switching frequency
approach, the filter current tends to ride either the upper or
lower hand depending on the switch duty cycle. Hence small
amount of low order harmonics are present in the filter current
and neutral wire current.
Using the instantaneous reactive power theory [Z], it has
been shown that the reactive power requirement of a threephase circuit can be compensated instantaneously without
the requirement of energy storage device. In modified form,
instantaneous reactive power theory [3] is also seen to compensate for reactive and harmonic components of load currents
in balanced and unbalanced system. But the drawbacks of
these schemes are expanded architecture, complex circuitry
and need for real time calculations.
Smedley and Qiao have proposed an approach based on
Unified Constant-frequency Integration (UCI) control 141. This
scheme gives satisfactory results to compensate reactive and
harmonic currents in a three-phase system [6]. This scheme
is not computation intensive and hence, there is no need for
high performance processors. Also there is no need to sense
utility voltages. Hence the information about zero crossing of
supply voltage is not needed. This control method is based on
one-cycle control and uses an integrator with reset to control
the pulse width of an ac-dc converter so that current drawn by
it, compensates the reactive and harmonic currents drawn by
the non-linear loads.
In this paper, an attempt is made to apply UCI control
for three-phase four-wire system containing single phase nonlinear loads. The scheme is applied for both three-leg and
four-leg invener topology. Simulation results are presented in
this paper to demonstrate the effectiveness of the proposed
modified scheme.
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Fig. 1.
Active Power Filter for four-wire system baaed on UCI contool with four-leg invener topdog)
11. CONTROL SCHEMES
The commonly used converter topologies for Active Power
Filter (APF) applications include both voltage and current
type converters, where the voltage type converters have been
reported more cost effective than their counterparts [ 5 ] . For
the compensation of three-phase four-wire system, the APF
could be of either four-leg inverter topology or split-capacitor
topology.
In four-leg inverter topology, three legs of inverter are connected to the three-phase conductors through series inductors
and the fourth leg is connected to the neutral conductor. The
second approach is to use a standard three-phase converter.
In this topology, the midpoint of DC lmk is connected to the
neutral conductor. In this paper, control strategies for both the
topologies are proposed.
A. Four-leg Inverter Topology
Reactive power and harmonic current requirement of nonlinear loads can be met by controlling the AF'F in such a way
that the effective load, consisting of the non-linear load and
APF, appears to be resistive.
Fig. 1 shows the schematic of the three-phase APF which
employs a three-phase four-legged bridge converter with the
proposed controller. The current references for each of three
phases are derived from UCI control scheme [6]. The current
references consists of the harmonic current components drawn
by the load. By forcing the filter phase current to follow the
reference, only a fundamental frequency sinusoidal current is
drawn from the supply, which is in phase with the supply
voltage. So the source experiences a resistive load in effect.
The control equations based on UCI control [6] are
R, . is, = V, - 2 . V, . d.,
R, .ish = V, - 2.vm.dbn
R, . i,, = V, - 2 V, . d,,
(1)
The above equations indicate the relationship between the
input phase currents, duty ratios of switches, and the output
of the dc-rail voltage compensator under unity power factor
condition. Unity power factor can be achieved by controlling
the switches Sa,, Sb,, etc. so that the duty ratios satisfy
the control equation (1) and thereby controlling the inverter
terminal voltages U A N , W B N and V C N .
All harmonic currents except zero sequence currents form
symmetrical sets in a balanced system and their sum is
zero. Hence, in addition to the high switching frequency
current components, a dominant uiplen harmonic current flows
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......
Fig. 2. Schematic of three-phase APF with Split-Capacitor inverter topology bared on UCI conuol.
through the load neutral. The zero sequence current can be
eliminated by controlling the fourth leg of inverter so that
it draws a current which is equal in magnitude and opposite
in direction to the zero sequence current flowing through the
neutral conductor of load. The three legs of APF are operated
based on the above control equation and it can he seen that
source current is sum of respective load current and current
injected by the APE
proposed controller. The driver signals to the two switches
in each arm are complementary and the converter is always in
continuous conduction mode (CCM).
Assuming that the switching frequency is much higher than
the tine frequency, the switching cycle average voltage at
nodes A, B, and C referred to the midpoint of the capacitor
“ N can he written as
VAN
.,i = i ~ , + i f .
+
izb = i f b
ifb
(2)
is,
= ik + i fc
To balance the source currents and to eliminate the zero
sequence current, the fourth leg of inverter is operated under
a simple constant hysteresis band controller. The current
reference for the fourth leg is a function of load neutral current
il, such that,
i f n = - il,
(3)
UBN
VCN
-
+
+
(4)
where dan,dbn. and d,, are the duty ratios for switches Sa,,
San,
and S,, respectively; V,, and Vczare the voltages across
the dc link capacitors.
The voltages at nodes A, B, and C referred to neutral point
“ N can be written as
UAN
The current through source neutral conductor reduces to a very
high frequency current of small magnitude. This current can
be easily filtered out by a small passive filter.
B. Split Capacitor To,rmIogy
Fig. 2 shows the schematic of the three-phase APF that
employs a three-phase standard bridge converter with the
+
= Vci - (Vci K2).dan
= Vci (h vc2). dbn
= VI (Vci K2) . d,,
UBN
UCN
= Z)a - j W L . if.
= lib - j W L . ifb
= ‘Vc - j W L . ifc
(5)
where L is source inductance (assuming all phases have the
same inductance L), and w is the line angular frequency.
Neglecting the voltage drop across the inductance, ( 5 ) can he
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I
where V , is the phase-neutral rms voltage. In order to achieve
unity power factor, the control goal for the active power filter
is
U , = Re . i s ,
U b = Re ' i s b
(8)
~g = Re . i s ,
03 ,1, 051
-m
'
em
01
o s
os4
0 1
0%
037
0-
032
os
0%
03s
056
017
011
Fig. 3. Simulation Results for four-leg tOpdOgy, (a) Source voltages, (b)
Load w m n t s , ( c ) APF currents. (d) Source Currents.
where Re is the emulated resistance. Combination of (7) and
(8) yields
Re i,, = &I - (Kl
O Y
m
il,
+ K2) d m
10
'
Re ' i a b = 1/,1 - (&I + Kz)
. dbn
Re i,, = v,, - (Kl + V,Z) . d,,
(9)
-10
'
where is,, i.b, and i,, are the input phase currents, and they
are the sum of nonlinear load phase currents and the filter
phase currents as shown in Fig. 2. Unity power factor is
achieved by controlling the switches Sa,, sb,, etc. so that
the duty ratios satisfy equation (9).
This control equation can be implemented based on a onecycle control circuit that uses an integrator with reset along
with other circuit elements. The voltage feedback compensator
regulates the voltage across both the complete capacitor branch
and also the individual capacitors in the APF converter during
each line cycle. As a result. there will ideally be no active
' converter and source.
power transfer between the AEF
Fig. 4. Simulation Results for neutral circuit with four-leg lopology. (a) Load
n e u f d currenf (b) Filter neutral current. (c) Source neural currenf.
111. SIMULATED
RESULTS
M
The complete model of APF has been implemented in
MATLABISimulink software package and simulation study
for above discussed topologies is carried ont. Three-phase
unbalanced load consists of a single-phase rectifier in phase
A and single-phase R-L load in phase B and C . Rectifier
consists of commutation inductance of 40mH and inductive
load (R = O.ln, L = 120mH) on DC side. R-L load for phase
B and C is modeled as R = IOR & L = 40mH.
Simulation results for the proposed control strategies are
shown in Fig. [3-7]. The supply voltages and loads are
identical for both cases.
A. Four-Leg Iimener Topology
The four-leg APF is simulated with DC link voltage of
700V. The coupling inductance of 5 mH is used. Simulation
results of the system compensating unbalanced load, are shown
in Fig. 3-4.
I
0 18
0 a*
0.
0.1
0 12
043
I
0.4
Fig. 5 . Simulation Results for a step change in rectifier load with four-leg
topology, (a) Source voltage, (b) Load current. (c) APF current, (d) Source
current.
As seen from above figures, APF is compensating the harmonics and the reactive power while balancing the load. The
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-,"
03
011
ou
o u
0%
011
0 1
017
B. Split-Capacitor Imaner Topology
Simulation results for three-leg topology with split-capacitor
for three-phase four-wire system are discussed in this section.ln order to achieve the performance similar to four-leg
APF, DC link is modified in three-leg APF. Capacitor in DC
link is split into two halves in such a way that net capacitance
of new topology is same as that of four-leg APE Fig. 6 shows
the simulation results for split capacitor topology and Fig. 7
shows the neutral currents.
It is found that the source neutral current consist of a
nominal fundamental frequency component. This is due to
unbalanced charging of the DC link capacitors. This unbalance
in DC link capacitor voltages depends upon the extent of
unbalanced load in the system.
Performance of this control scheme is also verified for step
change in load. It is observed that performance of this scheme
is similar to that of earlier scheme.
J
0 1
Fig. 6. Simulation Results for spliti.apacitor topology, (4Source volwges,
(b) Load currents, (c) APF c~rrents.(d) Source Currents.
IV. CONCLUSION
UCI control is verified for four-leg and split-capacitor
inverter topology. Though the performance of four-leg inverter
topology is found to be equivalent to conventional methods,
this scheme uses less complicated control circuitry. Even
though four-leg inverter topology gives satisfactory performance, the active switch count is high. In order to overcome
this problem, split-capacitor inverter topology is suggested
using UCI control. Due to uneven charging of the DC link
capacitors, there exists some nominal fundamental frequency
component in neutral conductor. This current is a function
of unbalance in the system. It is observed that performance
of split-capacitor inverter topology is very similar to that of
four-leg invener topology.
-10
-10
REFERENCES
Fig. 7. Simulation Results for neutral circuit using split-capacitor topology,
(a) Load neural current. (bJ Filter neutral cumnt. (c) Source ne~rralcurrent.
nominal high frequency harmonic content in source current
can be easily filtered out with small passive filter if required.
Also the neutral current is effectively compensated.
Performance of the proposed scheme is also evaluated for
a step change in load. Simulation results for a step change in
load at t = 400111s are shown in Fig. 5 .
It is seen that this scheme offers excellent dynamic response.
The DC link capacitor voltage for APF remains almost constant after initial transient. Thus, this scheme offers desired
performance under steady state and transient conditions.
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