Electrical Power and Energy Systems 44 (2013) 219–226
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Electrical Power and Energy Systems
journal homepage: www.elsevier.com/locate/ijepes
A novel hysteresis band current controller scheme for three phase AC chopper
Murat Kale a,⇑, Murat Karabacak b, Bilal Saracoglu a
a
b
Duzce University, Faculty of Technology, Electrical and Electronics Engineering Department, Konuralp, Duzce, Turkey
Duzce University, Duzce Higher Vocational School, Department of Electronics Technology, Duzce, Turkey
a r t i c l e
i n f o
Article history:
Received 2 August 2011
Received in revised form 13 June 2012
Accepted 5 July 2012
Available online 26 September 2012
Keywords:
Three phase PWM AC chopper
Hysteresis band current control
Pulse width modulation (PWM)
a b s t r a c t
This paper presents the application of the hysteresis band current controller (HBCC) technique to the
three phase pulse width modulation (PWM) AC chopper used for the purpose of controlling the magnitude of the sinusoidal currents and voltages applied to an AC load. If the HBCC technique used in the
inverters is directly employed in the three phase PWM AC chopper, it causes the AC chopper to fail to
provide balanced three phase sinusoidal currents for a three phase AC load. In return, this situation leads
some unavoidable and serious faults to occur in the hardware of the three phase PWM AC chopper. In
respect to this case, the detailed analysis expressing the related faults is presented. Consequently, for
the first time, a novel HBCC technique overcoming these faults is proposed for the three phase PWM
AC chopper. The proposed method is tested under various operating conditions and a very precise control
performance is achieved. Simulation results prove the feasibility and validity of the proposed method.
Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction
In order to obtain regulated AC supply, AC choppers are widely
used in the applications such as lightening control, industrial heating and soft starting of induction motors. The simplest way to control an AC chopper consisting of a pair of triacs is the phase angle
control (PAC) because of its simplicity and the ability of controlling
a large amount of power economically [1,2], which is called the
conventional AC chopper. However, it has several limitations due
to the inherent characteristics of the PAC. That is, a lagging power
factor appears at the supply side even for a resistive load [3,4]. As a
result of PAC, the harmonic content of the output voltage and current of the AC chopper is large, where requires a relatively large filtering stage [5]. Moreover, a discontinuity of power flow appears at
both the supply and load sides of the AC chopper as well, which
leads to another serious drawback in driving dynamic loads such
as electric motors [1]. In order to eliminate these drawbacks arising
from the inherent characteristics of these controllers, linecommutated conventional AC controllers can be replaced by
PWM AC choppers having better overall performance such as sinusoidal supply current with unity power factor, fast dynamics and
significant reduction in filter size [1]. Using the high frequency
switching devices such as IGBT and MOSFET, the supply voltage
can be chopped by changing the duty ratio of the PWM modulation
signal so as to regulate the load voltage [6].
⇑ Corresponding author. Tel.: +90 380 5421133x2248; fax: +90 380 5421134.
E-mail addresses: muratkale@duzce.edu.tr (M. Kale), muratkarabacak@duzce
.edu.tr (M. Karabacak), bilalsaracoglu@duzce.edu.tr (B. Saracoglu).
0142-0615/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.ijepes.2012.07.013
Downloaded from http://www.elearnica.ir
In the inverters, in order to control the load current, HBCC
among the various PWM techniques is widely used because of its
inherent simplicity and fast dynamic response [7–14]. In [15,16],
the AC load current is controlled by using HBCC in the single phase
AC chopper.
In [17], an adaptive HBCC technique is proposed for the three
phase PWM AC chopper. In that study, the HBCC technique is
established based on the claim that ‘‘the operation principle of
the HBCC technique of a three-phase AC chopper is the same one
as that of the three-phase inverter’’ [17]. In contrast to this claim,
the HBCC technique employed in a three phase PWM AC chopper
has to be structurally different from its counterparts in an inverter
and/or a single phase PWM AC chopper. Otherwise, it is inevitable
for the power switches such as IGBT or MOSFET of three phase
PWM AC chopper to be subject to some unavoidable and serious
faults since the continuity of load currents is not ensured. Therefore, in [17], the HBCC technique proposed for the three phase
PWM AC chopper lacks theoretical validation and so it is not possible to be implemented experimentally.
In the literature, there is not any study that proposes and evidently proves the application of HBCC technique to a three phase
PWM AC chopper. As a result, this case formed the motivation of
this study.
The novelty of this study is to present a detailed analysis interested in the faults mentioned above and accordingly propose a
novel HBCC technique eliminating them. The proposed HBCC technique for three phase PWM AC chopper, which is seen in Fig. 1, is
simulated in Matlab/Simulink and detailed results are obtained for
various operating points that also contain the case of unbalanced
supply voltages. Since all the faults are eliminated, it is guaranteed
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M. Kale et al. / Electrical Power and Energy Systems 44 (2013) 219–226
Voltage
Measurement
vSa
vSb
vSc
Current
Measurement R L
S1
R L
S2
R L
S3
vSabc
S3*
S2*
iLabc
S1*
Fig. 1. The power scheme of the three phase PWM AC chopper.
the load voltages and currents are stably remained balanced in all
the operating conditions.
Table 1
Possible switching states for three phase inverter and AC chopper.
2. The HBCC used in the inverters
In the inverter, the HBCC is only based on that the switching signals are obtained by means of comparing the desired sinusoidal
reference currents at the desired frequency and amplitude with
the actual load currents, which is clearly seen in Fig. 2.
Where iLa ; iLb and iLc are the reference three phase currents
aimed at applying to a three phase inductive AC load, iLa, iLb and
iLc are the actual three phase load currents. R and L are also resistance and inductance of the AC load respectively. Thanks to the fact
that the three phase current errors maintain within a hysteresis
band, it is ensured the actual load current vector follows the reference trajectory.
Due to the inherent nature of the HBCC, the switching signals of
each phase are exactly independent of each other [18]. This implies
that all the switching states given in Table 1 are possible to be performed at any moment in time according to the dynamics of the load
driven. Moreover, including all the initial conditions of the load currents, the continuity of the load currents are provided on account of
the inverse parallel diodes of the IGBTs. In this context, there is no possible fault to be able to occur as regards the switching sequence. In this
technique, the DC-bus voltage of the inverter and the phase angle of
the load are not required to be measured and/or calculated.
Besides, the width of the hysteresis band has a direct influence
on the switching frequency and peak to peak ripples in the load
currents. In the literature, there are many studies about adaptively
selecting the width of hysteresis band and thereby keeping the
switching frequency constant, called adaptive hysteresis band.
However, this is out of the scope of this study.
2.1. Analysis of thepossible faults interested in application of the HBCC
to the three phase PWM AC chopper
At this stage, we aim at applying the HBCC to the three phase
PWM AC chopper. In this respect, the HBCC technique used in
HB controller
iLa*
iLa
iLb
+
-
NOT
iLc
+
-
NOT
iLc*
1
2
3
4
5
6
7
8
S2
S3
S1
S2
S3
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
the three phase inverter is directly applied to the three phase
PWM AC chopper feeding a load with isolated neutral without
any modification or improvement. Correspondingly, it is inevitable
that some important and serious faults occur. In terms of analysis
of the faults, we assumed the assumption below is valid.
A1 In the course of the time t0, randomly selected polarities of
the phase A, phase B and phase C load currents are negative, positive and positive respectively. In this moment, the initial values of
phase A, phase B and phase C currents are iLa(0) = 9A, iLb(0) = 6A
and iLc(0) = 3A respectively.
It should be noted that, according to the dynamics of the load
driven, any of the eight possible switching states listed in Table 1
is possible to immediately be in effect as soon as the time t0 passes.
The general formulation of the phase voltages is given in the
following:
2
3
2
32 3 2
L1
0
ia
0 54 ib 5 þ 4 0
r3
0
ic
3
2
32
1 1 1
v Sa
1
þ 4 1 1 1 54 v Sb 5
3
v Sc
1 1 1
r1
v Sa
4 v Sb 5 ¼ 4 0
v Sc
0
0
r2
0
0
L2
0
32 diLa 3
0
6 dt 7
0 54 didtLb 5
diLc
L3
dt
ð1Þ
Therefore, after an infinitely small time following the time t0, we assumed the switching states given below are put into effect in order.
Switching Signals
for IGBTs
+
-
iLb*
State
State
State
State
State
State
State
State
S1
NOT
Three Phase
Two Level
Voltage Fed
Inverter
iLa R
L
iLb R
L
iLc R
L
Fig. 2. The HBCC in the three phase inverters.
Isolated
Neutral
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M. Kale et al. / Electrical Power and Energy Systems 44 (2013) 219–226
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Fig. 3. The phase current path relations in connection with the application of the HBCC to the AC Chopper.
2.1.1. Switching state 1
S1, S2 and S3 are off, which the form of the phase current paths is
given in Fig. 3a, then the load phase voltages are equal to zero as
the following:
2
3
2 3
2
0
1
v La
6
7 6 7 16
4 v Lb 5 ¼ 4 0 5 4 1
3
0
1
v Lc
32 3 2 3
0
0
1 1
76 7 6 7
1 1 54 0 5 ¼ 4 0 5
0
0
1 1
ð2Þ
It is clear that there is no fault.
2.1.2. Switching state 2
S1 and S2 are off and S3 is on. The form of the phase current
paths is given in Fig. 3b, which implies no fault.
2
3
2
3
2
v La
v Sa
1
6
7 6
7 16
4 v Lb 5 ¼ 4 0 5 4 1
3
1
v Lc
v Sc
1 1
32
v Sa
3
76
7
1 1 54 0 5
1 1
v Sc
2.1.3. Switching state 3
S1 and S3 are off and S2 is on. That means there is no fault. The
form of the phase current paths is given in Fig. 3c.
2
2
3
2
1
32
3
v Sa
76
7
1 54 v Sb 5
1 1
1 1
ð4Þ
0
2.1.4. Switching state 4
S1 is off and S2 and S3 are on. The form of the phase current
paths is given in Fig. 3d. There is no fault and resulting equation
yields:
2
ð3Þ
3
1
v La
v Sa
7 16
6
7 6
4 v Lb 5 ¼ 4 v Sb 5 4 1
3
1
v Lc
0
3
2
3
2
1
v La
v Sa
6
7 6
7 16
4 v Lb 5 ¼ 4 v Sb 5 4 1
3
1
v Lc
v Sc
1
1
32
3
v Sa
76
7
1 54 v Sb 5
1
v Sc
1 1
ð5Þ
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M. Kale et al. / Electrical Power and Energy Systems 44 (2013) 219–226
2.1.5. Switching state 5
In the previous modes, the overall three phase system is in the
closed loop, the way all three phase currents have a return path.
Therefore continuity of the load currents is ensured, since they follow their references as the three phase current errors maintain
within the hysteresis band. For first four switching states, it is
therefore clear that all inductive components of the three phase
load have a certain stored energy in the magnetic field and the fact
that no current path is broken prevents them from the instantaneous discharge, thus no voltage spike comes into existence in
the phases.
As for the switching state 5, the switches S1, S2 and S3 are on, off
and off respectively, which means the AC chopper encounters an
unavoidable fault. Namely, when the state 5 is put into practice,
the current conduction path for phase A is broken. The form of
the phase current paths related to this situation is given in
Fig. 3e. This implies the phase A current will immediately be fallen
equal to zero and, in turn, a very high reverse voltage spike is generated by the sharp change in the phase A current. In other words,
from the viewpoint of the laws of magnetic induction, an instantaneous discharge of the inductance of phase A occurs, which leads
to the voltage spike in phase A. In this case, the instantaneous variation in phase A current is iBRa = 9A. Furthermore, the phase B and
C have been in the closed loop, which has no connection with supply, thus, the both currents induce a new current. Its amplitude is
equal to the difference between them and the direction is same as
the higher one, which cause the instantaneous partial charge and
discharge of the inductance of phase B and C. Similarly, this also
leads to voltage spikes in phase B and C. If we call it iBRb-c (the
breakdown current between phase B and C), its amplitude will
be |ib–ic| = 3A and direction will be same as ib, which is being reverse direction to the phase C current. Then, it is clear the phase
B and C currents sharply change from ib = 6A and ic = 3A to
iBRb = (ib–ic) and iBRc = (ib–ic) respectively, where iBRb and iBRc are
the instantaneous variations in phase B and C currents. Since the
magnetic field is a function of electrical current, by definition,
the voltage spikes occurred in phase A, B and C can be expressed
through the instantaneous rate of change of the phase currents
passing through the phase inductances over an infinitely small
time interval following the course of switching state5:
2
3
2
r1
v La
6
7 6
4 v Lb 5 ¼ 4 0
0
v Lc
0
r2
0
32
3
2
L1
0
7 6
76
0 54 ðiLb iLc Þ 5 þ 4 0
r3
ðiLb iLc Þ
0
0
0
L2
0
32 iBRa 3
0
Dt
76 iBRb 7
7
0 56
4 Dt 5
iBRc
L3
ð6Þ
Dt
iBRa, iBRb and iBRc are the sharp variations in the phase currents during the course of the time Dt that is the infinitely small time interval. These voltage spikes can be supposed to be equal to infinite
since Dt can be approximately identical to zero and, in consequence, probably brings about the fault causing a severe damage
to the components in the AC chopper, especially power switches.
2
3
2
r1
v La
4 v Lb 5 ¼ 4 0
0
v Lc
2
0
r2
0
3
þ1
ffi 4 1 5
1
3 2
32
L1
0
0
0 54 ðiLb iLc Þ 5 þ 4 0
r3
ðiLb iLc Þ
0
0
L2
0
32 9 3
0
0
0 54 30 5
L3
60
ð7Þ
2.1.6. Switching state 6
S1, S2 and S3 are on, off and on respectively. The form of the
phase current paths is given in Fig. 3f; the phase B current path
is broken. The phase A and C have been in the closed loop; however, this closed loop is different from that in the switching state
5 since it has a connection to supply. In parallel with this case,
the formulation of the load phase voltages appears slightly different from the general formulation given before.
3 2
32
L1
0 0
ðiLa iLc Þ
4
5þ4 0
5
r2 0
0
0 r3
0
ðiLa iLc Þ
3
3
2
32
1 1 1
v Sa
v Sa
1
þ 4 0 5 4 1 1 1 54 0 5
3
v Sc
v Sc
1 1 1
2
3
þ1
ffi 4 1 5
þ1
2
3 2
r1
v La
4 v Lb 5 ¼ 4 0
0
v Lc
2
0
L2
0
32 3 3
0
0
0 54 60 5
9
L3
0
ð8Þ
2.1.7. Switching state 7
S1, S2 and S3 are on, on and off respectively. The form of the
phase current paths is given in Fig. 3g; the phase C current path
is broken. This is another variant of the fault expressed in the
switching state 6. The phase voltages are given in the following:
3 2
32
L1
0 0
ðiLa iLb Þ
4
5
r2 0
ðiLa iLb Þ 5 þ 4 0
0 r3
0
0
3
3
2
32
1 1 1
v Sa
v Sa
1
þ 4 v Sb 5 4 1 1 1 54 v Sb 5
3
0
0
1 1 1
2
3
þ1
ffi 4 þ1 5
1
2
3 2
r1
v La
4 v Lb 5 ¼ 4 0
v Lc
0
2
0
L2
0
32 6 3
0
0
0 54 90 5
30
L3
ð9Þ
2.1.8. Switching state 8
S1, S2 and S3 are on. The form of the phase current paths is given
in Fig. 3h. There is no fault and the phase voltages are:
2
3
2
3
2
1
v La
v Sa
6
7 6
7 16
4 v Lb 5 ¼ 4 v Sb 5 4 1
3
1
v Lc
v Sc
32
3
1 1
v Sa
76
7
1 1 54 v Sb 5
1 1
v Sc
ð10Þ
As seen from the analysis above, if the HBCC technique used in the
inverters is directly applied to a three phase AC chopper and any of
the switching states 5, 6 or 7 occurs at any moment in time according to dynamics of the load driven, it is inevitable that a serious
damage to power switches of the chopper takes place.
3. The proposed HBCC for the three phase AC chopper
Our task in this stage is to develop a HBCC technique for the
three phase PWM AC chopper which eliminates the faults mentioned in the previous section. The main difference of the AC chopper from the inverter is that the currents and the voltages at the
supply side of the AC chopper are AC signals. The AC chopper is obliged to produce output currents at only the same frequency and
the same waveform as supply voltages.
Besides, there is a load phase angle between the voltage and the
current space vectors of the supply according to the characteristic
of load. Consequently, the reference currents in the AC chopper
have to be same frequency as the supply voltages and phase angle
as the load [15].
The fact that the HBCC used in the inverters cannot be used for
the AC chopper was expressed quite clear in the previous section.
However, it can be modified to be applied to the AC chopper, which
requires two certain modifications. These modifications are carried
out by obtaining the reference currents and providing the continuity of the load current conduction paths.
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M. Kale et al. / Electrical Power and Energy Systems 44 (2013) 219–226
3.1. Obtaining the reference currents
vSa
The reference currents can be generated in two steps. First, the
frequency and the angle of the space vector of the supply voltages
are obtained via employing the synchronous reference frame PLL.
Second, it is required transforming the three phase load currents
into synchronous reference frame using Park Transformation in order to calculate the load phase angle, which is revealed in Eqs. (11)
and (12). It follows that d and q axis currents are passed through
first order low pass filters (LPF) to obtain the angle of the fundamental component of the load currents. Then, the phase difference
between the supply voltages and the load currents can be computed as shown in Eq. (13). The load phase angle and the angle
of the space vector of the supply voltages are added, which enables
the three phase reference currents at the same phase as the load
currents and the same frequency as the supply voltages to be produced. The maximum value of the reference currents is determined
by the user randomly, which is not in connection with the theory of
the proposed HBCC.
vSb
vSc
SHBA
S1
S1*
Fig. 5. Phase A switching signals obtained by minimum voltage algorithm.
Table 2
Possible switching states when the phase A voltage is minimum.
iLa ¼ Im sinðwt þ uÞ
iLb ¼ Im sinðwt ð2p=3Þ þ uÞ
ð11Þ
iLc ¼ Im sinðwt þ ð2p=3Þ þ uÞ
iLd
iLq
2 3
iLa
2 sinðxtÞ sinðxt 2p=3Þ sinðxt þ 2p=3Þ 6 7
¼
4 iLb 5
3 cosðxtÞ cosðxt 2p=3Þ cosðxt þ 2p=3Þ
iLc
ð12Þ
I
u ¼ tan1 Lq
ILd
ð13Þ
where Im is maximum value of the load currents, iLx (x = a, b, c) is the
load currents, iLd and iLq are the d and q components of the load currents respectively, ILd and ILq are the filtered d and q components of
iLd and iLq respectively, xt is the angle of the space vector of the supply voltages, u is the load phase angle.
3.2. Producing switching signals and providing the continuity of
current paths
It is possible to ensure the continuity of current conduction
paths through the diodes parallel connected to the IGBTs in the
inverters, but this situation is not sufficient for the AC chopper.
There are some techniques to guarantee continuity of the current
paths in the literature for the AC chopper [19,20]. Among them,
the algorithm called as ‘turns on the switches of the phase with
minimum voltage’ which is proposed in [19] is adapted for the
HBCC proposed in this study. It is then ensured that the right
power switch can be triggered according to the instantaneous values of the supply voltages, which eliminates the faults as guaranteeing the continuity of the current paths. Otherwise, it is
inevitable that the faults mentioned in the previous section occur.
vSa
vSb
vSc
1
2
3
4
S2
S3
S1
S2
S3
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
0
1
0
The measured load currents are subtracted from the reference
currents as in Eq. (11), with the result that the current errors of
each phase are acquired. The switching signals (SHBA, SHBB and SHBC)
of each phase are formed through applying the HBCC to these current errors. After the switching signals (SHBA, SHBB and SHBC) are
passed through the ‘Minimum Voltage Algorithm’, they can be applied to the switches in the AC chopper seen in Fig. 4. The output
signals of the HBCC (SHBA) and the switching signals (S1 and S1 ) obtained by the ‘Minimum Voltage Algorithm’ are shown in Fig. 5. As
two switches of the phase having minimum voltage are kept in
‘on’, the current control of three phase is implemented by the
switches of the other two phases. Since the current passing
through the phase having minimum voltage consists of sum of
the currents of the other two phases, it is indirectly controlled by
the currents of the other two phases that remain within the hysteresis band. In this way, HBCC of three phase currents can be
achieved due to the fact that all the current errors are maintained
within the hysteresis band. The two modifications applied to the
HBCC used in the inverters are clearly shown in Fig. 4, which also
depicts the real time implementation scheme of the proposed
controller.
3.3. Analysis of application of the proposed HBCC to the AC chopper
In order to analyze the proposed HBCC, the following assumption is supposed to be valid. The analyses can be expanded all initial conditions and all operating points.
iLa iLb iLc
ϕ
+
Im*
iLd
abc
dq
iLa + −
*
ωt +
PLL
ωt
iLa
iLb
iLc
State
State
State
State
S1
iLq
LPF
LPF
Calculation of
the Reference
Currents
(Equation 11)
iLb*
iLc*
+ −
+ −
HB
Controller
ILd
ILq
Load Angle
Calculation
(Equation 13)
Fig. 4. Real time implementation scheme of the proposed HBCC.
SHBA
SHBB
SHBC
Minimum
Voltage
Algorithm
S1
S2
S3
S1*
S2*
S3*
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M. Kale et al. / Electrical Power and Energy Systems 44 (2013) 219–226
R L
vSa
vSb
vSc
S1
R L
S2
S3
R L
S1*
S2*
R L
vSa
vSb
vSc
S1
R L
S2
R L
S3
S3*
S1*
(a)
vSc
R L
vSa
S1
R L
vSb
S2
R L
vSc
S3
S1*
S2*
S3*
(b)
vSa
vSb
S2*
R L
S1
R L
S2
R L
S3
S3*
S1*
S2*
S3*
(d)
(c)
Fig. 6. The phase current path relations in connection with the application of the proposed HBCC to the AC Chopper.
3.3.2. Switching state 2
S1, S3, S1 and S2 are on, S2 and S3 are off. The form of the phase
currents is given in Fig. 6b. The load phase voltages follow:
Table 3
The system parameters used in the simulations.
Parameters
Supply
Voltage (phase-neutral)
Frequency
3-Phase Load Inductances
3-Phase Load Resistors
Load
2
Value
VSabc
f
L
R
220 Vrms
50 Hz
20 mH
10 O
A2 The assumption A1 is valid here as well. For these initial values, the analysis results of the switching’s states given in Table 2
can be concluded in the following.
After an infinitely small time following the time t0, we assumed
the switching states given below are put into effect in accordance
with the dynamics of the proposed HBCC.
When the phase A voltage is minimum, all the switching states
given in Table 2 are possible to be performed at any moment in
time according to the dynamics of the load driven.
3.3.1. Switching state 1
S1, S1 , S2 and S3 are on, S2 and S3 are off. The form of the phase
current paths is given in Fig. 6a. It follows that:
2
3
2 3
2
1
0
v La
6
7 6 7 16
4 v Lb 5 ¼ 4 0 5 4 1
3
1
0
v Lc
32 3 2 3
0
0
76 7 6 7
1 1 54 0 5 ¼ 4 0 5
0
0
1 1
1 1
iLa
ð14Þ
iLb
3
2
3
2
1
v La
v Sa
6
7 6
7 16
4 v Lb 5 ¼ 4 0 5 4 1
3
1
v Lc
v Sc
1 1
32
v Sa
3
76
7
1 1 54 0 5
1 1
v Sc
ð15Þ
3.3.3. Switching state 3
S1, S2, S1 and S3 are on, S3 and S2 are off. The form of the phase
current paths is given in Fig. 6c. The load phase voltages are:
2
3
2
3
2
1
v La
v Sa
7 16
6
7 6
4 v Lb 5 ¼ 4 v Sb 5 4 1
3
1
v Lc
0
32
3
1 1
v Sa
76
7
1 1 54 v Sb 5
1 1
0
ð16Þ
3.3.4. Switching state 4
S1, S2, S3 and S1 are on. The form of the phase current paths is
given in Fig. 6d. In this state, the load phase voltages can be expressed as follow:
2
3
2
3
2
v La
v Sa
1
6
7 6
7 16
4 v Lb 5 ¼ 4 v Sb 5 4 1
3
1
v Lc
v Sc
iLc
Fig. 7. The three phase load currents in the case of Im ¼ 20A.
1
1
32
3
v Sa
76
7
1 54 v Sb 5
1
v Sc
1 1
ð17Þ
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M. Kale et al. / Electrical Power and Energy Systems 44 (2013) 219–226
25
Currents [A]
20
15
10
5
0
0
5
10
15
20
25
30
35
40
45
50
Harmonic Order
Fig. 8. Harmonic spectra of the phase A current.
Im*
iLa
Fig. 9. Dynamic responses of the phase A current for step changes in the amplitude of the reference currents.
vSa
vSb
vSc
iLa
iLb
iLc
Fig. 10. The load currents under unbalanced supply voltages.
226
M. Kale et al. / Electrical Power and Energy Systems 44 (2013) 219–226
With the proposition of the ‘turn on all the switches of the
phase with minimum voltage’, the instantaneous discharge of the
inductive components of the load is avoided and thus the continuity of three phase load current paths are accordingly ensured,
which is verified the analysis results above as well.
4. Simulation results
The simulation results are obtained by the Matlab/Simulink on
the basis of the parameters given in Table 3. In order to examine
the behaviors of the proposed HBCC, the simulations are carried
out for three different cases.
4.1. Case 1
In the case of the reference currents with constant amplitude,
20A, and balanced supply voltages, the load currents produced
with the proposed HBCC is shown in Fig. 7. The harmonic spectra
of the phase A current is shown in Fig. 8, which reveals the THD
is % 2.15. As can be concluded from the Figure, the THD of the currents is quite low and complies with the IEC 1000-3-2 Harmonic
Standards.
4.2. Case 2
In the case of the step changes in the amplitude of the reference
currents (Im ), from 15A to 10A and then to 20A, the dynamic responses of the load currents are plotted in Fig. 9 under balanced
supply voltages. It is clearly concluded from Fig. 9 that the load
currents follow the references with high performance and
accuracy.
4.3. Case 3
In the case of the reference currents with constant amplitude,
20A, the load currents are given in Fig. 10 under unbalanced supply
voltages. Since the PLL method used in the proposed HBCC can correctly track the angle of the voltage space vector of the supply even
in the case of unbalanced supply voltages, the reference currents
can be easily generated and thus the load side currents are stably
remained balanced at their reference values. The unbalances in
the supply voltages are chosen as VSa = 220 V, VSb = 240 V and
VSc = 205 V.
5. Concluding remarks and discussion
The direct application of the HBCC to three phase PWM AC
chopper leads to some serious and unavoidable faults which especially damage to the power switches of the chopper. In order to
eliminate these faults, a novel HBCC for the three phase PWM AC
chopper is proposed. The contributions obtained in the study can
be given in the following order:
1. The related faults interested in direct application of HBCC technique used in the three phase inverter to the three phase PWM
AC chopper are analyzed in detail.
2. Due to the two certain modifications in the HBCC technique
used in the three phase inverter, the related faults are eliminated and the application of the HBCC technique to the three
phase PWM AC chopper is achieved.
3. Despite the step changes in the amplitude of the reference currents and unbalanced supply voltages, it is clearly shown the
load currents track the reference currents with high performance and accuracy.
In order to demonstrate validity and performance of the proposed method, various operating points being possible to happen
in real world applications are taken into consideration in the simulations. As a result, it is obvious a very precise control performance is achieved. The simulation results prove the validity and
feasibility of the proposed HBCC for the three phase PWM AC
chopper.
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