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Adaptation of PWM and Reference Signal Tracking Methods for
27-Level Hybrid Multilevel Inverters
M. Emin MERAL1, Lütfü SARIBULUT2, Ahmet TEKE2 and Mehmet TÜMAY2
[email protected], [email protected], [email protected] and [email protected]
Yüzüncü Yıl University, Department of Electrical and Electronics Eng., Van, TURKEY
2
Çukurova University, Department of Electrical and Electronics Eng., Adana, TURKEY
1
Abstract: Multilevel inverters have become more popular due to reduced switching losses,
low costs, low harmonic distortion and high-voltage capability when compared to PWM
inverters. A new family of multilevel inverters that has decreased the number of separated
DC sources has emerged named as hybrid multilevel inverter. In this study, theories and
applications of three modulation methods for 27 level hybrid multilevel inverters are
examined. In addition, a new method for reference signal generation is proposed. The
comparative case studies are presented to validate the proposed modulation technique using
Power System Computer Aided Design Program (PSCAD).
Keywords: Hybrid multilevel inverters, H-bridge inverters, reference signal generation
1. Introduction
Multilevel inverters have gained much attention in recent years due to their various
advantages. The general concept of multilevel inverters involves the utilizing a higher
number of power electronics switches to perform the power conversion in small voltage
steps. The small voltage steps lead to obtain the low harmonic distortion and switching
losses, devices possessing low voltage ratings and higher efficiency. Also, it performs the
reduction of v t stresses on the load and gives the possibility of working with low speed
power electronic switches. Such multilevel inverter topology permits a significant reduction
of the output filter and an improvement of the efficiency [1-2]. The industrial drives and
distributed generation resources include the multilevel inverters [3]. Recently, multilevel
inverter topology has been applied to low-voltage applications, as well [4]. Diode-clamped,
flying capacitor and cascaded (H-bridge) are the fundamental multilevel inverter topologies
[5-7]. Among these inverters, the cascaded H-bridge inverter is useful for practical
applications owing to the advantages that the modularized circuit layout, it does not need
1
extra clamping diodes or voltage balancing capacitors and it requires the reduced number of
components to achieve the same number of output voltage levels among the conventional
multilevel inverters [8]. Another important topic is the increasing the level number of
multilevel inverter. Thus, the harmonic distortion can be reduced as much as possible while
keeping low switching frequency and switching losses.
The hybrid multilevel is the new structures, where the cascaded series inverters have
different internal DC bus voltages, use different switching devices and are modulated quite
differently in [9]. The hybrid multilevel inverter generates a larger number of levels with
the same number of power devices of the cascaded multilevel inverter, uses more
effectively the natural switching speed and voltage blocking characteristics are different
types of switching devices. If the level of hybrid multilevel inverters increases, the total
harmonic distortion (THD) of the output voltage decreases and the quality of the output AC
voltage improves [10]. The methods that are the selective harmonic elimination, space
vector modulation and sinusoidal PWM are the commonly used in the multilevel inverters
[11-13]. Many modulation algorithms have been adapted or created for hybrid multilevel
inverters in the literature. However, the conventional PWM method and phase shifted
carrier PWM method were adapted to cascaded multilevel inverters but not adapted to
hybrid multi-level inverters [14-15].
In this paper, a new control algorithm based on reference signal tracking using Clarke
transformation is proposed for hybrid multilevel inverters. The important PWM methods
such as the conventional PWM method and PSPWM method are applied to a 27 level
hybrid H-bridge inverter [14-16]. The operation principles of these methods are verified by
using PSCAD. Harmonic spectrums, THD and weighted THD (WTHD) values are also
presented with the help of designed PSCAD-MATLAB interface. Finally, simulation
results of presented methods are discussed and compared.
2. Topology of the Hybrid Multilevel Inverter
Hybrid multilevel inverter is used with an order-3 configuration varies in DC source ratio
with 1/3/9 [9]. The inverter given in Figure 1 consists of three H-bridge cells and DC link
2
voltage among the stages has the relationship of VDC, 3VDC and 9VDC. By using three Hbridge cells fed with separate DC sources and controlling the switching of the cells, an
output voltage with various levels can be generated. The output voltages of H-bridge cell
are given in Table 1.
Vt
V1
S11
S13
S21
S23
S12
S14
S31
S33
S32
S34
9Vdc
3Vdc
Vdc
V3
V2
S22
S24
Figure 1. Hybrid multilevel inverter topology with the ratio of 1/3/9
P and N denote the output voltages of the stages of VDC, 3VDC and 9VDC with positive
and negative voltage polarities, respectively. Z denotes that the related stage is in a
freewheeling state. Figure 2 illustrates the voltage polarities (positive, zero and negative
polarities) for the first H-bridge cell according to the switching states.
Output Voltage of
Each Cell
V1 (H-bridge cell 1)
V2 (H-bridge cell 2)
V3 (H-bridge cell 3)
States
Switches
Polarity
S11- S14 ON
P
S12- S14 ON
Z
S12- S13 ON
N
S21- S24 ON
P
S22- S24 ON
Z
S22- S23 ON
N
S31- S34 ON
P
S32- S34 ON
Z
S32- S33 ON
N
Value
+1Vdc
0Vdc
-1Vdc
+3Vdc
0Vdc
-3Vdc
+9Vdc
0Vdc
-9Vdc
Table 1. The output voltage of each H-bridge cell
3
S11
Vdc
+Vdc
S12
S13
S11
S13
Vdc
0
S14
S13
Vdc
-Vdc
S14
S12
A) Pozitive polarity
S11
S12
S14
C) Negative polarity
B) Zero polarity
Figure 2. Output voltage polarities and switching states for the first H-bridge cell
27 output levels can be obtained by various switching states of each H-bridge cell. The
switching states and the output values proposed hybrid inverter are given in Table 2. The
inverter switching losses of PWM inverters with H-bridge cell are significantly reduced
compared with other methods [9].
Table 2. Voltage levels of hybrid multilevel inverter with polarities
V
ou
t
V
1
V
2
V
3
V
ou
t
V
1
V
2
V
3
-13V
dc
N
N
N
+
13V
dc
P
P
P
-12V
dc
Z
N
N
+
12V
dc
Z
P
P
-11V
dc
P
N
N
+
11V
dc
N
P
P
-10V
dc
N
Z
N
+
10V
dc
P
Z
P
-9V
dc
Z
Z
N
+
9V
dc
Z
Z
P
-8V
dc
P
Z
N
+
8V
dc
N
Z
P
-7V
dc
N
P
N
+
7V
dc
P
N
P
-6V
dc
Z
P
N
+
6V
dc
Z
N
P
-5V
dc
P
P
N
+
5V
dc
N
N
P
-4V
dc
N
N
Z
+
4V
dc
P
P
Z
-3V
dc
Z
N
Z
+
3V
dc
Z
P
Z
-2V
dc
P
N
Z
+
2V
dc
N
P
Z
-1V
dc
N
Z
Z
+
1V
dc
P
Z
Z
0V
dc
Z
Z
Z
3. Commonly Used PWM Methods in the Hybrid Multilevel Inverter Topology
Two methods namely modified sinusoidal PWM (MSPWM) and modified phase shifted
carrier PWM (MPSPWM) method are commonly used in the hybrid multilevel inverter
topology [14-15]. These methods are examined in the following.
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3.1. Modified General Sinusoidal PWM Method
In MSPWM method, the amplitude of triangular carrier signal is equal to maximum
value of reference signal. The carrier signal frequency can be selected arbitrarily between
10 to 100 times of reference signal frequency. In this study, the comparison of reference
signal with carrier and the required switching positions of each H-bridge cell are given in
Figure 3 and Table 2, respectively. They are determined by control unit when the
magnitude variations of the reference signal, which passes through the one level to another
level are detected. In each sampling time, the control unit continuously compares the
reference signal with carrier signal.
Carrier
Reference Signal
13Vdc
A
P3
A
V dc
0.0
P2
V dc
P1
V dc
P0
0
V dc
-13Vdc
.
time
Figure 3. Carrier signal, reference signal and output voltage levels
In the comparison of these signals, the situations, that the magnitude of reference signal
is higher, equal or lower than the magnitude of carrier signal can be occurred. A simple
position example is given in the following. For an instance, the point p1 is the starting level
of +2VDC, the crossing point is p2 and the starting level of +3VDC level is p3. The reference
signal is higher than carrier signal until the reference signal passes from p0 to p1 or equal to
p2, the firing positions of IGBTs of each H-bridge cells are selected according to upper
level of the interval (+2VDC level) by the control unit. The reference signal is lower than the
carrier signal between p2 and p3, the firing positions are selected considering the lower level
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of the interval (+3VDC level). For negative levels, firing positions are symmetrical with the
firing positions of positive levels.
3.2. Modified Phase Shifted PWM Method for Hybrid Multilevel Inverter
The difference between MPSPWM and MSPWM methods is the usage of carrier signals.
The number of used carrier signals is defined proportional with the inverter level. For
instance, 27 triangular carrier signals are used for proposed hybrid inverter. The amplitudes
of all carrier signals are equal to the amplitude of reference signal and their phases are
angle shifted from the fundamental carrier signal as the calculated by (1). The reference
signal and carrier signals are given in Figure 4.
angle 
3600
n
(1)
where, n is the level of the hybrid inverter.
For each level of hybrid inverter, one carrier signal is used. The reference signal and the
related carrier signal are compared for each interval between two levels. As mentioned in
MSPWM method, IGBTs are switched by the control unit according to situations that the
reference signal is higher, equal or lower than the related carrier signal.
kV
0.30
-0.30
Carrier signals for positive levels
Reference Signal Carrier signal (1) Carrier signal (13)
Carrier signals for negative levels
kV Reference Signal Carrier signal (1) Carrier signal (13)
0.30
(s) -0.30
Figure 4. Carrier Signals for positive and negative levels
4. Proposed control method for 27 level hybrid multilevel
In PWM methods, the switching signals are obtained by comparing the carrier signal
with reference signal. In the proposed method, the calculations of switching depend on the
6
(s)
tracking of the reference signal magnitude without comparing the carrier signal with
reference signal. The phase angle (θ) of the three phase system is needed to calculate the
amplitude of the reference signal and to synchronize the inverter output with three-phase
system. It can be calculated by using phase locked loop (PLL) and Clarke transformation
(α-β). PLL gives the initial phase angle (not effected any disturbances) during the operation
of the system and protect its initial value during the all system working process. However,
the instant amplitude variations and angle shifted of the reference signal can be rapidly
realized by using α-β transformation. Hence, α-β transformation with is preferred to use in
the proposed method. In α-β transformation, the three-phase stationary coordinate system is
transformed into the two-phase stationary reference frame by (2).
V
V
T
1
1

1 
 
2
2
2 V V V 
 

3
3 an bn cn
3
0
 
2 
 2
(2)
where; Van , Vbn , Vcn are the phase voltages of the three phase system.
After the calculation of the α-β components, θ of the three phase system (for phase A)
can be found by using (3).
  tan 1 (
V
V
)
(3)
The amplitude of the reference signal can be calculated by (4).
VrefA  V cos( )
(4)
Likewise, (5) can be used for tracking phase B.
VrefB  V cos(  2 / 3)
(5)
7
V and θ of the reference signal obtained in the reference frame is given in Figure 5. The
reference signal is be calculated by utilizing (6) and is used for tracking of phase A.
V  V2  V2
(6)
harmoniccomp
Measurement of
Reference Voltages
and Generation of
Carrier Signal
g11
g13
g12
g14
Control Unit:
Generation of
Firing Pulses
using FORTRAN
Codes
A
Van
B
Vbn
C
Van
Vbn
Vcn
FFT
Vt
F = 50
B
C
Measurement of
Harmonic Components
and PSCAD-MATLAB
Interface
g31
g33
g32
g34
Vcn
31
Total
Harmonic
Distortion
31
Individual
Ph
(31)
A
g21
g23
g22
g 24
Mag
(31)
dc
harmoniccomp
interface.m
2
31
interface
inp
New Matlab Interface
carrier
Vt
V1
V2
g11
4
1
g22
g34
4
g33
g24
4
1
g21
g12
1
4
1
g23
g14
4
g13
1
Circuit of
Hybrid
Multilevel
Inverter
4
1
V3
g31
g32
Figure 5. Two-phase stationary reference frame
PSCAD is used to simulate the hybrid multilevel inverter. In this study, the control unit
of hybrid multilevel inverter is created with FORTRAN codes to decrease the used
components number. The power circuit and control unit of proposed 27-level hybrid
multilevel inverter is given in Figure 6.
8
Vbn
V
V

V
Van
Vcn
Figure 6. Simulation model of 27 level inverter and its control unit
The determination of VrefA with FORTRAN codes is given in Table 3(A). After that, the
maximum value of reference signal is divided to the levels. The amplitude of reference
signal is divided into 13 parts and the one of them is called unit amplitude (Eu) as given in
Figure 7. In the proposed method, the first step is to determine the voltage levels. For
instance, the zero voltage level is between the voltage levels of 0 and E0.5, the first voltage
level is between the voltage levels of E0.5 and E1.5, the second voltage level is between the
voltage levels of E1.5 to E2.5.
#LOCAL REAL D
#LOCAL REAL Q
#LOCAL REAL phase
#LOCAL REAL VrefA
#LOCAL REAL IVI
D = 0.6666 * ($phaseA- (0.5 * $phaseB) - (0.5 * $phaseC))
Q = 0.6666 * ((0.8660 * $ phaseB) - (0.8660 * $ phaseA))
Phase = 57.2974795 *ATAN2( Q , D)
IVI = SQRT(( D * D) + (Q * Q))
#LOCAL REAL step
#LOCAL REAL E0
#LOCAL REAL E1
#LOCAL REAL E2
#LOCAL REAL E3
step = IVI / 13
E0 = 0
E1 = step * 0.5
E2 = step * 1.5
E3 = step * 2.5
!******** If VrefA is between E0 and E1 **********
IF ( VrefA.GT.E0 .AND.LE.E1) THEN
$g11 = 0 : $ g12 = 0 : $g13 = 1 : $g14 = 1
$g21 = 1 : $g22 = 1 : $g23 = 0 : $g24 = 0
$g31 = 0 : $g32 = 0 : $g33 = 1 : $g34 = 1
!******** If VrefA is between E1 and E2 **********
ELSE IF ( VrefA.GT.E1 .AND. VrefA.LE.E2) THEN
$ g11 = 1 : $g12 = 0 : $g13 = 0 : $g14 = 1
$g21 = 0 : $g22 = 0 : $g23 = 1 : $g24 = 1
$g31 = 0 : $g32 = 0 : $g33 = 1 : $g34 = 1
…
…
END IF
VrefA= IVI * COS (0.01745 * phase)
The calculation of Vref in the control unit of
hybrid inverter by using FORTRAN codes
The calculation of zero, first and second
voltage levels and assignment of switching
position for IGBTs
(A)
(B)
Table 3. FORTRAN codes of the VrefA, calculation of the voltage level and assignment
the switching position of IGBTs
9
The second step is to assign the switching sequences given in the Table 2. Such as, if the
reference voltage is in the first level, the first stage is operated to obtain +1VDC and the
other stages are operated to obtain 0VDC. According to these levels, the positions of
switches S11, S14, S21, S24, S31, S34 are selected as logic one and the positions of switches S12,
S13, S22, S23, S32, S33 are selected as logic zero. The switching signals of IGBTs are given by
the control unit according to these sequences. The FORTRAN codes used to calculate the
zero, first and second voltage levels and to assign the switching position of IGBTS are
given in Table 3(B). FORTRAN codes of first two levels are given in Table 3(B). The
calculation procedure of other levels is similar to these two levels.
E3.5
E2.5
E1.5
E0.5
-E0.5
-E1.5
+2 Vdc level
0 Vdc level
-2 Vdc level
0. 0190
kV Reference Signal
0.30
0. 0200
0. 0210
Output of inverter
-0.30
(s)
Figure 7. Positive cycle of reference signal and output voltage levels
5. Simulation Results and Discussions
PSCAD/EMTDC simulation package is used to illustrate the output voltage waveforms.
Harmonic spectrums, THD and WTHD values are calculated and presented via PSCADMATLAB interface. The output voltages of each cell with reference voltage for the positive
10
levels (from +1VDC to +13 VDC and zero level) and inverter outputs of three methods are
given in Figure 8. V1, V2, V3 and Van are the waveforms of the first H-bridge cell, the
second H-bridge cell, the third H-bridge cell and reference phase-A voltages, respectively.
A large capacitor value for DC link is used to eliminate the transients and undesirable
oscillations of AC output voltage. The carrier signal frequency used in PWM methods is
selected as 2 kHz.
Obtaining the first 14 level by MGSPWM method
V1
V2
V3
Van
0.350
MGSPWM method
Vt
0.350
kV
kV
24 V
-0.100
-0.350
MPSPWM method
Obtaininig the first 14 level by MPSPWM method
V3
Vt
Van
0.350
positive levels
positive levels
0.350
V2
kV
negative levels
V1
kV
-0.350
-0.100
Obtaining the first 14 level by NEW method
0.350
V1
V2
V3
Vt
Van
kV
kV
-0.100
0.0000
NEW method
0.350
0.0020
0.0040
time
0.0060
-0.350
0.0000
time
0.0050
0.0100
0.0150
0.0200
Figure 8. Output voltages of each H-bridge cell and total output voltages for all methods
The value of interval between levels is 24V (The desired amplitude Am=311V/total
positive level number n=13, Am/n=24 V). All the modulation methods generate 27 level output
voltage. The proposed method produces the higher quality sinusoidal waveform compared
11
to the voltages of the other three methods. However, other methods have almost the same
voltage waveform.
Harmonic spectrums of output voltage for all methods are given in Figure 9 and the
following results can be obtained from harmonic spectrums of modulation methods.
 The proposed method generates the minimum 3rd harmonic component and the values
of all harmonic components are not higher than 0.5%.
 In MGSPWM method, the harmonic components higher than 15th have minimum
value compared to the MPSPWM method and the proposed method.
 In MPSPWM method, the values of harmonic components higher than 20th are
greater than MGSPWM method and the proposed methods.
 The values of even harmonics can be ignored in the proposed method but they are
relatively high in MPSPWM method and MGSPWM methods.
Figure 9. Harmonic spectrums of output voltage for all methods (for ma=1)
THD results of output voltages for three methods are calculated by (7).
1   2
THD   Vn 
V1 n2,3,... 
1/ 2
(7)
12
The presented methods are compared to each other for different modulation indexes. The
modulation index is defined as follows:
ma 
Am
Ac
(8)
where Am is the peak amplitude of the reference or modulation signal, Ac is the carrier
(triangular) peak value.
As shown in Figure 10a, THD values (32nd order of harmonics are taken into account) are
kept below the voltage distortion limits between 0.5-1.0 modulation indexes for all methods
[17]. When the modulation index is between 0.9-1.0, the proposed method produces the
superior output waveform with minimum THD value. For modulation indexes between 0.91.0, MSPWM method produces higher THD compared to proposed method but the THD
values are lower than MPSPWM method. However, for the lower modulation indexes,
MPSPWM method produces better output waveform with lower THD values.
Figure 10a. THD values of output voltage versus modulation indexes
Another measure is needed to compare harmonic distortions caused mainly by lower
order harmonics due to the importance of low order harmonics [14]. This is known as
13
WTHD and calculated by using (9). Up to 32nd order of harmonics are taken into account in
WTHD calculation and given in Figure 10b.
1   V 
WTHD    ( n ) 2 
V1 n2,3,... n 
1/ 2
(9)
where, V1 is the amplitude of fundamental component, n is the order of harmonics and Vn
is the amplitude of nth harmonic.
Figure 10b. WTHD values of output voltage versus modulation indexes
The proposed method produces an output waveform with minimum WTHD when the
modulation index is between 0.8-1.0 and lowers than 0.5 as given in Figure 10b.
6. Conclusions
In this paper, three modulation methods are adopted to 27 level hybrid multilevel
inverters. The first two methods are based on PWM methods. These methods are adapted to
hybrid multilevel inverter to provide output voltage with 27-levels. A new method based on
reference signal tracking algorithm is proposed as third method. In the proposed method,
the switching signals of power switches are obtained without comparing the carrier signal
with reference signal. The reference signal is obtained using Clarke transformation. The
magnitude of reference signal is divided to hybrid inverter levels and switching of IGBTs
14
for each H-bridge cell is determined according to these levels. The performances of
examined methods are verified through simulation studies. According to the results, the
proposed method gives superior THD, WTHD and output voltage waveform than the
conventional PWM methods. The proposed method has simple software to implement the
control algorithm because it does not need the necessity of PWM comparison. The
proposed method is very effective to decrease the voltage harmonics in the hybrid
multilevel inverter applications.
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