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7/28/2019 Inverter Topology and Control Strategies
1/34
Basic Three Phase Voltage Source
Inverter Topology
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Two Simultaneous Switch Gating
Scheme
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Two Switch Gating Scheme-Phase Voltag
M MM1,M6 M1,M2 M3,M2 M3,M4 M5,M4 M5,M6 M1,M6 M1,M2 M3,M2 M3,M4 M5,M4 M5,M6
R1
R2
R3
100V
M1,M6
R1
R2
R3
M1,M2
100V
R1
R2
R3
M3,M2
100V
R1
R2
R3
M3,M4
100V
R1
R2
R3
M5,M4
100V
R1
R2
R3
M5,M6
100V
M1 D1
M4D4
M3 D3 M5D5
M6 M2D2
R1 R2 R3
R Y B
N
100V
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Two Switch Gating Scheme-Phase Voltage
Spectra
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Two Switch Gating Scheme-Line Voltage
MM1,M6 M1,M2 M3,M2 M3,M4 M5,M4 M5,M6 M1,M6 M1,M2 M3,M2 M3,M4 M5,M4 M5,M6
R1
R2
R3
100V
M1,M6
R1
R2
R3
M1,M2
100V
R1
R2
R3
M3,M2
100V
R1
R2
R3
M5,M4
100V
R1
R2
R3
M5,M6
100V
R1
R2
R3
M3,M4
100V
M1 D1
M4D4
M3D3
M5D5
M6 M2D2
R1 R2 R3
R Y B
N
100V
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Two Switch Gating Scheme-Line Voltage
Spectra
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Three Switch Gating Scheme
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Three switch gating scheme- Phase voltage
MM1,M6,M5 M1,M6,M2 M1,M3,M2 M4,M3,M2 M4,M3,M5 M4,M6,M5 M1,M6,M5 M1,M6,M2 M1,M3,M2 M4,M3,M2 M4,M3,M5 M4,M6,M5
R1
R2
R3
100V
M1,M6,M5
R1
R2
R3
M1,M6,M2
100V
R1
R2
R3
M1,M3,M2
100V
R1
R2
R3
M4,M3,M2
100V
R1
R2
R3
M4,M3,M5
100V
R1
R2
R3
M4,M6,M5
100V
M1 D1
M4D4
M3 D3 M5D5
M6 M2D2
R1 R2 R3
R Y B
N
100V
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Three switch gating scheme- Line voltage
MM1,M6,M5 M1,M6,M2 M1,M3,M2 M4,M3,M2 M4,M3,M5 M4,M6,M5 M1,M6,M5 M1,M6,M2 M1,M3,M2 M4,M3,M2 M4,M3,M5 M4,M6,M5
R1
R2
R3
100V
M1,M6,M5
R1
R2
R3
M1,M6,M2
100V
R1
R2
R3
M1,M3,M2
100V
R1
R2
R3
M4,M3,M2
100V
R1
R2
R3
M4,M3,M5
100V
R1
R2
R3
M4,M6,M5
100V
M1 D1
M4D4
M3D3
M5D5
M6 M2D2
R1 R2 R3
R Y B
N
100V
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Comparison of the two schemes2 Switch Scheme
Six step L-L voltage Fourier Series:
...13,11,7,5,1
sin3
n
d
n
tnV
Quasi-square phase voltage Fourier Series:
...13,11,7,5,1
3
sin
3n
d
n
tn
V
3 Switch Scheme
Quasi-Square L-L voltage Fourier Series:
...13,11,7,5,1
sin32
n
dn
tnV
Six step phase voltage Fourier Series:
...13,11,7,5,1
3sin
2
n
d
n
tn
V
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Comparison of the two schemes(2)
2 SWITCH OR 1200
SCHEME
SIX STEP L-L VOLTAGE
3 SWITCH OR 1800
SCHEME
SQUARE L-L VOLTAGE
PHASE VOLTAGES
(BALANCED LOAD)
QUASI-SQUARE SIX-STEP
L-L RMS VALUEdV
2
1= 71 % of dV dV
3
2= 82% of dV
L-L FUNDAMENTAL
AMPLITUDE dV
3
= 95% of dV dV32
=110% of dV
RATIO OF mt
HARMONIC
AMPLITUDE TO
FUNDAMENTAL
m
1
m
1
dV = dc bus voltage. m (other than fundamental) = 6* any positive integer1.
Conclusion: The 3 switch scheme gives higher fundamental component of line-line
voltage. Thus it is preferred for 3 phase motor drives. However with the two switch
scheme the chances of a shoot-through fault is largely eliminated.
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Equivalent circuit of induction motors fed
from inverters
Harmonic supply voltage,1 = 1 .Harmonic synchronous speed, 1 = 1.(Please refer to section 9.2 of the textbook).(The negative sign because of reverse rotating magnetic field).
Harmonic slip, =11 =
11
111 =
1 1.
Examples: = 5, 5 = 515 = 1.2 ; = 7, 7 =71
7= 0.86; = 11, 11 = 11111 = 1.091; =
13, 13 = 13113 = 0.923.
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Equivalent circuit of induction motors
fed from inverters(2)
The magnitude of harmonic magnetizing current is negligible as nt harmonic current though it is1
2 of the fundamental current . Therefore, the magnetizing branch can be open circuited. As themagnitude of1 and2
are much larger than 1 and 2 the resistors can be neglected and the
equivalent circuit reduces to the one shown above.
Now1 = 1;2 = 2.
The harmonic stator current is given by
1 =1
(1+2 )=
121+2
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Example using the two switch
conduction scheme
A 3 phase, 3 hp, 208 V, 1740 rpm, 60 Hz, 4 pole, Y connected, induction motor is supplied froma constant 300 V dc bus 3 phase inverter in the six pulse mode (2 switches conducting
simultaneously). The motors equivalent circuit parameters are 1 =2 = 0.5 ,1=2 = 1 , =35 . Find the 1st, 5th, and 7th harmonic line current, output power, torque of the motorwhen it runs at 1740 rpm.
Solution:
For the 2 switch scheme, the Fourier series of the phase voltage is given by:
= 3 sin
3
=1,5,7.11.13 .
Thus the RMS value of the fundamental phase voltage is given by
1 ( ) = 32 = 32 300 = 117 V
5 ( ) =1( )
5=
117
5= 23.4 V
7 ( ) =1( )
7=
117
7= 16.7 V
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Problem continued
V1 =117
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Problem continued(2)1 = 32 22
1 = 3 7.29
2 14.5 = 2312
1 = 01
=2312
2
1740
60
= 12.69Nm.
For 5th
harmonic and 7th
harmonic frequencies the equivalent circuit gets modified.
Slip corresponding to 5th
harmonic
5 = 55 =518001740
51800 = 1.2
Slip corresponding to 7th harmonic
7 = 77 =718001740
71800= 0.86
Solving the harmonic equivalent circuit,
5 = 121+2 = 11725(2) = 2.34; 5 = 35 22 155 = 3 2.342 0.5 11.21.2 = 1.37 W;
5 = 1.3721740
60
= 0.071 Nm.
7 =1
21+2 =
117
49(2)= 1.194; 7 = 37 22
177
= 3 1.1942 0.5 10.850.85
=
0.377 ; 7 =0.377
2174060 = 2.07 103
Nm.
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Inverter Topologies For Induction Motor
Drives
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Limitations of the Two Switch or Three
Switch Gating Schemes
With two switch or three switch gating schemes only frequency variation is possible
through the inverter.
Voltage variation has to be achieved through controlled rectifiers or choppers which
supplies the dc bus powering the inverter.
When fundamental frequency is low these switching schemes will introduce harmonics that
will cause considerable torque and speed ripple. For example iff1 is 10 Hz,f5 is 50 Hz,
f7 is 70 Hz etc. All these 50 Hz, 70Hz, 110Hz, 130 Hz components can cause considerable
current in a 50 Hz or 60 Hz machine and hence torque and speed ripple.
To overcome this (separate voltage and frequency control and increase of lower order
harmonics at lower fundamental frequency ) v/f control through the inverter gating
alone can be achieved through various sinusoidal pulse width modulation
(SPWM) techniques. Some of them are discussed next.
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Sinusoidal PWM Inverters
The inverter topology is same as that of the six-step inverter (see figure, top left). However the
gating pattern is different.
For each phase, two synchronized sine and triangle (zero crossing of sine coincides with the zero
crossing or the peak of triangle) waveforms are compared (see figure, top right) to generate the
PWM output. This is called natural sampling.The sine is called the modulating wave and the
triangle is called the carrier wave. Free running sine and triangle waveforms give rise to sub
harmonics. However, the sine and the triangle can be free running only with low frequency of the
sine (about < 5 Hz) and high frequency of the triangle. As in the case of the utility supply, the
sine-waves of each phase are phase shifted by 1200
from one another as well.
If is the peak of the sine and the peak of the triangle, then the modulation index (M)=
defined as
. Usually is varied and is kept fixed. Also 0 1.
M1 D1
M4D4
M3D3
M5D5
M6 M2
D2
R1 R2 R3
A B C
N
Vd/2
Vd/2
O
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Sinusoidal PWM Inverters(2)If is the frequency of the sine and the frequency of the carrier, =
is called the carrier
ratio or the frequency ratio. For a three-phase sine-PWM inverter, = 9,15,21,27,3, =odd. This eliminates the even harmonics from the inverter voltage. Usually q is varied with
such that is within a certain band. Normally is around 4-5 kHz. This frequency is a good
compromise between stress level of motor insulation and THD of the motor current. The figure
below shows a typical versus relationship.
fc
fm
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Three-phase PWM waveforms and
harmonic spectrum
E i t l li lt ( i k) d li t (bl k) f 2 kW 4
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Experimental line voltage (pink) and line current (black) for a 2 kW, 4
pole, 60 Hz induction motor running at 1330 rpm in a closed-loop
slip controlled drive using a PWM inverter
Top : No Load . Bottom: Full Load
Experimental line voltage (pink) and line current (black) waveform for a
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Experimental line voltage (pink) and line current (black) waveform for a
2 kW, 4 pole, 60 Hz induction motor running at 1770 rpm in a closed-
loop slip controlled drive using a PWM inverter
Top : No Load . Bottom: Full Load
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Sinusoidal PWM Inverters(3)
If the peak of the sine wave and the frequency of the sine wave are changed simultaneously such
that their ratio is maintained constant, the inverter output voltage/frequency ratio is also kept
constant as they change. Thus a single control signal that controls the amplitude and frequency o
the sine wave is sufficient to obtain v/f control of the induction motor.
The RMS line-line fundamental voltage 1 =3
2 , =
3
22 = 0.612 .
0 1. For RMS line-line voltages of other line harmonic components, the plot and thetable as shown in the next two slides, has to be used as the relationship is not linear as the
fundamental.
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Plot of the normalized fundamental
and some higher harmonic components versus
modulation index (M)
qk=2q 1
3q
G li d h i f li li f
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Generalized harmonics of line-line for a
large q that is a multiple of 3
0.2 0.4 0.6 0.8 1.0
1 0.122 0.245 0.367 0.490 0.612
2 0.010 0.037 0.080 0.135 0.195
4 0.005 0.011
2 1 0.116 0.200 0.227 0.192 0.111
2 5 0.008 0.020
3 2 0.027 0.085 0.124 0.108 0.038
3 4 0.007 0.029 0.064 0.096
4 1 0.100 0.096 0.005 0.064 0.042
4 5 0.021 0.051 0.073
4 7 0.010 0.030
Example of PWM controlled induction motor drive
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Example of PWM controlled induction motor driveIn a three-phase sine-PWM converter, = 300 V, = 0.2, = 39,1 = 12 Hz. a) Calculate
the RMS values of the fundamental-frequency voltage and some dominant harmonics in the line-
line voltages and the THD. b) Calculate next the harmonics in the phase current of an induction
motor connected in delta and the THD for a slip frequency of 2 Hz. The motors equivalent
circuit parameters are 1 =2 = 0.5 , 1=2
= 1 , =35 at 60 Hz.
Harmonic Line-line voltage (V) Harmonic Frequency (Hz)
1 300*0.122=36.6 12 2 = 37 300*0.010=3 12*39= 444
+ 2 = 41 300*0.010=3 12*41= 492
2 1 = 77 300*0.116=34.8 12*77=924
2 + 1 = 79 300*0.116=34.8 12*79=948
3 2 = 115 300*0.027=8.1 12*115=1380
3 + 2 = 119 300*0.027=8.1 12*119=1428
4 1 = 155 300*0.1=30 12*155=1860
4 + 1 = 157 300*0.1=30 12*157=1884
a) From the earlier table the line-line voltages at fundamental and other higher frequencies can
be computed as follows using the values in the highlighted column corresponding to M=0.2
from the table in the previous slide.
Total Harmonic Distortion voltage =2 32 + 2 34.82 + 2 8.12 + 2 302
36.6
= 66.1236.6
= 1.81 or 181%
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b) = 212
=1
6
With this value of slip and inverter frequency of 12 Hz the motor equivalent circuit can be
redrawn as:
V1 =36.6
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Example of PWM controlled induction motor drive (3)
Using the harmonic equivalent circuit as shown above the harmonic currents can be computed as
37 =3
2 0.2 37= 0.2 A
39 =3
2 0.2 39= 0.18 A
77 =34.8
2 0.2 77= 1.13 A
79 =34.8
2 0.2 79= 1.10 A
115 =8.1
2 0.2 115= 0.176 A
117 =8.1
2 0.2 117= 0.170 A
155 =30
2 0.2 155= 0.484 A
157 =30
2 0.2 157= 0.478 A
Total Harmonic Distortion current
=0.22 + 0.182 + 1.132 + 1.12 + 0.1762 + 0.172 + 0.4842 + 0.4782
11.3
=1.756
11.3= 0.1554 or 15.54%
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Overmodulation (M>1)Vd
Normalized RMS value of the
Fundamental line-line voltage
(with respect to Vd , the dc bus
voltage), versus modulation
index M.
Overmodulation: M =1.55. Pulse dropping due to
overmodulation.
For values of M > 1, the relationship between M and the fundamental value of the RMS voltagebecomes nonlinear (Figure above, left). This is caused as Vm , the sine peak becomes higher
than Vc , the triangle peak (Figure above, middle). This also causes progressively narrowing
pulses and notches with increasing M. Eventually because of dead time requirement of the
switches they are eliminated by the control circuit (Figure above, right). Overmodulation finally
leads to a quasi-square line-line voltage (like the three switch scheme earlier) once M= 3.24.
Sinusoidal Modulation With Regular Sampling
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Sinusoidal Modulation With Regular Sampling
In this scheme a sampled version of the original sinusoidal reference in used. If the sampling is
done only at the positive peaks of the triangle it is called symmetrical sampling (Fig. a above).
If the sampling is done at both positive and negative peaks of the triangle it is called
asymmetrical sampling (Fig. b above). The PWM pattern can then be stored for different
values of modulating index M in a non-volatile memory. This scheme requires much
less memory compared to naturally sampled PWM scheme when implemented using amicrocontroller. It also solves arameter drift, dc offset etc. associated with analo electronics.
Optimal Pulse width Modulation
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Optimal Pulse-width Modulation
(Programmed Harmonic Elimination)Pre-determined notches are introduced in the switching patterns to eliminate certain harmonics
like 5,7,11,13 etc. in the inverter output voltage. The notches are introduced in such a way that the
quarter-wave symmetry is preserved. Because of the quarter-wave symmetry all cosine terms in
the Fourier series will be absent.
For example, if we want to eliminate the 5t
and the 7t
harmonic and keep the fundamental at a
certain value , then from the definition of Fourier series
=4
sin
2
0.
One needs to introduce three notches in the quarter cycle to write the following three equations:
= 1 =4
sin 1
0
4
sin +21
4
sin
4
sin3
3
32
=
4
cos1 + 1 cos1 + cos2 cos3 + cos2 cos3=
4
1 2cos1 + 2 cos2 2cos3
0 = 5 =4
51 2cos 51 + 2 cos 52 2cos 53
0 = 7 =4
71 2cos 71 + 2 cos 72 2cos 73
Solving the three equations will yield 1,2,3.
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Programmed Harmonic Elimination (2)
M1 D1
M4D4
M3D3
M5D5
M6 M2
D2
R1 R2 R3
A B C
N
Vd/2
Vd/2
O
If such a gating signal is applied to the inverter in the figure above (left)the normalize voltage
with respect to
2
will look like the figure above (right)
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Programmed Harmonic Elimination (3)
1,2,3 can be pre-computed as a function of percentage of the maximum fundamental voltage
and stored in the memory as a look-up table. The figure above shows a plot using the data from
the table.