Inverter Topology and Control Strategies

7/28/2019 Inverter Topology and Control Strategies

1/34

Basic Three Phase Voltage Source

Inverter Topology


2/34

Two Simultaneous Switch Gating

Scheme


3/34

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


4/34

Two Switch Gating Scheme-Phase Voltage

Spectra


5/34

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


6/34

Two Switch Gating Scheme-Line Voltage

Spectra


7/34

Three Switch Gating Scheme


8/34

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


9/34

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


10/34

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


11/34

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.


12/34

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.


13/34

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


14/34

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


15/34

Problem continued

V1 =117


16/34

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.


17/34

Inverter Topologies For Induction Motor

Drives


18/34

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.


19/34

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


20/34

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


21/34

Three-phase PWM waveforms and

harmonic spectrum

E i t l li lt ( i k) d li t (bl k) f 2 kW 4


22/34

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


23/34

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


24/34

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.


25/34

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


26/34

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


27/34

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%


28/34

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


29/34

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%


30/34

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


31/34

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


32/34

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.


33/34

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)


34/34

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.

Date post:	03-Apr-2018
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Inverter Topology and Control Strategies

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