02 pwm inverters part ii

8/12/2019 02 PWM Inverters Part II

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Pulse-Width-Modulated

PWM Inverter Part IICha ter 10 or 6

Pre ared b

Dr. Mohammad Abdul MannanAssistant Professor, Department of EEE

mer can n erna ona n vers y - ang a es



Current Source Inverter (CSI)

van age o as ompare1. Since the input dc current is controlled and limited, miss

firin of switchin devices or a short circuit would not be

series problems;

2. The peak current of power devices is limited;. e commu a on c rcu s or yr s ors are s mp er;

4. It has ability to handle reactive or regenerative load

without feedback or freewheeling diodes.

Disadvantage of CSI as Compared VSI

1. A CSI requires a relative large reactor (or inductor) to

exhibit current-source characteristics,

2. An extra converter stage is required to control the

,

3. The dynamic response is slower, and

4. Due to current transfer from one pair of switches to

another, an output filter is required to suppress the output

voltage spikes.



Single-Phase Transistorized CSI

e c rcu agram o a s ng e-p ase rans s or ze s s own nFig. 10-36(a).

Since there must be a continuous current flow from the source,

two switches must always conduct – one from upper and onerom ower sw tc es.

The conduction sequence is 12, 23, 34, and 41.

reverse voltage on the transistors.



The gate signals and output current waveshape is shown in

Fi . 10-36 b and c .

When two devices in different arms conduct, the source current

I L flows through the load.

When two devices in the same arm conduct, the source current

is bypassed from the load.rom q. . , e oa

current can be expressed as

∑== ,..5,3,1 sin2sin)( n t nn

nt oi ω π



Single-Phase Thyristorized CSI

e c rcu agram o a s ng e-p ase rans s or ze sshown in Fig. 10-36(a).

1 2 , 1

and C 2 are charged with polarity as shown.

Firin of T and T reverse biases T and T . T and T are

turned off by impulse commutation.



The current now flows through

T 3C 1 D1, load, and D2C 2T 4.The capacitors C 1 and C 2 are

sc arge an rec arge a a

constant rate determined by

= m

When C 1 and C 2 charged to the

load voltage and their currentsa s o zero, e oa curren

will be transferred from diode

.



Firing of T 1 and T 2 reverse

biases T 3 and T 4. T 3 and T 4 are

turned off by impulsecommutation.

The current now flows through

T 1C 1 D3, load, and D4C 2T 2.1 2

discharged and recharged at a

constant rate determined b

load current, I m= I L.

load voltage and their currents

falls to zero, the load currentwill be transferred from diode

D3 to D1 and D4 to D2.

e capac ors are now rea y

to turn off T 1 to T 2.



Three-Phase CSI

. - -current-source inverter.

The wave forms for gating signals

and line currents for a wye-

connected load are shown in Fi .

10-38(b).

At any instant only two thyristors

con uc a e same me. ac

device conducts for 120o.



The current for phase a can be expressed as:

∑∞

=

+=⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

,..5,3,1)79.10()

6(sin

6cos

2)(

nt nn

n

L I

t ai π ω π

π

The PWM, or SPWM, or MSPWM technique can be

a lied to var the load current and to im rove the ualit

of its waveform.

The current source inverter (CSI) is a dual of voltagesource inverter (VSI).

The line-to-line of a VSI is similar in shape to the line

.



Filter to Reduced Output Harmonics

o re uce e ou pu armon cs, ou pu ers are necessary.Fig. 10-40 shows the commonly used output filters.

A C -filter is very simple, but it draws more reactive power.

An LC -filter as in Fig. 10-40(b) can eliminate only onerequency.

A properly designed CLC -filer as in Fig. 10-40(c) is more

less reactive power.



Pulse Width Modulated (PWM) Inverter

quare-wave nver ers su ers rom wo ma or raw ac s:(i) The output voltage of the inverter cannot be controlled for a fixed-source

voltage. To achieve voltage control, the inverter must be fed either from

controlled ac-dc or dc-dc converter.

(ii) The output voltage contains appreciable harmonics (low-frequency range).

Also THD is ver hi h.

The problem of square-wave inverter can be minimized by using PWM

technique.

PWM techniques allows:(i) Variation of output voltage within the inverter by varying the gain of the

. .

(ii) Variations of output frequency either by varying the number of pulses per

half-cycle of the output or by varying the period for each half-cycle with fixednum er o pu ses n eac a -cyc e.

(iii) Simultaneous variation of out voltage and frequency is also possible. So

that V/f ratio can be kept constant. This feature is required in induction motor-

drives.

(iv) Control of harmonics at the output of the inverter.



Why the Output Voltage is Required to Control in

The control of output voltage is required in industrial applications for the

following reasons:

• To cope with the variation of dc input voltage,

• For voltage regulation of inverter, and

• For the constant volts/fre uenc control re uirement

In PWM technique the gate signal of switching devices of an inverter is

obtained b com arin a reference si nal with a carrier si nal.

The magnitude of the output voltage depends on the amplitude modulation

index and the frequency of the output voltage depends on the frequency of

.

Thus, the magnitude of output voltage can be controlled by varying the

modulation index and the frequency of output voltage can be controlled by

vary ng e requency o re erence s gna .



Control the Out ut Volta e B Var in the

Inverter Gain

There various pulse-width-modulation (PWM) techniques

1. Single-pulse-width-modulation,

2. Multiple-pulse-width-modulation,

3. Sinusoidal-pulse-width-modulation (SPM),4. Modified sinusoidal-pulse-width-modulation

,

5. Phase-displacement control



Single-Pulse-Width-Modulation

-is varied to control the inverter output voltage.

The followin fi ure shows the eneration of atin si nals and

output voltage of single-pulse full-bridge inverters.

The gating signals are generated

b com arin a rectan ular

reference signal of amplitude, A r, with a triangular carrier

wave o amp tu e, c.



The frequency of fundamental output voltage is determined by

the fre uenc of reference si nal.

By varying A r from 0 to A c, the pulse width, δ , can be varied

from 0o to 180o.

The ratio of A r to A c is control variable and defined as the

amplitude modulation index.The amplitude modulation index, or simply modulation index

is given by M = A r/ A c.

The rms output voltage can be found from:

2/1

π δ

π

δ π

ω π sV t d sV oV =∫

+

−

=

⎥⎥⎥⎥⎥

⎢⎢⎢⎢⎢

2)(

)(222

The Fourier series of output voltage

ields:∑

==

,..5,3,1sin

2sin)(

nt nn

n

st ov ω

π



Fig. 10-12 shows the harmonic

, .

The dominant harmonic is the

third, and the distortion factor

increases significantly at low

output voltage.

Example [2, p.654] A single-phase full-wave inverter uses

-

third harmonics from the output wave. Determine the width of pulse, .

Solution: From the Fourier series, we obtain the rms value of

third harmonics is:34 δ V 2233 π

To eliminate the third harmonics, V 3 =0, thus 023sin =δ °=180

23δ

°=°×= 12018032δ



Multiple-Pulse-Width-Modulation

each half-cycle of output voltage.

The eneration of atin si nals for turnin on and off of

transistor is shown in Fig. 10-13(a) by comparing a reference

signal with a triangular carrier wave.The frequency of reference signal, f r, sets the output frequency,

f o, and the carrier frequency, f c, determines the number of

- , .

The rms output voltage

modulation index (or

ratio .This type of modulation

is also known as uniform

pulse-width modulation

(UPWM).



The number of pulses per half-cycle is found

from: 22 f

mc f p ==

Where m f = f c/ f o is defined as the frequency modulation ratio

or index . The variation of modulation index M from 0 to 1

varies the pulse width from 0 to π / p and the output voltage

from 0 to V s.If δ is the width of each

pulse, the rms output δ δ π

p p

p =+

= ⎥⎥⎤

⎢⎢⎡

2/12)/(

22vo age can e oun

from: δ π π p− ⎥⎥

⎦⎢⎢

⎣ 2)/(2

The general form of Fourier

series for the instantaneous

∞= sin)( t n Bt v ω

= ,..5,3,1n



If the positive pulse of mth pair starts at ω t = m and ends at

ω t = m+π, the Fourier series coefficient for a pair of pulses is:

⎥⎥⎥⎥⎤

⎢⎢⎢⎢⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

∫ + ∫ +++−= )(cos)(cos1 δ α α

δ α π α π ω ω ω ω π

mm

mm

t td nt td nnb

⎥⎥⎥

⎦⎢⎢⎢

⎣ ⎥

⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ ++−+=2

sin2

sin2

sin2 δ α π δ α δ

π mnmnnn sV

The coefficient B n can be found by adding the effects of all

pulses:++−+= ⎥

⎤⎢⎡

⎟ ⎞

⎜⎛

⎟ ⎞

⎜⎛

pnnnsV B sinsinsin

2 δ α π δ α δ

= ⎦⎣ ⎠⎝ ⎠⎝

m 1



Advantages(i) Distortion factor are reduced com ared to sin le- ulse-

modulation.

(ii) As value of “p” increases amplitudes of lower harmonicre uces.

Disadvantagesncrease num er o pu ses, sw c ng osses are

increased.



Sinusoidal Pulse-Width-Modulation (SPWM)

proportion to the amplitude of a sine-wave evaluated at the

center of the same pulse.

By comparing a sinusoidal reference signal of frequency, f r, (of

amplitude, A r), with a triangular carrier wave of frequency, f c,o amp u e, c , e ga ng s gna s are genera e , as s own

in Fig. 0-15(a).

that two transistors

of the same arm

and Q4) cannot

conduct at the sametime, the

instantaneous output

the following figure.



If δ m is the width of mth pulse, the=

pmV V

δ

=m 1The Fourier series for the ∞

= sin)( t n Bt v ω ns an aneous ou pu vo age s: = ,..5,3,1n

2 ⎥⎤⎢⎡ ⎟ ⎞⎜⎛ ⎟ ⎞⎜⎛ p nV δ δ δ

..,.........7,5,3,1for 1 222

==

−=⎥⎥⎦⎢

⎢⎣

⎟⎟

⎠⎜⎜⎝

⎟⎟

⎠⎜⎜⎝

nm

mmnn π



The peak of fundamental output voltage for PWM and SPWM

The maximum eak am litude of the fundamental out ut

.or 1=

sm

voltage as V m1(max) = V s (when d =1).

u accor ng o e re a on o rms va ue o un amen a

output of bridge inverter, V m1(max) could be as high as

π= - s π s

Overmodulation ( d >1) basically leads

-

more harmonics as compared to

operation in the linear range (with d ≤1.0).

Overmodulation is normally avoided in

app ca ons requ r ng ow s or on

[e.g. UPS].



The same gating signals can be generated by using unidirectional

trian ular carrier wave as shown in Fi . 10-15 b Fi . 9.17 b of

Ref. 2].

Advantagesi The distortion factor is reduced si nificantl com ared to

that of multiple-PWM.(ii) SPWM eliminates all harmonics less than or equal to 2 p-1.

For p=5, the lowest-order harmonics is ninth.

(iii) Lower-order-harmonics is reduced significantly.

Disadvantages(i) With increased number of pulses, switching losses are

ncrease .

(ii) Control scheme is more complex.



Modified Sinusoidal Pulse-Width-Modulation (MSPWM)

n ec n que, e w o pu ses a are nearer e peaof the sine wave do not change significantly with the variation of

modulation index.

Thus, the SPWM technique can be modified so that the carrier

wave is applied during the first and last 60o

intervals per half-cyc e e.g. o to o an o to o . s type o mo u at on n

known as MSPWM and shown in Fig, 10-18.

half-cycle is found from:

36/ +=

The fundamental component is

characteristics are improved. It

reduces the number of

switching of power devices and

also reduces switching losses.



Phase-Displacement Control

Voltage control can be obtained by using multiple inverters

an summ ng e ou pu vo ages o n v ua nver ers.

A single-phase full-bridge inverter can be perceived as the sum

- .



A 180o phase displacement produces an output voltages as

-

angle of produces an output as shown in Fig. 10-20(e).

The rms output voltage:π β

sV oV =

Fig. 10-20



The instantaneous voltages equation can be expressed as

∑== ,..5,3,1sin

nt nn saov ω π ∑= −= ,..5,3,1

)(sinn

t nn sbov β ω π

∑∞

=−−=−= ⎥

⎦

⎤⎢⎣

⎡

,..5,3,1

)(sinsin2

n

t nt nnVs

bovaov

abv β ω ω

π

∑∞

=−=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

,..5,3,1)

2(cos

2sin4

nt nn

nVs

abv β ω β

π

The rms value of the fundamental output

volta e is: sin4

1nVsV =

The above equation indicates that the output voltage can bevaried by varying the delay angle .

This type of control is especially useful for high-power

app ca ons, requ r ng a arge num er o rans s ors n

parallel.



Advanced Modulation Techni ues

e w c s mos common y use , su ers

from drawbacks (e.g. low fundamental outputvo age .

The other techniques that offer improved

per ormances are:

• Trapezoidal modulation,

• a rcase mo u a on,

• Stepped modulation,

• armon c n ec on mo u a on, an

• Delta modulation



Delta ModulationIn delta modulation trian le wave is allowed to oscillate within a

defined window V above and below the reference sine wave v r.

The inverter switching function, which is identical to the output

vo age v o s genera e rom e ver ces o e r angu ar wave v c as

shown in Fig. 10-27. It is also known as hysteresis modulation.

If the frequency of the modulating wave is changed keeping the slope of thetriangle wave constant, the number of pulses and pulses widths of the

modulated wave would change.

e un amenta output

voltage can be up to V s and

is de endent on the eak

amplitude A r and frequency

f r

of the reference voltage.

e e a mo u a on can

control the ratio of voltage

to fre uenc v/f control ,

which is a desired feature in

ac motor control.



Harmonic Reductions-

inverters can be eliminated by introducing a pair of

symmetrically placed bipolar voltage notches as shown in Fig.

10.28.

The Fourier series of output voltage can be expressed as)46.10(

,..5,3,1sin)( ∑

==n

t nn Bt ov ω



1 2/ )(sin2 )(sin)(sin

4t td nt td nt td nsV

n B α π α ω ω α

α ω ω ω ω π ∫ ∫+∫−= ⎥⎥⎤

⎢⎢⎡

)47.10(2cos2

1cos214

n

nnsV

n Bα α

π

+−=

⎦⎣

Eq. (10.47) can be extended to m notches per quarter-wave, thenthe expression of n becomes:

4 ⎤⎡⎛ V

...

4

cos

3

cos

2

cos

1

cos⎥

⎥

⎦⎢

⎢

⎣

⎟

⎠

⎜

⎝

−−−=π

nnnn

nn



The third and fifth harmonics would be eliminated if B = B =0

and Eq. (10.47) gives the necessary equations to be solved.

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −−==+− 5.01

3cos1cos31

2or 0

23cos2

13cos21 α α α α

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

−−

==+− 5.025cos1

cos31

1or 025cos215cos21 α α α α

ese equat ons can e so ve terat ve y y n t a y assum ng

1 = 0 and repeating the calculation for 1 and 2. The result is

= o = o

2 . , 2 . .

A pair of unwanted harmonics at the output of single phase



A pair of unwanted harmonics at the output of single-phase

inverters can also be eliminated by introducing a pair of

symmetrically placed unipolar voltage notches.With unipolar voltage notches, the co-efficient B n is given by

1

0

2/

2

)(sin)(sin4

t td nt td nsV n B α π

α ω ω ω ω π ∫ ∫+=⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

)49.10(2cos

1cos14

n

nnsV

n Bα α

π

+−=

02

3cos1

3cos1 =+− α α 02

5cos1

5cos1 =+− α α

The result is

= o

and

2 = 37.97o.



The modified sinusoidal PWM techniques can be applied to

effectively in the output voltage as shown in Fig. 10-30.

02 pwm inverters part ii

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