INVERTERS

INTRODUCTION

• Converts DC to AC power by switching the DC input voltage (or current) in a pre-determined sequence so as to generate AC voltage (or current) output.

Half-bridge Inverter

• Consists of 2 choppers, 3-wire DC source• Transistors switched on and off alternately• Each provides opposite polarity of Vs/2 across the load

Half-bridge Inverter

• When Q1 ON When Q2 ON

When the load is highly inductive

Single-phase full-bridge inverter

• Consists of 4 choppers and a 3-wire DC source• Q1-Q2 and Q3-Q4 switched on and off alternately• Need to isolate the gate signal for Q1 and Q3 (upper)• Each pair provide opposite polarity of Vs across the load

Single-phase full-bridge inverter

Load current for a highly inductive load

For resistive load

Three-phase inverter

•Consists of 6 transistors and 6 diodes •Conducts for 120° or 180°•A three-phase inverter with star connected load is shown

180° Conduction Mode

Mode 1 Operation

1

1

1

32 223

2 323

eq

s s

eq

san cn

sbn

R RR R

V ViR R

Vi Rv v

Vv i R

03

t

Q1, Q5, Q6 conduct

Mode 2 Operation

2

2

2

32 223

23

2 3

eq

s s

eq

san

sbn cn

R RR R

V Vi

R R

Vv i R

Vi Rv v

23 3

t

Q1, Q2, Q6 conduct

Mode 3 Operation

23

t

3

3

3

32 223

223

eq

s s

eq

an bn

scn

R RR R

V ViR R

iv v

Vv i R

Q1, Q2, Q3 conduct

Waveforms for 180 Conduction

Phase Voltages for 180 Conduction

Fourier Series for Line-to-Line Voltages

1

5 56 6

56 6

1,3,5,...

( cos( ) sin( ))2

1 ( ) ( )

4 sin( )sin( )2 3

4 sin sin ( )3 6

oab n n

n

n s s

sn

sab

n

av a n t b n t

b V d t V d t

V n nbn

V nv n tn

For the other Line-to-Line Voltages

1,3,5,...

1,3,5,...

4 sin sin ( )3 2

4 7sin sin ( )3 6

sbc

n

sca

n

V nv n tnV nv n tn

Line-to-Line rms Voltage

12 23

2

0

2 ( )2

2 0.81653

L s

L s s

V V d t

V V V

Phase Voltages (Y-connected load)

1,3,5,..

1,3,5,..

1,3,5,..

4 sin( )sin( )33

4 2sin( )sin ( )3 33

4 4sin( )sin ( )3 33

saN

n

sbN

n

scN

n

V nv n tnV nv n tnV nv n tn

180° Conduction Mode

Phase

voltages

Line voltages

Voltage control of single phase inverters

• External control of ac output voltage• External control of dc input voltage• Internal control of inverter

External control of ac output voltage

• AC voltage control• Series inverter control

External control of dc input voltage• Controlled using fully controlled rectifiers, uncontrolled

rectifiers, choppers, inverters and filters

Internal control of inverters• Pulse width modulation control

Pulse Width Modulation

• Single pulse width modulation• Multiple pulse width modulation• Sinusiodal pulse width modulation• Modified-Sinusoidal-Pulse-Width Modulation• Phase-Displacement Control

Single pulse width modulation

One Pulse per Half-Cycle Pulse Width Controls the Output

Voltage

Carrier and Reference Signals

• Compare the Reference Signal with the Carrier• Frequency of the Reference Signal determines the

frequency of the Output Voltage• Modulation Index = M = Ar/Ac

Gate PulseGate Pulse

Gate Signals and Output

RMS value of the Output Voltage

12

22

2

2 ( )2

0 1800

o s

o s

o s

V V d t

V V

V V

Fourier Series for the Output Voltage

1,3,5,...

4( ) sin sin2

so

n

V nv t n tn

Times and angles of the intersections

11

22

(1 )2

(1 )2

S

S

Tt M

Tt M

Pulse width d (or pulse angle δ)

2 1 Sd t t MT

TS = T/2

Harmonic Profile

Multiple-Pulse-Width-Modulation

Multiple Pulses per Half-Cycle of Output Voltage

Gate Signal Generation

• Compare the Reference Signal with the Carrier• Frequency of the Reference Signal determines the Output

Voltage Frequency• Frequency of the Carrier determines the number of pulses per

half-cycle• Modulation Index controls the Output Voltage

Gate Signals and Output Voltage

Number of pulses per half cycle = p = fc/2fo = mf /2 where mf = frequency modulation ratio

RMS Value of the Output Voltage12( ) / 2

2

( ) / 2

2 ( )2

0 1

02

0

0

p

o s

p

o s

o s

pV V d t

pV V

MTp

pV V

Fourier Series of the Output Voltage

1,3,5,...

2

1

( ) sin

4 3sin sin ( ) sin (4 4 4

o nn

ps

n m mm

v t B n t

V nB n nn

The times and angles of the intersections

( )2

( 1 )2

m sm

m Sm

Tt m M

Tt m M

The pulse width d (or pulse angle δ)

1m m Sd t t MT

TS = T/2p

Harmonic Profile

Sinusiodal pulse width modulationModulating Waveform Carrier waveform

1M1

1

0

2dcV

2dcV

00t 1t 2t 3t 4t 5t

Amplitudes of the triangular wave (carrier) and sine wave (modulating) are compared to obtain PWM waveform. Simple analogue comparator can be used.

Sinusiodal pulse width modulation

waveformmodulating theofFrequency veformcarrier wa theofFrequency M

)(MRatio) (Frequency Ratio Modulation

veformcarrier wa theof Amplitude waveformmodulating theof AmplitudeM

:MDepth)n (ModulatioIndex Modulation

R

R

I

I

p

p

Bipolar Switching

Modulating Waveform Carrier waveform

1M1

1

0

2dcV

2dcV

00t 1t 2t 3t 4t 5t

SPWM With Bipolar Switching• In this scheme the diagonally opposite transistors S1, S2

and S3 , S4 are turned on or turned off at the same time. The output of leg A is equal and opposite to the output of leg B. The output voltage is determined by comparing the control signal, and the triangular signaltching pattern is as follows.

• In the bipolar PWM switching scheme there is only one modulation signal and the switches are turned ‘on’ or turned ‘off’ according to the pattern.

Unipolar switching 1

Unipolar switching scheme

A BCarrier waveform

(a)

(b)

(c)

(d)

1S

3S

pwmV

SPWM With Unipolar Switching• In this scheme, the devices in one leg are turned on or

off based on the comparison of the modulation signal Vr with a high frequency triangular wave.

• The devices in the other leg are turned on or off by the comparison of the modulation signal -Vr with the same high frequency triangular wave.

Harmonic Reduction in Inverters

• Harmonic reduction by PWM • Harmonic reduction by transformer connections• Harmonic reduction by stepped wave inverters

Current Source Inverters

• Input current is constant, but adjustable.• Converts input dc current to an ac current at its output

terminals.• Does not require any feedback diodes.• For ripple free current input L-filter is used before CSI.

Single phase Capacitor Commutated CSI with R load

Voltage and current waveforms for single phase CSI with R load

Single phase Auto-sequential Commutated Inverters (ASCI)

Voltage and current waveforms of single phase ASCI

Modes of single phase ASCI

Mode I Mode II

Equivalent circuit of Mode II

Resonant Converters• Resonant converters are used to convert dc-to-dc through an

additional conversion stage: the resonant stage. Resonant power converters contain resonant L-C networks whose voltage and current waveforms vary sinusoidally during one or more subintervals of each switching period.

• Advantages– natural commutation of power switches– low switching power dissipation– reduced component stresses, which in turn results in an increased

power efficiency and an increased switching frequency– higher operating frequencies result in reduced size and weight of

equipment and results in faster responses; hence, a possible reduction in EMI problems

Contd…

Fig 1 Typical block diagram of soft-switching dc-to-dc converter

Classification of Resonant Converters

• Quasi-resonant converters (single-ended)– Zero-current switching (ZCS)– Zero-voltage switching (ZVS)

• Full-resonance converters (conventional)– Series resonant converter (SRC)– Parallel resonant converter (PRC)

Series-Resonant Circuit

Fig 2 .Series-Resonant Circuit a) circuit b) waveforms

Parallel-Resonant Circuit

• Excited by a current source

Fig 3. Parallel-Resonant Circuit

ZCS Resonant-Switch Converter

Fig 4. ZCS Resonant-Switch Converter

ZCS Resonant-Switch Converter

Fig 5 Voi waveforms of ZCS Resonant-Switch Converter

• Waveforms; voltage is regulated by varying the switching frequency

ZVS-CV DC-DC Converter

Fig 6. ZVS-CV DC-DC Converter

• The inductor current must reverse direction during each switching cycle

Advantages and Disadvantages of ZCS and ZVS

• Power switch is turned ON and OFF at Zero-Voltage and Zero-Current• In ZCS topologies, the rectifying diode has ZVS• ZVS topologies, the rectifying diode has ZCS• Both the ZVS and the ZCS utilize transformer leakage inductances and

diode junction capacitors and the output parasitic capacitor of the power switch.

• Major disadvantage of the ZVS and ZCS techniques is that they require variable-frequency control to regulate the output

• In ZCS, the power switch turns-OFF at zero current but at turn-ON, the converter still suffers from the capacitor turn-ON loss caused by the output capacitor of the power switch.