Inverters

Introduction

• DC to AC converters

• Change DC input voltage to a symmetric ac

output voltage of desired magnitude and

frequency

• Ideal inverter output waveform should be

sinusoidal

• Simplest form of output: square wave

• Output voltage could be fixed or variable

• Fixed or variable frequency

• Normally the input DC voltage is fixed

• Variable output can be produced by pulse

width modulation (PWM) control within the

inverter

• Low and medium power applications square

wave voltages can be accepted

• For high power applications, low distorted

sinusoidal waveforms are required

• Harmonics can be reduced by using high speed

power semiconductor devices and switching

techniques

• Typical input sources:

– DC batteries

– Wind generator

– AC rectified output

• Used in industrial applications

– Variable speed ac motor dries

– Induction heating

– Standby power supplies

– UPS

Simple Example

Inverter

Requirement on the Switching

Network Switching network must be able to:

• Connect the load directly across the DC source

• Reverse connect the load across the DC source

• Short the load

Simple Example

• Load requires ac voltage of 50Hz

• Connect the load across the dc source for certain period of time (10ms)

• Reverse connect the load for an equal duration of time (10ms)

• Bipolar square wave across the load of period 20ms (50Hz)

• Square wave output having a fundamental frequency and harmonics can be found using Fourier series expansion

• Can remove harmonics using filter

• RL load

• 4 quadrant operation

• Should be able to provide +ve and –ve current

• Provide +ve and –ve voltages

Voltage Fed Inverter (VFI)

• Also called voltage source inverters (VSI)

• Input voltage remains constant

• Capacitor acts as input to the inverter

Half Bridge Inverter

• Triggering signal of switch 1 should be a logic

invert of the triggering signal of switch 2

• When diodes conduct, energy is fed back to

the dc source

• Diodes are called feedback diodes

• Transistor conducts for only 90

𝑎) 𝑉𝑜1(𝑟𝑚𝑠) = 0.45𝑉𝑠 = 0.45 × 48 = 21.6𝑉

𝑏) 𝑃𝑜 =𝑉𝑜

2

𝑅 =

(0.5 × 48)2

2.4 = 240𝑊

𝑐) 𝐼𝑝 = 242.4 = 10𝐴; 𝐼𝑎𝑣𝑔 = 0.5 × 10 = 5𝐴

𝑑) 𝑉𝐵𝑅 = 2 × 24 = 48𝑉

Single Phase Full Wave Inverter

Mode 1:𝑄1, 𝑄2 ON

Inductor energizes in forward current

Mode 2:𝐷3, 𝐷4 ON

Inductor de-energizes in forward current

Mode 3:𝑄3, 𝑄4 ON

Inductor energizes in reverse current

Mode 4:𝐷1, 𝐷2 ON

Inductor de-energizes in reverse current

Output Voltage

• Output RMS Voltage

• Fourier Series Expansion

• Fundamental Voltage RMS

Example

Repeat the same example of single phase half

wave inverter for single phase full wave inverter

Modulation Strategies

• Improve the

output waveform

by increasing the

switching

frequency

• Increase the

number of pulses

• Shape is more

sinusoidal

Voltage Control of Single Phase

Inverters

• Necessary to control the output voltage of

inverters:

– To compensate for changes in input dc voltage

– To fulfil the requirements of ac load

– To regulate voltage of inverter

– To satisfy the constant volts and frequency control

requirement

• Most efficient method to controlling the gain is

though pulse width modulation (PWM) control

Pulse Width Modulation Control

• Controlling the output voltage by controlling

the width of pulses

– Single pulse width modulation

– Multiple pulse width modulation

– Sinusoidal pulse width modulation

Single Pulse Width Modulation

Gate Signal for Transistor 𝑄1

Gate Signal for Transistor 𝑄4

𝐹𝑠𝑤 =1

𝑇𝑠𝑤

Single PWM

• One pulse per half cycle

• Changing the width of the pulse controls the output voltage of inverter

• Use comparator to compare the reference dc voltage 𝑉𝑟 with carrier signal 𝑉𝑐 (triangle waveform)

• Gate signal is generated

• Fundamental frequency of output voltage depends on frequency of reference signal

• By varying 𝑉𝑟 from 0 to 𝑉𝑐 , pulse width can be varied from 0 ° to 180°.

Single PWM

• Control variable: Amplitude modulation index:

𝑀 = 𝑉𝑟𝑉𝑐

• The rms value of output voltage:

where a is the pulse width

Multiple Pulse Width Modulation

• Extension of single pulse modulation

• Also called uniform pulse width modulation (UPWM)

• Several pulses of equal distances are used in each half cycle

• Gating signal is generated by turning on an doff the transistors by comparing the reference signal with a triangular carrier wave

• Frequency of reference signal 𝑓𝑟𝑒𝑓 controls output frequency 𝑓𝑜

• Carrier frequency 𝑓𝑐 determines the number of pulses per half cycle p

Multiple PWM

Multiple PWM

• Frequency modulation ratio:

𝑚𝑓 =𝑓𝑐𝑓𝑜

• Number of pulses in each HC:

𝑝 =𝑓𝑐2𝑓𝑜

=𝑚𝑓

2

• The rms value of output voltage:

Multiple PWM

Sinusoidal Modulation

• Multiple PWM has equal distance pulses

• Pulse width of each pulse is varied in proportion

to the amplitude o a sine wave

• Reference signal is a sinusoidal wave

• Several pulses per HC with different pulse

widths

• Most commonly used in industrial applications

𝑀 =𝑉𝑟𝑉𝑐

Effect of Switching Frequency