11. Inverters
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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