Table of contents  
Introduction 
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As we have already aware from the term Inverter which is an Electrical Setup used for daily purposes. In Inverter input DC is converted to AC power by switching the DC input voltage in a sequence so as to generate AC output. The Inverter is the power electronic circuit, which converts the DC voltage into AC voltage. The DC source is normally a battery or output of the controlled rectifier.
Typical Applications Uninterruptible power supply (UPS), Industrial (induction motor) drives, Traction, HVDC.
Inverters can be broadly classified into two types. They are
Voltage source inverter (VSI) with variable DC link
Sometimes, the DC input voltage to the inverter is controlled to adjust the output. Such inverters are called Variable DC Link Inverters. The inverters can have a single phase or threephase output.
Single phase voltage source inverters
Due to symmetry along xaxis
𝑎_{o} = 0 , 𝑎_{𝑛} = 0
𝑏_{𝑛} = 4Vs/nπ
The instantaneous output voltage
& = 0, For n = 2,4.....
The rms value of the fundamental output voltage
Assuming a lossless inverter, the ac power absorbed by the load must be equal to the average power supplied by the dc source.
𝑉_{01} = Fundamental rms output output voltage
𝐼_{0} = rms load current
𝜃_{1} = the load angle at the fundamental frequency
Single phase full bridge inverter
Instantaneous load current 𝑖0 for an RL load
Where θn = tan^{1}(nwL/R)
The rms output voltage is
The instantaneous output voltage in a Fourier series
Three Phase Voltage Source Inverter
When three singlephase inverters are connected in parallel a three phase inverter is formed.
The gating signal has to be displaced by 1200 with respect to each other so as achieve three phase balanced voltages.
A 3phase output can be achieved from a configuration of six transistors and six diodes.
Two type of control can be applied to transistors, they are such as 180^{o} & 120^{o} conduction
1. 180degree conduction.
Here Q_{1}Q_{2}Q_{3}Q_{4}Q_{5} & Q_{6} are the positions of thyristor When 𝑄_{1} is switched on, terminal a is connected to the positive terminal of dc input voltage.
When Q_{4} is switched on terminal a is brought to negative terminal of the dc source. There are 6 modes of operation is a cycle and the duration of each mode is 60^{o}.
The conduction sequence of thyristor or if we replace 123,234,345,456,561,612. The gating signals are shifted from each other by 60^{o} to get 3𝜑 balanced voltages.
2. Three phase 120^{o} mode VSI
The circuit diagram is same as that for 180^{o} mode of conduction.
Here each thyristor conducts for 120^{o}.There are 6 steps each of 60^{o} duration, for completing one cycle of ac output voltage.
Waveform & Harmonics of Square Wave Inverter
In square wave inverters, maximum output voltage is achievable. However there in NO control in harmonics and output voltage magnitude.
A better square wave notching is shown below this is known as PWM technique.
Both amplitude and frequency can be controlled independently. Very flexible.
1. PWMoutput voltage and frequency control
2. Output voltage harmonics
Total Harmonic Distortion (THD) is a measure to determine the “quality” of a given waveform.
Study of harmonics requires understanding of wave shapes. Fourier Series is a tool to analyse wave shapes.
3. Harmonics of squarewave
When n is even cos nπ = 1
When n is odd cos nπ = 1
bn = 4 V_{dc}/ nπ
4. Quasisquare wave
a_{n} = 0, Due to half wave symmetry.
If n is even then bn = 0
If n is odd then
In particular amplitude of the fundamental
In General n^{th} Harmonics will be eliminated if ⇒ α = 90^{o}/n
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