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- Un-interruptible power supply (UPS), Industrial (induction motor) drives, Traction, HVDC.
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 three-phase output.
Single phase voltage source inverters
Due to symmetry along x-axis
𝑎o = 0 , 𝑎𝑛 = 0
𝑏𝑛 = 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.
𝑉01 = Fundamental rms output output voltage
𝐼0 = rms load current
𝜃1 = 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 single-phase 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 3-phase 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 180o & 120o conduction
1. 180-degree conduction.
Here Q1Q2Q3Q4Q5 & Q6 are the positions of thyristor When 𝑄1 is switched on, terminal a is connected to the positive terminal of dc input voltage.
When Q4 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 60o.
The conduction sequence of thyristor or if we replace 123,234,345,456,561,612. The gating signals are shifted from each other by 60o to get 3-𝜑 balanced voltages.
2. Three phase 120o mode VSI
The circuit diagram is same as that for 180o mode of conduction.
Here each thyristor conducts for 120o.There are 6 steps each of 60o 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. PWM-output 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 square-wave
When n is even cos nπ = 1
When n is odd cos nπ = -1
bn = 4 Vdc/ nπ
4. Quasi-square wave
an = 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 nth Harmonics will be eliminated if ⇒ α = 90o/n
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