1. Inverters
Dr John Fletcher

2. Basics Inverters are DC to AC converters
We can use inverters to generate
A dc supply
Single-phase AC supply
Three-phase AC supply
from a single dc source.
The basic building block is the inverter ‘leg’.
An inverter leg is shown. Vdc is the input, Vout the output.

3. Inverter switching T1 and T2 are NEVER turned on together. Why?
T1 and T2 are switched using PWM in a complementary manner (T2 ON, T1 OFF)
Vout is then a switched waveform, just like the basic step-down converter earlier.

4. Pulse-width Modulation
T1,on
T2,on

5. Current Paths Current path if T2 ON, or T1 and T2 OFF
Two switches with freewheel diodes provides uni-directional voltage and bi-directional current control.
Only when T1 is ON is energy supplied from the source.
When T2 ON, a zero voltage loop is applied.
With positive current flow →
Current path if T2 ON, or T1 and T2 OFF
Current path if T1 ON

6. Current Paths
When T1 is ON (or T1 and T2 OFF) energy has to be absorbed by the source.
When T2 ON, a zero voltage loop is applied.
With negative current flow →
Current path if T2 ON
Current path if T1 ON, or T1 and T2 OFF

7. Bridge Leg V-I graph
The basic bridge leg can operate in two quadrants of the VI graph. I V

8. Average Output Voltage
A single inverter leg produces an average output voltage:
Define a duty cycle or modulation index
Hence
m must be between 0 and 1.
We can make m vary in time therefore we can produce any voltage and any frequency we desire (within the bounds fixed by the switching frequency and Vdc).

9. Switching Frequency
Switch frequency (1/Ts) of the pulse-width modulated (PWM) signal is usually chosen as high as possible to reduce current ripple in the load.
Max switching frequency is limited by losses and the ability to manage those device losses (remember lecture 2?)
In low power circuits, switching frequency can be as high as ~1 MHz
High power circuits (say >500kW) may use frequencies of 1kHz or less.

10. Single-phase H-bridge
Two inverter legs connected in parallel.

11. Single-phase H-bridge
From previous discussion on inverter legs
So the average output voltage
applied to the load
For a sinusoidal output (ma-mb) must vary sinusoidally.

12. Single-phase H-bridge
The modulation indices of both inverter legs vary sinusoidally in time with a modulation depth, m (0<m<0.5) and an offset. If we apply (2) and (3) to (1) we get
That is, the modulation depth, m, sets the magnitude of the ac output voltage and ωt sets the frequency.
Notice that the dc offset in the modulation indices is co-phasal and does not appear in the output voltage.
We can control the magnitude and frequency.

13. H-Bridge V-I graph
The H-bridge can operate in all four quadrants of the VI graph.
It can generate both polarities of voltage and control both polarities of current. I V

14. PWM Generation Ts t1 t2
(t1-t2)/2
Ts/2 m1 m2
Vload
Leg 1 output
Leg 2 output
Carrier waveform
Modulation indices of each leg are compared with a triangular carrier waveform.
Intersects define the turn-on and turn-off instant of each bridge leg.
With this scheme load sees two output voltage pulses per switching cycle.
Harmonic spectrum of the applied voltage has components around multiples of the switching frequency.

15. Three-phase inverters
Now if:

16. Three-phase inverters
Inserting modulation indices into (1-3) gives:
Three-phase output voltages
The circuit is a pulse-width modulated voltage source inverter (VSI).

17. Six-step Operation
The previous section looked at pulse-width modulated VSIs.
PWM VSIs can be used at all but very high power drives.
For high-power drives, often the switches are turned ON and OFF once during one fundamental cycle rather than many 100s of times with PWM.
The output voltage waveform is then ‘square wave’.

18. Six-step Line Voltages
Line voltages are stepped
Fourier analysis of output voltages gives
and line voltages
and phase voltage

19. Six-step Inverter Currents
Inverter currents are obviously non-sinusoidal. (Note: this load is inductive)
Result from the harmonic voltages in the output line voltage.
Harmonic currents causes additional loss components.
And also torque ripple if the load is a machine.