INVERTERS (DC-AC Converters)

1. INVERTERS (DC-AC Converters)

2. Square wave inverters (1-phase) • Amplitude and harmonic control (quasi square wave) • Total Harmonic Distortion INVERTERS for SEE 4433 • Pulse Width Modulation (PWM) (1-phase) • Bipolar and unipolar • Harmonics • 3-phase inverters • Square wave (six-step) • PWM

3. INVERTERS In SEE 4433, regardless of the control method, the circuit topology of single-phase inverter are of two types: Full-bridge and half-bridge A. Full-bridge inverter Q1 Q3 D1 D3 • Upper and lower switches cannot be ON simultaneously • Depending on the switches positions, there can be 3 possible output voltage: • (Vdc), (-Vdc) and 0 + vo − Vdc io Q4 D4 Q2 D2

4. INVERTERS In SEE 4433, regardless of the control method, the circuit topology of single-phase inverter are of two types: Full-bridge and half-bridge B. half-bridge inverter • The capacitors equally devide the voltage Vdc • Depending on the switches positions, the output voltage can be either (Vdc/2) or (−Vdc/2) Q1 D1 C1 + Vdc/2 − + vo − Vdc C2 + Vdc/2 − D2 Q2

5. INVERTERS Square-wave inverter (with full-bridge) S1, S2 S1, S2 S3, S4 • It can be shown that: • Can also be implemented using half-bridge inverters

6. INVERTERS Square-wave inverter (with full-bridge) Current path for inductive load: Q1 Q3 D1 D3 + vo − Vdc io Q4 D4 Q2 D2 SEE EXAMPLE 8-2

7. INVERTERS TOTAL HARMONIC DISTORTION • THD is used to measure the quality of the AC voltage or current • The closer the waveform to sinusoidal, the smaller is the THD • Can be applied to voltage or current SEE EXAMPLE 8-3

8. INVERTERS Quasi-square wave inverter – Amplitude and harmonic control Duration of ZERO output voltage is introduced and it can be shown that: • Amplitude of the fundamental component can be controlled (by controlling α) • Certain harmonic contents can be eliminated (also by controlling α !) Amplitude and harmonics cannot be controlled independently Cannot be implemented using the half-bridge inverter.

9. INVERTERS Quasi-square wave inverter – Amplitude and harmonic control Fourier series of the output voltage is given by: where

10. INVERTERS Quasi-square wave inverter – Amplitude and harmonic control Amplitude control Amplitude of fundamental component:  By changing α the amplitude of the fundamental will change Harmonic control The nth harmanic can be eliminated if its amplitude made zero For example, the amplitude of the third harmonic (n=3) is zero when α = 30o

11. INVERTERS Quasi-square wave inverter – Amplitude and harmonic control Simultaneous control of amplitude and harmonic In order to be able to control amplitude and harmonic simultaneously, variable Vdc has to be added Controlled via DC link Variable DC DC-DC converter Fixed DC voltage Load Inverter

12. INVERTERS Quasi-square wave inverter – Amplitude and harmonic control Switching signals (full-bridge inverter)        2 0 0  2 S1 S1 S2 S2 S3 S3 S4 S4

13. INVERTERS Pulse Width Modulation Is a method used to control the output voltage (amplitude and frequency) of an inverter by modulating the width of the pulses of the output waveform • Main advantages of PWM control: • Filter requirement is reduced • Amplitude and frequency can be control independently • Significant reduction in THD of load current (inductive load) • Disadvantages of PWM control: • More complex control circuit • Higher switching losses • In SEE4433, two switching scheme for single-phase inverter will be discussed: • Bipolar switching scheme • Unipolar switching scheme

14. INVERTERS Pulse Width Modulation Bipolar switching scheme (vsine > vtri) : Q1 and Q2 ON; vo=Vdc (vsine < vtri) : Q3 and Q4 ON; vo=-Vdc

15. INVERTERS Pulse Width Modulation Bipolar switching scheme fsine Frequency modulation index ftri Vm,tri Vm,sine Amplitude modulation index The amplitude of the fundamental component of vo is proportional to ma: V1=maVdc

16. INVERTERS Harmonics in PWM single-phase inverter

17. INVERTERS Harmonics in PWM single-phase inverter : Bipolar switching scheme • If mf is chosen as odd integer with the triangular wave synchronize with the modulating signal, then the PWM output is an odd quarter-wave symmetry. • an = 0 and bn exist only for odd  Graphically, this can be represented using frequency spectrum diagram : OR using a normalized Fourier coefficients table:

18. INVERTERS Pulse Width Modulation Unipolar switching scheme (vsine > vtri) : Q1 ON, Q4 OFF; va= Vdc (vsine < vtri) : Q1 OFF, Q4 ON; va= 0 (-vsine > vtri) : Q3 ON, Q2 OFF; vb= Vdc (-vsine < vtri) : Q3 OFF, Q2 ON; vb= 0 Vab = va - vb

19. INVERTERS Harmonics in PWM single-phase inverter : Unipolar switching scheme • The frequency of the output voltage is doubled. • If mf is chosen as even integer then the first cluster of harmonics appear around 2mf(the harmonic at 2mf itself is zero) Graphically, this can be represented using frequency spectrum diagram : Or using a normalized Fourier coefficients table:

20. INVERTERS Harmonics in PWM single-phase inverter : Comparison between square wave and PWM SQUARE-WAVE • Contains harmonics at relatively low frequency: 3rd, 5th, 7th, 9th, etc. • In order to improve the THDV , a low pass filter can be employed  filter will be bulky since cutoff frequency is low  difficult to remove harmonics since at the same time must ensure fundamental component is not attenuated. PWM • Harmonics appear around mfwhich is further away from fundamental. • To improve THDV, filter with higher cutoff can be used  smaller in size  easier to filter out harmonics. PWM mf = 21 Square wave 1 3 5 7 9 11 13 n 1 3 5 7 9 11 13 15 17 19 21 23 25

21. INVERTERS Three-phase inverters Six-step inverter S1 S5 S3 S1 S2 S3 A Vdc S4 n B S5 C S6 S4 S2 S6 Vdc vAo o • THDV of line-line and line-n are both 31% • THDI of line current depends on load, however it will be smaller than the single phase vBo vCo vAB vAn

22. INVERTERS Three-phase inverters PWMinverter mfis chosen to be multiple of 3 so that the harmonic at multiple of 3, including mf (and its multiple) are suppressed (or canceled out) in the line-line voltage