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Ch7 Inverters (converting DC to AC) Introduction ․Converting DC to AC

Ch7 Inverters (converting DC to AC) Introduction ․Converting DC to AC ․ Applications: adjustable-speed AC motor drives. Uninterruptible power supply (UPS). AC appliances run from an automobile battery. 7.1 The full-bridge converter.

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Ch7 Inverters (converting DC to AC) Introduction ․Converting DC to AC

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  1. Ch7 Inverters (converting DC to AC) Introduction ․Converting DC to AC ․Applications: adjustable-speed AC motor drives. Uninterruptible power supply (UPS). AC appliances run from an automobile battery.

  2. 7.1 The full-bridge converter • Basic circuit to convert DC to AC • AC output is synthesized fro DC input by closing and opening the switches in appropriate sequence. • Output voltage vo can be positive, negative or zero depending on which switches are closed.

  3. 7.2 The square-wave Inverter • Simplest switching scheme to produce a square wave • Switches connect the load to +Vdc when S1 and S2 are closed or to –Vdc when S3 and S4 are closed. • Periodic switching of load voltage between +Vdc and –Vdc produced a square wave across the load. • Even this alternating output is nonsinusoidal, it may adequate ac waveform for some application. • Load current waveform depending on load component. • For R load, load current waveform matches the shape of output voltage. • For RL load, current waveform have more sinusoidal quality than the voltage because of filtering properties of inductance.

  4. RL load Assume S1 and S2 closed at t=0 and voltage across RL load become +Vdc Current expressed as the sum of natural response and forced response

  5. At t=T/2 S1 and S2 open and S3 and S4 close Voltage across RL load become –Vdc.

  6. For steady state By symmetry

  7. Full – bridge inverter using BJTs

  8. 7.3 Fourier Series Analysis With no dc component in the output In square wave output

  9. Example The inverter have Vdc=100 V, R = 10 Ω , L = 25 mH and f = 60 Hz. Determine the amplitude of the Fourier series term for the square wave load voltage, the amplitudes of the Fourier series term for load current, and the power absorbed by the load.

  10. 7.4 Total harmonic distortion (THD) • To describe a quality of the AC output voltage or current. • Assuming no dc component in the output

  11. 8-7 Amplitude and harmonic control By adjusting the interval , the output voltage can be controlled. Fig.8-4

  12. ∵Half – wave symmetry Harmonic content can also be controlled by adjusting α Harmonic n is eliminated if

  13. Amplitude control and harmonic reduction may not be compatible. To control both amplitude and harmonic, it is necessary to have control over the dc input voltage. Fig 8-5 A graphical representation of the integration in the Fourier series coefficient.

  14. 8-8 The half – bridge Inverter Fig 8-7

  15. A square-wave output or bipolar pulse-width-modulated (PWM) output. The voltage across an open switch is twice the load voltage

  16. 8-9 pulse-width-modulated (PWM) output Advantage：Reduced filter requirements to decrease harmonics and the control of the output voltage amplitude can be realized Disadvantage：more complex control circuits for switches and increased losses due to more frequent switching. Sinusoidal PWM requires: (1). a reference (modulating or control) signal-sinusoidal. (2). a carrier (triangular wave) signal that controls the switching fre. Bipolar switching: Fig 8-8 S1 and S2 are on when Vsine>Vtri S3 and S4 are on when Vsine < Vtri

  17. Unipolar Switching： One (First) Fig 8-9 S1 is on when Vsine>Vtri S2 is on when -Vsine<Vtri S3 is on when -Vsine>Vtri S4 is on when Vsine<Vtri Another (second) Fig 8-10 S1 is on when Vsine>Vtri (high fre) S4 is on when Vsine<Vtri (high fre) S2 is on when Vsine> 0 (low fre) S3 is on when Vsine< 0 (low fre)

  18. 8-10 PWM definitions and considerations. • Frequency modulation ratio： The Fourier series of the PWM output voltage has a fundamental fre. which is the same as that of the reference signal. Harmonic frequencies exist at and around multiple of the switching fre. A simple low-pass filter can be effective in removing those (harmonics). Higher losses in switches (2) Amplitude modulation ratio： If , then , (linearly). If , the amplitude of the output increases with , but not linearly. (3). Swithes：carrying current in either direction. Feedback.diode allowing for switching times in the control. (4). Reference voltage：sinusoidal, non-sinusoidal

  19. 8-11 PWM harmonics Bipolar switching：(Fig 8-8) If mf =odd integer, the PWM output then exhibits odd symmetry For the k-th pulse of the PWM output. (Fig 8-11)

  20. Normalized frequency spectrum： Fig 8-12 Normalized Fourier coefficients ： Table 8-3

  21. Unipolar switching：(Fig 8-9) If mf =even integer, some harmonics that were in the spectrum for the bipolar scheme are absent. (seeing Fig 8-13 and Table 8-5)

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