1. For the waveform shown below, obtain expressions for Fourier components for fundamental, 5th, 7th, and 11th elements, write out (using Taylor Series and Newton - Raphson method, you are not required to write the program) formulae for iterative evaluations of α1, α2 , α3 and α4 such that the resultant waveform gives fundamental at 0.85 Vd and eliminates 5th and 7th and 11th harmonics.

2.(a). In the single-phase interface for a bi-directional power flow, VS =240 V(rms) at 50 Hz and LS = 3.5 mH.. The switch-mode converter is PWM controlled in its linear range with . The converter is controlled such that iS is either in phase or out of phase with VS. Calculate the minimum value of Vd if the power flow through the converter is 5 kW (a) from the ac to the dc side and (b) from the dc to the ac side.

2.(b) For the converter above the DC side voltage is maintained to , Determine the phase angle between the inverter fundamental voltage,VC1, and grid side voltage such that the power delivered to the grid is 10 kW and the fundamental current leads VS by 150°. Calculate the reactive power to the grid and draw the phasor diagram.

3. A three-phase inverter is used for interfacing a PV power generator to the grid of 420 VLL (max) and 50 Hz. The per phase input filter inductor LS =2.0mH and the DC-bus voltage is controlled to 740 V. The converter is controlled such that the power angle is 7.44 degree leading and the real power supplied to the grid is 20 kW. The converter supplies reactive power to the grid.

Calculate the converter voltage VC1, reactive power, the converter phase current and modulation index.

4. A three-phase inverter is used for interfacing a PV power generator to the grid of 415 VLL (rms) and 50 Hz. The input filter inductor LS =4.0mH and the DC -bus voltage is controlled to 800 V. The converter is controlled such that the phase angle between the fundamental phase current and system phase voltage is 165 degree and iDC is 25 A.
Calculate the power and reactive power supplied to the grid, the converter voltage and modulation index and the power angle δ

5. A single phase-controlled converter is used to connect a renewable power source to the grid. The sinusoidal waveforms of the grid side voltage VS and current IS are shown in Fig. Q5 , where IS is chopped at phase angle 45° with respect to VS.

Show that the rms value of the current IS is , where is the peak current. (The identity may be used.)
The fundamental component of IS can be shown to have a magnitude of and 10º lagging phase shift with respect to VS,

Calculate the power factor.