Hi.

I am confused. When should i use Vrms, Vmax or Vaverage in my calculation.

Is it correct that Vrms is used for power?

For example, when i calculate duty cycle for buck converter, should I use Vmax or Vaverage for the Vout and Vin?

Thank you.

 

For example, when i calculate duty cycle for buck converter, should I use Vmax or Vaverage for the Vout and Vin?

Vout and Vin for a buck converter are DC so I don't understand your question, since Vmax and Vaverage are the same.
The theoretical duty cycle (ignoring losses) is simply Vout/Vin when both values are the DC voltages.

Vrms is the equivalent AC voltage as that value DC voltage which generates the same power into a resistive load, i.e., 120Vrms generates the same resistive heat as 120Vdc.

 

When you are considering things like losses in inductor windings, the switch and capacitor ESR, you generally use RMS currents.
If the switch is a FET, which behaves as a resistance, this includes both the AC and DC contributions to RMS.
For the inductor, you want to know each part separately. The average DC current (equal to the output current in a buck) contributes to resistive loss in the winding and influences the effective permeability of the core for many core types. The RMS AC component (the triangular current ripple riding on the average DC) contributes to resistive loss in the winding ("skin effect" and "proximity effect" must be considered) and hysteresis and eddy current losses in the core.
For the input and output capacitors the RMS currents must be considered since they cause heating due to the ESR of the capacitors. For the output capacitor, normally just AC RMS of the ripple current is considered. For the input cap the full effect of the pulsed nature of the current from it needs to be considered and is more difficult to evaluate because of issues with the input power source.

For actual duty cycle, you would use "instantaneous" voltages. For example, if the input were from rectified and filtered AC, the instantaneous voltage would vary from the bottom of the ripple to the peak of the ripple. Don't forget that the simple equation for duty cycle (Vout/Vin) applies only if the inductor current does not drop fully to zero. As soon as the inductor current drops to zero each switching cycle ("discontinuous current" operation), that equation no longer applies.