When should the AC resistance of a diode be taken into account in a practical circuit?
A diode can be represented by the series connection of a fixed voltage source \$V_{T0}\$ in series with a dynamic resistance \$r_d\$. The source level depends on the technology: around 0.6 V for a silicon diode and 0.4 V for a Schottky diode. The below picture shows you this equivalent model:



You can see that the total drop label \$V_f\$ is the sum of \$V_{T0}\$ and the resistive drop. The dynamic resistance is determined by calculating the slope at the diode dc operating point. Obviously, when a current flows in this structure, it incurs power dissipation. The formula describing these conduction losses are as follows: \$P_d=V_{T0}I_{d,avg}+r_dI^2_{d,rms}\$. The first contributor is the average current while the second is the rms current. If the current flowing in the diode has a weak ac component (not much ripple around the dc value), then the formula \$P_d\approx V_fI_{d,avg}\$ gives good results. However, if the current contains a strong ripple, like in a heavy discontinuous mode-operated switching converter, then you must account for the diode dynamic resistance for power computation.