The definition of ripple voltage related to harmonics is valid for AC systems. It is analysed with Fourier series expansions of odd signals. Even signals are naturally eliminated by themselves as known. On the other hand, any DC waveform should not contain odd or even content. If we care this aspect, the ripples seen in DC are related to inappropriate rectification and it can be solved by filtering the output. Thus, Mohan's equivalent is valid for this situation. At this point, you need to add a low pass filter to output of the rectification stage. The sqrt(sum(Vhigher_order_harmonics^2)) that is given incomplete expresses the total harmonic distortion ratio and the right equation should be like this; sqrt(sum(Vhigher_order_harmonics^2)/Vmean)

Mr. Kabalci thank you very much for your explanatory answer. In my model i have included a low pass filter to eliminate high order harmonics. Because the rectifier is twelve pulse only voltage harmonics of order h=12n would be present and they are attenuated or eliminated from the filter. I was also curious about the correctness of the first expression as it seemed like a "customised" equation of THD. And THD is valid only for AC systems. So I am going to use Mohans equation. Also I would like to ask you if you are aware of a limit of DC ripple for high power DC systems.

THD is only defined by Standards on the AC side. On the DC side there is not a definition of the ripple factor, but the evaluation of the peak-to-peak ripple voltage, Vripple, due to commutations. The simpliest way to calculate Vripple is to calculate the istantaneous difference between the max and minimum value of the pulsed voltage, taking into account the actual delay of the firing angle alfa, at commutation time. As an example, for a 12 pulses bridge with alfa=0, Vripple~0,034*Vmax, without any filter. The filtering effect of a capacitance C across the DC terminals depends on the load. In the case of a resistive load R, Vripple can be well evaluated as Vripple~Vmax*T/(12*C*R) where T is the period of the AC voltage

Mr. Kourmpelis thank you for your reply. The ripple limit in HVDC systems are mostly defined with a testing voltage measurement that is used in a lower level of actual operation voltage. And the voltage ripple limit in the testing system should be lower than 5% of measurement voltage. On the other hand, the harmonic orders seen in an 12-pulse rectifier are 12n±1 ordered (11th, 13th, so on) those are injected to DC side by the transformer. This is another discussion issue and can be discussed together if required.

in my opinion Mohans "Power electronic devices" technique is good.