Just came across this thread, and I agree with the conclusions made. After many years experience in designing and working with soft starters I can confirm that the current waveform is a double humped waveform as shown above with the forst hump being the current flowing from phase A to phase C and the second hump being the current flowing from phase A to phase B. As you reduce the conduction angle, the OFF time increases and the humps become more prominant. As the conduction time is increased, the humps blend into a single hump and at 180 degree conduction angle we have the traditional sinewave we are so familiar with.
When the SCR is conducting, we have the same voltage input and output minus tha voltage drop across the SCRs which is typically around 1 - 1.2 volts per SCR. The current is the same, so at each instant that the SCR is ON, the VA input equals the VA output minus the conduction losses of the SCR. For each instant that the SCR is OFF, the VA input equals the VA output, so the laws of conservation etc are fully met.
The difficulty comes when considering discontinuous waveforms. At that time, you can not take the average voltage times the average current to get the average power. This is a stunt commonly pulled by the promoters of energy savers!!
Unfortunately, much of the technical literature about SCR control of induction motos shows waveforms that are true for an SCR based controller with a resistive load. This shows the current waverform to be very different from reality and the commutation occuring at 0 and 180 degrees.
The reality is that the current is smoothly rounded and takes on the double hump, and it commutates at an angle which reflects the power factor of the motor, hence the commutation angle changes with slip.
During the non conduction period, the voltage on the motor terminals does not fall to zero as logic would suggest. The spinning motor acts as a generator and creates it's own voltage profile to fill in the gap. The actual voltage seen is dependant on the voltage generated, but can make the waveform "applied" to the motor seem prety wicked at times. The rality is that the waveform applied to the motor is only the portion where the SCRs are conducting.
So in calculating power and VA, we need to take the integral of the products of the instanteous values to get meaningful results.
Returning to the OP, for voltage drop calculations, is is usually sufficient to consider the average start current to get reasonable results. The maximum start current flows around the voltage zero crossing at zero shaft speed and increases higher up the sinewave as the motor reaches full speed. This is the same for a standard induction motor starter. The major difference is that there is a non conduction period before the voltage crest that can at times include the voltage crest.
So treat the soft starter like a full voltage starter with a reduced average start current. - somewhat like a primary resistance starter with a very small power loss.
Best regards,
Mark Empson