1 to 3 Phase Transformation

This is an theoretical approach on how can we transform one single-phase electrical system into three-phase system. Assume that we have one single-phase generator of electrical energy, it can be voltage or current generator. If we send the energy from this generator to pass into three blocks which have to shift the phase of the voltage (current), and if we choose these blocks in such a way that they will be shift phases on from each other for 1/3 of the period T of the alternate voltage (current), where T = 1/f, then, after this blocks we will have three phases, or in other words, we will have 3-phase system.

Picture 1: Transformation from 1 to 3 phase electrical system



The block-diagram on the Picture 1, is actually one-pole schematic of the transformation system. The three blocks PS1, PS2 and PS3 are the "Phase Shifters" for each of the three lines. These blocks can be implemented easily with appropriate electronics. The function of the PS block is to shift the phase of the voltage (current). The PS1 block have to shift the phase of the voltage from the generator for whole period T or not to shift at all (which is same), or to delay this voltage for the T amount of time (or 0 when no shift). On the second line, the PS2 block have to shift back the phase for T/3, or delay the voltage from generator for T/3 amount of time. Finally, on the third line of the system, the PS3 block have to shift back the phase for 2T/3, or to add the delay of the voltage from generator for 2T/3 amount of time. If we assume that the frequency of the alternating voltage from the generator is 50 Hz, then the period will be 20 miliseconds. So, the second line should be delayed for 6.66 ms, and the third line should be delayed for 13.33 ms. This way, we got three phases from only one. Phase A that we got on the first line is actually the first phase of the 3-phase system (R), Phase B that we got on the second line is the second phase (S) and Phase C that we got on the third line is the third phase of our 3-phase system (T). It's good to mention here that all three lines need to be well synchronized.

If the active power of the single phase generator is P, and if we assume that there is no power loss during the transformation (actually, here we only transform the number of phases and there is no energy transformation, so, the prediction that we have no energy/power loss is logical), then the active power of each "virtual" phase generator A, B and C will be about P/3.


In practice, there are devices which transform single-phase to three-phase electrical energy. They are good for use in cases where the supply network is single-phase but we want to use 3-phase consumer device (~3 EM motor or any kind of ~3 machine).