If one phase power is 220V, why is three phase 220V, not 660V.

In a three-phase system, the voltage between two phases is not simply the sum of the individual phase voltages (220V + 220V = 440V) because the phases are shifted by 120 degrees from each other.

This means the voltages don't reach their peak values at the same time. When calculating the voltage between two phases, you must use vector addition (or phasor addition), which takes into account the phase difference. The resulting line-to-line voltage in a 3-phase system is approximately 1.732 (the square root of 3) times the phase voltage, which is why a 220V phase voltage results in a 380-400V line voltage, not 660V. 

Elaboration:

1. Phase Shift:

In a three-phase system, each phase voltage is 120 degrees out of phase with the others. This means they don't reach their peak positive or negative values simultaneously. 

2. Vector Addition:

When calculating the voltage between two phases (line-to-line voltage), you are essentially finding the resultant voltage of two vectors (phasors) that are 120 degrees apart. 

3. Square Root of 3:

The line-to-line voltage in a balanced three-phase system is calculated by multiplying the phase voltage by the square root of 3 (approximately 1.732). For example, if the phase voltage is 220V, the line voltage would be approximately 220 * 1.732 = 381V, which is typically rounded to 400V.

4. Why not 660V?

If you were to simply add the phase voltages arithmetically (220V + 220V + 220V = 660V), you would be ignoring the phase shift and assuming they all reach their peak values at the same time, which is not the case in a three-phase system.

5. Practical Considerations:

While the theoretical line-to-line voltage is 400V, the actual measured voltage can vary slightly due to factors like system loading and voltage drops, according to an electrical forum.