Why use vector sum for calculating neutral current?

Question

In a three phase system, we use a vector sum to calculate resulting neutral current.

I don't understand why we use vector sum. The resulting neutral current is actually the sum of instantaneous values of 3 phase currents right? So even if we use a phasor diagram to represent the currents, it should not be a vector sum; it should just be the sum of the y axis components (sin components) of the currents.

Also, when we are given 3 phase current values to calculate the resultant neutral, are we given RMS or instantaneous values, or the maxima? It cannot be instantaneous because otherwise neutral would be a simple addition of them.

I am not a physics student; I am just trying to understand this for a use-case project, so it would be helpful if someone helps me reconcile all these facts. Thanks!

Answer 1

If you just sum the instantaneous currents of three phases, and they do not sum to zero due to imbalance, you get the instantaneous current running in the neutral wire.

But that is also a sine wave, with some amplitude and some phase. So it is a vector sum. So having a single point in time might add up that neutral current is 0 at some instant, but in reality it is a sine wave which just happened to be at the zero crossing at that instant and it does not mean the current is 0 since it has amplitude and phase.

Answer 2

To answer " Why use vector sum for calculating neutral current? " you need to know that the numbers we read from the ammeter and voltmeter are not instantaneous, but RMS or Max values. KCL says the sum of instantaneous currents connected to a node is zero, that means they are measured at the same time. However, KCL doesn't work if one current is measured now, and the the other one is measured later. The peak values ( MAX or RMS) don't happen at the same time but at different times. How do we know that? Use vectors and see the phase angle between them! Phase angle in vector analysis is an indication of time shift in time domain analysis. If the peaks of two signals are 2 milliseconds apart, that means they have a phase shift of (Frequency)(360 Degrees)*(0.002 Sec) . For example if the frequency is 60 Hz, the phase shift is : Theta = (60 Hz)(360)(0.002) = 43.2 Degrees. So, in a system at 60 Hz, a phase shift of 43.2 degrees is equal to a delay of 2 milliseconds. In conclusion: The vector summation of the AC signal is to find their instantaneous values at one instant and add them. This is true for balanced and unbalanced signals.