Okay so we’re going to take these
phasors and substract phase a current
with phase c current and then
look at what our line current A looks like.
Alright.
So here is phase A current and here is phase C current.
Now if we want to perform phase a current plus phase C current,
we would do this through what we call the head to tail method.
And how that works is very simple.
We would pick up phase C current
and add it to the head of phase a current.
And the resultant vector starts from the origin and go towards the
head of phase C current.
So this right here is our resultant vector.
And this resultant vector equals
phase A current plus phase C current.
However, this is not what we want.
What we want to equate is this equation.
Phase A current minus phase C current.
So let’s clean this up a little bit and put phase C current back
to where it was.
Okay because there is a minus sign
that’s associated with the Phase C current,
we have to pick up phase C current and rotate it 180 degrees.
So phase C current becomes like this.
So this phasor here is negative phase C current.
So now, let’s pick this up again and
connect it to the head of phase A current
so now we’re going to connect it like that.
Okay. Now the resultant vector starts from the origin
and ends at the head of negative phase C current.
Now notice that the resultant vector longer now right?
And the resultant vector represents
phase A current minus phase C current.
Now believe it or not,
this phasor diagram actually represents
this particular equation alright.
And this resultant vector is actually
representing this line current here.
So what we’re saying when comparing line current with phase current A.
Now remember, this is phase current A here
and this is line current here.
So let’s label that a little better.
We see that the line current is
a lot larger than our phase current right?
This is our phase current here and this is our line current.
So the magnitude of our line current which starts
from the origin
and ends at this tip here
that is a lot larger than our phase current.
In fact, if we compare the two,
we will find that the line current is actually
the square root of 3 times larger than our phase current.
So if we take our phase current here and line it up with our line current,
we would be at this point here.
But then we would have to stretch it
or we would have to multiply it,
by the square root of 3 or 1.73
to make it equal to our line current.
So that’s the first observation.
That our line current is the square root of 3
times larger than our phase current.
Okay.
Now, also notice that our line current
has a phase shift associated with it.
Alright?
So if all the phasors were rotating in the counter clockwise direction
which they should according to
international standards,
they were all rotating in the counter clockwise direction,
we will see that the line current has a 30 degrees phase shift
okay.
So number 2,
line current has a 30 degree phase shift with respect to phase current.
Before we conclude here,
when I was first learning this,
this particular phasor analysis
was very complicated.
It didn’t sit with me very well.
So lets take a step back
and walk through this step by step.
So what we’re actually doing with this phasor analysis
is we’re trying to compute this particular equation.
And what we’re saying is if we subtract
phase current A
minus phase current C,
we’ll get line current A.
And this is exactly what we did.
We took phase current A and we substracted
phase current C
and what we got right here is line current A.
Okay.
And all we’re saying is that if we compare phase current A,
which is this phasor here…
with line current A which is this phasor here,
we’ll see that the line current is a lot larger than our phase current.
Not only is it larger,
but it also has a 30 degrees phase shift.
This line current has a 30 degree phase shift.
So going back to our diagram,
what we’re saying is that this line current here,
if we compare this line current with this phase current.
Which is the phase current that’s flowing through the primary phase A winding.
This line current is going to be square root of 3 times
larger than this phase current.
And this line current is also going to have a 30 degree phase shift
with this phase A current.
Okay?
So let’s take another step back and ask ourselves,
why is our line current different from our phase current?
Besides the fact that we have a delta connection.
And we’re electrically combining two different phase (phase A and Phase C) currents.
Is because, when we set our phase A, B, and C current,
we said that we would have a balanced system.
And in this balanced system,
we have 120 degree phase shift between our three phasors.
So phase A is 120 degree apart from phase B.
And Phase B is 120 degrees apart from phase C.
Now because, we have a balanced system,
and because the phase currents are a 120 degrees apart,
when we’re subtracting one phase current with another phase current,
the angle is the magic that
get’s you the square root of 3 times larger
and the 30 degree phase shift.
So it’s the angle of phase A current which is at 0 degrees right?
Which we defined here.
And the angle of phase C current,
which is at 120 degrees which we defined here.
That’s what’s causing the square root of 3 times different and
the 30 degrees phase shift between the phase current and the line current.
Thank you
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