Calculating phasors from sensor readings

[TerGrim]

Hi!

I am working on a project (hobby basis) and with limited EE background.
I wish to make a polar plot, showing the current and voltage phasors for each phase (unbalanced 3-phase, 3 wire system (IT system), se picture below.).

I have obtained the following readings (instantaneous values):

• Phase to phase voltages (U12, U23, U31)
• phase to ground voltages (U1, U2, U3)
• currents (i1, i2, i3) I believe these are measured as line currents, so have to divide by sqrt(3) to get the phase currents as my setup is connected in wye config (not grounded).
• power factor for each phase, so I can calculate the phase difference between the voltage and current phasor.

Based on this readings, how should I go if I want to calculate the voltage and current phasors for each phase, is it possible with this readings?

For the voltage phasors, I could use the following cosine, since I have the phase-to-phase, and phase to ground voltage readings.

For the currents, since I read the instantaneous currents, is the length of my current phasor equal to this value? And to get the angle, I would use the angle of voltage phasor, and then shift it again using the angle calculated from the power factor?

Am I on the right track?

Sorry if my post is messy, give me feedback if anything has to change.

Best regards from Germany :)

 

[jim hardy]

see if this link is any help

https://www.electronics-tutorials.ws/accircuits/phasors.htmli'm confused by this conflict, though

and what do you mean by "instantaneous values" ?

 

[TerGrim]

Thanks, I will have a look at the link once I get home.

I should have written phase to neutral point, I think(?). I am testing this on a setup that is earthed like an IT system, i.e. the neutral point is not connected to earth. Sorry for not beeing clear, lack of EE/math knowledge is holding me down, but I thought this was a good way to get some more knowledge :)

see if this link is any help
and what do you mean by "instantaneous values" ?

Thanks, my manual (in german) says "instant value", but I need to find out if this is the "instant" rms value or any value on the sine wave.

I believe its RMS, but then again, I find it abit weird when they say "instant value" if its rms, because to calculate rms you need more than one reading?

 

[anorlunda]

Thanks, my manual (in german) says "instant value", but I need to find out if this is the "instant" rms value or any value on the sine wave.

Digital: RMS generally means a calculation based on an entire cycle. However at each sampling interval, you could calculate a rolling RMS for the preceding cycle. 100 samples per second, 100 RMS calculations per second. That can be what they mean by instantaneous RMS.

Analog: AC analog meters inherently measure RMS.

 

[Babadag]

I think instantaneous current it is i(t)=√2*Irms*cos(ω*t+φ). For any t we'll get another i. [Imax=√2*Irms]. The phasor will be Irms[cos(φ)±jsin(φ)]Usually we take one of the voltage as φ=0 then we can consider φ from here.
We can read the instantaneous current on a recorder tape [or oscilloscope] since the values are changing fast at the industrial frequency[50-60 hz] using an d.c.meter. An a.c. avometer usually will give you a r.m.s. value only as anorlunda already said.

 

[jim hardy]

I wish to make a polar plot, showing the current and voltage phasors for each phase

Did you take a look at that tutorial?

• Phase to phase voltages (U12, U23, U31)

• phase to ground voltages (U1, U2, U3)

That's a good start.

It's important to be rigorous in your naming and your drafting.

Draw a triangle with sides of length U12, U23, and U31.

Next find where is the Neutral, which i hope is what you called "Ground".
Do that with a compass by drawing lines of length U1 U2 and U3 from the respective vertices to wherever they intersect.
You should get something resembling this

Now add your arrowheads .
This is where rigor pays off , and that's the secret to success in learning to work with three phase.

Decide which end of each phasor you want to call FROM and which end to call TO,
and always write their names that way.
I use the convention subscript them From-To
For example,
if you decide to call the end with an arrowhead TO and the other end FROM
( we call them Head and Tail as with arrows)
then we should make the sketch look like this
(well, leave your arrowheads black)
and my convention would be 'write their names U_From-To'

I could equally well have named those interior phasors UN1 UN2 and UN3 and put their arrowheads out at the vertices ,
and probably would have but i wanted you to see the mechanics of construction
and i wound up with too many overlapping arrowheads out there at the vertices - it was ugly

Here's the beauty of three phase - it's all 30 and 60 and 90 and 120 degree angles, so the geometry works out quite convenient.
Observe in a balanced system that
Angle between any two phase to phase voltages is 60 degrees
Angle between any two phase to neutral voltages is 120 degrees
Angle between any phase-to-phase and any phase-to-neutral voltage ie either 30 or 90 degrees.
So the only cosines you have to remember are 0.5 and ½√3 .

Now it's time for you to practice picking any phasor and writing its name.
Form the habit now of being rigorous in naming and drawing.

Now here's a pill to swallow
Every textbook author is free to define his naming and arrowhead convention
and here on PF you will see posts from disparate textbooks
so establish early what is the convention in use for a conversation.
I cannot overstress the importance of that point

Now
you have to imagine that triangle rotating at frequency of the system you're studying.
US power is of course 60hz
yours is probably 50 hz
in airplanes you'll find 400 hz
in car alternators it's in proportion to (engine speed X pulley ratio X number of poles) so quite variable.
By agreement(!) among power engineering folks we almost universally draw our phasor diagram rotating CCW
so the phase sequence of that sketch we made would be 123 because that's the order in which the vertices would go by an observer standing near the triangle.
On engineering drawings there's usually a little arrow showing the direction of rotation just as a reminder..

That's enough to absorb in one sitting, i think.

 

[jim hardy]

If your system is unbalanced your triangle won't be so symmetric as the example above
But knowing all those voltages you can construct it using just high school geometry..

Keep us posted ?

old jim

 

[jim hardy]

• currents (i1, i2, i3) I believe these are measured as line currents, so have to divide by sqrt(3) to get the phase currents as my setup is connected in wye config (not grounded).

• power factor for each phase, so I can calculate the phase difference between the voltage and current phasor.

it's not clear where you took those measurements.

can you draw a sketch (maybe in Paint?) and upload it ?

For the currents, since I read the instantaneous currents, is the length of my current phasor equal to this value?

Proportional to it. Pick a scale factor cm per amp that fits your page...

And to get the angle, I would use the angle of voltage phasor, and then shift it again using the angle calculated from the power factor?

You could try that.
Is your load connected phase to phase or phase to neutral ?

 

[Babadag]

What do we need it is a a.c. voltmeter, an ampermeter and a single phase wattmeter.
Let's say we take voltage U1o and I1o and the power P1o=U1o*I1o*cos(φ1o) so we have φ1o. If I want to measure φ12 between U1 and U2 I need a known R inserted between U2 terminals and so we have a current in phase with U2 so the wattmeter will show cos(φ12). A phasor diagram as Jim indicates it could be done now.