Calculating Phase Currents for Unbalanced Loads

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mivey

Senior Member
mea03wjb,

Scanning through the other posts, it looks like others have put a lot more thought into it. Unfortunately, I have not taken the time to read through them.

I am curious as to what you are trying to accomplish. Assuming you get the phase currents, what are you going to do with them?

Another thought: If it is a delta-connected motor, why not just assume a balanced load, calculate the power delivered, divide by three to get the power in each phase, then use the power and line-line voltage to calculate the phase current?
 

Smart $

Esteemed Member
Location
Ohio
mea03wjb,

Scanning through the other posts, it looks like others have put a lot more thought into it. Unfortunately, I have not taken the time to read through them.

I am curious as to what you are trying to accomplish. Assuming you get the phase currents, what are you going to do with them?

Another thought: If it is a delta-connected motor, why not just assume a balanced load, calculate the power delivered, divide by three to get the power in each phase, then use the power and line-line voltage to calculate the phase current?
He's attempting to detect any early-stage degradation in the windings. He'll need an accurate phase current value to make that determination.

W...
Can you post or otherwise upload or furnish some instantaneous data that you have for at least a cycle?
 

jghrist

Senior Member
I only used the instantaneous values - How are the phase angles used?
Do not use instantaneous values. You can't extract useful information on a sinusoidal quantity from a single instantaneous value. Use the equations in my Post #21 to convert two instantaneous values into magnitude and angle. You can put the samples into a spreadsheet and calculate magnitude and angle for each sample (along with the previous sample from 1/4 cycle earlier) to see how it varies.

If you want to get fancy, you can also calculate harmonics using a discrete Laplace transform, but the fundamental should suit your purposes.

Is your system 50 Hz or 60 Hz? I ask because you said the instantaneous values were 0.0002 seconds apart which is not an integral number of samples per cycle at 60 Hz. To get values 1/4 cycle apart, you'd like to sample in multiples of 4 per cycle.

Please post example magnitudes and angles (or a series of instantaneous values) so that we can have some real numbers to mess around with.
 

jghrist

Senior Member
The answer would be easy if the currents were balanced. The load current would be line current divided by sqrt(3)

This is the key to the solution. Use sequence components to solve as balanced currents.

First, find the sequence line currents.
Divide the pos-sequence by sqrt(3) and shift the angle +30?.
Divide the neg-sequence by sqrt(3) and shift the angle -30?.
Calculate the phase load currents.

Example:

IA = 20 @ -10?
IB = 17 @ -130?
IC = -IA - IB = 18.68 @ 118?

Line sequence components:

IL0 = 0
IL1 = 18.52 @ -7.32?
IL2 = 1.73 @ -40?

Delta load sequence components:

ID0 = 0
ID1 = 10.69 @ 22.68?
ID2 = 1 @ -70?

Delta load phase currents

IAB = 10.69 @ 17.32?
IBC = 9.87 @ -94.18?
ICA = 11.59 @ 144.95?
 

topgone

Senior Member
The answer would be easy if the currents were balanced. The load current would be line current divided by sqrt(3)

This is the key to the solution. Use sequence components to solve as balanced currents.

First, find the sequence line currents.
Divide the pos-sequence by sqrt(3) and shift the angle +30?.
Divide the neg-sequence by sqrt(3) and shift the angle -30?.
Calculate the phase load currents.
Maybe jghrist meant to say "The answer would be very easy if the currents were resistive or PF = unity".
 

mivey

Senior Member
Do not use instantaneous values. You can't extract useful information on a sinusoidal quantity from a single instantaneous value. Use the equations in my Post #21 to convert two instantaneous values into magnitude and angle. You can put the samples into a spreadsheet and calculate magnitude and angle for each sample (along with the previous sample from 1/4 cycle earlier) to see how it varies.
Sorry, but I'm not following. I don't see how samples taken a 1/4 cycle value will give you the magnitude and angle of the sinusoid. Are you targeting specific points on the wave or just any two readings 1/4 cycle apart? Are we talking about some other sinusoidal function?
 

jghrist

Senior Member
Sorry, but I'm not following. I don't see how samples taken a 1/4 cycle value will give you the magnitude and angle of the sinusoid. Are you targeting specific points on the wave or just any two readings 1/4 cycle apart? Are we talking about some other sinusoidal function?
Any two points 1/4 cycle apart. Any pure sinusoid. See Understanding and Analyzing Event Report Information by David Costello. Download at https://www.selinc.com/literature/literature.aspx?fid=282 (may require registration).

Generate a sample sinusoid in Excel and test it.
 

skeshesh

Senior Member
Location
Los Angeles, Ca
Any two points 1/4 cycle apart. Any pure sinusoid. See Understanding and Analyzing Event Report Information by David Costello. Download at https://www.selinc.com/literature/literature.aspx?fid=282 (may require registration).

Generate a sample sinusoid in Excel and test it.

I see reference to 1/4 cycle in the article but not the reason why that is the relevant sampling rate. Does this have something to do with the criteria required to recover a sin. wave correctly from data points (digital to analog)?
 

Smart $

Esteemed Member
Location
Ohio
Any two points 1/4 cycle apart. Any pure sinusoid. See Understanding and Analyzing Event Report Information by David Costello. Download at https://www.selinc.com/literature/literature.aspx?fid=282 (may require registration).

Generate a sample sinusoid in Excel and test it.
Haven't read the linked document... just glanced through it. But it seems to me, this 1/4 cycle approach makes the assumption the phase currents are exactly 120? out-of-phase. What if there is a deviation in power factor across the cormers, where the phase currents have some unequal level of deviation from nominal... The currents' phasing will not be exactly 1/4 cycle apart other than by extraordinary coincidence.

And then of course, there is the assumption of having a pure sinusoidal waveform. I believe that to be something that rarely exists in true measurements also...!!!

Perhaps I need to give the issue more consideration, I don't know. But short of changing my current impression, I'd be more inclined to determine phase angle by peaks and/or zero crossings.
 
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mivey

Senior Member
Any two points 1/4 cycle apart. Any pure sinusoid. See Understanding and Analyzing Event Report Information by David Costello. Download at https://www.selinc.com/literature/literature.aspx?fid=282 (may require registration).

Generate a sample sinusoid in Excel and test it.
I follow you now.

When I first saw your post, I did not pay close attention. I made a quick scribble of a sin wave, picked two points and thought "how would the average of those two ever get you anything useful?". :roll:

Thanks for the info.

Brings to memory a nyquist sample rate but I would have to go back and look at my text book.
 

jghrist

Senior Member
Haven't read the linked document... just glanced through it. But it seems to me, this 1/4 cycle approach makes the assumption the phase currents are exactly 120? out-of-phase.
There is no assumption on phase current angles. The two samples are from the same current. To get the phase relationship between two currents, take two samples from each current at the same times.

And then of course, there is the assumption of having a pure sinusoidal waveform. I believe that to be something that rarely exists in true measurements also...!!!

Perhaps I need to give the issue more consideration, I don't know. But short of changing my current impression, I'd be more inclined to determine phase angle by peaks and/or zero crossings.
Using peaks and zero crossings for phase angles may also give errors if the waveform is not a pure sinusoid.

The equations are actually a cosine filter for 4 samples per cycle. A cosine filter output is the fundamental with all harmonics rejected. You can get a closer approximation of the fundamental of a distorted wave by using a cosine filter with more samples. A 16 sample/cycle cosine filter is often used in protective relays. See How Microprocessor Relays Respond to Harmonics, Saturation, and Other Wave Distortions by Stanley E. Zocholl and Gabriel Benmouyal. Download at http://www.selinc.com/literature/literature.aspx?fid=282
 

Smart $

Esteemed Member
Location
Ohio
There is no assumption on phase current angles. The two samples are from the same current. To get the phase relationship between two currents, take two samples from each current at the same times.
I don't have enough time to study it right now. Perhaps you can just show me. I created a graphical scenario starting with delta load currents of differing magnitudes and power factors (so the currents' phase angles are not 120? out-of-phase). Then I vector added to get the line current magnitudes and angles. Next I advanced the timing to 18? for line samples 1 then to 108? (i.e +90? or a 1/4 cycle) for line samples 2. The following are the magnitudes at those instances:
I1.1 = 9.9109935363
I2.1 = -3.3283763153

I1.2 = -0.5122323416
I2.2 = 11.833679776​
The ".x" indicates the sample number.

From this information, can you tell me the I12 leg of the load's current and angle?


Using peaks and zero crossings for phase angles may also give errors if the waveform is not a pure sinusoid.

The equations are actually a cosine filter for 4 samples per cycle. A cosine filter output is the fundamental with all harmonics rejected. You can get a closer approximation of the fundamental of a distorted wave by using a cosine filter with more samples. A 16 sample/cycle cosine filter is often used in protective relays. See How Microprocessor Relays Respond to Harmonics, Saturation, and Other Wave Distortions by Stanley E. Zocholl and Gabriel Benmouyal. Download at http://www.selinc.com/literature/literature.aspx?fid=282
Not concerned with non-sinusoidal scenarios right now... perhaps later ;)
 

jghrist

Senior Member
I don't have enough time to study it right now. Perhaps you can just show me. I created a graphical scenario starting with delta load currents of differing magnitudes and power factors (so the currents' phase angles are not 120? out-of-phase). Then I vector added to get the line current magnitudes and angles. Next I advanced the timing to 18? for line samples 1 then to 108? (i.e +90? or a 1/4 cycle) for line samples 2. The following are the magnitudes at those instances:
I1.1 = 9.9109935363
I2.1 = -3.3283763153

I1.2 = -0.5122323416
I2.2 = 11.833679776​
The ".x" indicates the sample number.

From this information, can you tell me the I12 leg of the load's current and angle?

Assuming that I1 is current into load terminal 1, I2 is current into load terminal 2, I12 is load current from terminal 1 to terminal 2.

I12 = 4.267 @ 133? (rms value)
I23 = 5.511 @ 8?
I34 = 4.648 @ -123.239?
 

Smart $

Esteemed Member
Location
Ohio
Assuming that I1 is current into load terminal 1, I2 is current into load terminal 2, I12 is load current from terminal 1 to terminal 2.

I12 = 4.267 @ 133? (rms value)
I23 = 5.511 @ 8?
I34 = 4.648 @ -123.239?

Hmmm... you nailed the magnitudes, but your angles are a bit off :confused:
4.26681288869444 @ -335? (or 25?)
5.51135192129047 @ -100?
4.64804813713548 @ -231.2391388721?
 

jghrist

Senior Member
Hmmm... you nailed the magnitudes, but your angles are a bit off :confused:
4.26681288869444 @ -335? (or 25?)
5.51135192129047 @ -100?
4.64804813713548 @ -231.2391388721?

I expected that. The phase angle relationships are the same:

I23 lags I12 by 125?
I34 lags I23 by 131?
I12 lags I34 by 104?

It's the relative angles that count. If you had voltages sampled at the same times, the angles between the current and voltage would be correct, so the power factors would be correct. You can start T=0 anytime to change the angle of all currents by a constant time or angle. Note that the difference is 108?, the angle that you shifted for sample 2.
 

Smart $

Esteemed Member
Location
Ohio
I expected that. The phase angle relationships are the same:

I23 lags I12 by 125?
I34 lags I23 by 131?
I12 lags I34 by 104?

It's the relative angles that count. If you had voltages sampled at the same times, the angles between the current and voltage would be correct, so the power factors would be correct. You can start T=0 anytime to change the angle of all currents by a constant time or angle. Note that the difference is 108?, the angle that you shifted for sample 2.
So it is...

...but if you expected that, you should have nailed the angles, too!!!! :D

Nevertheless, a very nice recovery ;)

...but I must say, I don't care much for those report type solutions like the one you attached above. It looks like report stuff pasted from an analytic electrical program.
 

mea03wjb

Member
Data to analyse

Data to analyse

All,

Sorry for late reply here is some measured data for you to play with, .txt file.

The sampling rate is 5kHz, the supply freq. is 50Hz.
Voltages are line-to-neutral (volts), currents are line (amps).

I will try and get my head around the latest few posts then get back to you.
 

jghrist

Senior Member
...but I must say, I don't care much for those report type solutions like the one you attached above. It looks like report stuff pasted from an analytic electrical program.
It's part of a Mathcad workbook saved to .rtf then saved in Word. For some reason, I couldn't get the .pdf attachment to work. I know it would be easier to follow with full equations spelled out, but this was easy because I already had the A matrix in a general workbook and solutions with matrices are easier in Mathcad.
 

Smart $

Esteemed Member
Location
Ohio
It's part of a Mathcad workbook saved to .rtf then saved in Word. For some reason, I couldn't get the .pdf attachment to work. I know it would be easier to follow with full equations spelled out, but this was easy because I already had the A matrix in a general workbook and solutions with matrices are easier in Mathcad.
That's called the "easier" factor :D

Speaking of easier, I believe I've come up with a simple calculation for the magnitude of phase currents... knowing the magnitude of the line currents. As I mentioned the Fermat Point previously was on the basis the load legs all had an equal power factor.

In my vector analysis of your "1/4 cycle" math, I noticed the angles and associations between them seemed to indicate where power factors are different, the point we are looking for is the triangle centroid, and it follows in my theorizing that when power factors are equal, the Fermat Point coincides with the triangle centroid.

Anyway, I came up with the following formulas and need someone to verify them...

Deltacurrentfromlinecurrentcalculation2.gif
 
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