Calculating Phase Currents Based on Measured Line Currents - Delta Heater Load

[mivey]

Just to give a little more info - I have some metering class CT's ordered so I can get more accurate line current measurements.

Great. Then just measure the currents and phase angles and be done with it as it is just vector math after that.

 

[gar]

110122-2143 EST

iceworm:

The WYE-DELTA transform I referenced is a transform from a 3 terminal delta to a 3 terminal wye network where the mid-point of the wye is not constrained, not connected to anything.

If the corners of the delta are labeled A, B, and C; and the impedances between them are Zab, Zbc, and Zca, then the transform from delta to wye where the wye impedances are Za, Zb, and Zc, is

Zsum = Za + Zb + Zc

Za = Zab * Zca / Zsum
Zb = Zab * Zbc / Zsum
Zc = Zbc * Zca / Zsum

I am going to change my previous example to resistors of the following values:
Zab = 90 ohms
Zbc = 110 ohms
Zca = 800 ohms

Zsum = 1000 ohms

Za = 90 * 800 / 1000 = 72 ohms
Zb = 90 * 110 / 1000 = 9.9 ohms
Zc = 110 * 800 /1000 = 88 ohms

The transform is from resistive to resistive, but the line currents are not in phase with a balanced Y voltage source because of the unbalanced nature of the load. However, within any single resistive load the current thru that resistor is in phase with the voltage across that resistor as it must be.

.

 

[gar]

110123-1326 EST

I believe the goal is to find the bank of heaters where a failure has occurred.

If we assume there is a failure in only one bank, then the current magnitude in one line will not change, at least adjusted for any nominal line voltage change. Also assuming all line-to-line voltages remain with the same relative balance.

The line with the unchanged current, call it C, is opposite the the bank with the failed heater element. Thus, the failed bank in this case is A-B.


Back to the SCR question. A pair of back-to-back SCRs with their gates continually biased on or off are close to the equivalent of a mechanical contact. A single SCR biased on is roughly equivalent to a diode. How the SCRs are wired in the heater circuit will determine whether to treat them as a switch or a controlled rectifier. Also note a Triac is somewhat equivalent to a back-to-back pair of SCRs.

If the SCRs are used as controlled rectifiers in this heater circuit, then simple phasor analysis won't work, non-sinusoidal waveform.

.

 

[david luchini]

Great. Then just measure the currents and phase angles and be done with it as it is just vector math after that.

I think its a bit more difficult than just vector math. As has been already pointed out, you need to solve 3 simultaneous equations with 3 unknowns.

However, I think there is a fourth unknown that hasn't been discussed. While it is known that the angles between the load current will be 120[FONT=&quot]? [/FONT]apart, the angle between the line and phase currents will also be unknown.


For instance, if we assign the angle θ to the load current from A-B, and θ-120 to the load current B-C and θ-240 to the load current C-A. And we then measure the line current to be Ia=102.38<0, Ib=110.48<-118.56, and Ic=108.96<-242.96. The vector equations for Ia=Iab-Ica, Ib=Ibc-Iab, and Ic=Ica-Ibc become:


Ia=(Iab*cos(θ)+jIab*sin(θ)) - (Ica*cos(θ-240)+jIca*sin(θ-240))
Ib=(Ibc*cos(θ-120)+jIbc*sin(θ-120)) - (Iab*cos(θ)+jIab*sin(θ))
Ic=(Ica*cos(θ-240)+jIca*sin(θ-240)) - (Ibc*cos(θ-120)+jIbc*sin(θ-120))


So even if you measure the line currents and their associated angles, you will need to solve 3 simultaneous equations with 4 unknowns (Iab, Ibc, Ica and θ) in order to determine the load currents.

 

[rattus]

I think its a bit more difficult than just vector math. As has been already pointed out, you need to solve 3 simultaneous equations with 3 unknowns.

So even if you measure the line currents and their associated angles, you will need to solve 3 simultaneous equations with 4 unknowns (Iab, Ibc, Ica and θ) in order to determine the load currents.

The line current angles must be referenced to the voltage angles. That is, we must also know the voltage angles, then we would know the value of theta. Still a messy problem to solve.

 

[david luchini]

The line current angles must be referenced to the voltage angles. That is, we must also know the voltage angles, then we would know the value of theta. Still a messy problem to solve.

The phase current angles would be referenced to the phase voltage angles (they'd be the same angles) but the line current angles are NOT referenced to voltage angles or to the phase current angles in this unbalanced case.

As an example, for line currents Ia=102.38<0, Ib=110.48<-118.56, you can see that the line currents are not 120[FONT=&quot]? [/FONT]apart. If the phase angles for currents Ia, Ib and Ic are not a constant angle apart, how can you possibly know the phase angle difference between Ia and Iab, etc? By simply measuring (as suggested in the OP) the line currents (assuming magnitudes and angles,) the angle (theta) of the load current, as it relates to the line currents, is an unknown.

 

[gar]

110124-1414 EST

The original post in combination with a subsequent post implies the purpose of the measurements is to identify on which load there is a failed heater.

In a previous post I pointed out that if you make the assumption that failure probabilities are not very high, and the cause of a failure in one element does not cause a failure of an element in another phase, then for a failure in a single phase there will be one line current that likely remains unchanged. This in turn points to the heater bank with the problem.

If one needs to calculate the resistance change in the failed bank, then the problem is much simpler to solve than if all three currents change. In this case you know the current and phase angle of the currents in the unchanged two banks. Note, if one current only changes in proportion to supply voltage change, then that is still a current that does not change for the purpose here.

The line with the unchanged current, call it C, is opposite the the bank, A-B, with the failed heater element.

If you need more information than this, and actually want to know the current thru bank A-B, then the currents in banks B-C and C-A can be calculated and therefore the current in A-B can be calculated.

Iab = 240 + j0 / Rab
Ibc = -120 - j207.9 / Rbc
Ica = -120 + j207.9 / Rca

and

Ia = Iab - Ica
Ib = Ibc - Iab
Ic = Ica - Ibc

Both Ibc and Iba are known. Proceed from here. I have not spent the time to create a simple solution from this point.

.

 

[rattus]

The phase current angles would be referenced to the phase voltage angles (they'd be the same angles) but the line current angles are NOT referenced to voltage angles or to the phase current angles in this unbalanced case.

As an example, for line currents Ia=102.38<0, Ib=110.48<-118.56, you can see that the line currents are not 120[FONT=&quot]? [/FONT]apart. If the phase angles for currents Ia, Ib and Ic are not a constant angle apart, how can you possibly know the phase angle difference between Ia and Iab, etc? By simply measuring (as suggested in the OP) the line currents (assuming magnitudes and angles,) the angle (theta) of the load current, as it relates to the line currents, is an unknown.

David, I am saying that the measured line current angles must be referenced to something, and that something must be a voltage angle. For example, let Vab be at zero degrees. We would assume a separation of 120 degrees, but that could be measured as well. Then, since the loads are resistive, we know all the angles--three equations, three unknowns.

 

[david luchini]

David, I am saying that the measured line current angles must be referenced to something, and that something must be a voltage angle. For example, let Vab be at zero degrees. We would assume a separation of 120 degrees, but that could be measured as well. Then, since the loads are resistive, we know all the angles--three equations, three unknowns.

The measured line current angles could be referenced to the phase voltage angles, they could be referenced to the phase current angles (as they are the same for the resistive load.) But arbitrarily assigning an angle, such as saying Vab is at zero degrees doesn't work if the measured angles of the line currents is the starting point. You can't measure Ia=102.28<0 and then decide Vab is at zero arbitrarily.

The OP mentioned that he could easily measure the line currents (and presumably the angular relationship between those currents.) But with only those line current measurements (which are not separated by 120 degrees since the load is not balanced) the angle of the phase currents and phase voltages relative to the line currents is an unknown.

We know that the phase currents and voltages will be 120 degrees separated from each other, but we do not know how much Ia is separated from Iab, etc. That is why there are four unknowns, not three.

 

[rattus]

The measured line current angles could be referenced to the phase voltage angles, they could be referenced to the phase current angles (as they are the same for the resistive load.) But arbitrarily assigning an angle, such as saying Vab is at zero degrees doesn't work if the measured angles of the line currents is the starting point. You can't measure Ia=102.28<0 and then decide Vab is at zero arbitrarily.

The OP mentioned that he could easily measure the line currents (and presumably the angular relationship between those currents.) But with only those line current measurements (which are not separated by 120 degrees since the load is not balanced) the angle of the phase currents and phase voltages relative to the line currents is an unknown.

We know that the phase currents and voltages will be 120 degrees separated from each other, but we do not know how much Ia is separated from Iab, etc. That is why there are four unknowns, not three.

David, there must be a common reference for all angles. I would assign one of the L-L voltage angles to be zero which then is the common reference for ALL other angles. If this is done, then "theta" is no longer an unknown.

 

[Smart $]

The measured line current angles could be referenced to the phase voltage angles, they could be referenced to the phase current angles (as they are the same for the resistive load.) But arbitrarily assigning an angle, such as saying Vab is at zero degrees doesn't work if the measured angles of the line currents is the starting point. You can't measure Ia=102.28<0 and then decide Vab is at zero arbitrarily.

The OP mentioned that he could easily measure the line currents (and presumably the angular relationship between those currents.) But with only those line current measurements (which are not separated by 120 degrees since the load is not balanced) the angle of the phase currents and phase voltages relative to the line currents is an unknown.

We know that the phase currents and voltages will be 120 degrees separated from each other, but we do not know how much Ia is separated from Iab, etc. That is why there are four unknowns, not three.

David....

The calculation basis changed when mivey responded to jakeself's statement that he had some metering class CT's ordered. I believe the assumption was made that line-line voltage was/is also being measured and angles (phase relationship) determined.

With phase angles known and say θ_Vab arbitrarily assigned 0?, θ_Va = -30? and θ_Vac = -60?. Essentially all line voltage angles can be calculated from the three measure angles (or from one if assuming an exact 120? phase relationship). All we have to do from there is reference line current angle to voltage angles, determining φ for each... and the rest is just vector math.

...but this all assumes voltage angles are being determined. If not, you are correct.

 

[david luchini]

David, there must be a common reference for all angles. I would assign one of the L-L voltage angles to be zero which then is the common reference for ALL other angles. If this is done, then "theta" is no longer an unknown.

OK, let me try it this way...If I measure the line currents of an unbalanced, delta connected, resistive load and tell you that the currents are as follows:

Ia=102.37<0
Ib=110.48<-118.56
Ic=108.96<117.04

What is the phase current angle of Iab? I don't even want to know the magnitude of Iab. Just the angle. How are you going to determine the angle of Iab with only the information I have given you? As far as I can tell, that angle is an unknown.

You cannot arbitrarily assign an angle of zero to one of the L-L voltages. In this example, you would have Vab at angle zero, Iab at angle zero, and Ia at angle zero. This is not possible.

 

[david luchini]

David....

The calculation basis changed when mivey responded to jakeself's statement that he had some metering class CT's ordered. I believe the assumption was made that line-line voltage was/is also being measured and angles (phase relationship) determined.

I see nothing to suggest that the line-line voltage and phase relationship is also being measured. The quote in post 29 was:

Just to give a little more info - I have some metering class CT's ordered so I can get more accurate line current measurements.

The only information offered as the starting point for finding the load currents is the measured Line Currents. I've made the assumption that the angular relationship between the line currents was also measured (if not, finding a solution is even more difficult.) The angular relationship between the line currents and phase currents is unknown.

 

[Smart $]

OK, let me try it this way...If I measure the line currents of an unbalanced, delta connected, resistive load and tell you that the currents are as follows:

Ia=102.37<0
Ib=110.48<-118.56
Ic=108.96<117.04

What is the phase current angle of Iab? I don't even want to know the magnitude of Iab. Just the angle. How are you going to determine the angle of Iab with only the information I have given you? As far as I can tell, that angle is an unknown.

You cannot arbitrarily assign an angle of zero to one of the L-L voltages. In this example, you would have Vab at angle zero, Iab at angle zero, and Ia at angle zero. This is not possible.

Ibc=60.00<30.50?
Ica=67.50<-89.50?
Iab=58.20<149.50?

As I mentioned earlier, the first fernat point is the geometric solution (restrictions apply).

 

[Smart $]

I see nothing to suggest that the line-line voltage and phase relationship is also being measured. The quote in post 29 was:



The only information offered as the starting point for finding the load currents is the measured Line Currents. I've made the assumption that the angular relationship between the line currents was also measured (if not, finding a solution is even more difficult.) The angular relationship between the line currents and phase currents is unknown.

I agree. That's why I said I believe that assumption was made. But there is a solution as noted in my other post... and line current phase relationships need not be known.

 

[Smart $]

Ibc=60.00<30.50?
Ica=67.50<-89.50?
Iab=58.20<149.50?
As I mentioned earlier, the first fernat point is the geometric solution (restrictions apply).

Ooops!!! That should have been...

Iab=60.00<30.50?
Ibc=67.50<-89.50?
Ica=58.20<149.50?

 

[david luchini]

Ooops!!! That should have been...

Iab=60.00<30.50?
Ibc=67.50<-89.50?
Ica=58.20<149.50?

I agree that your geometric solution would be the way to go. Solving 3 simultaneous equations with 4 unknowns would be too much math for me.

However, I think your method led you astray somewhere. For the values of Iab, Ibc, and Ica that you list above, I come up with:

Ia=101.85<0.51
Ib=110.48<-117.5
Ic=109.50<117.6

Probably just a add/subtract error somewhere.

 

[gar]

110125-0944 EST

If three current transformers are added to the system, then the logical location is one on each load bank rather than the supply lines and now direct measurements of the desired currents are possible. This also provides a convenient means of measuring load bank power, especially if phase shift modulation of current is in use.

In the present system if the SCR switches are individually controllable, then the load could be limited to one or two banks at a time and appropriate line currents would directly read load current.

.

 

[jakeself]

Thank you for continuing the discussion. I still have not come up with a mathematical solution that I could implement within my PLC. The excel solver in the spreadsheet I previously attached seems to be the best way to backtrack and find the phase current magnitudes based on the line current magnitudes so far. (Which is still not a great solution because I will be required to get the data into excel each time to calculate the wattage between phases.)

As I am continuing to work on this machine and reading through some of your posts, I have a few things to clarify:

• I am only able to measure line current RMS magnitude. (not phase angles). I would like to translate this into phase current RMS magnitude to find the wattage between phases. Similar to what is shown in the excel screenshot previously posted.
• There are multiple heaters in parallel between each pair of phases. One heater going bad will change the wattage between those phases, but will not completely disconnect the load between those phases.
• Our SCRs are 3-phase with 2 controlled legs using a contactor style input control signal. It is part# DC21-24C0-0000 listed at this link if you are interested: http://www.watlow.com/downloads/en/specsheets/windmc0309.pdf
• We have a few different setups using these SCRs. A couple of them are inherently unbalanced even when all of the elements are working. I tried to simplify the problem in my early explanations, but a couple of the responses on here are assuming a balanced load when everything is working properly. I wanted to point out that in these scenarios, the load is unbalanced even when all elements are working. This is due to the fact that these setups have a mixture of 1000W and 650W elements and it was not possible to complete balance them.

Let me know if there is any other information I can provide to help out. Is it possible to do what I am asking? Is my excel solver really calculating phase current magnitudes properly when only line current magnitudes are typed in?

The machine is currently being re-wired. Once this is completed, I will be able to conduct some tests and see if the equations used in my excel solver match up to the test conditions. I will be able to get some data with all heaters working and disconnect some heaters and see the results at that time.

 

[Open Neutral]

I have an unbalanced IR Heater load setup as a delta load. Voltage is 3-phase 240VAC. There are multiple heaters in parallel between each pair of phases. We are simply looking for a method to tell how many bad heating elements there are.

Contrarian approach:

CT's or Hall Effect sensors on each heater, maybe?