Power Calculation Unbalanced 3 Phase

[StephenSDH]

I see what you mean with the power factor not equal to 1. Perhaps backing into the KW is more difficult then I thought.

I came up with a formula to calculate KW. Not exact. I first calculate power based on average current and then multiply by an unbalanced factor. It is exact for balanced and single phase loads, but in-between it appears to be around 2 percent off.

 

[GoldDigger]

Why not just measure the baseline currents for each zone at a time when the elements are operating properly instead of trying to calculate a theoretical number?
If you insist on calculating, you can use a spreadsheet or graphing calculator to determine the line to line currents given the line currents.
It is a system of three vector equations in three unknowns and a unique solution must exist.
Having a closed form formula is nice, but not at all necessary.
The power, and therefore the normal line to line current for each heater is known, but only to the extent that the power rating of each heater will have a value inside a manufacturing tolerance range. Just remeasure each time a new heat strip is installed.

 

[winnie]

Is there some un-mentioned factor that is forcing you to work with power values rather than current values?

You have CTs connected to your PLC. They measure current.

If you calculate the _expected_ current given the proper resistors and compare that with the _measured_ current values, doesn't this also tell you if you've lost a resistor?

If you want to calculate currents correctly, you have to represent all of the currents at a given node using vectors, and then do the vector addition.

If you want to calculate phase power, then you need to represent the voltage at the phase nodes using vectors, and you have to take the 'dot product' of voltage and current.

If you pm me with an e-mail address, I will send you a very rough spread sheet that takes any combination of L-L or L-N resistive loads, calculates the current through those loads, and does the vector math to figure out the phase current and phase watts. This is not a finished product that you can use to do your engineering calculations, just an example that you can use to reference the math.

-Jon

 

[gar]

141123-0924 EST

StephenSDH:

In an earlier post of mine I suggested that you probably don't want to do the vector math to determine the power in each leg of your delta load from the delta line currents. To do this in your PLC is probably a waste of effort.

I later suggested, and partially by implication, that you compare the known correct currents, obviously by having measured the mold when it was known to be good at a known voltage, and during operation comparing the actual currents with the reference currents. Implied was that these current values at the known voltage must be adjusted for the actual voltage.

For a single resistance failure I indicated how you could know the delta leg where the failure was.

To make this work in your PLC you have a normalized table for the current in each phase at 600 V for each different mold. A separate table for each different mold. The table is generated experimentally. When heaters are replaced in a mold, then a new table has to be created for that mold, and updated in the PLC.

We have to assume that all phase voltages have a 1 to 1 relationship, but vary together as line voltage varies. Otherwise the problem gets difficult. If we assume the tables have been normalized to 600 V, then a voltage measurement is needed in addition to the three line currents. Each measured line current is adjusted by Vin/600 and compared with its associated table value. This is a relatively simple operation in a PLC, easily understood, and convient for trouble shooting.

Since the mold has temperature feedback control we can assume that resistance values are constant. It is not clear if there is a single temperature sensor and only one contactor per mold. The current probably should be measured near the turn off time of the contactor. If your measuring resolution is such that accuracy is in the range 0.1% of nominal maximum expected current, then I would expect that a 1% change in resistance could be detected, this is just an off hand judgement.

.

 

[StephenSDH]

Winnie & Golddigger,

I will record the current for each phase and that will be helpful. I need to display wattage so the operator can compare the actual to the specs. Showing the 3 current values would be hard for them to make sense of. They are telling me a large percentage of the heaters are not the original size and they are buried in the mold. I'm not sure what phases they have the heaters connected to. It would be hard to come up with a correct base line. Winnie I'll PM you for the spreadsheet. Thanks!

Gar,

Like you suggested, I do have a recipe for each mold and I will log the current values for each zone & phase to the recipe table. Each zone has 1 contactor, 1 thermocouple, and 2-4 heaters. So there are 32 Contactors, 32 Thermocouples and approx. 100 heaters strips depending on the mold. I am planning on CT monitoring the mains and turning on each zone individually for a duration to capture the current draw.


Thanks for the help everyone. In retrospect I should have purchased a power meter and let the meter calculate the true power. I was mistaken to think calculating KW, would be easy.

Thanks, Steve

 

[GoldDigger]

With a power meter, you would still have to measure current at some point to figure out which heater was bad.
But at least you would know to take that mold out of service immediately.

 

[gar]

141123-1248 EST

StephenSDH:

You have only given pieces of the story as this thread has progressed.

What do you really know and want to do?

Now we have 32 contactors, 32 controllers, and 32 thermocouples. I have to assume the controllers are not and really can not be totally synchronized with each other. Thus, with a bang-bang control function and just measuring the total power input to the mold you have a problem.

Originally your post was about detecting failed heaters. Now it has grown to providing information to the operator.

With independent zones (a particular controller and thermocouple with a few heating elements) it seems logical to measure each zone independently.

Put a 3 phase power monitor on each zone. For example a Load Controls PH-3A. For each zone measure the short time average power when the zone is on. This is used to evaluate whether the heating elements are OK. In addition add (accumulate) samples of the short time average over a time period long enough to encompass one or more on-off cycles of the contactor synchronized to start a new accumulation at the start of ON and to stop at the start of another ON. Determine the average power, accumulator value divided by the number of samples.

Previously I mentioned measuring the current near the end of the on cycle, but I now think it would better shortly after the start of ON to look for bad heaters. You only have a few heaters per zone. Thus, this won't be important.

To determine average power you need many samples per on-off period.

Also the ratio of ON power to average power could be an indicator of a failed heater.

.

 

[StephenSDH]

141123-1248 EST

StephenSDH:

You have only given pieces of the story as this thread has progressed.

What do you really know and want to do?

Now we have 32 contactors, 32 controllers, and 32 thermocouples. I have to assume the controllers are not and really can not be totally synchronized with each other. Thus, with a bang-bang control function and just measuring the total power input to the mold you have a problem.

Originally your post was about detecting failed heaters. Now it has grown to providing information to the operator.

With independent zones (a particular controller and thermocouple with a few heating elements) it seems logical to measure each zone independently.

Put a 3 phase power monitor on each zone. For example a Load Controls PH-3A. For each zone measure the short time average power when the zone is on. This is used to evaluate whether the heating elements are OK. In addition add (accumulate) samples of the short time average over a time period long enough to encompass one or more on-off cycles of the contactor synchronized to start a new accumulation at the start of ON and to stop at the start of another ON. Determine the average power, accumulator value divided by the number of samples.

Previously I mentioned measuring the current near the end of the on cycle, but I now think it would better shortly after the start of ON to look for bad heaters. You only have a few heaters per zone. Thus, this won't be important.

To determine average power you need many samples per on-off period.

Also the ratio of ON power to average power could be an indicator of a failed heater.

.

Gar,

My original posts all said I am looking to calculate KW based on unbalanced 3 phase heat load and need help with the calculation. There is no story. If you don't know how to calculate KW for an unbalanced heater load that's fine, because I don't either. I tried to provide enough detail on the first post so I do not waste people's time, but based on the questions I guess I failed at this. In the future I will try to be more clear about the question and provided a drawing from the beginning.

Happy Thanksgiving,

Steve

 

[gar]

141123-1414 EST

StephenSDH:

It is not that I don't know how to calculate the total power, it is a lot of work, but rather I think you may have a faulty system design. Now that you have introduced the fact that there are 32 zones with individual controllers, and you only want to monitor three line currents, then I believe you have major problems for total power measurement to detect a single heater failure. Power measurement is not needed to detect a heater failure. This comment is modified by my rereading your first post. See below.

If all you want is total power, then the Load Controls device will directly provide this information with one signal for your total system. This automatically uses all three currents and three voltages to calculate total power. Because of the design of the power monitor there is compensation for differences in the three phase voltages.

I do not have good information on accuracy and repeatability, but it is listed as 2.5% of full scale for accuracy, and 0.25% for repeatability. Minimum response time is 15 milliseconds (one full 60 Hz cycle). Nothing on zero drift or temperature coefficient.

Your present approach of measuring current is going to produce some time varying ripple resulting from the random operation of the various contactors.

Going back and rereading your original post I see you mention individually switching the zones to measure one zone at a time, and that there were several heaters per zone. Several meaning not very many, apparently about three. Thus, to sense that a heater element has failed will show up as a change in two of the three currents. The change will be at least moderate because of only a few heating elements. Easy to detect. Now from later posts we know individual zones have individual controllers and contactors.

winnie is apparently sending you a spreadsheet with the solutions to the simultaneous equations. He has done all the work for the simultaneous equations solution.

.

 

[Phil Corso]

Stephen,

Power measurement is an excellent way to detect element failure. It can even be done with just line-current measurement!

If interested in an EXCEL approach, contact me at " Cepsicon@aol.com "

Phil Corso

 

[Smart $]

...

It is not that I don't know how to calculate the total power, ...

What I'm wondering is: are the CT's on each zone or are there only three providing total system current. If the latter, with temp' controllers kicking zones on and off at discrete times, there would be no realistic way to determine single heater failure during an operation. The CT's must monitor each zone separately.

 

[gar]

141123-2350 EST

Smart $:

What I conclude from all the information provided is:

1. There are 32 zones each with a thermocouple, controller, and the bang-bang controller contactor. It is not clear if the PLC has control of the contactors, or if the controller function is performed in the PLC.

2. There are only a few heater elements per zone, possibly not much more than three.

3. Apparently all zones can be turned off except for a single zone to be tested.

4. I believe three CTs are used to simultaneous monitor all 32 zones under normal operation, and thus, under a test condition could monitor a single zone with contactor control. With very few heaters per zone there should be no problem to detect failure of one or more heaters of the zone.

5. I believe the total heating elements in a mold may approach 100, and some of these may be substantially smaller than others. Therefore, even with long term averaging of total power input it is likely difficult to get accuracy or resolution that can detect 0.1% or less change in total power. The random variations of needed power by the mold may swamp out any meaningful signal from a small heater being lost. By testing only one zone at a time with only a few heaters the test becomes feasible.

6. I believe direct power measurement is a far better way to monitor this system than to try to work back from the three phase line currents.

.

 

[Smart $]

1. There are 32 zones each with a thermocouple, controller, and the bang-bang controller contactor. It is not clear if the PLC has control of the contactors, or if the controller function is performed in the PLC.

Agree.

2. There are only a few heater elements per zone, possibly not much more than three.

IIRC, he said 2 to 4 per zone.

3. Apparently all zones can be turned off except for a single zone to be tested.

That's what it sounds like... which leads me to believe the PLC has control, regardless of whether it is the temperature controller or not.

4. I believe three CTs are used to simultaneous monitor all 32 zones under normal operation, and thus, under a test condition could monitor a single zone with contactor control. With very few heaters per zone there should be no problem to detect failure of one or more heaters of the zone.

Agree. In post #25 he said CT's monitoring the mains.

5. I believe the total heating elements in a mold may approach 100, and some of these may be substantially smaller than others. Therefore, even with long term averaging of total power input it is likely difficult to get accuracy or resolution that can detect 0.1% or less change in total power. The random variations of needed power by the mold may swamp out any meaningful signal from a small heater being lost. By testing only one zone at a time with only a few heaters the test becomes feasible.

Feasible, yes. I have to assume there is down time between casts which would be the ideal time to do the testing. If down time is too short, it'll have to be on-the-go.

6. I believe direct power measurement is a far better way to monitor this system than to try to work back from the three phase line currents.

Perhaps... perhaps not. To determine loss of a single heater would still have to resort ot testing each zone separately. So IMO no gain in awareness. Just easier implementation in setting up a visual output in kW.

I still say all that is necessary is to take each zone's line current measurements, compare to expected line currents (whether calculated or measured) to verify all heaters are functioning or trigger an alarm if any value is below a predetermined threshold value. The alarm could easily be set up to notify which zone a faulty heater is located and to which lines it is connected. I don't believe the operator really needs to know the ON wattage for comparison. Displaying zone wattage is a matter of form vs. function.

I understand the need. One may think temperature would suffice. But if the zone is made up of 4 heaters for example, the controller will just try to compensate by keeping the other three on longer... and likely result in three too-hot spots and one too-cold spot.

 

[StephenSDH]

141123-1414 EST

StephenSDH:

It is not that I don't know how to calculate the total power, it is a lot of work, but rather I think you may have a faulty system design. Now that you have introduced the fact that there are 32 zones with individual controllers, and you only want to monitor three line currents, then I believe you have major problems for total power measurement to detect a single heater failure. Power measurement is not needed to detect a heater failure. This comment is modified by my rereading your first post. See below.

If all you want is total power, then the Load Controls device will directly provide this information with one signal for your total system. This automatically uses all three currents and three voltages to calculate total power. Because of the design of the power monitor there is compensation for differences in the three phase voltages.

I do not have good information on accuracy and repeatability, but it is listed as 2.5% of full scale for accuracy, and 0.25% for repeatability. Minimum response time is 15 milliseconds (one full 60 Hz cycle). Nothing on zero drift or temperature coefficient.

Your present approach of measuring current is going to produce some time varying ripple resulting from the random operation of the various contactors.

Going back and rereading your original post I see you mention individually switching the zones to measure one zone at a time, and that there were several heaters per zone. Several meaning not very many, apparently about three. Thus, to sense that a heater element has failed will show up as a change in two of the three currents. The change will be at least moderate because of only a few heating elements. Easy to detect. Now from later posts we know individual zones have individual controllers and contactors.

winnie is apparently sending you a spreadsheet with the solutions to the simultaneous equations. He has done all the work for the simultaneous equations solution.

.

Gar,

Here is the drawings of the complete system, if your interested.

https://www.dropbox.com/s/spqecw0h168x8r2/E31606.pdf?dl=0
Sheet 2 is the Contactors, Sheet 22 is the coils, Sheet 20 is the thermocouples

The PLC controls the zones not a temp controller. The PLC will first turn off all the zones so there is 0 KW and get a base line. Then it will energize just 1 zone and log the 3 current values and make a KW calculation. I will leave it energized for 2-3 seconds, however long it takes for current to be steady state. Then I will turn that zone off and energized the next zone. Rinse Repeat for 32. There will be no switching during the measurements.

Steve

 

[StephenSDH]

Agree.


IIRC, he said 2 to 4 per zone.


That's what it sounds like... which leads me to believe the PLC has control, regardless of whether it is the temperature controller or not.


Agree. In post #25 he said CT's monitoring the mains.


Feasible, yes. I have to assume there is down time between casts which would be the ideal time to do the testing. If down time is too short, it'll have to be on-the-go.


Perhaps... perhaps not. To determine loss of a single heater would still have to resort ot testing each zone separately. So IMO no gain in awareness. Just easier implementation in setting up a visual output in kW.

I still say all that is necessary is to take each zone's line current measurements, compare to expected line currents (whether calculated or measured) to verify all heaters are functioning or trigger an alarm if any value is below a predetermined threshold value. The alarm could easily be set up to notify which zone a faulty heater is located and to which lines it is connected. I don't believe the operator really needs to know the ON wattage for comparison. Displaying zone wattage is a matter of form vs. function.

I understand the need. One may think temperature would suffice. But if the zone is made up of 4 heaters for example, the controller will just try to compensate by keeping the other three on longer... and likely result in three too-hot spots and one too-cold spot.

Sounds like you got everything right. I think monitoring current would be more accurate and repeatable. I just don't know the phases the heaters are connected to and if they have the right heaters installed now. They have over a dozen molds with 32 zones and they are always repairing heaters so even if the phasing changes the KW should stay the same. I do like monitoring the current, I'll have the see how it goes.

The operator has a sheet of paper that shows the kw for each zone, so if I can display KW to them they can determine if it matches.

Here is a sketch of the zones.
https://www.dropbox.com/s/eyorv2060zhyvft/20141124_083411.jpg?dl=0

The heaters are against a steel plate and the product is on the other side of the plate. If one heater strip fails or the heater strip is the wrong wattage the zone will still make temp at the thermocouple position, but you end up with cold/hot spots.

 

[StephenSDH]

Stephen,

Power measurement is an excellent way to detect element failure. It can even be done with just line-current measurement!

If interested in an EXCEL approach, contact me at " Cepsicon@aol.com "

Phil Corso

Thanks. Emailing.

 

[Phil Corso]

Stephen,

On its way.

Phil

 

[Phil Corso]

To all...

Finally, an appropriate 1-page EXCEL program was sent to StephenSDG today!

If others are interest my No-Cost offer still stands! But, anonymity wont get you a copy!

Regards, Phil Corso