kW Meter hook-up (2 element) 3

[JBinCA]

Hi,

On a recent project, I was asked to check operation of a panelmount kW meter at the last minute. Since we didn't have a manual defining the test, I attempted to draw out the phasors of the meter and devise a test of my own.

The connections to the meter (per the diagram on the side) are are as follows (system is 12kV 3 wire / ungrounded):

open delta - open delta PTs with B phases grounded.

A and C phase CT inputs.

Since the meter is a 2 element meter, a single phase test is possible with one PT and one CT input being injected from the relay test set. This would yield 1/2 of the calculated primary kw (V * I * sqrt (3) * PTR * CTR). This single element test did produce 1/2 the indicated power of the dual element test.

The problem I can't explain is the phase angles involved. Since the meter is "looking at" phase to phase voltages, it seems to me that unity pf would occur with some phase angle between the voltage and current of a particular elemet. Testing proved that unity pf occured with voltage and current in phase (maximum kW reading at given voltage and current magnitude occured when voltage and current were in phase).

As I analyze things, A - N voltage (on primary) should be in phase with A phase current (on primary) at Unity pf. It follows that A-B voltage should lead A phase current by 150 deg on the secondary at unity pf.

Admittedly, it's been a long time since I've regularly had to draw out phasors. I'm certain the error is with my analysis and that the meter is operating properly.

I would appreciate it if someone is able to tell me where I went wrong or suggest an online reference that they believe breaks down phasors for kW (MW) metering satisfactorily.

Best Regards,

JBinCA

 

[davidbeach]

In the two wattmeter method you won't get half the power in each element except for unity power factor. Google two watt metermethod and see if you don't find a good analysis.

 

[stevenal]

The beauty of this is that both the balanced three phase loads and the line to line connected single phase loads will be metered correctly. Balanced three phase loads at unity do not have the same current angles as the single phase loads do at unity, but one, the other, or any combination will all be metered at unity. The only error I see is the assumption that you can simulate balanced three phase loading with a single phase test set. Since no neutral is available, you cannot. Draw it out and do the math. At unity, if one element leads, the other lags equally so the total vars are zero.

 

[waross]

Think of the connection first as two single phase transformers.
These may be metered with two watt meters or a two element watt meter. In a two element watt meter there is no interaction between the two elements. The reading should be the same as the sum of the readings of two single watt meters.
Now connect the transformers in open delta. This takes one jumper and the jumper should form a common point for both transformers and both PTs. The CTs should be on the leads that are not commoned. Each element of the meter is still measuring the output of same transformer.
The current and voltage angles are determined by the loads.
now if you add a third transformer and close the delta, the phase angles through the transformers change as the third transformer takes its share of the load, the load phase angles remain the same. The metering is on the load lines, thus the metering is accurate for both open delta and closed delta.
respectfully

 

[JBinCA]

Davidbeach,

Thank you for the recommendation on what to google. This first hit that google returns has certainly been helpful and I will reference it for further discusstion.

https://www.ohiosemitronics.com/pdf/tech_papers/Two-wattmeter-method(E).pdf

Please see the graphs on page six (2 and three element instantaneous power). The load power remains constant (= 1.5). You will find that the each element's contribution in the first graph (which is equal to the RMS value of the waveform) is 0.5. Each element is reading 1/3 of the power.

You will find that the each element's contribution in the second graph (which is equal to the RMS value of the waveform) is .75. Each of the two elements is reading 1/2 of the power.

This is what I was referring to when I mentioned that each of the elements was responsible for 1/2 of the total indicated power.

You will also find that the graphs on pages 7-10, which illustrate non-unity pf's, show that the RMS value of each waveform is at 1/2 the total power.

Thanks again for the help.

JBinCA

 

[JBinCA]

Stevenal,

Thank you for your response. You are correct in stating that one cannot simulate balanced three phase loads with a single phase test set. However, as waross points out, there in no interraction between the two elements of a 2 element watt meter. Therefore, there is no need to simulate balances three phase conditions. It is actually quite common to test the meters with a single phase source that sends voltage in parallel and current in series to the meter inputs.

I have always thought that a 2 element meter would only accurately meter a balanced three phase system, but after reading the white-paper I referenced above I am now of the oppinion that the 2 element meter will accurately meter all kW except those lost due to ground leakage.

https://www.ohiosemitronics.com/pdf/tech_papers/Two-wattmeter-method(E).pdf

Thanks again.

JBinCA

 

[JBinCA]

Waross,

I'm going to have to do some sketching in order to digest your explanation. I would like to get your oppinion on the following point though:

I know that electro-mechanical 2 element kW meters have no interraction between the two elements. If I understand you correctly, this is true of solid state and microprocessor based meters as well. Is that your understanding?

Thanks and best regards,

JBinCA

 

[waross]

Hello JBinCA;
That is my understanding. I have not researched it though. Perhaps someone else can give us some info.
I was checking the hookup and multiplier factor on an installation last week. I had done the original install, and then in 2001, they lost one phase of an undersea cable. I used a two element meter and an open delta 480 volt transformer connection. The only PTs available were 240 to 120. so I took 240 volts of the center tap of the 240:480 volt transformer windings. Fed that to the 240/120 PTs and got 120 volta for the meter.
No problem. Then in 2005, the undersea cable was repaired, and the plant wanted to change the voltage to 240 volts. The crews did not realise that when they reconnected the transformers, the multiplier changed from 240 to 120.
I had a delightfull visit to a tropical island to sort it out and help determine when the deed occured. It's such a small utility that the general manager personally supervises the men when they are changing transformer taps. There was no record of the date of the transformer change, but it was just before the season started. When I pointed out a jump in the billing of over 580% from one month to the next, it was agreed that that was the time of the error. Prior to the transformer reconnection, the plant went on their own generators when they had a heavy load.
Incidently, that connection will also meter a wye transformer bank, if there are no loads connected to the neutral. The phase to phase, load phase angles are the same as for a delta bank.
respectfully

 

[swn1]

When checking the calibration of a two-element meter with a single-phase source, you need to energize both potential coils. There is an adjustable shading coil on the potential coil cores that is used to generate torque to cancel the friction in the shaft bearings and register. Your low-power calibration will be way off if you only energize one potential coil, or if you use a voltage significantly different from the usual operating point of the system.

With typical load power factors one element or the other is responsible for essentially all of the positive torque. The other element adds or subtracts a small amount, depending on just what the PF is. So just doing the series/parallel test isn't a very good test. You should at least follow it up with a "buck" test, with the elements hooked up to produce equal and opposite torques. If you get significant drift, adjust the balance.

The bureau of reclamation has a pretty thorough procedure for calibrating electromechanical energy meters. You can also piece together a good notion of what to do by reading the instruction manuals for six to ten different meters. Unfortunately, no one meter's manual is going to educate you by itself.

Note that your source is probably not calibrated accurately enough to calibrate an energy meter to revenue accuracy. You'll want to use a reference energy meter to in series (CT) / parallel (PT) with your meter to get to that level of accuracy.

Finally, the most accurately calibrated meter in the world is worthless if it is wired incorrectly or if the instrument transformer ratios do not match the nameplate or any of a large number of other possible application problems. You need to verify it at the system level as well.

 

[JBinCA]

Hi SWN1,

Thanks for the response. The procedures you've described sound like the same one's we use for calibration of watt-hour demand meters (energy meters). We typically use a watt-hour standard in the test circuit.

This is a panel mount power meter, and one just used for operator indications, so none of the revenue grade bells and whistes are there.

I guess it would make sense to rephrase my question this way:

What phase angle would we expect between A phase current and Va-b at the meter input terminals at unity load pf?

I expected a 30 deg phase shift (or 150 degree) the way I analyze the system, but upon testing I found that 0 degree phase shift corresponded to maximum indicated power (with fixed secondary voltage and current magnitude).

Thanks to all for viewing and responding to this thread.

Regards,

JBinCA

 

[stevenal]

"What phase angle would we expect between A phase current and Va-b at the meter input terminals at unity load pf?"

This is equivalent to a single phase load connected a - b. If this is a unity pf load, the angle will zero.

 

[JBinCA]

Stevenal,

Thanks for the response. I agree that the meter would be wired the same as for a single phase load, but it is not measuring a single phase load. Since it's not intended to measure a single phase load, I expected that it would have a characteristic phase shift between L-L voltage and line current.

Another way to illustrate:

1. Power 3ph = 3 * V _l-n * I _l * cos theta.
theta is between l-n voltage and current.

2. Power 3ph = sqrt(3) * V_l-l * I _l * cos theta

Theta (in eq 2) is still between l-n voltage and current, correct?

A meter measuring based upon equation 1 would not be looking for a characteristic phase shift between the voltage and current inputs.

A meter measuring based upon equation 2 would be looking for a characteristic phase shift between the voltage and current inputs since there is a phase difference between the Vl-l and V l-n.

Am I wrong here?

Thanks again to all for responding

 

[JBinCA]

I don't know if my OP stated my question sufficiently, but I now have the answer and thought I'd post it here in case anyone is interested.

Here's the proof.

First, power in a 3P3W or balanced 3P4W system can be calculated by either of the two equations below.

1. P_3ph = V_L-L * I_L * sqrt(3) * cos (theta)

2. P_3ph = V_L-N * I_L * 3 * cos (theta)

I have confirmed with Yokogawa's tech support their belief that all solid-state 2 element kw meters are made such that each element contributes independently to total kw. This mimics the operation of the electromechanical meters they have come to replace.

A 3 element kW meter works by employing equation 2 above. Each phase's L-N voltage is multiplied by that phase's current and maximum power occurs when the two are in phase. The calculated powers are then summed to obtain total power.

A 2 element kW meter works by employing equation 1 (sort of). 2 of the exact same individual elements described above are utilized, which means maximum power reading in each element still occurs when the voltage and current inputs to each element are in phase. The elements are wired such that their voltage input comes from a phase to phase voltage (which does have a 30 deg phase shift relative to the phase to N voltage) and the current inputs remain the same. The total power equation becomes:

P_3ph = V_L-L * I_L * cos (30) * 2 * cos (theta)

which equals equation 1 since

cos(30) = .8660 and 2 *.8660 = 1.732 = sqrt (3).

Therefore, the 2 element wattmeter can be tested by secondary injection of X volts and y amps in phase with one another or X * sqrt(3) volts and y amps 30 degrees apart because the increase in voltage is offset by the phase shift. This second arrangement is what the meter sees when placed in service in 3P3W or balanced 3P4W system.

But the big lesson learned is .... Don't expect your work to make sense if you try drawing phasors at the end of an 18 hour shift!

 

[stevenal]

I'm confused about your use of the word "intent". Does this apply to your project or the meter? This metering configuration is "intended" to accurately measure power to single phase loads, three phase loads, and any combination of the above that can be connected to the three wires. Revenue grade accuracy can be achieved. Blondel works.

 

[waross]

Almost all the meter connections that I am aware of have no intentional phase shift between the voltage and current.
Any phase shift is due to the power factor of the load and is interpretted as such by the meter.
An exception is the delta CT connection to measure 4 wire wye installations with unbalanced currents with a two element meter. This works but is affected by voltage unbalance.
respectfully

 

[stevenal]

Waross,

I gotta disagree with the guy with the star. With 2 element metering on a balanced three phase resistive load, each element will independently a 30 degree shift. One leads while the other lags, though, and the resultant is zero reactive power and pf=1.

Two elements on a 4 wire violates Blondel.

 

[waross]

"A" Phase is measured as a single phase transformer with one element.
"B" Phase is measured as a single phase transformer with the other element.
Here's where it gets tricky.
You are familiar with resolving currents into the real power and the reactive power components.
"C" Phase current may be resolved into an "A" Phase component and a "B" Phase component.
The CT on "C" phase is wired so that the CT secondary current flows through both elements of the meter.
"A" Phase extracts the "A" Phase component and adds it to the "A" Phase total. (The element will only respond to that component of the current that is in phase with the "A" Phase voltage.
The "B" Phase element does the same.
If the voltages to neutral are not balanced, there will be corresponding errors with the "C" phase energy.
Reference: Westinghouse Fourth edition, Meter and Instrument Transformer Application Guide and condensed Metering Course.
This metering method may be used with the third phase CT connected in delta, or with two CTs. The third p[hase conductor is passed through the other two CTs in the reverse direction. Westinghouse gives the connections but the explanation is mine.
The first time I used this connection, I hid a comparison meter with different connections for a few months to reassure myself that it would indeed work, and that I had not made any connection errors. I am not called upon to do revenue metering very often but it happens. If the connection has CTs and/or PTs I hit the books for a few hours of refresher and then double check my work with a hidden check meter. One time my check meter was a 100 amp residential meter driven be a CT on one phase. The normal multiplier was multiplied by 3 to account for the other 2 phases. Normally mistakes in metering connections are in whole number ratios or are related to sqrt. 3. I tracked within about 3% for 3 months. Actually, feeding a meter with 15 test amps with 2 or 3 amps or less depending on the load, I was surprised to track that close.
respectfully

 

[swn1]

When you hook up a two element meter to a three-phase circuit with the typical open-delta PT arangement the voltage triangle is offset because the B corner is grounded.

This is irrelevant when computing energy in a three-wire load circuit, in principle.

In practice, the effect is that the energy is "allocated" to one element more than another. There is zero energy allocated to the B phase, so no element is phycially present. The potential of P is used as the reference for the other phases and the current in B is ignored.

At unity power factor you have one element 30 degrees leading and the other 30 degrees lagging. Which is which depends on the phase rotation direction and is essentially irrelevant.

As the power factor begins to lag, one element picks up more of the energy because its current phasor rotates into alignment with the offset potential phasor. Simultaneously the other element picks up less energy because its current phasor is rotating away from the offset potential vector.

The electronic meters are almost all very poorly documented. As far as I have been able to ascertain, telling them they have a delta PT arrangement simply disables the display of individual phase power and energy and phase-to-ground voltage values. It may also disable B-phase computation on some models but not on the ones I've tested.

At least one manufacturer recommends checking for equal response in the power readings when pulling the PT fuses on each phase as a means of verifying corrent installation. This only works with a unity power factor load or with a balanced load and wye PTs. We seldome see either.

 

[JBinCA]

Swn1,

Thanks for the information. Good stuff.

I have run into a few meters / relays that will disable calculation of certain values based upon the power system configuration settings.

I also agree, that the low end of the meter market is intollerably poorly documented.

Thanks again.

JB