2 Watt Meter for 4 wire circuit?

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mull982

Senior Member
For a balanced 3phase system with 3 conductors I know you can use the "2 wattmeter" method for determining the total power in the system with only 2CT's and 2PT's.

What about for a 3 phase 4-wire unbalanced wye system. Can you still use the "2 wattmeter method" or must you add additional CT's and PT's?
 

mull982

Senior Member
I've given this some thought and am thinking that only (2) PT's and (2) CT's would still be needed (2 wattmeter) for determining the total power in a 4 wire circuit since the neutral will only carry the unbalanced current and not necessarily change the total power in the circuit? Is this correct?

To back this up I also read somewhere that an n phase system can have its total power measured with n-1 wattmeters. Even though this is a 4 wire system it is still a three phase system so I would think that its power can be measured with 3-1=2 wattmeters.
 

jim dungar

Moderator
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Location
Wisconsin
Occupation
PE (Retired) - Power Systems
I've given this some thought and am thinking that only (2) PT's and (2) CT's would still be needed (2 wattmeter) for determining the total power in a 4 wire circuit since the neutral will only carry the unbalanced current and not necessarily change the total power in the circuit? Is this correct?
Not quite.
Suppose your (2) CTs are on phases A and C but your unbalanced load is on B to neutral.

This type of circuit requires a 'modified Two-Element meter' This is fairly easy to do with a mechanical device where the line current flows directly through the 'field' coils. But it would require (3) CT's and (3) PT's when not direct connected.
 

jtester

Senior Member
Location
Las Cruces N.M.
Not quite.
Suppose your (2) CTs are on phases A and C but your unbalanced load is on B to neutral.

This type of circuit requires a 'modified Two-Element meter' This is fairly easy to do with a mechanical device where the line current flows directly through the 'field' coils. But it would require (3) CT's and (3) PT's when not direct connected.

I have an old Westinghouse meter course, that shows 2 CT's being used, and it claims that the accuracy is equal to a 2 1/2 stator meter. I tried to scan it, but can't get the dimension of the picture small enough to post.

I'll try to describe the connection. A phase goes into the polarity side of CT #1, and out to the load, C phase goes into the polarity side of CT #2 and out to the load, B phase goes into the nonpolarity side of CT #2, out and then into the nonpolarity side of CT #1, out and then to the load. The CT secondary leads are wired in a wye, and the neutral lead is fed into 2 of the current terminals on the meter, the other 2 leads feed the other 2 meter current terminals.

I have always believed that metering is as much black magic as it is science. I don't pretend to understand it, but there it is.

Jim T
 

mivey

Senior Member
I've given this some thought and am thinking that only (2) PT's and (2) CT's would still be needed (2 wattmeter) for determining the total power in a 4 wire circuit since the neutral will only carry the unbalanced current and not necessarily change the total power in the circuit? Is this correct?
no

To back this up I also read somewhere that an n phase system can have its total power measured with n-1 wattmeters. Even though this is a 4 wire system it is still a three phase system so I would think that its power can be measured with 3-1=2 wattmeters.
That is incorrect. What you read was that an n-wire system can be accurately measured with n-1 wattmeters if the common point for the voltages in the wattmeters was one of the wires. We are concerned with the number of current-carrying conductors.
 

mivey

Senior Member
I have an old Westinghouse meter course, that shows 2 CT's being used, and it claims that the accuracy is equal to a 2 1/2 stator meter. I tried to scan it, but can't get the dimension of the picture small enough to post.

I'll try to describe the connection. A phase goes into the polarity side of CT #1, and out to the load, C phase goes into the polarity side of CT #2 and out to the load, B phase goes into the nonpolarity side of CT #2, out and then into the nonpolarity side of CT #1, out and then to the load. The CT secondary leads are wired in a wye, and the neutral lead is fed into 2 of the current terminals on the meter, the other 2 leads feed the other 2 meter current terminals.

I have always believed that metering is as much black magic as it is science. I don't pretend to understand it, but there it is.

Jim T
Nothing magical about it as it is just math. It may appear magical if you don't recognize that the math is only a model of the physical reality.

The key to the 2-1/2 stator meter is that you have three currents and two voltages. The missing third voltages is produced by inverting the two measured voltages and summing them. This is done with the assumption that the voltages are all equal in magnitude and have even phase displacements. Any deviation produces an inaccuracy but it might be considered acceptable in many cases as the voltages may be reasonably balanced.

The question is: How do we measure three currents and two voltages but only use two CTs and two PTs ?

The math is:
#1) 3 Stators: (Van ? Ia) + (Vbn ? Ib) + (Vcn ? Ic)

#2) Approximate "b" voltage with sum of inverted voltages: (Van ? Ia) + ([– Van – Vcn] ? Ib) + (Vcn ? Ic)

#3) You may also use the inverted "b" current with a positive voltage sum approximation: (Van ? Ia) + ([Van + Vcn] ? -Ib) + (Vcn ? Ic)

#4) Run the inverted current (i.e. run it backwards) through the other two CT's (denoted with "{}": (Van ? {Ia-Ib}) + (Vcn ? {Ic-Ib})

FWIW, this is a real application of real inverted voltages and currents, not just some math trick. It is a physical reality, as are the inherent inaccuracies. #1 is the accurate way to meter the circuit.
 

jtester

Senior Member
Location
Las Cruces N.M.
My hat is off to Mivey, your explanation is brilliant. I still think this is black magic, you just have proven to be an accomplished practitioner.

Thanks for the information.

Jim T
 
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