Two-Element (Two-Stator) Meter
The three-wire, three-phase delta service is usually metered with a two-stator meter in accordance with Blondel’s Theorem. The meter used has internal components identical to those of network meters, but may differ slightly in base construction.

Typical meter connections are shown in Figure 7-4. In the top element (stator) of the meter the current sensor carries the current in line lA and the voltage sensor has load voltage AB impressed on it. The bottom element (stator) current sensor carries line current 3C and its corresponding voltage sensor has load voltage CB impressed. Line 2B is used as the common line for the common voltage-sensor connections.

The phasor diagram of Figure 7-4 is drawn for balanced load conditions. The phasors representing the load phase currents IAB, IBC, and ICA are shown in the diagram lagging their respective phase voltages by a small angle . By definition, this is the load power-factor angle. The meter current coils have line currents flowing through them, as previously stated, which differ from the phase currents. To determine line currents, Kirchhoff’s Current Law is used at junction points A and C in the circuit diagram. Applying this law, the following two equations are obtained for the required line currents:

The operations indicated in these equations have been performed in the phasor diagrams to obtain I1A and I3C. Examination of the phasor diagram shows that for balanced loads the magnitude of the line currents is equal to the magnitude of the phase currents times the sqrt of 3.

The top element (stator) in Figure 7-4 has voltage EAB impressed and carries current I1A. These two quantities have been circled in the phasor diagram and inspection of the diagram shows that for the general case the angle between them is equal to 30° . Therefore, the power measured by the top element (stator) is EABI1Acos(30° ) for any balanced-load power factor. Similarly, the bottom element (stator) uses voltage ECB and current I3C. These phasors have also been circled on the diagram and in this case the angle between them is 30° . The bottom element (stator) power is then ECBI3Ccos(30° ) for balanced loads. The sum of these two expressions is the total metered power.

Examination of the two expressions for power shows that even with a unity
power factor load the meter currents are not in phase with their respective
voltages. With a balanced unity power factor load the current lags by 30° in the top
element (stator) and leads by 30° in the bottom element (stator). However, this
is correct metering. To illustrate this more cleanly, consider an actual load of
15 amperes at the unity power factor in each phase with a 240-volt delta supply.
The total power in this load is:
3 EPhase IPhase cos 3 240 15 1 10,800 watts
Each element (stator) of the meter measures:
Top Element EABI1Acos(30° )
Since I1A 3 IPhase
Top Element 240 3 15 cos(30° 0°)
240 3 15 0.866 5,400 watts
Bottom Element ECBI3Ccos(30° °)
Since I3C 3 IPhase
Bottom Element 240 3 15 cos(30° 0°)
240 3 15 0.866 5,400 watts
Total Meter Power Top Element Bottom Element 5,400 5,400
10,800 watts Total Load Power
When the balanced load power factor lags, the phase angles in the meter vary
in accordance with the 30° expressions. When the load power factor reaches
50%, the magnitude of is 60°. The top stator phase angle becomes 30° 90°
and, since the cosine of 90° is zero, the torque from this stator becomes zero at this
load power factor. To illustrate this with an example, assume the same load current
and voltage used in the preceding example with 50% load power factor.
Total Load Power 3 240 15 0.5 5,400 watts
Top Element 240 3 15 cos(30° 60°)
240 3 15 0 0 watts
Bottom Element 240 3 15 cos(30° 60°)
240 3 15 0.866 5,400 watts
Total Meter Power 0 5,400 5,400 watts Total Load Power.
With lagging load power factors below 50%, the top element power reverses
direction and the resultant action of the two elements (stators) becomes a differential
one, such that the power direction is that of the stronger element (stator).
Since the bottom element (stator) power is always larger than that of the top
element (stator), the meter power is always in the forward direction, but with
proportionately lower power at power factors under 50%. Actually on a balanced
load, the two elements (stators) operate over the following ranges of power factor
angles when the system power factor varies from unity to zero: the leading
element (stator) from 30° lead to 60° lag, the lagging element (stator) from 30° lag
to 120° lag.

As such, the watt metering formula for any instant in time is:
Watts (Vab Ia) (Vcb Ic) Accumulating the watts over time allows the metering of watthours.

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