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Data Collection

Fairchild Application Note "The power factor can vary from 0 to 1 and can be either inductive..." in lede paragraph.

Metering phasors

Where:

a,b,c represent phase identifiers

Ean, Ebn, Ecn represent phase to neutral voltages (volts)

Eab, Ebc, Eca represent phase to phase voltages (volts)

Ia, Ib, Ic represent phase line currents (amperes)

In represents neutral current (amperes)

$\theta$ represents the phase angle each current lags the listed potential (degrees)

$Pt$ represents total system power (watts)

3 phase 4 wire (wye) using 3 element metering

See Measurement Canada Standard Drawing

$Pt=IaEan*cos(\theta )+IbEbn*cos(\theta )+IcEcn*cos(\theta )$

Each line current and respective voltage is metered as three single phase circuits and then totalized in the meter.

3 phase 4 wire (wye) using 2.5 element metering

See Measurement Canada Standard Drawing

$Pt=IaEan*cos(\theta )-IbEan*cos(\theta )-IbEcn*cos(\theta )+IcEcn*cos(\theta )$

Ia and Ic currents are metered with their respective voltages as two single phase circuits. Ib is fed, polarity reversed, through an additional (split) winding on each element. Since the reversed Ib is 60° out of phase (at system unity PF) from each potential each element will meter cos(60°) or 50% of Ib, resulting in 100% metering for Ib. The two elements are totallized in the meter. Balanced system voltages are a requirement for technique accuracy.

3 phase 4 wire (wye) using 2.0 element metering and delta connected CTs

See Measurement Canada Standard Drawing

$Pt=(Ia-Ib)Ean*cos(\theta )+(Ic-Ib)Ecn*cos(\theta )$

Ia and Ic currents are metered with their respective voltages as two single phase circuits. Ib is fed, polarity reversed, via a current transformer delta connection through each element. Since the reversed Ib is 60° out of phase (at system unity PF) from each potential each element will meter cos(60°) or 50% of Ib, resulting in 100% metering for Ib. The two elements are totallized in the meter. Balanced system voltages are a requirement for technique accuracy.

3 phase 3 wire (delta) using 2 element metering

See Measurement Canada Standard Drawing

$Pt=IaEab*cos(\theta )+IcEcb*cos(\theta )$

Two phase line currents are metered with phase to phase voltages. The odd combination of each current and voltage results in using voltages 1.732 higher and shifted by 30° resulting in 1.732 EI * cos(30°) = 1.5EI (at system unity pf) on each element. The elements are totalized to 3EI * cos($\theta$) and correct metering. Balanced system voltages are a requirement for technique accuracy.