Estimating Line-to-Line Voltages

(Redirected from Estimating Phase-to-Phase Voltages)

This is the published version, checked on 29 November 2011.

Accuracy	Basic
Depth	Basic
Readability	Basic

The energy measurement IC in the WNB and WNC series WattNode^® meters does not directly measure the line-to-line (or phase-to-phase) voltage. They can be estimated mathematically, and the WattNode Modbus meter computes the estimated line-to-line voltages for standard three-phase and residential configurations. See the WattNode Modbus manual for details, particularly the PhaseOffset register documentation.

For firmware versions 15 and lower, WattNode Modbus only estimates line-to-line voltages for 120/240 residential services and for standard three-phase circuits, not including four wire delta circuits (aka "wild leg" or "high phase"), and not including grounded delta circuits. Firmware versions 16 and later add estimated line-to-line voltages for four-wire delta and grounded delta circuits. See the PhaseOffset register in the WattNode Modbus manual for details.

Standard Three-Phase Circuits

The following equations should provide accurate estimated line-to-line voltages provided the three phases are separated by 120° and the neutral (or ground if neutral is absent) to line voltages are well balanced (within a few percent).

$V_{AB} = \sqrt{V_A^2 + V_B^2 + V_A V_B}$

$V_{BC} = \sqrt{V_B^2 + V_C^2 + V_B V_C}$

$V_{AC} = \sqrt{V_A^2 + V_C^2 + V_A V_C}$

Residential Circuits

North American residential circuits typically use two 120 VAC lines that are 180° apart, with a line-to-line voltage of 240 VAC. Because of the 180° angle between the two lines, the individual voltages can be added to accurately estimate the line-to-line voltage.

$V_{AB} = V_A + V_B$

Three-Phase Grounded Delta Circuits

Three-phase three-wire grounded delta circuits (also called "corner-grounded delta" or "grounded leg") have one of the phases tied to ground.

Assuming phase B is the grounded leg, the following equations compute the line-to-line voltages. If a different phase is grounded, the equations can be shifted up or down a phase to get the correct answer:

$V_{AB} = V_A$

$V_{BC} = V_C$

$V_{AC} = \sqrt{V_A^2 + V_C^2 - V_A V_C}$

Four-Wire Delta Circuits

Four-wire delta circuits (also called "wild leg" or "high leg") have one phase with a higher line-to-neutral voltage than the other two. Most commonly, the line-to-neutral voltages are 120, 120, and 208 VAC, while the line-to-line voltages are all 240 VAC.

Assuming phase B is the high (or wild) leg, the following equations compute the line-to-line voltages. If a different phase is grounded, the equations can be shifted up or down a phase to get the correct answer:

$V_{AB} = \sqrt{V_A^2 + V_B^2}$