# Why is the Theoretical Calulated Three-Phase Apparent Power Values (ΣVA and ΣS) Different From the Measured Values?

This is due to measurement and calculation error, or differences in calculation methods.

On the WT, the three-phase apparent power (ΣS) equation is calculated under the assumption of a balanced condition (the absolute value of each phase is the same, and the phase angle is 120°). When balanced, the line to line voltages U1, U2, and U3 in three-phase three-wire or 3V3A configuration result in phase voltages of √3 times UR, US, and UT. Considering the three-phase apparent power, three-phase four wire is simply the sum of each phase:
Three-phase four-wire ΣS = S1+S2+S3

For three-phase three-wire and three-phase three-wire (3V3A), the apparent power is, in princicple, not measured. Therefore when balanced, a coefficient is used such that the same value as three-phase four-wire ΣS, and the following equations are used:
Three-phase three-wire ΣS = √3/2(S1+S3)
3V3AΣS = √3/3(S1+S2+S3).

Consequently, when unbalanced, since the phase-to-phase phase angle is not 120°, and the votlage value of each phase is of a different size, the line to line voltages U1, U2, and U3 above do not result in phase voltages of √3 times UR, US, and UT. Therefore, ΣS calculated for three-phase three-wire or 3V3A can differ from the value of ΣS determined in a three-phase four-wire configuration.

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