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Dran-View 6 User Guide

Normalized Phase A = 343 - 343 = 0

Normalized Phase B = 223 - 343 = -120 + 360 = 240

Normalized Phase C = 103 - 343 = -240 + 360 = 120

Note that for phases B and C we add 360 degrees back in because, by convention,

we always resolve angles to positive modulo 360. If we were to use these

normalized angles in the sine expansion equation given above to generate f(t), we

would get approximately the original signals except that their time origins would be

shifted left 343 degrees. Alternatively you could view it as shifting the time axis

forward (to the right) -343+360 = 17 degrees. Imagine it as clipping 343 degrees

from the end of the cycle and pasting it to the front, or clipping 17 degrees from the

front of the cycle and pasting it to the end.

Normalization to the fundamental of a single channel does not change the channel

to channel phase offsets. This is important because the channel to channel phase

offsets are used to compute Harmonic Watts. If you “Normalize to Own

Fundamental” you are essentially “zeroing out” the fundamental phase angles of all

the channels. This will destroy the true phase to phase relationships between

channels and thus change the hand computed Harmonic Watts from their true

values. This is very important to remember! Because of the potential to corrupt the

Harmonic Watts computations, we recommend that you exercise caution when

using the “Normalize to Own Fundamental” option. In order to insure that the

harmonic watts computations are correct, Dran-View always internally uses the un-

normalized voltage and current phase angles to compute watts.

The following equations are used in normalization.

To Compute a Normalized Phase Angle from the UN-Normalized Expression

Below is the general formula that may be used to normalize un-normalized phase

angles which were intended to be used in expressions of the form sin (ωt ±δ) or cos

(ωt ±δ). Remember, δ

is unsigned modulo 360!

Normalized

= b * (nφ - δ

UnNormalized

)

For Dran-View the equation above resolves to two forms:

Normalized

= nφ − δ

UnNormalized

Used for cosine expansion

Normalized

= δ

UnNormalized

- nφ Used for sine expansion

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