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Dran-View 6 User Guide

Expressed in the cos(ωt-δ) form preferred by mathematicians these phasor angles

would become 90, 210 and 330, respectively. Confusing, to say the least. Most non-

mathematicians visualize and speak of sine waves not cosine waves. Phasors in the

power industry almost always come from sine transforms.

NOTE: In the expansions above (and throughout most of this document) the contribution of

the DC component (harmonic zero) has been ignored. To be technically correct, it

should be included but it is typically discarded because in AC circuits it is usually

close to zero. The DC component is simply the algebraic average of all the data

points in the cycle. If the DC component is significant, then f(t) may be more

accurately computed by including the average voltage or current in the summation.

19.1.4. Phase angles and Normalization

Normalization, as used by Dranetz-BMI, refers to the process of recomputing the

phase offsets output by the harmonic transform in order to relocate the expression

of the signal to a new origin. Since the phase angles generated by a harmonic

transform are dependent on both the start point of the sample window and the form

of the transform (whether it is sine or cosine, whether the phase angle is added or

subtracted, etc.) it is possible to get a bewildering set of equivalent phase angle data

sets for the same set of waveforms. Normalization attempts to standardize the

expression of a (set of) waveform(s) by always referencing the data to the same

point. The most useful application of this option is in referencing the phase angles

of the harmonic transform to the positive zero crossing of the voltage sample

synchronization channel fundamental. This is particularly helpful when viewing the

fundamental phasors of highly distorted signals in a three phase system. In the

presence of high distortion, typical sampling hardware may not synchronize itself

exactly to the zero crossing of a sync channel fundamental. This could cause the

phase offsets of the fundamentals that are returned from the un-normalized sine

transforms to be, for example, 343, 223 and 103 degrees for channels A, B and C,

respectively. Normalizing this data to the fundamental of channel A will yield a

familiar 0, 240, 120 degree sequence that we easily recognize as a positive

sequence three phase system. This is calculated as follows. Since we wish to

normalize to the sync channel (Channel A) we must “subtract out” the phase offset

of the sync channel from each of the channels as follows:

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