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Dran-View 6 User Guide

19.1.7. Important Notes about θ:

Because cos(θ) is equal to cos (-θ) the computation of watts is correct if you

reference current to volts or volts to current, either way. As we shall see, this

flexibility sets the stage for endless confusion. The reactive power, VAR, is

computed as sin(θ). Since sin (-θ) is equal to –sin(θ) we can see that the

computation of VAR is greatly affected by how you compute the phase difference,

θ, between volts and current. Referencing current to voltage will give a different

reactive power than if you reference volts to current. To further confuse the issue,

the way in which you express the signals also affects your results. For example, the

phase angles from the signals expressed as sin (ωt +δ) must be handled differently

than if you take the phase angles from the same signals expressed as cos (ωt -δ

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if you wish to get the same results. Obviously, we need to establish a convention if

we ever wish to get consistent power calculations.

19.1.8. Statement of Power Convention

When the current signal lags the voltage signal that is driving it, we say that it is

inductive and by convention, we assign the reactive power (VAR) to be positive.

When the current signal leads the voltage signal that is driving it, it is considered

capacitive and by convention, the reactive power is assigned to be negative. This is

the standard used on all Dranetz-BMI products. This power industry standard is

reasonable when you consider that most real world loads are inductive. If you

accept that “normal” should be positive then it is reasonable to assign positive to

inductive (normal) loads. The terms leading and lagging are taken from phasor

notation. The phasors are imagined to be rotating in a counter clockwise direction.

They are conventionally shown starting at some arbitrary phase offset equivalent to

time t equal zero. The phase offset is the phase angle offset gotten when the signals

are expressed in the form sin (ωt +δ). Expressed in this fashion the leading signal is

the signal with the greatest unsigned phase offset unless the difference between the

larger and the smaller δ

is greater than 180 degrees. In this case the signal with the

smaller δ

is the leading signal. Remember, we always express δ

in unsigned

modulo 360 format. Using this carefully constructed convention the phase

difference between volts and current is correct for computing both active power,

watts, and reactive power, VAR, when the signals are expressed in sin (ωt +δ)

format and the current phase angle offset is subtracted from the voltage phase

angle.

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