# Power Uncertainty calculation for a non-standard Power Factor value

The phase angle at 0.8 pf is not mentioned in the specs.  I can guess it is going to be right between 35 and 40 degrees (based on WATTS - 50 and 55 based on VARs I am using WATTS in these examples). First method, start with a specified phase angle that's close in value and determine if the contribution is significant:

I will take a known power factor,  like the specs from one of the two phase angles that is nearest in value.  The difference may not have a large contribution on the uncertainty.  Let's look at the math.  I'll use a power factor of 0.766. I could also use 8.66, but since it's uncertainty is lower I'll take the more conservative approach.  I'll also use the 1 year of accuracy 100V and 1 Amp  @ 60Hz as my power output.

Here is the math (again, based on a power factor of .766 or 40 degrees):

Total Power Uncertainty (expressed in %) is:
The RSS of the AC Voltage spec + the AC Current spec + the adder.  (Again, using a 1 Year spec for AC Voltage, Current and Power Uncertainty Phase Error Adder.)

The total will be the square root of (0.053^2 + 0.06^2 + 0.22^2)
= square root of 0.054809
= 0.234% (resolved to 3 digits you may want more want).

The math is not too complicated.  Now if you know the exact phase angle you can use the calculation on page 1-20 to figure out the EXACT adder.  But the difference between the 35 and 40 degree (watts) spec adder is only about 0.037%.

if that amount contributes too much uncertainty we can calculate it another way.

Second method, start with a known Power Factor, calculate the phase angle and find the exact adder:

Again - if you know the phase angle then you can use the formula below to get your adder and plug it into the rss formula above.

To calculate exact AC Watts power adders due to phase uncertainty for values not
shown, use the formula below: (The following excerpt is from the 5520A User's manual) If we go back to the 0.8 power factor example, you'll calculate the phase angle from that power factor.  Again, here is the math:

Determine the inverse cosine of the power factor (or the Arccosine).

The Arccosine of 0.8 = 0.643501109

Now we have to convert this number from Radians to Degrees.

0.643501109 * 180/pi = 36.8698976

Now we can plug the phase angle of 36.8698976 into the formula to calculate the adder.

100(1- (0.79842646439408859170837352979009/0.80000000048007746813463608767146)

= 0.196692010630575300200522839807

= .2 (rounded)

So now I can determine the total power uncertainly with a more exact adder

The total will be the square root of (0.053^2 + 0.06^2 + 0.2^2)

= square root of 0.0.046409

So the Total Power Uncertainty is = 0.215%

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