1. Power Factor Uncertainty or The Design Engineer’s Challenge
TCE Sales & Service
Yokogawa Europe B.V.
1 December 2018

2. What is the consequence of the internal power factor uncertainty of a power meter?
The average electric power for a sinusoidal waveform is:
Pavg = Urms . Irms . cos [W]
Every multiplication factor contributes in its own way to the total uncertainty:
Pavg, = (Urms, error) . (Irms, error) . (cos error) [W]
When measuring power, many small errors occur. For a total inaccuracy figure we have to sum them all together. Many small possible errors could result in one big uncertainty figure, so we better pay attention to all of them.
Factors that influence the total error for power are: Current shunt drift by continuous high currents
Amplitude
Frequency of the fundamental of the input signal
Crest Factor of the input signal (BW)
Crest Factor setting of the Power Meter
Power Factor
Temperature
Use of filters
Use of protection diodes
TCE Sales & Service
Yokogawa Europe B.V.
1 December 2018
CS_10_PF Uncertainty

3. Effect of internal power factor at cos  = 1
(Urms,error) & (Irms, error) & (cos  =1 error)
When we measure voltage and current, there is an uncertainty about the amplitude caused by the FREQUENCY CHARACTERISTICS (= BW=BANDWIDTH) of the measuring instrument itself.
Furthermore, every RANGE SETTING incorporates unique components, so every range will contribute differently to the total accuracy. This error is called the RANGE ERROR.
WITHIN A RANGE it makes a difference if the actual measurement value is close to 0% or 100% of the maximum range value. The instrument itself is often calibrated at the 100% value, so this would give the best result. Close to 0% (entering the “noise floor”) the worst. This error is called the READING ERROR.
For Voltage, Current and Power measurements, the Error is specified as:
(Error as % of reading) x reading value + (Error as % of range) x range value.
Basically this uncertainty is measured and calculated at the condition of cos=1. See the specifications as published in the Product Bulletins and the User Manuals.
TCE Sales & Service
Yokogawa Europe B.V.
1 December 2018
CS_10_PF Uncertainty

4. Effect of internal power factor error at cos   1
(Urms,error) & (Irms, error) & (cos  1 error)
If cos 1, there is an ADDITIONAL ERROR caused by the different phase and frequency characteristics of the voltage and current inputs circuitry’s.
Voltage can be measured immediately, but to measure current (Coulombs/s) is very difficult. Current for that reason is first converted to a voltage value with help of a resistor. Although often all the current is running through this resistor (direct current measurement), this resistor is often called the internal current shunt. This current shunt generates, by having a few nH inductance, a little extra phase shift (delay) that the voltage input doesn’t have.
Even when PF=1 this error occurs, but its effect is then negligible in relation to the reading value while the product (Urms x Irms) is at its max. value. This influence is included in the basic uncertainty specifications for power.
Also small changes in  around 0° result in negligible changes in cos  :
cos(0°) =
cos(0.4°)=
cos(0.5°)=
So the uncertainty has little or no effect on the power meter accuracy.
Around a phase shift of 90°, the impact of cos  uncertainty is much bigger.
WHY?
TCE Sales & Service
Yokogawa Europe B.V.
1 December 2018
CS_10_PF Uncertainty

5. Effect of internal power factor error at cos  1
(Urms,error) & (Irms, error) & (cos  1 error)
Small changes in , around 90° result in significant changes in cos  and consequently effects the power meter accuracy:
cos(90°) =
cos(89.6°)=
cos(89.5°)=
With a 0.1 delta in degrees, we see the third digit behind the comma already changing.
CONCLUSION:
When PF  1 an additional error has to be added to the power meter measurement, in addition to the amplitude errors of U & I at PF = 1.
The error is expressed as a % of the range and will result in an absolute value, to be added to the error found at PF=1.
TCE Sales & Service
Yokogawa Europe B.V.
1 December 2018
CS_10_PF Uncertainty

6. U & I different Delay = Phase Shift!
Input circuitry of the digital power meter
Normalisation Circuitry
u(t)
Attenuator
Amplifier
A/D
DSP
i(t) u(t) SHUNT
i(t)
The VOLTAGE input often needs a big attenuation (e.g. 600V to 3V).
The small voltage drop across the CURRENT-shunt on the other hand needs a very high gain (e.g. mV to 3V).
OPAMPs are designed with different amplitude gain characteristics.
Consequently there will be an additional internal phase shift between the voltage and current input.
Main part of the phase delay is caused by this shunt due to its, although very small, inductance.
TCE Sales & Service
Yokogawa Europe B.V.
1 December 2018
CS_10_PF Uncertainty

7. The Impact on Paverage
Before U(t) and I(t) are fed into the A/D converter the signals are so called “Normalised” for optimal ADC input level (e.g. 3 Volt). The electrical circuits for u(t) and i(t) are not identical and consequently i(t) undergoes in the power meter an extra delay resulting in a phase error of  degrees.
This has no consequences for Urms and Irms, but it has a consequence for the measurement of active power. As from the following drawing can be seen p(t)  p(t), then also Pav  Pav.  
u(t)
i(t)
i(t)
p(t)
p(t) t
u(t) = Upksin(t) i(t) = Ipk sin(t- ) i(t) = Ipksin(t- (+ ))
TCE Sales & Service
Yokogawa Europe B.V.
1 December 2018
CS_10_PF Uncertainty

8. If the frequency increases, the relative impact increases.
Frequency Characteristics of Amplifiers and Attenuators
An unwanted phase-shift is caused by the different phase and frequency characteristics of the voltage and current inputs circuitry’s.
The current shunt generates, by having a few nH inductance, a little extra phase shift to the current input. The voltage input does not have this component.
Even when PF=1 this error occurs but its effect is neglectable at 50/60Hz in relation to the reading value while the product Urms and Irms is at its max. value.
At every frequency we have a phase delay error related to the range. This error is measured in degrees, but later specified as a % of the range for ease of use.
Freq 1
degrees
freq
Urms, range1
Irms, range1
Phase error at freq 1 in range 1 (100 VA)
Urms, range2
Irms, range2
Phase error at freq 1 in range 2 (1000 VA)
If the frequency increases, the relative impact increases.
At higher frequencies an extra error has to be added to the total power error. Even for the PF = 1 condition this error is no longer neglectable.
TCE Sales & Service
Yokogawa Europe B.V.
1 December 2018
CS_10_PF Uncertainty

9. How to measure  at a certain frequency (e.q. 50Hz)?
Pavg = Urms x Irms x cos [W]
When =90°, then cos=0 and we expect:
Pavg = Urms . Irms . 0 = 0 [W]
Reality tells us different:
Pavg, at (cos =0) = some value !
In order to MEASURE this internal error as good as possible, we measure with input signals equal to the maximum value of the calibrated measurement range;
UFS-rms and IFS-rms.
The product of UFS-rms and IFS-rms is equal to the apparent power SFS in [VA].
These input signals are not normal daily measuring conditions for industry applications. These conditions will allow us to measure  as good as possible.
TCE Sales & Service
Yokogawa Europe B.V.
1 December 2018
CS_10_PF Uncertainty

10. How to measure ? How to apply  in accuracy calculations?
error by the internal phase angle
TCE Sales & Service
Yokogawa Europe B.V.
1 December 2018
CS_10_PF Uncertainty

11. How to measure ? How to apply  in accuracy calculations?
error by the internal phase shift and cabling delay
Ideal Situation:
ABS-error!
The Measurement of δ:
ABS-error!
TCE Sales & Service
Yokogawa Europe B.V.
1 December 2018
CS_10_PF Uncertainty

12. Relation  and W
The WT-series measure only the instantaneous voltage applied to the load and the resulting current. The Power Factor (former cos) is calculated in the following way.
TCE Sales & Service
Yokogawa Europe B.V.
1 December 2018
CS_10_PF Uncertainty

13. Relation  and W
Because of  there is an uncertainty in W and consequently in “cos ” itself.
VA=constant VA VA
var
var
var W W W 2 3
±DW
TCE Sales & Service
Yokogawa Europe B.V.
1 December 2018
CS_10_PF Uncertainty

14. Yokogawa’s Measurement Philosophy
Wide & Zoom
Wide & Zoom：
Watch the total Picture, analyze the details at same time.
TCE Sales & Service
Yokogawa Europe B.V.
1 December 2018
CS_10_PF Uncertainty