Power Factor Uncertainty
or
The Design Engineer’s
Challenge
What is the consequence of
the internal power factor uncertainty of a power meter?
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
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.
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]
) phi I cos(
U
P 2 err2 2err
err error
,
avg
Effect of internal power factor at cos = 1
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.
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.
Furthermore, every RANGE SETTING incorporates unique components, so every range will contribute differently to the total accuracy.
This error is called the RANGE 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.
(Urms,error) & (Irms, error) & (cos =1 error)
Effect of internal power factor error at cos 1
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.
If cos 1, there is an ADDITIONAL ERROR caused by the different phase and frequency characteristics of the voltage and current inputs circuitry’s.
(Urms,error) & (Irms, error) & (cos 1 error)
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°) = 1.0000000
cos(0.4°)= 0.9999756 cos(0.5°)= 0.9999619
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?
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.
(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°) = 0.0000000 cos(89.6°)= 0.0069812 cos(89.5°)= 0.0087265
With a 0.1 delta in degrees, we see the third digit behind the comma already changing.
Effect of internal power factor error at
cos 1
Attenuator
Amplifier
A/D
DSP i(t) u(t) A/D
SHUNT
u(t) i(t)
Input circuitry of the digital power meter
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. V 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.
U & I different Delay = Phase Shift!
Normalisation Circuitry
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.
u(t)
i(t) i(t) p(t) p(t)
t
u(t) = Upksin(t) i(t) = Ipk sin(t- ) i(t) = Ipksin(t- (+ ))
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 Pav.
The Impact on P
averageIf 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.
Freq 1
degrees
freq
Urms, range1 Irms, range1
Phase error at freq 1 in range 1 (100 VA)
Urms, range2 Irms, range2
degrees
Phase error at freq 1 in range 2 (1000 VA)Freq 1 freq 0
0
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.
Frequency Characteristics of
Amplifiers and Attenuators
How to measure at a certain frequency (e.q. 50Hz)?
These input signals are not normal daily measuring
conditions for industry applications. These conditions will allow us to measure as good as possible.
Reality tells us different:
Pavg, at (cos =0) = some value !
When =90°, then cos=0 and we expect:
Pavg = Urms . Irms . 0 = 0 [W]
Pavg = Urms x Irms x cos [W]
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].
How to measure ?
How to apply in accuracy calculations?
sin
and
1 cos
1
] [
) sin . sin cos
. (cos I
U
sin sin
cos cos
) cos(
] [
) cos(
I U
dt P .
T P 1
rms - FS rms - FS
rms - FS rms - FS T
0 (t) avg
W W
error by the internal phase angle
] W [ sin
. .I
U . cos
. I
. U
Pavg FS-rms FS-rms FS-rms FS-rms
How to measure ?
How to apply in accuracy calculations?
[W]
tan .
cos .I
U cos
.I U
Pavg FS-rms FS-rms FS-rms FS-rms
error by the internal phase shift and cabling delay
] [W . .I
U
Pavg FS-rms FS-rms
ABS-error!
1 sin
0 cos
90
0 sin
1 cos
0
] W [ sin
. .I
U . cos
. I
. U
Pavg FS-rms FS-rms FS-rms FS-rms
ABS-error!
1 cos 0
90 90
0
] [W .I
U
Pavg FS-rms FS-rms
) P of value reading
P cos I
U (
W P
tan δ P
: Add
: USAGE PRACTICAL
THE
tan . P tan
. cos .I
U P
avg rdg
rms - FS rms
- FS
rdg err
abs
rdg rms
- FS rms - FS err
abs
W
δ P
Pabserr S-FS
Ideal Situation:
FS - S FS
- S
err -
abs .100 %of P
P
δ P
The Measurement of δ:
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.
VA
W
U I P
P U I
rms rms T
0
) avg (
T
0
2 ) ( rms
T 0
2 ) ( rms
s
] T [
1
) T (
1 T
1
P dt
t d dt
t
t t
u i
Relation and W
) cos ( Factor Power
VA W .
I
U P
rms rms
av
Because of there is an uncertainty in W and consequently in “cos ” itself.
VA W cos W
VA
cos
1W
1
Relation and W
2 1 3 2
VA=constant VA VA
var
var
W W W
var
W 3
Yokogawa’s Measurement Philosophy
Wide & Zoom Wide & Zoom ：
Watch the total Picture,
analyze the details at same time.
