8. Power of single-phase load
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8. POWER AND POWER FACTOR MEASUREMENT
FOR SINGLE PHASE LOAD
Tasks of the measurement
1.
Measure active power, power factor and apparent power consumption of the singlephase load. Use universal clamp digital meter for the measurement. Active power
should be measured also using analogue wattmeter and current instrument transformer
(CT). Evaluate B-type expanded uncertainty (k = 2) of active power measurement for
both cases. Compensate methodical error in case of measurement by means of
analogue meter. Current transformer transformation error is negligible. Find whether
the difference of the measurement results corresponds to their reported accuracy.
2.
Measure the voltage on the secondary winding of the current transformer and check if
the transformer is not overloaded.
Measurement hints
- Use the power supply of 120 V, 50 Hz (voltage between any two terminals of the 3 ×120 V
power line system at the switchboard).
- Since the load current is higher than 5 A at 120 V, a current instrument transformer (CT)
has to be used.
- Do not leave the load connected to the source for more than 2 minutes. It is not designed
for permanent usage.
- The secondary winding of the current transformer cannot be left open if primary winding is
connected to measured current. For connections of primary and secondary windings of the
CT, the thick wires with connection clips are to be used to assure minimal transition
resistance.
Schematic diagram
120 V/50 Hz
LOAD
I1
KL
V
COM
Fig.1 Active power, power factor and apparent power measurements using universal clamp meter
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8. Power of single-phase load
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I
1
CT
K
k
L
l
U kl
120 V, 50 Hz
V3
V1
U1
Z
A
I2
W
Fig. .2 Schematic diagram for measurement of active power consumption using analogue wattmeter
List of the equipment used
KL
A
V1
W
CT
120 V
Z
- universal digital clamp meter PK 430.1;
- iron-vane ammeter, accuracy class. ..., measurement range used ...;
- PMMC voltmeter with rectifier, accuracy class ..., measurement range used ...,
input resistance ...;
- electrodynamic wattmeter, accuracy class ..., voltage measurement range ... V,
current measurement range ... A, voltage coil resistance ... 
- instrument current transformer, transformation ratio ..., accuracy class ...;
- AC power supply - switch board;
- measured load
Theoretical background and measurement steps
Power consumption or energy measurements are based on knowledge of nominal voltage of
the source and approximate current going through the load. If an universal clamp meter is
used, the correspondence of its voltage and current ranges to those before-mentioned values
must be checked. In case of analogue (electrodynamic) wattmeter utilisation, the
measurement range is limited by its current range. Instrument current transformer (CT) with
suitable transformation factor must be used for measurements where the current going
through the load is higher that the current measurement range of the wattmeter. In our case,
the load current is measured by clamp meter according the Fig. 1.
Measurement using universal clamp meter
The values of current I 1 , active power P, power factor cos  and apparent power S can be
measured as shown in the Fig. 8.1 by means of universal digital clamp meter PK 430.1. Its
technical parameters are given in the introductory part of this textbook, Chap. 0. The device is
switched on by the setting of the rotary switch to the position where the yellow mark on the
switch points to symbol of the measured parameter. After switching the device on, short autotest runs. During this time all the display segments are activated. Auto-calibration follows
(the display shows “CAL“). During auto-calibration (cca 15 s) the clamp magnetic circuit is
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8. Power of single-phase load
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compensated for residual magnetic field. The clamp must not be attached around any
(powered) wire during this period. The device is set to automatic range selection mode after
auto-calibration and “AUTO” is shown on the display. True RMS measurements (TRMS) in
case of current or voltage measurements are indicated by means of symbol “AC + DC“. If the
measured value cannot be read immediately form the display, the function “HOLD” can be
used (which freezes the displayed value until its next push). Should the measured value
appear outside the measurement range, the L L L L L symbols are displayed.
Current measurement is performed after the calibration is finished. The rotary switch must be
set to “A” position and the clamp must be put around the wire where the measured current
flows. The sign of the reading will be correct if the current enters the clamp magnetic circuit
in the direction indicated inside the clamp by arrow. The device sensitivity can be increased
by winding the wire with the measured current around the magnetic clamp. True current value
is then calculated by dividing the reading by number of turns.
During voltage measurements, the rotary switch is in the position “V” and measured voltage
is connected to the inputs “V“ and “COM”.
For active or apparent power consumption measurements, the rotary switch must be set to
“kW” or “kVA” position, respectively. If the voltage input „V“ is connected in the right way
with respect to the wire going through the clamp and if the current flows through the clamp in
the direction that corresponds to the arrow (see arrows in Fig. 1), the displayed value will be
positive if the energy is consumed and negative if the energy is delivered (generated). If one
of the inputs (voltage or current) will be reverted, also the reading will have the opposite sign.
Also in this case the device sensitivity can be increased by winding the current wire around
the clamp. In this case the reading must be divided by number of turns.
In case of power factor measurement, the switch is to be set to “cos “ position and the device
is connected in the same way as for power measurements (Fig. 1). The positive sign will
correspond to energy consumption and negative sign will correspond to energy
generation again (in case of the same connection as described above). The symbols L or C in
the last display position mean inductive or capacity load character. Considering the fact that
power factor is measured for currents higher than 40 A, more turns of wire carrying the load
current are to be used. The number of turns multiplied by the measured current should be than
higher than 40 A.
Active power measurement uncertainty evaluation
Considering the fact that the meter reading is affected by relative error P R (%) of the
measurement range P R (W) only, and expecting uniform error distribution, the standard
uncertainty of active power can be expressed in the form
uP 
PR  PR
100 3
(W)
(1)
and expanded uncertainty (coverage factor k = 2) in the form
U P  k u P  2u P
(W)
(2)
The value of the measured active power can be expressed as
PS  PM  U P
(W)
(3)
Active power measurement using analog wattmeter
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8. Power of single-phase load
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It is obvious from previous clamp meter measurements that the load current is higher than the
current range of the analogue wattmeter available. Therefore, it is necessary to utilise
instrument current transformer (CT) according the Fig. 2.
Rules for usage of instrument current transformer
The accuracy class of the CT or corresponding transformation error (sometimes called current
error) and phase error (sometimes called angle error) shown on the device label are valid only
in case that nominal values of apparent power S j on the secondary transformer winding does
not exceed a certain value that is also shown on the transformer label and usually ranges in 5
to 30 VA. The value of S j is given as
S j  U klj I 2j  Z 2 j I j2 (VA; V, A, , A)
(4)
where I 2j
U klj
is nominal value of current in the secondary winding of the CT (usually 5 A),
is voltage drop on k - l outputs of CT (see Fig. 2) that corresponds on
consumed current I 2j and nominal impedance Z 2j connected to the secondary
winding of the CT.
The true value of the constant load Z 2 can be calculated from the voltage drop U kl on the
secondary winding of the CT its current I 2 . There is
Z2 
where Z 2
U kl
I2
Sj
U kl
 2
I2
I2j
(; V, A; VA, A)
(5)
is the impedance of serial connection of current coil of the watt-meter and
ammeter connected to the secondary winding of the CT
is voltage drop on k - l outputs of the CT corresponding to the I 2 ,
measured value of the current of the secondary winding of the CT.
Rules of correct CT connection that must be followed:
a) Secondary CT circuit must not be disconnected if current goes through its primary
winding.
b) Secondary CT circuit must be connected by means of wires with suitably high diameters
and clips assuring minimal transition resistances. The wires must not increase
significantly the CT load Z 2 .
c) The beginning of primary winding (labelled "K") is to be connected to the power supply,
the beginning of the secondary winding (labelled "k") is to be connected to the beginning
of the current coil of the wattmeter, usually labelled by arrowhead.
Active power measurements
Active power P m (Fig. 8.2) can be calculated using the equation
Pm  U 1 I 1 cos   PW  p I  k W  p I (W; V, A, -; W/d, -)
(6)
where P W is wattmeter reading (W);
kW
wattmeter constant (W/division);

wattmeter deflection (division);
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8. Power of single-phase load
pI 
I1 j
I2j
I 1j , I 2j
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is transformation factor of the CT;
are nominal values of primary and secondary windings of the CT (-).
The value of P m is affected by methodical error – the power consumption of parallel
combination of wattmeter voltage coil and voltmeter. It is possible to compensate for this
error by the formula
PK  Pm 
where P k
Pm
U1
R nW
RV
U 12
RnW  RV  (W; W, V, )
RnW RV
(7)
is compensated active power consumed by the load (W),
measured power (W),
load voltage (V),
resistance of the wattmeter voltage coil (,
voltmeter resistance (.
The voltage drop U kl on the secondary winding of the CT is checked by V 3 to keep the total
CT load within range defined by (8.5).
Measurement uncertainty evaluation
After compensating for methodical error, the measurement uncertainty depends only on
wattmeter and CT accuracy classes. We neglect the phase error (in the range of one to tens of
angle minutes) and we expect that only transformation error p I (called also current error)
affects the current transformation. The compensating part of the (7) is not considered when
evaluating measurement uncertainty due to the fact that its value is significantly lower than
the measured power P m .
Measurement uncertainty of the power consumed by load can be calculated using the equation
Pm  PW p I (W; W, -)
where
Pm
PW
pI
(8)
is a power consumption of the load (W),
wattmeter reading (W),
CT transformation, defined in (8.6) (-).
The standard measurement uncertainty according to (8.8) can be evaluated using the equation
2
u Pm
where
u Pm
u PW
AC W
MW

 Pm
  P


u PW    m u pI 

 PW
  p I
u PW 
AC W  M W
100 3
;
2

u pI 
 p I  u PW 2  PW  u pI 2
AC CT  p I
100
3
(9)
(10)
is standard measurement uncertainty of the active power (W),
standard uncertainty of the wattmeter reading (W),
wattmeter accuracy class (%),
wattmeter measurement range (W),
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8. Power of single-phase load
u pI
AC CT
pI
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CT transformation uncertainty (-),
CT accuracy class (%),
CT transformation (-).
The true value of the measured power can be expressed as (for coverage factor k = 2)
Ps  Pk  2u Pm (W)
(11)
Comparison of active power measurement results obtained by clamp meter and
analogue wattmeter
The active power measurements can be considered as correct and uncertainties as relevant if
the results of (3) and (11) overlap.
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