Task 11, Three-phase power
AE1B38EMB
11. MEASUREMENT OF POWER CONSUMPTION OF
THE NONBALANCED THREE-PHASE LOAD
Task of the measurement
1.
Measure the active power and the reactive power of the nonsymmetrical 3-phase load in
Y-connection. Do not connect the common node of the load to the common point of 3
wattmeters voltage coils.
Measure the active power:
a) using three wattmeters;
b) using two wattmeters; verify by three measurements the Blondel theorem.
Measure the reactive power using three wattmeters.
Make correction of the error of the method where appropriate. Estimate the expanded
uncertainty of measurement in all measurements (k = 2).
2. Verify the function of the three-phase electronic (static) watt-hour meter and compare the
reading of the Wh-meter with results gained by other measuring instruments.
Schematic diagram
Connection for measurement of the active power is shown in Figs. 17a.1 and 17a.2.
Connection for the measurement of the reactive power is shown in Fig. 17a.3 and connection
for verification of the Wh-meter function in shown in Fig. 17a.1.
L1
L1
L1
L2
L2
L3
L3
L
W1
I2
V
A2
Wh-METER
L3
U
A1
ELECTRONIC
L2
I1
W2
I3
W
A3
W3
Fig. 1 Connection for measurement of the active power of the three-phase load using three
wattmeters, and for verification of functions of electronic Wh-meter.
I1
L1
U
W1
I2
L2
V
A2
W2
I3
L3
L
A1
W
A3
Fig.2 Example of connection for measurement of active power
using two wattmeters - Aaron connection
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Task 11, Three-phase power
AE1B38EMB
I1
L
1
U
A1
W1
I2
L
W2
I3
3
V
A2
2
L
L
W
A3
W3
Fig. 3 Connection for measurement of reactive power of the non-symmetrical
three-phase load using three wattmeters
Notes to the measurement:
a)
Check correct connection (with respect to the phase sequence) of power supply and the
load.
b)
The 3  120 V voltage system is used in delta connection.
c)
Take care in all measurement of the correct connection of beginnings of current and
voltage coils of wattmeters and of the electronic watt-hour-meter.
d)
Do not let the load connected to the power line source for more than 5 minutes. Load
might be damaged if connected to power line for longer time.
e)
Do not disconnect the electronic Wh-meter, let it connected in all measurements, even if
it is not shown in the schematic diagrams.
List of the equipment used
A1
A2
A3
W1
- iron-vane ammeter, accuracy class …, measurement range used: …;
- iron-vane ammeter, accuracy class …, measurement range used: …;
- iron-vane ammeter, accuracy class …, measurement range used: …;
- electrodynamic wattmeter, accuracy class …, voltage measurement range used: …V,
current measurement range used: …A, voltage coil resistance: ... ;
W2
- electrodynamic wattmeter, accuracy class …, voltage measurement range used: …V,
current measurement range used: …A, voltage coil resistance: ... 
W3
- electrodynamic wattmeter, accuracy class …, voltage measurement range used: …V,
current measurement range used: …A, voltage coil resistance: ...  ;
L 1 , L 2 , L 3 - power line AC source 3  120 V;
L
- the measured load;
electronic WH-meter EMU 30, ZPA Trutnov, Czech Republic.
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Task 11, Three-phase power
AE1B38EMB
Theoretical background
Measurement of the active power using three wattmeters
Connection in Fig. 17a.1 will be used for measurement of active phase powers P 1 , P 2 , P 3 ,
consumed by load in phases L 1 , L 2 , L 3. If not only the total three-phase load active power
should be measured but also the individual phase active powers should be measured, then
(since the measurement here takes place in three-wire system without neutral wire)
wattmeters with identical voltage coil resistances should be chosen. In this case the common
point of the ends of wattcmeters voltage coils in Fig.17a.1 is the power line neutral point (socalled „artificial neutral“), and voltages across voltage coil on every wattmeter is the same
and equal to power-line phase voltage. There is an ammeter in series with the current coil of
every wattmeter. According to the readings of these ammeters the current measurement
ranges of the corresponding wattmeters should be selected. The total measured active power
P Cm consumed by the load is given by the sum of the active powers of individual phases:
PCm  P1  P2  P3  K W1 1  K W2  2  K W3  3 (W)
(1)
where K W1 to K W3 are wattmeter constants (W/division),
are wattmeter deflections (divisions).
 1 to  3
The methodical error (error of the method) is here caused by power consumption of voltage
coils of individual wattcmeters
Pn1  Pn2  Pn3 
U p2
Rn
(W)
(2)
where U p is the phase voltage, voltage across the wattmeter voltage coil (V),
R n is resistance of the wattmeter voltage coil (more exactly wattmeter voltage
circuit, since it includes the series resistor setting the voltage range); in this
measurement voltage coil resistances are in all tree wattmeters identical (.
Error of the method shall be corrected by subtraction of the total power consumption of all
three voltage coils:
PC  PCm  3
U p2
Rn
(W)
(3)
Standard uncertainty of the reading by measurement of the active power using three
wattmeters is
2
2
u P  u P21  u P2
 u P3
(W)
(4)
The term expressing correction of the methodical error in expression (17a.3), that is the term
( 3U p2 / Rn ) is disregarded in standard uncertainty estimation, since it is much lower than the
total measured power P Cm .
If three identical wattmeters (identical type and measurement ranges) are used for
measurement of total active power, then the standard uncertainty of each wattmeter reading is
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Task 11, Three-phase power
AE1B38EMB
u P1  u P2  u P3  u P 
where AC W
MW
AC W  M W
100 3
(W)
(5)
is accuracy class of the wattmeter,
is wattmeter measuring rang (W).
Expanded uncertainty of the P C for the coverage factor k = 2 is then
U Pc  2
3 u P2
(W)
(6)
The result of measurement of the total active power shall be expressed in the
P  PC  U Pc (W)
(7)
Measurement of active power using two wattmeters
According to Blondel theorem, (n - 1) wattmeters are necessary for measurement of active
power in n-wire system. One of possible connections for the case of the 3-wire net is shown in
Fig. 17a.2 (the so-called Aaron connection). This scheme can be applied subsequently to all
three combinations of two wattmeters connection. The total active power measured by two
wattmeters is after correction of the methodical error (caused by power consumption of two
wattmeter voltage coils with resistances R n1 and R n2 ) given as
2
2
U 23
U 13
(W)
PC  K W1 1 
 K W2  2 
Rn2
Rn1
(8)
where R n1 and R n2 are resistances of voltage coils of the used wattmeters (),
U 12 and U 13 are line voltages in the three-phase voltage system used (V).
Since voltage coil resistances of all wattmeters are identical here and identical are also the line
voltages in the 3  120 V power line net, there is
PC 2
2
U 13
 K W1 1  K W2  2  2
(W)
Rn1
(9)
and if both wattmeters are identical and using the same measuring ranges, the expanded
measurement uncertainty can be estimated (for k = 2) as
U PC2  2
2 u P2
(W)
(10)
where u P is given by the equation (5). The term correcting in the relation (9) the methodical
2
error ( 2U 13
/ Rn1 ) is not taken into account by estimating uncertainty of measurement since it
is much smaller than the sum K W1  1 + K W2  2 .
Result of measurement using two wattmeters should be again expressed in the form
P  PC2  U PC2 (W)
(11)
Measurement of reactive power using three wattmeters
Connection for measurement of the reactive power is shown in Fig. 3. Voltage coils of the
wattmeters are connected to line voltage lagged (delayed) by /2 with respect to the phase
voltage of the phase where is connected the current coil of the corresponding wattmeter.
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Task 11, Three-phase power
AE1B38EMB
Deflection of each wattmeter is proportional to the reactive power of the corresponding phase
multiplies by 3 , since magnitude of the line voltage connected to its voltage coil is 3 times larger than the phase voltage (the voltage system is symmetrical). The reading of each
wattmeter must be therefore divided by 3 , and the total reactive power is therefore given by
the expression
QC  Q1  Q2  Q3 
N1 N 2 N 3 K W11  K W2 2  K W33



3
3
3
3
(VAr),
(12)
where N 1 , N 2 and N 3 are readings of wattmeters and other symbols have the same meaning as
in relation (17a.1).
Standard uncertainties of individual wattmeter readings can be estimated (as in (17a.5)) as
uN 
where AC W
MW
uN
AC W  M W
100
(VAr),
3
(13)
is accuracy class of the used wattmeter (%),
is measurement range of the used wattmeter (VAr),
is uncertainty of the wattmeter reading (VAr).
Uncertainty of the reactive power measured by each wattmeter can be using (12) estimated as
u
uQ  N (VAr)
(14)
3
The expanded uncertainty (k = 2) of the total measured reactive power Q C is given as
U QC  2 u Q21  u Q2 2  u Q2 3 (VAr)
(15)
If all three wattmeters are identical (both type and range), the expanded uncertainty U Qc (for
k=2) can be expressed as
U QC  2
u 
3  N 
 3
2
 2 uN
(VAr)
(16)
and the result of measurement of reactive power shall be expressed in the form
Q  QC  U QC
(17)
Phase shifts of phase voltages with respect to phase currents can be found for all three phases
from the equation
Q
i  arctg i () , i = 1, 2, 3
(18)
Pi
Note: For wattmeters with voltage and current coils connected according to Fig. 17a.3
positive wattmeter deflections correspond to positive reactive powers. If some of the
wattmeters read negatively (deflection tends to be out of scale in negative direction) it
is necessary to commutate the polarity of the voltage coil and take the wattmeter
reading as negative. Quadrant in which lies the phasor of current I i , respectively to it
corresponding phase shift  i can be found according to the signs of both P i and Q i .
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Task 11, Three-phase power
AE1B38EMB
Demonstration of the three-phase static (electronic) watt-hour meter EMU 30,
manufacturer ZPA cz Trutnov, Czech Republic
According to Fig. 17a.1, part of the measuring circuit is also a three-phase electronic (socalled „static“) watt-hour meter. This watt-hour meter allows measurement of large number of
parameters in the three phase net. The Wh-meter is for common energy consumer
programmed usually so that the readings of the active energy rotate in each 10 s in individual
(in altogether 4) tariffs. The watt-hour meters EMU 30 used in this task were free of charge
supplied to our department by the company ZPA cz Trutnov (www.zpa.cz). Wh-meters were
programmed so that after switching on they show the total energy consumed in all phases
(kWh). After repeated pushbutton switching there are in sequence displayed following
readings, demonstrating broad measurement ability of the meter:


























Total reactive energy (kVArh),
Total apparent energy (kVAh),
Instantaneous active power in all phases (1,2,3) (kW),
Instantaneous active power in phase 1 (kW),
Instantaneous active power in phase 2 (kW),
Instantaneous active power in phase 3 (kW),
Instantaneous reactive power in all phases (1,2,3) (kVAr),
Instantaneous reactive power in phase 1 (VAr),
Instantaneous reactive power in phase 2 (VAr),
Instantaneous reactive power in phase 3 (VAr),
Instantaneous apparent power in all phases (1,2,3) (kVA),
Instantaneous apparent power in phase 1 (VA),
Instantaneous apparent power in phase 2 (VA),
Instantaneous apparent power in phase 3 (VA),
Phase voltage of phase 1 (V),
Phase voltage of phase 2 (V),
Phase voltage of phase 3 (V),
Line voltage 1-2 (V),
Line voltage 2-3 (V),
Line voltage 1-3 (V),
Current in phase 1 (A),
Current in phase 2 (A),
Current in phase 3 (A),
cos  in phase 1,
cos  in phase 2,
cos  in phase 3.
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