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FACULTY OF ENGINEERING
LAB SHEET
EEL1196 Instrumentation & Measurement Techniques
TRIMESTER 2 2013-2014
IM2: Power Measurement Using Two Wattmeter Method
*Note: On-the-spot evaluation may be carried out during or at the end of the experiment.
Students are advised to read through this lab sheet before doing experiment. Your
performance, teamwork effort, and learning attitude will count towards the marks.
Objective:
1. To examine the methods of power measurement in DC circuit and three-phase circuits, using
wattmeter.
Apparatus required:
Multi-range wattmeter: 3 V, 10 V, 30 V, 100 V, 300 V, 500 V
0.1 A, 0.3 A, 1 A, 3 A, 10 A
Ammeters: a.c .0-5 A, d.c. 0-1 A.
Voltmeter: a.c. 0-500 V, d.c. 0-10 V.
Resistors: 1 box-unit containing three 1800 , 150 W resistors.
Capacitors: 1 box-unit containing three capacitors of 4.2 µF each.
D.C. Power supply: 0-240 V,
A.C.Power supply: Three phase and single phase, 50 Hz supply
1.Theory:
1.1 Power
Power in an electrical system is the product of the voltage v and current i. In SI-units, v is in
volts, i is in amperes and the power P is in watts. In d.c. circuits, v and I do not vary with time
and are normally represented as upper-case letters V and I. The power P is also constant in d.c.
circuits. We can write:
P = V.I
In a.c. circuits, we have an instantaneous power, p and an average power, P. These are given
by:
p = v. i.
P
=
…
1 T
 v.i.dt
T o
(1.1)
…
(1.2)
If v and I vary sinusoidally with time as
v = √2 V cos  t …
and
i
= √2 I cos ( t -  ), …
(1.3a)
(1.3b)
the instantaneous power is
p = v.i = 2 V I cos  t . cos ( t - ) …
where V and I are the effective (R.M.S.) values of the voltage and current.
(1.4)
In equations (1.3 b) and (1.4), a ‘+’ sign denotes a capacitive load (current leading the voltage)
and a ‘−’ sign denotes an inductive load (current lagging behind the voltage).
The average power is
P
1T
=
 v.i.dt
To
= V.I. cos  …
(1.5)
In an a.c. circuit, the voltage and current are represented by phasors. The term cos is called
power factor. If v and i are of different frequencies, the value of the integral in equation (1.2)
will be zero. P = VI is the appetence power and P = V.I. cos is the active power of the load.
1.2 Wattmeter terminals:
A wattmeter is an indicating instrument, which takes v and i, and performs the multiplication,
integration and averaging indicated in equation (1.2). The average power P, (also called true
power) is shown on the instrument by a pointer-position (or digitally). For connection into the
circuit, a wattmeter has four terminals - two current terminals and two potential terminals. The
connections are made such that, the ‘current-element’ of the wattmeter is connected in series
with the load circuit. The load current is sent into the current-element of the instrument in a
specified direction. This direction is usually marked on the wattmeter. In the same way, the
direction of voltage-drop to be applied to the potential terminals is also given on the instrument.
If the reference current direction and voltage drop are properly taken into account, the meter will
give positive reading in a load that consumes power.
Wattmeter
O
I
A.C. Source
ZL
U
Load
Figure 1.1 Connecting a Wattmeter in a circuit.
1.3 Three phase power measurement
1.3.1 Voltage and Currents in Star- and Delta-Connected Loads:
In a three-phase ac system consists of three voltage sources that supply power to loads connected to
the supply lines, which can be connected to either delta (Δ) or star (Y) configurations as shown in
the figure 1.2.
Figure 1.2 Load configurations.
In balanced three-phase systems, the voltages differ in phase 120°, and their frequency and
amplitudes are equal. If the three-phase loads are balanced (each having equal impedances), the
analysis of such a circuit can be simplified on a per-phase basis.
The voltage and current relationships in three-phase ac circuits (in a balanced three-phase system)
can be simplified as shown in Table 1-1.
Table 1-1. Voltage and current relationships in three-phase circuits.
Star-Connected Balanced Load
Delta-Connected Balanced Load
Phase current: I P 
Phase current: I1p = I1L, I2p = I2L, I3p = I3L
Line current: IL = I1L = I2L = I3L
IL
3
Line current: IL = I1L = I2L = I3L
and Ip = I12p = I23p = I31p
Phase voltage: VP 
VL
3
Line voltage: VL = V12 = V23 = V31
Phase voltage: V12 = V12p, V23 = V23p,
V31 = V31p
Line voltage: VL = V12 = V23 = V31
and Vp = V1p = V2p = V3p
1.3.2 Three Phase Power Measurement using Two Wattmeter
Figure 1.3 shows the two wattmeter connection may be used to determine the power in a threephase three-wire circuit (balanced or unbalanced).
W1
W1
IA = IBA - IAC
IA
O
I
O
U
I
U
Z1
IBA
VAB
VBA
Z2
IB
Z3
IAC
Z1
Z2
IB = ICB - IBA
Z3
ICB
VCB
IC
U
O
VCB
IC = IAC - ICB
I
W2
U
O
I
W2
Fig. 1.3 Measurement of 3 power using two wattmeter.
Star connection:
Power indicated by W1 :
P1 = VAB IA cosAB-A
(1.6)
AB-A is the phase difference between VAB and IA. VAB = VAN - VBN (Potential drop across W1)
Power indicated by W2 :
P2 =
VCB IC cosCB-C
(1.7)
CB-C is the phase difference between VCB and IC. VCB = VCN - VBN (Potential drop across W2)
Sum of the powers measured by the two wattmeters W1 and W2 would equal:
PT = P1 + P2
(1.8)
The total power measured (P1+P2) is the sum of real power consumed in the three phases.
1.3.3 Three Phase Power Measurement – Analysis in the Balanced Case
Star connection:
The voltage, VAB = VAN – VBN and is indicated by the phasor diagram in Fig. 1.4.
Phase difference between VAB and VAN is 30°. If the load is assumed to be inductive, the current is
lagging behind their respective phase voltage by , the phase difference between IA and VAB is =
(30°+).
VAB

VA
IA
30o
-VB
VBC
IC
N
VB
VC
IB
VCA
Fig. 1.4 Phasor diagram for balanced
case.
For a balanced system the magnitudes VAB = VCB = V L (line voltage:voltage between any pair of
terminals, eg. VAB).
For a balanced supply and three-phase load:
Power indicated by wattmeter W1:
P1
= VABIA cosAB-A = VL.IL.cos(+30o)
(1.9)
where VL is the magnitude of the line voltage and IL that of the line current.
Power indicated by wattmeter W2:
P2
= VCBIC cosCB-C = VL.IL.cos(-30o)
(1.10)
The sum of the two wattmeter readings:
P1 + P2 = VL.IL.cos(+30o) + VL.IL.cos(-30o) = VL.IL.[cos(+30o) + cos(-30o)]
= 3 VL IL cos 
(1.11)
This is the total power PT consumed by the load. Hence, the sum of the readings of the two meters
gives the total power PT consumed by the load. In this method, the reading of the wattmeter W1 can
become negative if  is greater than 600 (refer equation 1.9).
For a balanced three-phase system, the reactive power:
Q=
3 VLILsin 
Caution:
HIGH VOLTAGE!!!. Please make sure that all the connections are correct before switch on
the power supply.
You are required to get the permission from the instructor to switch on the power supply.
2 Experimental Procedure:
2.1 Power Measurement in DC Circuit
1. Establish the connections for power measurement in DC circuit according to the circuit diagram
shown in Fig. 2.1 and select the ranges on the wattmeter as indicated.
2. Adjust the source voltage to 10V such that the current through the circuit is 0.1A. Adjust the
resistor such that the resistance is 100Write down the reading of the wattmeter, taking into
account its multiplication factor.
Wattmeter
(10V, 1.0 A)
A
O
I
U
10Vd.c.
V
V1
100 
I1

Fig. 2.1 Connection of a wattmeter in a d.c. circuit
Wattmeter reading =
W.
Calculate the average power from theory and compare the measure value.
2.2 Power Measurement in Three-Phase Circuits
2.2.1: a) Establish the connection for power measurements in a three-phase star connection load
according to the circuit diagram shown in Fig. 2.2(a). (Note that in this circuit
arrangement, a three-phase balanced supply feeding a balanced three-phase load.)
b) Adjust the load to 470  and connect in star connection. (The load consists of three equal
resistances.)
c) Use wattmeter, W1 and W2, to measure the power between line A and line B, and between
line B and line C. The current circuit of W1 is connected in series with line A, and that of
W2 is connected in series with line C of the three-phase circuit. The potential circuit of
W1 gets the voltage VAB applied across it. The potential circuit of W2 has the voltage VCB
across it.
d) Adjust the three phase supply voltage to be 250 V line-to-line. Read the corresponding
values measured, I of the ammeter, V of the voltmeter and P1 and P2 of wattmeter W1 and
W2. Record the measured values in table 2.1. Calculate the total power P consumed by
the load using the formula:PT = P1 + P2
e) Repeat the measurement of (d) by adjusts the three phase supply voltage to be 150 V and
100 V. Record the measured values in table 2.1.
I1
A
A
W1
(300V, 1 A, UPF)
O
I
V
415V
3
470 per phase
U
V1
B
U
C
O
I
W2
(300V, 1 A, UPF)
Fig 2.2(a) Two-wattmeter method of power measurement in a three-phase, three-wire
system. Resistive load in star- Symmetrical.
2.2.2: a) Establish the connection for power measurements in a three-phase delta connection load
according to the diagram shown in Fig 2.2(b).
b) Adjust the three phase supply voltage to be 150 V line-to-line.
c) Read the corresponding values measured, I of the ammeter, V of the voltmeter and P1 and
P2 of wattmeter W1 and W2. Record the measured values in table 2.1.
I1
W1
(300V, 1A, UPF)
A
A
O
I
V
415V
3
470  per phase
U
V1
B
U
C
O
I
W2
(300V, 1A, UPF)
Fig 2.2(b) - Resistive load in Delta – Symmetrical.
2.2.3 a) Connect three capacitors of equal value of 4.2 µF each in delta as shown in Fig. 2.2(c).
b) Adjust the three phase supply voltage to be 150 V line-to-line.
c) Read the corresponding values measured, I of the ammeter, V of the voltmeter and P1 and
P2 of wattmeter W1 and W2. Record the measured values in table 2.1. (NOTE: One of the
wattmeter is a negative reading as the pointer will shows value less than zero.)
d) Modify the wattmeter connection to obtain the reading for the wattmeter that gave
negative reading.
I1
A
A
W1
(300V, 1A, UPF)
O
I
U
V
415V
3
V1
B
U
C
O
I
W2
(300V, 1 A, UPF)
Fig.2.2(c). Capacitors in Delta – Symmetrical.
TABLE 2-1: EXPERIMENTAL RESULTS
S.NO
NATURE OF
LOAD
I1
Amps
V1
Volts
P1
Watts
P2
Watts
TOTAL POWER
P= P1+P2 (W)
Experimental
1
2
3
4
5
Theoretical
Resistive load in
star (symmetrical)
R =470 Ω /ph
V = 250 V
Resistive load in
star (symmetrical)
R =470 Ω /ph
V = 150 V
Resistive load in
star (symmetrical)
R =470 Ω /ph
V = 100 V
Resistive load in
 (symm.)
Rph= 470 Ω/ph
Capacitive load in
 (Symmetrical)
C=4.2 µF/ph
3. Answer the following questions:
a) Compute theoretically the values of total power for all cases following table 2.1.
b) For the case covered by section 2.2.1, Based on the phasor diagram given in the theory
showing all the voltages and currents, draw the phasor of VCB (in star connection). Find the
phase angle between the voltage and current associated with each wattmeter and hence
calculate the readings of P1 and P2.
c) What is the power factor at which the reading of one of the wattmeters would be zero?
d) Under what load conditions do the two wattmeters indicate readings of equal magnitude (a)
with the same sign (b) with opposite sign?
e) Design a balanced three-phase star connection load (resistive load) with supply voltage to be
150 V line-to-line and total power consumed by the load equal to the total power measured in
the three-phase delta connection load as shown in Fig 2.2(b).
4. Laboratory Report
The report should contain the following:
a) Objective.
b) Schematic diagrams and Basic Theory.
c) Tabulation of observed and computed data.
d) Answers to the exercise questions.
e) Your own results and conclusions.
Important:

You are given one week to prepare, write and submit your lab report to the same
laboratory.

All reports must be neatly handwritten. Neatness and carefulness are counted.

Write your own report and use your own findings and results, similar reports won’t
be given marks for both the original and the copied ones.

Late submission of your lab report will not be entertained