FACULTY OF ENGINEERING
LAB SHEET
EEL1196 Instrumentation & Measurement Techniques
TRIMESTER 2 2016-2017
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:
To examine the methods of power measurement using wattmeter in a DC circuit and three-phase circuits.
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 W, 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 … (1.0)
In a.c. circuits, we have an instantaneous power, p and an average power, P. These are given by:
p = v.i … (1.1)
… (1.2)
If v and i vary sinusoidally with time as
v = √2 V cos w t … (1.3a)
i = √2 I cos (w t - j ), … (1.3b)
the instantaneous power is
p = v.i = 2 V I cos w t . cos (w t - j) … (1.4)
where V and I are the effective (R.M.S.) values of the voltage and current.
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
= V.I. cos j … (1.5)
In an a.c. circuit, the voltage and current are represented by phasors. The term cosj is called power factor. If v and i are of different frequencies, the value of the integral in equation (1.5) will be zero. P = VI is the apparent power and P = V.I. cosj 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 to the circuit, a wattmeter has four terminals - two current terminals and two potential terminals as shown in figure 1.1. 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.
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:
A three-phase ac system consisting of three voltage sources that supply power to loads connected to the supply lines, which can be connected in either delta (Δ) or star (Y) configurations, are as shown in the figure 1.2.
Figure 1.2 Load configurations.
In balanced three-phase systems, the voltages differ by a phase of 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: I1p = I1L, I2p = I2L, I3p = I3L
Line current: IL = I1L = I2L = I3L / Phase current:
Line current: IL = I1L = I2L = I3L
and Ip = I12p = I23p = I31p
Phase voltage:
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 three-phase three-wire circuit (balanced or unbalanced).
Star connection:
Power indicated by W1 :
P1 = VAB IA cosfAB-A … (1.6)
fAB-A is the phase difference between VAB and IA. VAB = VAN - VBN (Potential drop across W1)
Power indicated by W2 :
P2 = VCB IC cosfCB-C … (1.7)
fCB-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 Analysis in the Balanced 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 f, the phase difference between IA and VAB is = (30°+f).
For a balanced supply and three-phase load system, the magnitudes VAB = VCB = VL (line voltage: voltage between any pair of terminals, eg. VAB).
Power indicated by wattmeter W1:
P1 = VABIA cosfAB-A = VL.IL.cos(f +30o) … (1.9)
where VL is the magnitude of the line voltage and IL is that of the line current.
Power indicated by wattmeter W2:
P2 = VCBIC cosfCB-C = VL.IL.cos(f -30o) … (1.10)
The sum of the two wattmeter readings:
P1 + P2 = VL.IL.cos(f +30o) + VL.IL.cos(f -30o) = VL.IL.[cos(f +30o) + cos(f -30o)]
=VL IL cos f … (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 f is greater than 600 (refer equation 1.9).
For a balanced three-phase system, the reactive power:
Q = VL IL sin f … (1.12)
Caution:
HIGH VOLTAGE!!!. Please make sure that all the connections are correct before switching 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 a DC Circuit
a) 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.
b) Adjust the source voltage to 10V such that the current through the circuit is 0.1A. Adjust the resistor such that the resistance is 100W. Write down the reading of the wattmeter, taking into account its multiplication factor.
Figure 2.1 Connection of a wattmeter in a d.c. circuit
Wattmeter reading = W.
Calculate the theoretical average power and compare with the measured value.
2.2 Power Measurement in Three-Phase Circuits Using Two Wattmeter
2.2.1: Resistive Load in Star Connection – Symmetrical
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 is feeding a balanced three-phase load.)
b) Adjust each of the resistances to 470 W and connect them in star. (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, respectively. 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 measured values: I of the ammeter, V of the voltmeter and P1 and P2 of the wattmeters, which are W1 and W2 respectively. 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 step (d) by adjusting the three phase supply voltage to 150 V and 100 V. Record the measured values in table 2.1.
W2
(300V, 1 A, UPF)
Figure 2.2(a) Resistive load in Star - Symmetrical.
2.2.2: Resistive Load in Delta Connection - Symmetrical
a) Establish the connection for power measurements in a three-phase delta connected 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 measured values: I of the ammeter, V of the voltmeter and P1 and P2 of wattmeter, W1 and W2, respectively. Record the measured values in table 2.1.
W2
(300V, 1A, UPF)
Figure 2.2(b) Resistive load in Delta – Symmetrical.
2.2.3: Capacitive Load in Delta Connection - Symmetrical
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 measured values: I of the ammeter, V of the voltmeter and P1 and P2 of wattmeter, W1 and W2, respectively. Record the measured values in table 2.1. (NOTE: One of the wattmeter will show a negative reading as the pointer will show a value less than zero.)
d) Modify the connection of the wattmeter showing the negative reading to obtain a positive reading.
TABLE 2-1: EXPERIMENTAL RESULTS
NO. / NATURE OF LOAD / I1(Amps) / V1
(Volts) / P1
(Watts) / P2
(Watts) / TOTAL POWER
P = P1+P2 (W)
Experimental / Theoretical
1. / Resistive load in star (symmetrical)
R = 470 Ω /ph
V = 250 V
2. / Resistive load in star (symmetrical)
R = 470 Ω /ph
V = 150 V
3. / Resistive load in star (symmetrical)
R = 470 Ω /ph
V = 100 V
4. / Resistive load in D (symm.)
Rph = 470 Ω/ph
V = 150 V
5. / Capacitive load in D (Symmetrical)
C = 4.2 µF/ph
V = 150 V
3. Answer the following questions:
a) Compute the theoretical values of total power for the different types of load in table 2.1.
b) For the case covered by section 2.2.1, based on the phasor diagram given in the theory section 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 connected load (resistive load) with a supply voltage of 150 V line-to-line and with the 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) Summary of the experimental procedure.
d) Tabulation of observed and computed data.
e) Answers to the exercise questions.
f) 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 in preparing report are taken into account when awarding marks.
· 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 (strictly no plagiarism, references should be properly cited).
· Late submission of lab report will be penalized through deduction of marks.