Transcript LECTURE 8 - Gunadarma University

PERTEMUAN 13
PENGUKURAN DAYA
Introduction
• Power may be defined as the rate at which energy is transformed oe
made available
• In almost all cases the power in a d.c. circuit is best measured by
separately measuring quantities, V and I and by computing P=VI
• In case of a.c. circuits the instantaneous power varies continuously
as the current and voltage go through a cycle of values
• The fact that the power factor is involved in the expression for the
power means that a wattmeter must be used instead of merely an
ammeter and voltmeter.
Wattmeter
• A wattmeter is essentially an inherent combination of an ammeter
and a voltmeter and, therefore , consists of two coils known as
current coil and pressure coil.
• Wattmeter connection:
Wattmeter Errors
•
Error due to inductance of pressure coil
True power 
•
cos
 Re adingof wattm eter
cos cos   
Error due to pressure coil capacitance
sin 
sin   cot
•
Error due to Eddy currents : soild metal parts are removed as far away from
the current coil as possible
•
•
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Error due to power loss in pressure coil or current coil
There are two method of connecting wattmeters in the circuit for
measurement of power, as shown in figure below (a) and (b).
Fig (a) :
Wattmeterreading  W  I r
•
Fig (b) :
2
c
Wattmeterreading  W 
V2
R  rp
Measurement of Power in Single Phase A.C. Circuit
•
3-voltmeter method
P
•
V32  V12  V22
2R
V32  V12  V22
cos 
2V1V2
Disadvantages : (i) Even small errors in measurement of voltages may
cause serious errors in the value of power, (ii) Supply voltage higher than
normal voltage is required
•
3-Ammeter method

R 2
P
I 3  I 12  I 22
2
•

cos 
I 32  I 12  I 22
2I 1 I 2
The disadvantages of measurement of power by 3 voltmeters are overcome
in this method
Measurement of power in conjuction with instrument
transformers
• This method is used when the currents and voltages of the circuits
to be measured are high
• Figure below shows a measurement of power with wattmeter in
conjunction with instrument transformers in single phase A.C.
circuits
•
Vector diagram for inductive load
      
K
•
cos
cos cos       
Vector diagram for capasitive load
     
K
cos
cos cos       
Measurement of Power in 3-Phase Circuit
•
Measurement of power in 3phase, 4-wire circuits-----------
•
P=W1+W2+W3
•
Measurement of power in 3phase, 3-wire circuits-------------
•
P=W1+W2+W3
•
•
•
•
3-wattmeter method of measuring
3-phase power of delta connected
P=W1+W2+W3
1-wattmeter method of measuring
balanced 3-phase power (a) star
connected, (b) delta connected
P=3W
•
2-wattmeter method of measuring
3-phase 3-wire power :
– (a) star connected,
– P=W1+W2
– (b) delta connected
– P=W1+W2
Determination of P.F. from Wattmeter Reading
•
•
If load is balanced, then p.f. of the
load can be determined from the
wattmeter readings
Vector diagram for balanced star
connected inductive load -----
cos  cos tan1
3W1  W2 
W1  W2
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The watt-ratio Curve ----------
•
p.f. can be determined from
reading of two wattmeters