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1. MEASUREMENT OF
POWER & ENERGY

2. A Wattmetter

3. POWER IN DC CIRCUIT
• The power taken by a load from dc source is
P=VI watts
• The ammeter and voltmeter takes power for
their operation, It must be taken into
considerations.
• Power indicated by the instrument= Power
consumed in load + Power loss in voltmeter

4. POWER IN AC CIRCUIT
• Instantaneous power varies continuously as the current and
voltage goes through a cycle
• We measure average value over a cycle. Energy is
calculated multiplying the power by time.
The instantaneous power is given by p=vi both current and voltage are sinusoidal &
current lags by angle then v=V sin and i=I sin( )
Instantaneous power p=vi=V sin sin( )
p=V sin sin(
m m
m m
m m
t t
I t t
I
   
  
 


 
2
0
V
) = [cos cos(2 )]
2
V Vcos cos(2 )
Average power over a cycle P= cos cos
2 2 2
m m
m m m m
I
I I
VI

   
  
 

 
  
   


5. ELECTRODYNAMOMETER
WATTMETER
• The fixed coil or the field coils are connected in
series with the load and so carry the current in the
circuit i.e. the current coil (C.C.)
• The moving coil is connected across the voltage
and carries a current proportional to the
voltage. A high non inductive resistance is
connected in series with the moving coil to limit
the current to a small value. It is called the
pressure coil (P.C.) or voltage coil

6. Construction of
Electrodynamometer Wattmeter
Fixed Coil
Moving Coil
Control
Damping
Scales and Pointers

7. Theory of Electrodynamometer
Wattmeter
1 2
The instantaneous torque of electrodynamoteter instrument is
T /
and I are the rms value of voltage and current instantaneous voltage
i i i dM d
V

v= 2 sin
For a purely resistive pressure coil i , pressure coil current is in phase
with voltage / = 2 sin / 2 sin
/ rms value of current in pressure coil
is the res
p
p p p
p p p
p
V t
i v R V t R I t
I V R
R

   
 
istanc epressure coil

8. If the current coil lags the voltage in phase by instantaneous value of current
through the coil = 2 sin( )
Instantaneous torque T 2 sin( ) 2 sin /
2
i p
p
i I t
I t I tdM d
II

 
   

 
 sin( )sin /
[cos cos(2 )] /
There is a component of power that varies the twice the fundamental frequency
1
Average deflection Torque T [cos co
p
d p
t tdM d
II t dM d
II
T
   
   


  
 
0
s(2 )]( / ). ( )
cos . / ( / )cos . /
Controlling Torque of Spring- T
T
p p
c
t dM d d t
II dM d VI R dM d
K
   
   


 



9. Spring constant and = final steady deflection
Since the moving system cannot follow the rapid
variation in torque due to double freq, it will take a
position at which the average deflection is equ
K 
1
1
al to
the restoring torque to the spring
At balance cos . /
cos .( / ) /
=( cos / ).( / )
( . / )
cos ;
p
p
p
K II dM d
II dM d K
VI R K dM d
K dM d P
P VI K
  
  
 


 
 

 1 pR K

10. Shape of Scale
• The deflection is directly proportional to the
power measured and the scale is essentially
uniform over the range in which dM/dθ is
constant.
• By suitable design the mutual inductance between
fixed and moving coil can be made to vary
linearly with the angle over a range of 400 to 500
on ether side of zero mutual inductance position.
The scale will be uniform over the range 800 to
1000 which cover almost entire scale range
1( . / )K dM d P 

11. • Pressure coil Inductance
• Pressure coil Capacitance
• Error due to mutual inductance effects
• Error caused due to connections
• Eddy currents error
• Stray magnetic field error
• Error caused by vibration of Moving systems
• Temperature error
Errors in Electrodynamometer Wattmeter

12. • If a network is supplied through n conductors, the
total power is measured by summing the
readings of n wattmeter's so arranged that a
current element of a wattmeter is in each line and
corresponding voltage element is connected
between that line and common point
• If the common point is located on one of the lines,
then the power may measured by n-1 wattmeter
Power in Poly-phase System
Blondel’s Theorem

17. Measurement of Power in Three
Phase Circuits. 3 Wattmeter Method
• The connections shown in fig….In this case
the common point and neutral point
coincide, Hence, v=0
1 1 2 2 3 3
1 2 3 1 1 2 2 3 3
1 1 2 2 3 3
, v=0 and ; ;
of the instantaneous reading of the wattmeters
instantaneous power of the load
Hence, these three wattmeters masures t
Hence v v v v v v
Some
p p p p v i v i v i
The v i v i v i
    
     
  
he power of load

18. Two Wattmeter Method
In 3 phase 3 wire system we require 3 elements. If
the common pt of the pressure coils coincides with
one of the lines then n-1=2 elements are reqr
1 1 2 2 3 3Instantaneous power consumed by the load v i v i v i  

19. The sum of the wattmeter readings is equal to
the power consumed by the load irrespective of
load is balanced or unbalanced
Two Wattmeter Method
Delta Connection
1 3 1 3
2 2 2 1
1 2 3 1 3 2 2 1 2 2 3 3 1 2 3
1 1 2 2 3 3 1 2 3
Instantaneous reading ( )
Instantaneous reading ( )
Sum of the instantaneous reading
( ) ( ) ( )
; Since, 0
p v i i
p v i i
p p v i i v i i v i v i i v v
v i v i v i v v v
  
 
         
     

20. The Load is Balanced
1 2 3 1 2 3
1 2 3
13 23 12
1 2 3
1 2
, , , , , , be rms value of phase voltage
and phase currents. The load is balanced, so
phase voltages
voltages V V V 3
Currents
Line Currents
Let V V V I I I
v v v V
line V
Phase i i i I
I I
  
  
  
  3
1 1
0
13 1 13
1
And pf. =cos
phase current lags the phase voltage
The current through wattmeter P is I and voltage across
its pressure coil is V . I leads V by and angle (30 - )
Reading of P wattmeter
I I
The



 0
1 13 1
0
1
P V . I cos(30 - )
P 3V. Icos(30 - )



 

21. 2 2
0
23 2 23
0
2 2 23 2
0
2
The current through wattmeter P is I and voltage across
its pressure coil is V . I lags V by and angle (30 )
Reading of P wattmeter P V . I cos(30 )
P 3V. Icos(30 )
of reading of twoSum




  
  
0 0
1 2
0 0
1 2
1 2
1 2
wattmeters=Total power of the loads
P P 3V. Icos(30 - )+ 3V. Icos(30 ) 3VIcos
Difference of reading of two wattmeters
P -P 3V. Icos(30 - )- 3V. Icos(30 ) 3VIsin
P -P 3VIsin tan
P P 3VIcos 3
  
  
 


   
  
    

1 1 2
1 2
1 1 2
1 2
P -P
tan 3
P P
P -P
Factor=cos cos tan 3
P P
Power 


 
 
 
  
      

22. 0 0
1
0 0
2
1 2
UNITY PF cos =1 and =0
Reading of Two Wattmeters are
P 3V. Icos(30 - ) 3V. Icos30 3/ 2
P 3V. Icos(30 ) 3V. Icos30 3/ 2
P +P 3 At unity pf total power P= 3 VI cos =3VI
Thus at unity pf th
WITH
VI
VI
VI
 



  
   
 
e reading of two wattmeters are equal
and each wattmeter reads half the total power

23. 0
0 0
1
0 0
2
1 2
PF cos =0.5 and =60
Reading of Two Wattmeters are
P 3V. Icos(30 - ) 3V. Icos30 3/ 2
P 3V. Icos(30 ) 3V. Icos90 0
P +P 3/ 2 At 0.5 pf total power P= 3/ 2
Thus at 0.5 pf one wattmeters rea
When
VI
VI VI
 


  
   
 
ds 0 and another
wattmeter reads the Total power

24. • It is noted that when the power factor is below 0.5 one of
the wattmeter will give negative indication. Under this
conditions, to read the wattmeter we must either reverse
the current or pressure coil connections. The wattmeter
will then give positive reading BUT this must be taken as
negative for the calculation of total power
0
0 0
1
0 0
2
1 2
PF cos =0 and =90
Reading of Two Wattmeters are
P 3V. Icos(30 - ) 3V. Icos60 3 / 2
P 3V. Icos(30 ) 3V. Icos120 3 / 2
P +P 0 At 0 pf reading of two wattmeters are
equal but opposite in sig
When
VI
VI
 


  
    
 
n

25. Measurement of Power Using IT
Connection diagram of CT and PT

26. • Both the CT and PT are subjected to ratio and
phase angle error, these errors are negligible in
modern instruments but must not be ignored in
precision job
• Voltmeter and ammeter are effected by only ratio
errors while wattmeter's are influence in addition
by phase angle error. Correction can be made for
these errors if test information is available about
the IT and its burden
Measurement of Power Using IT

27. • Considering the phasor diagram of current and
voltage of load and in the wattmerer coils
a. Load with lagging pf
b. Load with leading pf
Measurement of Power Using IT
, V= Voltage across the load
I= load current
= phase angle between current and voltage
= Phase angle between currents in the current and pressure coils of wattmeters
Let


V = Voatage across secondary winding of the PT
=Voltage across the pressure coil ckt of wattmeter
I = secondary winding current of CT= Current in wattmeter current coil
s
s
I = Current in the wattmeter pressure coil
=Angle by which lags on acount of inductance of pressure coil
= Phase angle of PT
=Phase angle of CT
P




28. Measurement of Power Using IT
lagging pf: The phase angle of CT is +ve (I revesed leads I)
and the phase of PT is -ve (V reversed lags V)
Phase angle of load is = + +
Phase angle of PT may be positive or negative
for
s
s
For
The
     
the positive phase angle of PT
Phase angle of load is = + +
Leading pf: The phase angle of CT is +ve and that of PT is -ve
for such a case; Phase angle of load = =
if the phase angl
For
    
    
 
  
e of PT is +ve Phase angle of load is = +      

29. Correction Factor
correction factor -neglecting for the present, the ratio of transformer
cos
K=
cos cos
actual ratio of PT x actula ratio of CT x Wattmere reading
=K x
The
Power K x

 

RFC of PT x RFC of CT x nominal ratio of PT x nominal rato
of CT x wattmeter reading

30. Three Phase Wattmeter
• A dynamometer type three phase wattmeter consists of two separate
wattmeter movements mounted together in one case with the two
moving coils mounted on the same spindle.
• The arrangement as in fig……..
– There are two current coils and two pressure coils
– A current coil together with its pressure coil is known as an element. Therefore a
three phase wattmeter has two elements
– the connections of two elements of three phase wattmeter are the same as that
for two wattmeter method using two single phase wattmeter's
– The torque on each element is proportional to the power being measured by it.
– The total torque deflecting the moving system is the sum of the deflecting of the
two elements

31. • Deflecting torque of element 1 ∞ P1
• Deflecting torque of element 2 ∞ P2
• Total Deflecting torque of elements 1 ∞ (P1+P2)
• Hence the total deflecting torque on the moving system is
proportional to the total power
• For correct reading of 3 phase wattmeter, there should not
be any mutual interference between the two elements. A
laminated iron shield may be place between the two
elements to eliminate the mutual effects
• Resistance R may be adjusted to compensate for error cause
my mutual interference.
Three Phase Wattmeter

32. Measurement of Reactive Power
• The reactive power Q=VI sinΦ
• In load monitoring, it gives the idea to the
operator the nature of the load. The reactive
power gives the idea of pf
sinQ 
2 2
, the ratio of the ractive and active power is tan =
apparent power S=VI, Determines the line and generator capacity
Apparent Power S=
Since Q P
The
P Q



33. • In a single phase ckt reactive power can be
measured by a varmeter. This is an electrodynamic
wattmeter in whose pressure coil circuit a large
inductive reactance is substituted fro the series
resistance so that the pressure coil current is in
quadrature with the voltage; under this condition
the wattmeter reads
•
Measurement of Reactive Power
Single Phase Varmeters
0
cos(90 ) sin Re Power
do not read correctly if harmonic present or
frequency is different from the calibrating one
VI VI active
Varmeter
   

34. Poly-phase Varmeter
• In 3-p circuits phase shifting necessary fro the measurement of
reactive power is usually obtained from phase shifting
transformer. This phase shifting may be done by two auto
transformers connected in “open delta”
• The CC usually connected in series with the lines as usual.
• The PC are connected as in fig…. The phase line 2 is connected to
the common terminals of the two auto-transformers and phase 1
and 3 lines are connected to 100% taps on the transformers
• Both transformers will produce 115.4% of line voltage across the
total winding
• The pressure coil of wattmeter 1 is connected fro 57.7 % tap on
transformer 1 to 115.4 % tap on transformer 2, Which produces
a voltage equal to line voltage but shifted by 900

35. • The pressure coil of wattmeter 2 is connected in
a similar manner. Since both the coils receive a
voltage equal to the line voltage but displaced
by 900, the wattmeter read the reactive power
consumed by the load.
• The arithmetic sum of the two wattmeter gives
the total reactive power supplied to the load
Poly-phase Varmeter

36. • In a balanced three phase circuit it is simple to use a
single wattmeter to read the reactive power.
• The CC of the wattmeter is connected in one line and the
PC is connected across the other two lines as shown in
fig….
Reactive Power Measurement in
Three Phase Circuit
2
13
0 0
13 2
per the phasor diagram, Current through the CC=I
across the PC =V
Re of wattmeter
=V I cos(90 ) 3 cos(90 ) 3 sin
volt-amp of the circuit Q=3 sin
( 3) Re of Watt
As
Voltage
ading
VI VI
Total VI
x ading
  


    
  1
meter; And, Phase angle =tan
Q
P
 

37. MEASUREMENT OF ENERGY

38. • Energy is the total power delivered or consumed over a
time interval i.e.
• Motor Meters Used both in ac and dc ckt. The meter
may amp-hour meter or watt-hour meter. The moving
system revolves continuously. The speed of the rotation
is directly proportional to the energy
• Meter constant: Defined as the no of revolution made
per kilowatt-hour power, usually marked on the meter.
0
x Time
W=
t
Enrgy Power
vidt

 

39. Braking
• In a motor meter the speed of the moving system is
controlled by a braking system. The braking system
consists of a permanent magnet/braking magnet so
placed that it induces eddy currents in some part of
the moving system.
• The eddy current produce a braking/retarding
torque which is proportional to the speed of moving
system. The part in which eddy currents are
produced is usually an aluminum disc and mounted
on the moving system. When the moving system
revolves the disc cuts through the field of
permanent magnet

40. Braking
1
1
1
generate in the disc e=K
of the permanent magnet n= speed of rotation and
K a constant
, r be the resistance of the eddy current path;
the eddy current produced=i=e/r=K /
br
emf n
flux
Let
n r
The

 


aking torque produced by the interaction of the eddy current
and field of the permanent magnet. This torque is directly proportional
to the product of the flux of magnet, magnitude of eddy current
and
2 2
2 2 1 3
2
4
the effective radius R from the axis of the disc
Braking Torque T K / K /
the radius R of the disc is constant T K /
moving system attains a steady speed when the drivin
B
B
K ir K nR r nR r
If n r
The
      
 
2
5 3
2 2
3 3 6
2
6 3
g torque is
equal to the braking torque, where K K /
, be the driving torque at steady state speed N
T T K / ( / K )T T K
K ( / K ) tan
B d d d
R r
Let
NR r N r R
r R cons t
 
      
  

41. • Td is directly proportional to r and inversely proportional
to…..
• The strength of braking magnet shall always remain
constant
• Temperature change, changes r and braking torque reduces
• It is necessary that the steady speed of meter should be low
and in order to achieve this the disc resistance be low and
that flux of the magnet and the effective radius of the disc
be large
• The braking torque can be adjusted by using a magnetic
shunt whose distance from the magnet can be changed
Braking

42. Friction
• Error caused by friction are considerably more
important in motor meters than the corresponding
errors in the indicating instruments
• Static Friction. This friction force will also cause
serious errors at low loads, as the friction is
comparable with the load. Static friction may be
considered as a constant when the meter is running
and may be compensated by providing small
driving torque

43. Running Friction:
when the meter is running normally , a
friction torque is applied to the moving
system and the magnitude of this torque is
proportional to the speed of the moving
system. This friction torque adds to the
braking action and may cause serious errors
and therefore has to be compensated