Measurement of Power and Energy | Electrical and Electronic Measurements - Electrical Engineering (EE) PDF Download

 Page 1


 
 
 
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MEASURMENT OF POWER & ENERGY 
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Dynamometer type wattmeter works on very simple principle and this principle can be stated as when 
any current carrying conductor is placed inside a magnetic field, it experiences a mechanical force and 
due to this mechanical force deflection of conductor takes place. 
Construction and Working Principle of Electrodynamometer Type Wattmeter 
Now let us look at constructional details of electrodynamometer. It consists of following parts. 
Moving Coil 
Moving coil moves the pointer with the help of spring control instrument. Limited of current flows 
through the moving coil so as to avoid heating. So in order to limit the current we have connected the 
high value resistorin series with the moving coil. The moving is air cored and is mounted on a pivoted 
spindle and can move freely. In electrodynamometer type wattmeter, moving coil works as pressure 
coil. Hence moving coil is connected across the voltageand thus the current flowing through this coil 
is always proportional to the voltage 
Fixed Coil 
The fixed coil is divided into two equal parts and these are connected in series with the 
load, therefore the load current will flow through these coils. Now the reason is very 
obvious of using two fixed coils instead of one, so that it can be constructed to carry 
considerable amount of electric current. These coils are called the current coils of 
electrodynamometer type wattmeter. Earlier these fixed coils are designed to carry 
the current of about 100 amperes but now the modern wattmeter are designed to carry 
current of about 20 amperes in order to save power. 
Control System Out of two controlling systems i.e. 
1. Gravitycontrol 
2. Spring control, only spring controlled systems are used in these types of wattmeter. 
Gravity controlled system cannot be employed because they will be appreciable amount 
oferrors. 
Damping System Air friction damping is used, as eddy current damping will distort the 
weak operating magnetic field and thus it may leads to error. Scale There is uniform 
scale which is used in these types of instrument as moving coil moves linearly over a 
Page 2


 
 
 
?
  
MEASURMENT OF POWER & ENERGY 
?
Dynamometer type wattmeter works on very simple principle and this principle can be stated as when 
any current carrying conductor is placed inside a magnetic field, it experiences a mechanical force and 
due to this mechanical force deflection of conductor takes place. 
Construction and Working Principle of Electrodynamometer Type Wattmeter 
Now let us look at constructional details of electrodynamometer. It consists of following parts. 
Moving Coil 
Moving coil moves the pointer with the help of spring control instrument. Limited of current flows 
through the moving coil so as to avoid heating. So in order to limit the current we have connected the 
high value resistorin series with the moving coil. The moving is air cored and is mounted on a pivoted 
spindle and can move freely. In electrodynamometer type wattmeter, moving coil works as pressure 
coil. Hence moving coil is connected across the voltageand thus the current flowing through this coil 
is always proportional to the voltage 
Fixed Coil 
The fixed coil is divided into two equal parts and these are connected in series with the 
load, therefore the load current will flow through these coils. Now the reason is very 
obvious of using two fixed coils instead of one, so that it can be constructed to carry 
considerable amount of electric current. These coils are called the current coils of 
electrodynamometer type wattmeter. Earlier these fixed coils are designed to carry 
the current of about 100 amperes but now the modern wattmeter are designed to carry 
current of about 20 amperes in order to save power. 
Control System Out of two controlling systems i.e. 
1. Gravitycontrol 
2. Spring control, only spring controlled systems are used in these types of wattmeter. 
Gravity controlled system cannot be employed because they will be appreciable amount 
oferrors. 
Damping System Air friction damping is used, as eddy current damping will distort the 
weak operating magnetic field and thus it may leads to error. Scale There is uniform 
scale which is used in these types of instrument as moving coil moves linearly over a 
 
 
 
range of 40 degrees to 50 degrees on either side. Now let us derive the expressions for 
the controlling torque and deflecting torques. In order to derive these expressions let us 
consider the circuit diagram givenbelow: 
 
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We know that instantaneous torque in electrodynamic type instruments is directly 
proportional to product of instantaneous values of currents flowing through both 
the coils and the rate of change of flux linked with the circuit. Let I1 and I2 be the 
instantaneous values of currents in pressure  and current coils respectively. So the 
expression for the torque can be written as: 
 
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Where, x is the angle. Now letthe applied value of voltage across the pressure coil 
be Assuming the electrical resistanceto the pressure coil be very 
high hence we can neglect reactance with respect to its resistance. In this the 
impedance is equal to its electricalresistancetherefore it is purely resistive. The 
expression for instantaneous current can be written as I2 = v / R p where R p is the 
resistance of pressurecoil 
Page 3


 
 
 
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MEASURMENT OF POWER & ENERGY 
?
Dynamometer type wattmeter works on very simple principle and this principle can be stated as when 
any current carrying conductor is placed inside a magnetic field, it experiences a mechanical force and 
due to this mechanical force deflection of conductor takes place. 
Construction and Working Principle of Electrodynamometer Type Wattmeter 
Now let us look at constructional details of electrodynamometer. It consists of following parts. 
Moving Coil 
Moving coil moves the pointer with the help of spring control instrument. Limited of current flows 
through the moving coil so as to avoid heating. So in order to limit the current we have connected the 
high value resistorin series with the moving coil. The moving is air cored and is mounted on a pivoted 
spindle and can move freely. In electrodynamometer type wattmeter, moving coil works as pressure 
coil. Hence moving coil is connected across the voltageand thus the current flowing through this coil 
is always proportional to the voltage 
Fixed Coil 
The fixed coil is divided into two equal parts and these are connected in series with the 
load, therefore the load current will flow through these coils. Now the reason is very 
obvious of using two fixed coils instead of one, so that it can be constructed to carry 
considerable amount of electric current. These coils are called the current coils of 
electrodynamometer type wattmeter. Earlier these fixed coils are designed to carry 
the current of about 100 amperes but now the modern wattmeter are designed to carry 
current of about 20 amperes in order to save power. 
Control System Out of two controlling systems i.e. 
1. Gravitycontrol 
2. Spring control, only spring controlled systems are used in these types of wattmeter. 
Gravity controlled system cannot be employed because they will be appreciable amount 
oferrors. 
Damping System Air friction damping is used, as eddy current damping will distort the 
weak operating magnetic field and thus it may leads to error. Scale There is uniform 
scale which is used in these types of instrument as moving coil moves linearly over a 
 
 
 
range of 40 degrees to 50 degrees on either side. Now let us derive the expressions for 
the controlling torque and deflecting torques. In order to derive these expressions let us 
consider the circuit diagram givenbelow: 
 
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?
?
?
?
We know that instantaneous torque in electrodynamic type instruments is directly 
proportional to product of instantaneous values of currents flowing through both 
the coils and the rate of change of flux linked with the circuit. Let I1 and I2 be the 
instantaneous values of currents in pressure  and current coils respectively. So the 
expression for the torque can be written as: 
 
?
?
?
Where, x is the angle. Now letthe applied value of voltage across the pressure coil 
be Assuming the electrical resistanceto the pressure coil be very 
high hence we can neglect reactance with respect to its resistance. In this the 
impedance is equal to its electricalresistancetherefore it is purely resistive. The 
expression for instantaneous current can be written as I2 = v / R p where R p is the 
resistance of pressurecoil 
 
 
 
.   
If there is phase difference between voltage and electric current, then expression 
for instantaneous current through current coil can bewrittenas 
As current through the pressure coil is very 
very small compared to the current through current coil hence current through the 
current coil can be considered as equal to total load current. Hence the 
instantaneous value of torque can be writtenas 
Average value of deflecting torque can be obtained by integrating the 
instantaneous torque from limit 0 to T, where T is the time period of the cycle. 
 
Controlling torque is given by Tc = Kx where K is spring constant and x is final 
steady state value of deflection. 
Advantages of Electrodynamometer Type Wattmeter 
Following are the advantages of electrodynamometer type wattmeter and they 
are written as follows: 
1. Scale is uniform upto a certainlimit. 
2. They can be used for both to measure ac as well dc quantities as scale is calibrated forboth. 
Errors in Electrodynamometer Type Wattmeter 
Following are the errors in the electrodynamometer type watt meters: 
 
1. Errors in the pressure coilinductance. 
2. Errors may be due to pressure coilcapacitance. 
3. Errors may be due to mutual inductanceeffects. 
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Page 4


 
 
 
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MEASURMENT OF POWER & ENERGY 
?
Dynamometer type wattmeter works on very simple principle and this principle can be stated as when 
any current carrying conductor is placed inside a magnetic field, it experiences a mechanical force and 
due to this mechanical force deflection of conductor takes place. 
Construction and Working Principle of Electrodynamometer Type Wattmeter 
Now let us look at constructional details of electrodynamometer. It consists of following parts. 
Moving Coil 
Moving coil moves the pointer with the help of spring control instrument. Limited of current flows 
through the moving coil so as to avoid heating. So in order to limit the current we have connected the 
high value resistorin series with the moving coil. The moving is air cored and is mounted on a pivoted 
spindle and can move freely. In electrodynamometer type wattmeter, moving coil works as pressure 
coil. Hence moving coil is connected across the voltageand thus the current flowing through this coil 
is always proportional to the voltage 
Fixed Coil 
The fixed coil is divided into two equal parts and these are connected in series with the 
load, therefore the load current will flow through these coils. Now the reason is very 
obvious of using two fixed coils instead of one, so that it can be constructed to carry 
considerable amount of electric current. These coils are called the current coils of 
electrodynamometer type wattmeter. Earlier these fixed coils are designed to carry 
the current of about 100 amperes but now the modern wattmeter are designed to carry 
current of about 20 amperes in order to save power. 
Control System Out of two controlling systems i.e. 
1. Gravitycontrol 
2. Spring control, only spring controlled systems are used in these types of wattmeter. 
Gravity controlled system cannot be employed because they will be appreciable amount 
oferrors. 
Damping System Air friction damping is used, as eddy current damping will distort the 
weak operating magnetic field and thus it may leads to error. Scale There is uniform 
scale which is used in these types of instrument as moving coil moves linearly over a 
 
 
 
range of 40 degrees to 50 degrees on either side. Now let us derive the expressions for 
the controlling torque and deflecting torques. In order to derive these expressions let us 
consider the circuit diagram givenbelow: 
 
?
?
?
?
?
We know that instantaneous torque in electrodynamic type instruments is directly 
proportional to product of instantaneous values of currents flowing through both 
the coils and the rate of change of flux linked with the circuit. Let I1 and I2 be the 
instantaneous values of currents in pressure  and current coils respectively. So the 
expression for the torque can be written as: 
 
?
?
?
Where, x is the angle. Now letthe applied value of voltage across the pressure coil 
be Assuming the electrical resistanceto the pressure coil be very 
high hence we can neglect reactance with respect to its resistance. In this the 
impedance is equal to its electricalresistancetherefore it is purely resistive. The 
expression for instantaneous current can be written as I2 = v / R p where R p is the 
resistance of pressurecoil 
 
 
 
.   
If there is phase difference between voltage and electric current, then expression 
for instantaneous current through current coil can bewrittenas 
As current through the pressure coil is very 
very small compared to the current through current coil hence current through the 
current coil can be considered as equal to total load current. Hence the 
instantaneous value of torque can be writtenas 
Average value of deflecting torque can be obtained by integrating the 
instantaneous torque from limit 0 to T, where T is the time period of the cycle. 
 
Controlling torque is given by Tc = Kx where K is spring constant and x is final 
steady state value of deflection. 
Advantages of Electrodynamometer Type Wattmeter 
Following are the advantages of electrodynamometer type wattmeter and they 
are written as follows: 
1. Scale is uniform upto a certainlimit. 
2. They can be used for both to measure ac as well dc quantities as scale is calibrated forboth. 
Errors in Electrodynamometer Type Wattmeter 
Following are the errors in the electrodynamometer type watt meters: 
 
1. Errors in the pressure coilinductance. 
2. Errors may be due to pressure coilcapacitance. 
3. Errors may be due to mutual inductanceeffects. 
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4. Errors may be due connections.(i.e. pressure coil is connected after currentcoil) 
5. Error due to Eddycurrents. 
6. Errors caused by vibration of movingsystem. 
7. Temperature error. 
8. Errors due to stray magnetic field. 
What is Low Power Factor Wattmeter? 
As the name suggests the low power factor meterare the instruments that measures 
lower values of power factor accurately. 
There are two main reasons that would suggests us that we should not use ordinary 
wattmeter in measuring the low value of power factor. 
1. The value of deflecting torque is very low even though we fully excite the 
current and pressure coils. 
2. Errors due pressure coilinductance. 
 
 
some modification or adding some new features we can use modified 
electrodynamic wattmeter or low power factor to measure the low power factor 
accurately. 
(1) The electrical resistanceof the ordinary wattmeter's pressure coil is reduced to 
low value such that current in the pressure coil circuit is increased, thus it leads to. 
In this category two cases diagrams arises and these are shownbelow: 
 
 
Page 5


 
 
 
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MEASURMENT OF POWER & ENERGY 
?
Dynamometer type wattmeter works on very simple principle and this principle can be stated as when 
any current carrying conductor is placed inside a magnetic field, it experiences a mechanical force and 
due to this mechanical force deflection of conductor takes place. 
Construction and Working Principle of Electrodynamometer Type Wattmeter 
Now let us look at constructional details of electrodynamometer. It consists of following parts. 
Moving Coil 
Moving coil moves the pointer with the help of spring control instrument. Limited of current flows 
through the moving coil so as to avoid heating. So in order to limit the current we have connected the 
high value resistorin series with the moving coil. The moving is air cored and is mounted on a pivoted 
spindle and can move freely. In electrodynamometer type wattmeter, moving coil works as pressure 
coil. Hence moving coil is connected across the voltageand thus the current flowing through this coil 
is always proportional to the voltage 
Fixed Coil 
The fixed coil is divided into two equal parts and these are connected in series with the 
load, therefore the load current will flow through these coils. Now the reason is very 
obvious of using two fixed coils instead of one, so that it can be constructed to carry 
considerable amount of electric current. These coils are called the current coils of 
electrodynamometer type wattmeter. Earlier these fixed coils are designed to carry 
the current of about 100 amperes but now the modern wattmeter are designed to carry 
current of about 20 amperes in order to save power. 
Control System Out of two controlling systems i.e. 
1. Gravitycontrol 
2. Spring control, only spring controlled systems are used in these types of wattmeter. 
Gravity controlled system cannot be employed because they will be appreciable amount 
oferrors. 
Damping System Air friction damping is used, as eddy current damping will distort the 
weak operating magnetic field and thus it may leads to error. Scale There is uniform 
scale which is used in these types of instrument as moving coil moves linearly over a 
 
 
 
range of 40 degrees to 50 degrees on either side. Now let us derive the expressions for 
the controlling torque and deflecting torques. In order to derive these expressions let us 
consider the circuit diagram givenbelow: 
 
?
?
?
?
?
We know that instantaneous torque in electrodynamic type instruments is directly 
proportional to product of instantaneous values of currents flowing through both 
the coils and the rate of change of flux linked with the circuit. Let I1 and I2 be the 
instantaneous values of currents in pressure  and current coils respectively. So the 
expression for the torque can be written as: 
 
?
?
?
Where, x is the angle. Now letthe applied value of voltage across the pressure coil 
be Assuming the electrical resistanceto the pressure coil be very 
high hence we can neglect reactance with respect to its resistance. In this the 
impedance is equal to its electricalresistancetherefore it is purely resistive. The 
expression for instantaneous current can be written as I2 = v / R p where R p is the 
resistance of pressurecoil 
 
 
 
.   
If there is phase difference between voltage and electric current, then expression 
for instantaneous current through current coil can bewrittenas 
As current through the pressure coil is very 
very small compared to the current through current coil hence current through the 
current coil can be considered as equal to total load current. Hence the 
instantaneous value of torque can be writtenas 
Average value of deflecting torque can be obtained by integrating the 
instantaneous torque from limit 0 to T, where T is the time period of the cycle. 
 
Controlling torque is given by Tc = Kx where K is spring constant and x is final 
steady state value of deflection. 
Advantages of Electrodynamometer Type Wattmeter 
Following are the advantages of electrodynamometer type wattmeter and they 
are written as follows: 
1. Scale is uniform upto a certainlimit. 
2. They can be used for both to measure ac as well dc quantities as scale is calibrated forboth. 
Errors in Electrodynamometer Type Wattmeter 
Following are the errors in the electrodynamometer type watt meters: 
 
1. Errors in the pressure coilinductance. 
2. Errors may be due to pressure coilcapacitance. 
3. Errors may be due to mutual inductanceeffects. 
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4. Errors may be due connections.(i.e. pressure coil is connected after currentcoil) 
5. Error due to Eddycurrents. 
6. Errors caused by vibration of movingsystem. 
7. Temperature error. 
8. Errors due to stray magnetic field. 
What is Low Power Factor Wattmeter? 
As the name suggests the low power factor meterare the instruments that measures 
lower values of power factor accurately. 
There are two main reasons that would suggests us that we should not use ordinary 
wattmeter in measuring the low value of power factor. 
1. The value of deflecting torque is very low even though we fully excite the 
current and pressure coils. 
2. Errors due pressure coilinductance. 
 
 
some modification or adding some new features we can use modified 
electrodynamic wattmeter or low power factor to measure the low power factor 
accurately. 
(1) The electrical resistanceof the ordinary wattmeter's pressure coil is reduced to 
low value such that current in the pressure coil circuit is increased, thus it leads to. 
In this category two cases diagrams arises and these are shownbelow: 
 
 
 
50 
 
 
 
 
 
both the ends of the pressure coil is connected to supply side (i.e. current coil is in 
series with the load). The supply voltage is equal to the voltageacross the pressure 
coil. Thus in this case we 
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have power shown by the first wattmeteris equal to the power loss in the load plus 
power loss in the current coil. 
 
 
In the second category, the current coil is not in series with the load and the 
voltage across the pressure coil is not equal to the applied voltage. The voltage 
across pressure coil is equal to the voltage across the load. In this power shown by 
the second watt meter is equal to the power loss in the load plus the power loss in 
the pressure coil. 
 
 
From the above discussion we conclude that in both cases we have some amount 
of errors hence there is need to do some modification in above circuits to have 
minimum error. 
 
The modified circuit is shown below: We have used here a special coil called 
compensating coil, it carries current equal to the sum of two currents i.e load 
current plus pressure coil current. The pressure coil is placed such that the field 
produced by the compensating coil is opposed by the field produced by pressure 
coil as shown in the above circuit diagram.