MODULE 3 MEASUREMENT OF RESISTANCE, POWER,...

MODULE 3 MEASUREMENT OF RESISTANCE, POWER,

POWER FACTOR AND ENERGY

1

Measurement of resistance

Measurement of low resistance

(upto 1 ohm)

Measurement of medium resistance

(1 to 0.1M )

Measurement of high resistance

(greater than 0.1M )

Measurement of earth resistance

2



Ammeter Voltmeter method

Potentiometer method

Kelvin Double Bridge method

Ohm meter method

Series type

Shunt type

Crossed coil Ohm meters

Fixed magnet moving coil Ohmmeter

Crossed coil moving magnet Ohmmeter

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Ohm meter method

Series type

Shunt type





=

=

So to find resistance

Measure potential across the resistance using voltmeter

Measure current through the resistance using Ammeter

5


6


Connection (a)

Voltmeter resistance is infinite

7


Connection (a)

If ammeter resistance is zero, then measured value is the actual value of unknown resistance

If Rx>>>RA Ammeter effect

becomes negligible

8


Connection(b)

Voltmeter reading is the true voltage across resistance

Ammeter reads total current which is sum of current through resistance and voltmeter

9


10


11


Actual value of resistance is measured if (Rm/RV)=0

Which means voltmeter resistance is infinite

If Rx


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Ohm meter method

Series type

Shunt type





14


R-rheostat

B- battery

S- standard resistance

X- unknown resistance

15


Circuit is connected as shown in figure

Rheostat R- regulate current

Voltage drop across standard resistance and unknown resistance is measured with the help of potentiometer (Vs and Vx )

=

=

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Advantage

High accuracy

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Ohm meter method

Series type

Shunt type





19

Kelvin Double Bridge(contd)

Why it is called double bridge??

it is because it incorporates the second set of ratio arms as shown

20


In this the ratio arms p and q are used to connect the galvanometer at the correct point between j and k to remove the effect of connecting lead of electrical resistance t.

Under balance condition voltage drop between a and b (i.e. E) is equal to F (voltage drop between a and c)

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It is used to measure resistances as low as 0.00001

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Ohm meter method

Series type

Shunt type




Ohm meter method

An ohmmeter is an electrical instrument that measures electrical resistance, the opposition to an electric current.

Micro-ohmmeters (microhmmeter or microohmmeter) make low resistance measurements.

Megohmmeters (aka megaohmmeter or in the case of a trademarked device Megger) measure large values of resistance.

The unit of measurement for resistance is ohms ().

27

http://en.wikipedia.org/wiki/Electricityhttp://en.wikipedia.org/wiki/Measuring_instrumenthttp://en.wikipedia.org/wiki/Electrical_resistancehttp://en.wikipedia.org/wiki/Electric_currenthttp://en.wikipedia.org/wiki/Meggerhttp://en.wikipedia.org/wiki/%CE%A9

Ohm meter method

Instead of measuring current and voltage , if one quantity is kept constant, then resistance is proportional to other quantity

Principle of Ohmmter

If current is kept constant, then resistance is proportional to voltmeter reading connected across the resistance

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Ohm meter method

Series type

Shunt type




Series type Ohm meter

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Current flowing through the meter depends on unknown resistance

Meter deflection is proportional to value of resistance

32


To mark zero on the scale

A-B is shorted

R2 is adjusted so that current (Ifsd) through the meter gives full scale deflection

This position is marked as zero

33


To mark infinity

A-B is opened

No current flows throgh the circuit

So pointer does not deflect

This point is marked as infinity

Rh is half scale resistance marking

34


For half scale deflection,

Since total resistance

presented to battery is 2Rh

35


To produce full scale deflection, current required is

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Ohm meter method

Series type

Shunt type




Shunt type Ohmmeter

40

Shunt type Ohmmeter

Consists of battery in series with adjustable resistance R1 and meter

Switch- provided to disconnect the battery when instrument is not in use

Unknown resistance is connected in parallel with meter hence the name shunt type Ohmmeter

41

Shunt type Ohmmeter

A-B shorted Entire current passes though

short, hence meter reads zero Pointer position is marked as

zero

A-B opened Entire current passes through

the meter and the deflection of the pointer is marked as infinity.

A-B some unknown resistance Meter will show

intermediate readings

42

Shunt type Ohmmeter

AB is opened

Current flowing through meter is:

=

1 +

43

Shunt type Ohmmeter

If AB is shorted

Current flowing through the meter:

= 0 mperes

44

Shunt type Ohmmeter

If unknown resistance is connected across AB

At node 1 = +

=

1 +

+

45

=( + )

( + )1+

Shunt type Ohmmeter

Current through meter is

=

+

46

=(+)

1(+)+ *

+

Shunt type Ohmmeter

For full scale deflection, = 0

= 0 Amperes

47

Shunt type Ohmmeter

For half scale deflection,

=

Current through meter is:

=

21+

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Ohm meter method

Series type

Shunt type




Crossed coil Ohmmeters

These instruments are also called ratiometers

It consists of two rigidly fixed coils at an angular seperation of 900

Indication depends on ratio of currents through two coils

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Ohm meter method

Series type

Shunt type




Fixed Magnet Moving Coil Ohmmeter

52


The two moving coils moves in permanent magnetic field.

53


Torque produced is:

54


The two torques produced acts in opposite directions

55


At equilibrium,

56


Current I1 is proportional to voltage drop across unknown resistance X

1 =

57


That means deflection

tan =1

2

That means deflection depends on value of X

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If X is not in circuit then pointer will set parallel to voltage coil which means X= infinity ohms

If X is shorted, maximum current flows through current coil , which will set the pointer parallel to current coil, which means X= zero ohms

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Ohm meter method

Series type

Shunt type




Crossed coil Moving magnet type Ohm meter

61


Consists of :

Two fixed coils

Pivoted magnetic needle attached with a pointer

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Case 1) Terminal ab is opened

No current flows through current coil

Bottom portion of the magnetic needle moves in the direction of pressure coil

Pointer shows resistance is zero ohms

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Case 2) Terminal ab is shorted

Current flowing through current coil is maximum

Bottom portion of magnetic needle move towards current coil

Resistance shown by the magnetic needle is zero

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Case 3) If unknown resistance X is connected across ab

Deflection of the magnetic needle will be proportional to ratio of currents through pressure coil and current coil

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Substitution method

Wheatstone bridge method

Carey Foster Bridge method

Ohmmeter method

66




Substitution method



Ohmmeter method

67


Same as measuring low resistance

68




Substitution method



Ohmmeter method

69

Substitution method

Method 1

R is variable resistance

X is unknown resistance

First X is put in the circuit, value of current is noted

Then X is removed and value of current is noted

70

Substitution method

Method 2

Initially switch is at position 1, current is measured

Then switch put to position 2, current is measured

71




Substitution method



Ohmmeter method

72

Wheatstones Bridge

73

Wheatstones Bridge(contd)

For measuring accurately any electrical resistance Wheatstone bridge is widely used.

There are two known resistors, one variable resistor and one unknown resistor connected in bridge form as shown below.

By adjusting the variable resistor the current through the Galvanometer is made zero.

When the electric current through the galvanometer becomes zero, the ratio of two known resistors is exactly equal to the ratio of adjusted value of variable resistance and the value of unknown resistance.

In this way the value of unknown electrical resistance can easily be measured by using a Wheatstone Bridge.

74


It is a four arms bridge circuit where arm AB, BC, CD and AD are consisting of electrical resistances P, Q, S and R respectively.

Among these resistances P and Q are known fixed electrical resistances and these two arms are referred as ratio arms.

An accurate and sensitive Galvanometer is connected between the terminals B and D through a switch S2

75


The voltage source of this Wheatstone bridge is connected to the terminals A and C via a switch S1 as shown.

A variable resistor S is connected between point C and D.

The potential at point D can be varied by adjusting the value of variable resistor S.

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Suppose current I1 and current I2are flowing through the paths ABC and ADC respectively. If we vary the electrical resistance value of arm CD the value of current I2 will also be varied as the voltage across A and C is fixed.

77


If we continue to adjust the variable resistance one situation may comes when voltage drop across the resistor S that is I2.S is becomes exactly equal to voltage drop across resistor Q that is I1.Q.

Thus the potential at point B becomes equal to the potential at point D hence potential difference between these two points is zero hence current through galvanometer is nil.

Then the deflection in the galvanometer is nil when the switch S2 is closed.

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Now potential of point B in respect of point C is nothing but the voltage drop across the resistor Q.

80


Again potential of point D in respect of point C is nothing but the voltage drop across the resistor S .

81


Equating, equations (i) and (ii) we get,

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The electrical resistances P and Q of the Wheatstone bridge are made of definite ratio such as 1:1; 10:1 or 100:1 known as ratio arms and S the rheostat arm is made continuously variable from 1 to 1,000 or from

1 to 10,000

Wheat stones bridge can be used for measurement of resistances upto 100000ohms

83

Wheatstones bridge mthod

Limitations

While measuring low resistance, resistance of leads and contacts become significant resulting in error

While measuring high resistances, galvanometer becomes insensitive to imbalance

Change in resistance of bridge arms due to heating effect

84




Substitution method



Ohmmeter method

85

Carey Foster Bridge

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Carey Foster Bridge

In the diagram to the right, X and Y are resistances to be compared.

P and Q are nearly equal resistances, forming the other half of the bridge.

The bridge wire EF has a jockey contact D placed along it and is slid until the galvanometer G measures zero.

The thick-bordered areas are thick copper busbars of almost zero resistance.

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Carey Foster Bridge

Place a known resistance in position Y.

Place the unknown resistance in position X.

Adjust the contact D along the bridge wire EF so as to null the galvanometer.

This position (as a percentage of distance from E to F) is l1.

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Carey Foster Bridge

Swap X and Y. Adjust D to the new null point. This position is l2.

If the resistance of the wire per percentage is , then the resistance difference is the resistance of the length of bridge wire between l1 and l2:

89

Carey Foster Bridge

90

Carey Foster Bridge

Two resistances to be compared, X and Y, are connected in series with the bridge wire.

Thus, considered as a Wheatstone bridge, the two resistances are X plus a length of bridge wire, and Y plus the remaining bridge wire.

The two remaining arms are the nearly equal resistances P and Q, connected in the inner gaps of the bridge.

91

Carey Foster Bridge

Let l1 be the null point D on the bridge wire EF in percent.

is the unknown left-side extra resistance EX

is the unknown right-side extra resistance FY

is the resistance per percent length of the bridge wire:

92

Carey Foster Bridge

93

Carey Foster Bridge

Equations 1 and 2 have the same left-hand side and the same numerator on the right-hand side, meaning the denominator on the right-hand side must also be equal

94

Carey Foster Bridge

95


Advantages high accuracy, unaffected by thermoelectric emfs

Limitations unsuitable for measuring low resistances

96




Substitution method



Ohmmeter method

97

Ohm meter method

Same as measuring low resistance using ohm meter

98



Direct deflection method

Megger method

Loss of charge method

Mega Ohm bridge method

99

Problems associated with measurement of high resistances

1) Leakage that occurs over and around the component or specimen under test , or over the binding posts by which the component is attached to the instrument or within the instrument

- If not controlled resistance measured will be a combined effect

- Effect of leakage paths on measurements can be removed by Guard circuit

100

Problems associated with measurement of high resistances

2) Electrostatic effect stray charges appear in the measuring circuit- so errors

3) Absorption by insulating materials- current falls fairly and steeply in the beginning and gradually thereafter

4) Resistance of insulating materials- falls rapidly with increasing temperature

5) Galvanometer employed should be highly sensitive 6) Voltage supply of 100V or more should be applied

depending on breakdown voltage of the component 7) One point of the circuit should be effectively

grounded obtaining definite ratios in the potential distribution

101

Guard circuit

102

Guard circuit

Case (a) without guard circuit

High resistance is measured by Ammeter- Voltmeter method

Micro ammeter carries sum of leakage current and resistance current (IR+IL)

So reading in the ammeter will not be accurate due to error caused by leakage current.

103

Guard circuit

Case (b)- With guard

Guard terminal surrounds the resistance entirely and is connected to battery side of micro ammeter

So current through micro ammeter is IR only and hence resistance can be measured accurately

104

Simple guard circuit

105

Guarded wheat stones bridge

106


Measurement of high

resistance

Direct deflection

method

Megger method



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Measurement of insulation resistance of a cable


Case (a) cables with metal sheath

Galvanometer G measures the current between core and metal sheath

Leakage currents over the surface of insulating material are carried by the guard wire wound on the insulation and does not flow through the insulation

The ration of voltage applied between the core and metal sheath and current flowing between them(galvanometer deflection) gives insulation resistance of the cable

109


Case (b)

Cable is immersed in water for at least 24hrs, so that it enters pores of the cable

Initially galvanometer should be shunted, if possible it should be connected in series with a high resistance(MegaOhms)

Leakage current flows through guard wire

Ration of voltmeter reading to galvanometer deflection gives the value of insulation resistance

110


Limitations

Galvanometer should be highly sensitive

Galvanometer should be prevented from initial inrush of currents

Battery should be at least 500V and its emf should remain constant

111


Measurement of high

resistance


Megger method



112

MEGGER METHOD

113

MEGGER METHOD

Working principle: Electromagnetic induction

When a current carrying conductor is placed in a magnetic field it experiences force whose magnitude depends on strength of current and magnetic field

114

MEGGER METHOD

It consists of three coils:

Current coil or deflection coil

Pressure or control coil

Compensating coil

Coils are mounted on a central shaft and is free to rotate along a C shaped structure

115

MEGGER METHOD

It also consists of

Permanent magnet to Ohmmeter and dc generator

116

MEGGER METHOD

The coils are connected to the circuit with flexible leads called ligaments

Current coil is connected in series with resistance R1 connected to T2 and one generator terminal

In the event of short, R1 protects the current coil

117

MEGGER METHOD

Potential coil

One end connected to compensating coil in series with protective resistance R2

Other end is connected to generator

Compensating coil is used for better scale operations

118

MEGGER METHOD

When the test terminals T1 T2 is open, no current flows through current coil

Some current flows through voltage coil, so the pointer move towards infinity ohm reading

119

MEGGER METHOD

If test terminals are shorted, high current passes through current coil and the scale reading will be zero ohms

120

MEGGER METHOD

When a high resistance is connected between T1 and T2 deflection of pointer is proportional to ratio of currents through pressure coil and current coil

Guard terminal is provided to eliminate leakage current

121

MEGGER METHOD APPLICATIONS


Measurement of insulation resistance

Used for testing continuity, pointer shows full deflection if continuity is there between two points in a circuit

122


Measurement of high

resistance


Megger method



123


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Step 1: Capacitor C is charged by battery- by keeping switch in position 1

Step 2: Capacitor C is discharged via Rx and Rleak

125


Step 3: Time (t) taken for the potential difference to fall from V1 to V2 is noted during discharge.

=

+

126


At the time of discharge:

=

=

=

127


=

=

128


=

0

21

2

1=

2

1= ( )

From the above

expression Reff can be determined

129


The test is then repeated with Rleak only.

So value of Rleak is found and from the expression of resistance RX that is unknown value of resistance is found.

130


131

Measurement of high

resistance


Megger method



Mega Ohm Bridge Method

132


It consits of:

Power supply

Bridge members

Amplifier

Indicating instrument

133


Sensitivity for high resistance is obtained by :

1) using high voltages of

500V or 1000V

2) Use of sensitive null

indicating arrangement

such as high gain

amplifier with CRO or

electronic voltmeter

134


Dial R2 is calibrated as

1- 10 100 1000M

Dial R2 1-10 is in logarithmic scale

Unknown resistance is

3 =142

Junction of arms R1and R2 is brought out on the main panel and designated as Guard Terminal

135

EARTHING AND MEASUREMENT OF EARTH RESISTANCE

What is meant by earthing?

How will you measure earth resistance?

136

EARTHING

The connection of electrical machinery/equipment to a general mass of earth, with a conducting material of low resistance is called earthing or grounding

The conducting material used is known as earth electrode

137

ADVANTAGES OF USING EARTH ELECTRODE

All parts of the electrical equipment will be at zero potential.

Leakage current flows through low resistance path provided by the earth electrode so human protection

Voltage spikes/ current spikes due to lightning or short circuits or other faults will easily get dissipated to earth.

138

ADVANTAGES OF USING EARTH ELECTRODE

In the case of three phase system, neutral is earthed which helps to maintain line voltage constant

For telephone and traction work, earthing acts as return path. So cost of cable and cast of such cable is avoided.

Earth electrode ensures low resistance path and hence able to carry leakage currents without deterioration.

139

MEASUREMENT OF EARTH RESISTANCE

Measurement of earth resistance

Fall of potential method

Megger earth tester

140


Measurement of earth

resistance

Fall of potential

method

Megger earth tester

141

FALL OF POTENTIAL METHOD

142


Potential E is applied

Current I circulates through the E and Q

Voltage between E and P is noted

143


Pattern of current flow through earth:

144


Current diverge from E

Current converge at Q

Current density is high near E and Q

Near electrodes, voltmeter reads high, where as between the electrodes

145


The potential V rises near E and Q due to current density

In the middle section V remains constant

146


Value of earth resistance is given by:

=

147


The measurement of VEP is done at various points between E and Q

The potential variation curve is shown in fig

Resistance RE is determined when the potential curve is absolutely flat To get accurate reading,

distance between P and Q should be large

148


Variation of resistance with distance is shown

149


Measurement of earth

resistance

Fall of potential method

Megger earth tester

150

MEGGER EARTH TESTER

151

MEGGER EARTH TESTER

It consists of

DC generator

Current reverser

Rectifier

Current coil

Potential coil

Electrodes E,P and Q

152

MEGGER EARTH TESTER

Current reverser and rectifier have L type commutators

These are mounted on the shaft and rotated with handle

Two brushes of commutator are arranged so that it they make contact alternately with each segment of the commutator

153

MEGGER EARTH TESTER

Other two brushes of commutator are placed in such away that they always make contact with the commutator

154

MEGGER EARTH TESTER

Earth tester consists of the terminals P1, C1, P2,C2

P1 andd C1 is shorted and connected to common point E

P2 and C2 are connected to auxiliary electrodes P and Q respectively

155

MEGGER EARTH TESTER

The ratio of voltage sensed by voltage coil and current passing through current coil, directly gives the value of earth resistance RE

Deflection of the pointer gives RE

It can be used for dc purposes only, but to measure ac reverser and rectifier is used

156

MEGGER EARTH TESTER

AC current through soil prevents back emf in the soil due to electrolytic action

157

MEASUREMENT OF POWER

Measurement of power is done by wattmeters

Wattmeter is a combination of Ammeter and Voltmeter.

So it contains current coil and voltage coil(pressure coil)

158


159

Wattmeters

Dynamometer type

Induction type

Electrostatic type

Wattmeter

160

Current coil carries load current

Pressure coil carries current proportional to voltage

Inductance of pressure coil should be minimum to avoid phase lag between current and voltage


161

Wattmeters

Dynamometer type

Induction type

Electrostatic type

Dynamometer type wattmeter

162


Fixed coil current flowing is proportional to load current

Moving coil- current flowing is proportional to load voltage

163


Strength of magnetic field- proportional to currents through two coils

164


165

V- supply voltage

I load current

R- resistance of moving

coil circuit


Fixed coil current: =

Moving coil current:

=

Deflecting torque:

=

166


For dc circuit deflecting torque is proportional to power

For ac circuit deflecting torque is proportional to voltage, current and power factor

=

167


1

2

M- mutual inductance between

two coils

Instantaneous torque is given by:

= 12

168


Instantaneous voltage in pressure coil is:

= 2

Instantaneous current through pressure coil is:

=2

= 2

- resistance of

pressure coil

169


Current through current coil lags voltage by an angle

= 2 I sin

170


Instantaneous torque is given by:

171


Average deflecting torque is given by:

172


Control torque is =

K- spring constant

- final steady state deflection

At balance position

= ()

173


At balance condition:

174

Shape of scale of dynamometer wattmeter

175


Deflection is proportional to power measured

and scale is uniform since

is constant.

Wattmeters are designed such that

remains over 40 to 50 degree on each side

of zero mutual inductance position.

M varies linearly in this zone with respect to

176


If zero mutual inducatnce position is kept in the middle then M varies linearly for deflection upto 80 to 100 degrees

177


178


Ranges:

Current coil: 0.25A to 100A

Pressure coil : 5V to 750V

179



Suspended coil torsion type

Pivoted coil indicating type

180

Suspended coil torsion type dynamometer wattmeter

181


The moving, or voltage, coil is suspended from a torsion head by a metallic suspension which serves as a lead to the coil.

This coil is situated entirely inside the current or fixed coils and the winding in such that the system is a static.

Errors due to external magnetic fields are thus avoided. The torsion heads carries a scale, and when in use, the

moving coil is bought back to the zero position by turning this head; the number of divisions turned through when multiplied by a constant for the instrument gives the power.

Eddy currents are eliminated as far as possible by winding the current coils of standard wire and by using no metal parts within the region of the magnetic field of the instrument.

182


The mutual inductance errors are completely eliminated by making zero position of the coil such that the angle between the planes of moving coil and fixed coil is 90 degree. i.e. the mutual inductance between the fixed and moving coil is zero.

The elimination of pivot friction makes possible the construction of extremely sensitive and accurate electrodynamic instruments of this pattern.

183

Pivoted coil indicating type dynamometer wattmeter

184


In these instruments, the fixed coil is wound in two halves, which are placed in parallel to another at such a distance, that uniform field is obtained.

The moving coil is wound of such a size and pivoted centrally so that it does not project outside the field coils at its maximum deflection position.

The springs are pivoted for controlling the movement of the moving coil, which also serves as currents lead to the moving coil.

185


The damping is provided by using the damping vane attached to the moving system and moving in a sector-shaped box.

The reading is indicated directly by the pointer attached to the moving system and moving over the calibrated scale.

The eddy current errors, within the region of the magnetic field of the instrument, are minimized by the use of non-metallic parts of high resistivity material.

186

Electrodynamometer type wattmeter

Advantages:

1) In dynamometer type wattmeter, the scale of the instrument is uniform (because deflecting torque is proportional to the true power in both DC as well as AC and the instrument is spring controlled.)

2) High degree of accuracy can be obtained by careful design; hence these are used for calibration purposes.

187

Electrodynamometer type wattmeter

Disadvantages:

1) The error due to the inductance of the pressure coil at low power factor is very serious (unless special features are incorporated to reduce its effect)

2) In dynamometer type wattmeter, stray field may affect the reading of the instrument. To reduce it, magnetic shielding is provided by enclosing the instrument in an iron case.

188

Errors in dynamometer type wattmeter

Errors

Due to pressure coil inductance

Due to pressure coil capacitance

Due power loss in pressure coil and current coil

Due to Eddy current

Due to friction

Due to temperature

Due to stray fields

189


Errors




Due to Eddy current

Due to friction

Due to temperature

Due to stray fields

190

Error due to pressure coil inductance

Current through pressure coil will be in phase with voltage applied

Due to inductance of pressure coil, current in pressure coil lags behind supply voltage

So there will be error in reading

191


192


Pressure coil current lagging behind voltage by an angle

193


Let power factor be lagging

194


195


196


197


If power factor is leading:

198


199


200

Compensation for Error due to pressure coil inductance

201


202


203


Errors




Due to Eddy current

Due to friction

Due to temperature

Due to stray fields

204

Error due to pressure coil capacitance

Pressure coil has capacitance as well as inductance

Capacitance is due to inter-turn capacitance in the high values of series resistor.

The effect produced is same as that of inductance circuit except that pressure coil currents leads applied voltage

So wattmeter will read low on lagging power factors of load, by increasing angle between load and voltage coil currents

205

Error due to pressure coil capacitance

Effect of frequency: vary angle between V and pressure coil current, the angle is increasing with frequency.

If inductive reactance of pressure coil = capacitive reactance of pressure coil, there will be no error

206


Errors




Due to Eddy current

Due to friction

Due to temperature

Due to stray fields

207

Error due to power loss in pressure coil and current coil

Let Rp be the resistance of pressure coil

Rc be resistance of current coil

208


There are two methods of connecting wattmeter

209


Voltage applied to the pressure coil = voltage across load + voltage drop across current coil

So wattmeter measures power loss in current coil in addition to power consumed by load

210


211


Current coil carries current to the load and current to pressure coil

So wattmeter reads:

power consumed by load + power loss in pressure coil

212


213


Power loss in pressure coil is less comapared to current coil

Connection (a) is preferred for small currents

Where as vice versa for high currents

214

Compensation for Error due to power loss in pressure coil

Compensating coil is used to eliminate error due to current coil carrying pressure coil current in addition to load current

Compensating coil is coincident and identical to current coil

If compensating coil is connected in series with current coil, current passed through two coils produces resultant magnetic field = zero

215


Compensating coil is connected in series with pressure coil so that magnetic field opposes that of current coil and neutralize pressure coil component of current in current coil

So if no load current flows through instrument, deflection will be zero

216


217


Errors




Due to Eddy current

Due to friction

Due to temperature

Due to stray fields

218

Error due to eddy currents

Eddy currents are induced in solid metal parts of instrument by alternating magnetic field

The phase of induced emf will be 90 degree behind inducing flux

Eddy currents are practically in phase with its emf and it sets up a magnetic field which is combined with that of current coil

So a resultant magnetic field is produced which is less than current coil alone and which lags behind current coil by small angle

219

Error due to eddy currents

Eddy current error cannot be easily calculated

If metal parts are more in instrument it is significantly high

220


Errors




Due to Eddy current

Due to friction

Due to temperature

Due to stray fields

221

Error due to friction

Deflecting torque is very less in the instrument

So there is frictional error

To reduce frictional error

Weight of moving parts should be reduced

Greater care must be taken on pivoting

222


Errors




Due to Eddy current

Due to friction

Due to temperature

Due to stray fields

223

Error due to temperature

As temperature changes

Resistance of pressure coil changes

Stiffness of springs changes

The above effects are opposite in action

So they neutralize

If pressure coil composed of copper and of resistance alloy having negligible resistance, temperature coefficient is 1: 10

224


Errors




Due to Eddy current

Due to friction

Due to temperature

Due to stray fields

225

Error due to stray fields

Dynamometer wattmeter has weak operating field

It is affected by stray magnetic fields resulting in errors

So these instruments are shielded against effect of stray magnetic fields

Lamination sheets are used in portable lab equipments, steel cases for switch board instruments

Precision type is not shielded to keep down eddy current errors

226

Low power factor electrodynamometer wattmeter

Ordinary electrodynamometer wattmeter are not suitable for measuring power at low power factors due to:

1) Small deflecting torque on the moving system even when pressure coil and current coil are excited.

2) Introduction of large error due to inductance of pressure coil

227


So features incorporated in lpf meters are:

228


229


230


231

POWER FACTOR METER

232

POWER FACTOR METER

But due to errors in meters used, the method mentioned is not accurate

So a meter is necessary to measure power factor directly which is called power factor meter

233

POWER FACTOR METER

Construction of power factor meter is similar to that of wattmeter

Current circuit carries current or fraction of current whose power factor needs to be measured

Voltage coil is split into two parts

Inductive

Non inductive

234

POWER FACTOR METER

The currents in two paths of are proportional to voltage across the circuit

Deflection depends on current through current circuit and currents in two branches of voltage circuit

235

TYPES OF POWER FACTOR METERS

Power factor meters

Electrodynamometer type

Moving iron type

Rotating field type

Alternating field type

236

ELECTRODYNAMOMETER TYPE POWER FACTOR METER

237


Construction is same as that of wattmeter

F1-F2 fixed coils connected in series

A-B moving coils with their axes in quadrature

A-B moves together and carries the pointer showing power factor

238


F1-F2 carries main current

If current is high, then a portion of current is passed through it

Magnetic field produced around F1-F2 is proportional to current

239


Coil A is connected in series with R

Coil B is connected in series with L

Values of R and L are adjusted so that coils A and B carries equal currents at normal frequency

At normal frequency

R = L

240


Current in coil A is in phase with supply voltage due to R

Current in coil B is in quadrature with supply voltage due to L

Current in coil B is frequency dependent due to L

Current in coil A is frequency independent due to R

241


Current in coils A and B produces magnetic fields of equal strength displaced by 90 degrees

242

ELECTRODYNAMOMETER TYPE POWER FACTOR METER- working

X-X uniform magnetic field produced by fixed coils

Due to interaction of magnetic fileds produced by each coils, torque is developed

Torque experienced by coil A and coil B are opposite to each other

Pointer attains equilibrium when two torques are equal

243


244


245


So angular position taken up by moving coil is equal to system power factor angle

Operation of meter is depended only on frequency and wave form

246

MOVING IRON POWER FACTOR METER

247

Disadvantage: Accuracy is less

MOVING IRON POWER FACTOR METER TYPES

Rotating field type

Alternating field type

248

ROTATING FIELD TYPE MOVING IRON POWER FACTOR METER

249


Consists of three fixed coils F1,F2 and F3 displaced by 1200

These coils are fed from three CTs

Coil F1- phase R

Coil F2- phase Y

Coil F3 phase B

250


Coil Q- kept in middle of F1,F2 and F3 and is connected across any two lines of the supply through a series resistance

251


Inside coil Q there is a short pivoted iron rod

The rod carries two sector shaped vanes I1, I2

The rod also carries damping vanes and the pointer

252

ROTATING FIELD TYPE MOVING IRON POWER FACTOR METER Coil Q and soft iro system

produces alternating flux

This flux interacts with fluxes produced by F1,F2 and F3

Due to R current through coil Q is in phase with supply

So deflection of moving system is proportional to power factor angle

253

ROTATING FIELD TYPE MOVING IRON POWER FACTOR METER Coils F1, F2, F3

displaced by 120 degrees produces rotating field by induction motor action

It keeps the system rotating

Due to high resistivity iron parts this motion is reduced by reducing induced currents

254


This meter can be used for balanced loads

It is also called

Westinghouse power factor meter

255

ALTERNATING FIELD TYPE MOVING IRON POWER FACTOR METER

256


Spindle carries pointer, damping vanes and three moving irons

The moving irons are sector shaped

Moving iron have 120 degrees with respect to each other

Q1,Q2,Q3- iron sectors

257


Iron sectors are magnetized by voltage coils P1,P2 and P3

Current coil is divided into two equal parts F1 and F2

Current coil carries one of the three line currents

258

ALTERNATING FIELD TYPE MOVING IRON POWER FACTOR METER When connected in

circuit, moving system moves and attains a position in which mean torque in one of the iron pieces is neutralized by other two

At this position deflection is proportional to phase angle between currents and voltages in three phase system

259


The voltage coils are at different levels hence resultant flux is alternating

This instrument is also called Nalder-Lipman power factor meter

260

ENERGY

261

ENERGY

262

ENERGY METER TYPES

263

Energy meter

Single phase

Three phase

SINGLE PHASE ENERGYMETER CONSTRUCTION

264

SINGLE PHASE ENERGYMETER CONSTRUCTION- PARTS

265

Driving system

Moving system

Braking system and

Registering system.

Driving system

consists of two electromagnets, called shunt magnet and series magnet, of laminated construction.

266

Driving system

A coil having large number of turns of fine wire is wound on the middle limb of the shunt magnet.

This coil is known as pressure or voltage coil and is connected across the supply mains.

This voltage coil has many turns and is arranged to be as highly inductive as possible.

In other words, the voltage coil produces a high ratio of inductance to resistance.

This causes the current, and therefore the flux, to lag the supply voltage by nearly 900.

267

Driving system

An adjustable copper shading rings are provided on the central limb of the shunt magnet to make the phase angle displacement between magnetic field set up by shunt magnet and supply voltage is approximately 90degrees.

The copper shading bands are also called the power factor compensator or compensating loop

268

Driving system

The series electromagnet is energized by a coil, known as current coil which is connected in series with the load so that it carry the load current.

The flux produced by this magnet is proportional to, and in phase with the load current.

269

Moving system

The moving system essentially

consists of a light rotating aluminium disk mounted on a vertical spindle or shaft.

The shaft that supports the aluminium disk is connected by a gear arrangement to the clock mechanism on the front of the meter to provide information that consumed energy by the load

270

Moving system

The time varying (sinusoidal) fluxes produced by shunt and series magnet induce eddy currents in the aluminium disc.

The interaction between these two magnetic fields and eddy currents set up a driving torque in the disc.

The number of rotations of the disk is therefore proportional to the energy consumed by the load in a certain time interval and is commonly measured in killowatt-hours (Kwh).

271

Braking system

Damping of the disk is provided by a small permanent magnet, located diametrically opposite to the a.c magnets.

The disk passes between the magnet gaps.

272

Braking system

The movement of rotating

disc through the magnetic field crossing the air gap sets up eddy currents in the disc that reacts with the magnetic field and exerts a braking torque.

By changing the position of the brake magnet or diverting some of the flux there form, the speed of the rotating disc can be controlled.

273

Registering or Counting system

The registering or counting system essentially consists of gear train, driven either by worm or pinion gear on the disc shaft, which turns pointers that indicate on dials the number of times the disc has turned.

274

Registering or Counting system

The energy meter thus determines and adds together or integrates all the instantaneous power values so that total energy used over a period is thus known.

Therefore, this type of meter is also called an integrating meter

275

Working/operation of single phase energy meter

276


Induction instruments operate in alternating-current circuits and they are useful only when the frequency and the supply voltage are approximately constant

The rotating element is an aluminium disc, and the torque is produced by the interaction of eddy currents generated in the disc with the imposed magnetic fields that are produced by the voltage and current coils of the energy meter.

277


Let us consider a sinusoidal flux (t) is acting perpendicularly to the plane of the aluminium disc, the direction of eddy current (Ie) by Lenzs law is indicated in figure

278


279

=0 since reactance of Al dsc is zero


So in all induction type meters, two eddy currents are there so that resultant torque will be there

280


281


Current coil produces two fluxes in opposite directions

So torques produced by the interaction of eddy current due to voltage and current coil is opposite at two points.

Hence the disc will start to rotate

282

Derivation of Torque equation

Phasor Diagram

283


284


285


286


287

ENERGYMETER CONSTANT

288

SOURCES OF ERRORS IN SINGLE PHASE ENERGYMETER

Incorrect magnitude of fluxes due to abnormal voltages and load currents

Incorrect phase relation of fluxes due to defective lagging, abnormal frequencies, changes in iron loss

Unsymmetrical magnetic structure disc rotates when pressure coils alone is excited

289

SOURCES OF ERRORS IN SINGLE PHASE ENERGYMETER

Changes in resistance of disc due to change in temperature

Changes in strength of drag magnets due to temperature and ageing

Phase angle errors due to lowering of power factor

Abnormal deflection of moving parts

Badly distorted waveform

Changes in retarding torque of the disc

290

ERRORS IN SINGLE PHASE ENERGY METER

Erro

rs

Phase error

Frictional Error

Creeping

Speed Error

Temperature error

Overload compensation

Voltage compensation

291

Phase error

An error due to incorrect adjustment of the position of shading band results an incorrect phase displacement between the magnetic flux and the supply voltage (not in quadrature)

This is tested with 0.5 p.f. load at the rated load condition

292

Compensation for phase error

By adjusting the position of the copper shading band in the central limb of the shunt magnet this error can be eliminated.

293

Compensation for phase error

A lag coil is placed as shown in figure so that phase angle between Voltage and flux is exactly 90 degrees

This kind of compensation is called

Power factor adjustment or Quadrature adjustment

Or Inductive load adjustment

294

Frictional Error

Frictional forces at bearings and registering mechanism give rise to unwanted braking torque on the disc

So additional driving torque is required

295

Compensation for frictional error

The two shading bands on the limbs are adjusted to create this extra torque.

This adjustment is done at low load (at about 1/4th of full load at unity p.f.).

296

Creeping Error

In some meters a slow but continuous rotation is seen when pressure coil is excited but with no load current flowing.

This slow revolution records some energy.

This is called the creep error.

This slow motion may be due to

(a) incorrect friction compensation,

(b) stray magnetic field

(c) for over voltage across the voltage coil.

297

Compensation for creeping error

This can be eliminated by drilling two holes or slots in the disc on opposite side of the spindle.

When one of the holes comes under the poles of shunt magnet, the rotation being thus limited to a maximum of 180 degrees

298

Compensation for creeping error

In some cases, a small piece of iron tongue or vane is fitted to the edge of the disc.

When the position of the vane is adjacent to the brake magnet, the attractive force between the iron tongue or vane and brake magnet is just sufficient to stop slow motion of the disc with full shunt excitation and under no load condition.

299

Speed Error

Due to the incorrect position of the brake magnet, the braking torque is not correctly developed.

This can be tested when meter runs at its full load current alternatively on loads of unity power factor and a low lagging power factor

300

Compensation for speed error

The speed can be adjusted to the correct value by varying the position of the braking magnet towards the centre of the disc or away from the centre and the shielding loop.

If the meter runs fast on inductive load and correctly on non-inductive load, the shielding loop must be moved towards the disc.

On the other hand, if the meter runs slow on non-inductive load, the brake magnet must be moved towards the center of the disc.

301

Temperature Error

Energy meters are almost inherently free from errors due to temperature variations.

Temperature affects both driving and braking torques equally (with the increase in temperature the resistance of the induced-current path in the disc is also increases) and so produces negligible error.

A flux level in the brake magnet decreases with increase in temperature and introduces a small error in the meter readings

302

Compensation for temperature error

This error is frequently taken as negligible, but in modern energy meters compensation is adopted in the form of flux divider on the brake magnet

303


When the disc rotates in the field of series magnetic field under load conditions, it cuts series flux and dynamically induced emfs is produced on the disc

This produces eddy currents on the disc

Due to interaction of eddy current flux and series magnet flux, braking torque is produced

This is proportional to square of current

304


This braking torque is called self braking torque and if load is high it causes serious errors in the instrument

To minimize this braking torque, full load speed of the disc is limited to 40rpm

The current coil series flux is kept minimum with respect to shunt coil flux

305


Practically an overload compensating device in the form of saturable magnet shunt is used

At high loads, shunt saturates and diverts some series magnetic flux.

This compensates for self braking torque

306


When supply voltage varies, energymeter causes errors

This is due to:

Non linear magnetic characteristics of shunt magnet core

Braking torque is proportional to square of supply voltage

307


Voltage compensation is provided by saturable magnetic shunt

It diverts a large proportion of flux into the active path when supply voltage increases

This is done by increasing side limb reluctance and providing holes in side limbs

308

ADVANTAGES OF INDUCTION TYPE ENERGYMETER

309

DISADVANTAGES OF INDUCTION TYPE ENERGYMETER

310

THREE PHASE ENERGYMETER

Three phase system

Four wire Three element energy meter

Three wire Two element energy meter

311

THREE PHASE THREE ELEMENT ENERGYMETER

312


It consists of three elements

Each element is similar to that of single phase energy meter

Pressure coils are P1,P2 and P3

Current coils are C1, C2 and C3

All elements are mounted in a vertical line in common case and have a common spindle, gearing and recording mechanism

313


The coils are connected in such a manner that the net torque produced is equal to sum of torques produced by each element

These are employed for three phase four wire system, where fourth wire is the neutral wire

Current coils are connected in series with the lines where as pressure coils are connected in parallel across line and neutral

314


One unit of three phase energy meter is cheaper than three individual units

Due to interaction of eddy currents between all elements, errors are produced which are reduced by suitable adjustments

315

THREE PHASE TWO ELEMENT ENERGYMETER

316

THREE PHASE TWO ELEMENT ENERGYMETER

It is provided with two discs for an element

Shunt magnet is carrying pressure coil

Series magnet is carrying current coil

Pressure coils are connected in parallel

Current coils are connected in series

Torque is produced in same manner as that of single phase energy meter

The total torque on registering mechanism is sum of torques on two discs

317

ELECTRONIC ENERGY METER

318


Average power = mean product of instantaneous voltage across the load and instantaneous current through load

Potential divider- for making voltage to required level

Voltage is scaled in the required range using voltage scaling device

Current scaling device scales load voltage which is proportional to load current

319


Both scaled voltages are connected to voltage and current multiplier unit

Voltage and current multiplier unit outputs current as a result of product of ac voltage and current

The current is proportional to instantaneous power applied to voltage controlled oscillator

VCO works on the principle of constant current charging capacitor

320


VCO basically voltage to frequency converter Output of VCO is square wave The frequency of square wave is proportional to

output current of VCO So power dependent current and frequency

dependent current decides the value of consumed energy

ADC (analog to digital converter) converts analog signal to digital signal

Display unit displays energy in watt-hour

321

ADVANTAGES OF ELECTRONIC ENERGYMETER

High sensitivity

No frictional losses

Less loading effect

Low load, full load, creeping adjustments are not required

High frequency range

High accuracy of 1%

322

MAXIMUM DEMAND METER

ASSIGNMENT

What is maximum demand meter?

Explain the following meters with neat figures

1) Merz price maximum demand indicator

2) Thermal type maximum demand indicator

3) Digital Maximum demand indicator

323

TRIVECTOR METER

324

TRIVECTOR METER

325

TRIVECTOR METER

326

TRIVECTOR METER

Ratchet coupling is linked to main common register shaft to which final drive from each gear system is connected

Shaft is always driven by direct drive which has the maximum speed

At that time all other slower shafts are idle on ratchets.

327

TRIVECTOR METER

As power factor changes, other gear drive drives the shaft at higher speed and drive shifts to another ratchet

For a given V-I product, speed of kWh meter varies as power factor varies

328

TRIVECTOR METER VARIATION OF PERCENTAGE SPEED vs

PHASE ANGLE

329

TOD METER

Electric company supplies electricity to various loads such as domestic, industrial and commercial purposes

These loads varies over various time periods

For some time load is maximum and for sometime load is minimum

The hours in which load is maximum is called peak load hours

330

TOD METER

The hours in which load is minimum is called off-peak hours

During on-peak hours company has to generate more power to supply for the demand.

This causes difficulties

331

TOD METER

Time of delay rate is special service offered by electric company that allows consumer to take advantage of lower electricity price during a certain time period

Consumer can save money being on TOD rate

To lessen the load during a particular time of a day, company offers special rate to the consumers who are willing shift the load or portion of the load to off-peak hours

332

TOD METER

A special metering arrangement is done to measure energy consumption during different time zones of the day including on-paek and off-peak hours

Trivector meter itself is provided with capability required

It is provided with a time of delay registser (TOD register) which is capable of being progarammed during off-peak and on-peak hours

333

TOD METER

TOD meters are time- of delay meter which is suitable of recording and indicating consumption during specific time periods of the day

Trivector meter with such an arrangement is called TOD meter

334

TOD METER

335

MODULE 3 MEASUREMENT OF RESISTANCE, POWER,...

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