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
(1Ω to 0.1M Ω)
• Measurement of high resistance
(greater than 0.1M Ω)
• Measurement of earth resistance
2
Measurement of low resistance
Measurement of low resistance
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
3
Measurement of low resistance
4
Me
asu
re
me
nt
of
low
r
esi
st
an
ce
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
Ammeter Voltmeter method
• 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 =𝑉𝑜𝑙𝑡𝑎𝑔𝑒
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑅 =
𝑉
𝐼
• So to find resistance
– Measure potential across the resistance using voltmeter
– Measure current through the resistance using Ammeter
5
Ammeter Voltmeter method
6
Ammeter Voltmeter method
• Connection (a)
• Voltmeter resistance is infinite
7
Ammeter Voltmeter method
• 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
Ammeter Voltmeter method
• Connection(b)
– Voltmeter reading is the true voltage across resistance
– Ammeter reads total current which is sum of current through resistance and voltmeter
9
Ammeter Voltmeter method
10
Ammeter Voltmeter method
11
Ammeter Voltmeter method
• Actual value of resistance is measured if (Rm/RV)=0
• Which means voltmeter resistance is infinite
• If Rx<<<RV then Rm/RV
becomes negligibly small hence actual value of resistance can be measured
12
Measurement of low resistance
13
Me
asu
re
me
nt
of
low
r
esi
st
an
ce
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
Potentiometer method
14
Potentiometer method
• R-rheostat
• B- battery
• S- standard resistance
• X- unknown resistance
15
Potentiometer method
• 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 )
•𝑋
𝑆=
𝑃𝑜𝑡𝑒𝑛𝑡𝑖𝑜𝑚𝑒𝑡𝑒𝑟 𝑟𝑒𝑎𝑑𝑖𝑛𝑔 𝑎𝑐𝑟𝑜𝑠𝑠 𝑋
𝑃𝑜𝑡𝑒𝑛𝑡𝑖𝑜𝑚𝑒𝑡𝑒𝑟 𝑟𝑒𝑎𝑑𝑖𝑛𝑔 𝑎𝑐𝑟𝑜𝑠𝑠 𝑆=
𝑉𝑋
𝑉𝑆
16
Potentiometer method
• Advantage
– High accuracy
17
Measurement of low resistance
18
Me
asu
re
me
nt
of
low
r
esi
st
an
ce
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
Kelvin Double Bridge method
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
Kelvin Double Bridge(contd…)
• 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)
21
Kelvin Double Bridge(contd…)
22
Kelvin Double Bridge(contd…)
23
Kelvin Double Bridge(contd…)
24
Kelvin Double Bridge(contd…)
• It is used to measure resistances as low as 0.00001Ω
25
Measurement of low resistance
26
Me
asu
re
me
nt
of
low
r
esi
st
an
ce
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
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 (Ω).
27
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
28
Measurement of low resistance
29
Me
asu
re
me
nt
of
low
r
esi
st
an
ce
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
Series type Ohm meter
30
Series type Ohm meter
31
Series type Ohm meter
• Current flowing through the meter depends on unknown resistance
• Meter deflection is proportional to value of resistance
32
Series type Ohm meter
• 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
Series type Ohm meter
• 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
Series type Ohm meter
• For half scale deflection,
– Since total resistance
presented to battery is 2Rh
35
Series type Ohm meter
• To produce full scale deflection, current required is
36
Series type Ohm meter
37
Series type Ohm meter
38
Measurement of low resistance
39
Me
asu
re
me
nt
of
low
r
esi
st
an
ce
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
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:
𝐼𝑚 =𝑉
𝑅1 + 𝑅𝑚
43
Shunt type Ohmmeter
• If AB is shorted
• Current flowing through the meter:
𝐼𝑚 = 0 𝐴mperes
44
Shunt type Ohmmeter
• If unknown resistance 𝑅𝑥 is connected across AB
• At node 1 𝐼 = 𝐼𝑚 + 𝐼𝑅
𝐼 =𝑉
𝑅1 +𝑅𝑚𝑅𝑥
𝑅𝑚 + 𝑅𝑥
45
𝐼 =(𝑅𝑚 + 𝑅𝑥)𝑉
(𝑅𝑚 + 𝑅𝑥)𝑅1+𝑅𝑚𝑅𝑥
Shunt type Ohmmeter
• Current through meter is
𝐼𝑚 =𝐼𝑅𝑥
𝑅𝑚 + 𝑅𝑥
46
𝐼𝑚 =(𝑅𝑚+𝑅𝑥)𝑉
𝑅1(𝑅𝑚+𝑅𝑥)+𝑅𝑚𝑅𝑥 *
𝑅𝑥
𝑅𝑚+𝑅𝑥
Shunt type Ohmmeter
• For full scale deflection, 𝑅𝑥 = 0
𝐼𝑚 = 0 Amperes
47
Shunt type Ohmmeter
• For half scale deflection,
𝑅𝑚 = 𝑅𝑥
• Current through meter is:
𝐼𝑚 =𝑉
2𝑅1+𝑅𝑀
48
Measurement of low resistance
49
Me
asu
re
me
nt
of
low
r
esi
st
an
ce
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
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
50
Measurement of low resistance
51
Me
asu
re
me
nt
of
low
r
esi
st
an
ce
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
Fixed Magnet Moving Coil Ohmmeter
52
Fixed Magnet Moving Coil Ohmmeter
• The two moving coils moves in permanent magnetic field.
53
Fixed Magnet Moving Coil Ohmmeter
• Torque produced is:
54
Fixed Magnet Moving Coil Ohmmeter
• The two torques produced acts in opposite directions
55
Fixed Magnet Moving Coil Ohmmeter
• At equilibrium,
56
Fixed Magnet Moving Coil Ohmmeter
• Current I1 is proportional to voltage drop across unknown resistance X
𝐼1 =𝐸
𝑋
57
Fixed Magnet Moving Coil Ohmmeter
• That means deflection
• tan θ =𝐾1𝐸
𝑋𝐼2
• That means deflection depends on value of X
58
Fixed Magnet Moving Coil Ohmmeter
• 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
59
Measurement of low resistance
60
Me
asu
re
me
nt
of
low
r
esi
st
an
ce
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
Crossed coil Moving magnet type Ohm meter
61
Crossed coil Moving magnet type Ohm meter
• Consists of :
– Two fixed coils
– Pivoted magnetic needle attached with a pointer
62
Crossed coil Moving magnet type Ohm meter
• 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
63
Crossed coil Moving magnet type Ohm meter
• 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
64
Crossed coil Moving magnet type Ohm meter
• 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
65
Measurement of medium resistance
Measurement of medium resistance
Ammeter Voltmeter method
Substitution method
Wheatstone bridge method
Carey Foster Bridge method
Ohmmeter method
66
Measurement of medium resistance
Measurement of medium resistance
Ammeter Voltmeter method
Substitution method
Wheatstone bridge method
Carey Foster Bridge method
Ohmmeter method
67
Ammeter Voltmeter method
• Same as measuring low resistance
68
Measurement of medium resistance
Measurement of medium resistance
Ammeter Voltmeter method
Substitution method
Wheatstone bridge method
Carey Foster Bridge 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
Measurement of medium resistance
Measurement of medium resistance
Ammeter Voltmeter method
Substitution method
Wheatstone bridge method
Carey Foster Bridge method
Ohmmeter method
72
Wheatstone’s Bridge
73
Wheatstone’s 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
Wheatstone’s Bridge(contd…)
• 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
Wheatstone’s Bridge(contd…)
• 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.
76
Wheatstone’s Bridge(contd…)
• 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
Wheatstone’s Bridge(contd…)
• 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. 78
Wheatstone’s Bridge(contd…)
79
Wheatstone’s Bridge(contd…)
• Now potential of point B in respect of point C is nothing but the voltage drop across the resistor Q.
80
Wheatstone’s Bridge(contd…)
• Again potential of point D in respect of point C is nothing but the voltage drop across the resistor S .
81
Wheatstone’s Bridge(contd…)
• Equating, equations (i) and (ii) we get,
82
Wheatstone’s Bridge(contd…)
• 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 Ω or from
1 to 10,000 Ω
• Wheat stone’s bridge can be used for measurement of resistances upto 100000ohms
83
Wheatstone’s 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
Measurement of medium resistance
Measurement of medium resistance
Ammeter Voltmeter method
Substitution method
Wheatstone bridge method
Carey Foster Bridge method
Ohmmeter method
85
Carey Foster Bridge
86
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.
87
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.
88
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 σ, 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.
• α is the unknown left-side extra resistance EX
• β is the unknown right-side extra resistance FY
• σ 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
Carey Foster Bridge method
• Advantages – high accuracy, unaffected by thermoelectric emfs
• Limitations – unsuitable for measuring low resistances
96
Measurement of medium resistance
Measurement of medium resistance
Ammeter Voltmeter method
Substitution method
Wheatstone bridge method
Carey Foster Bridge method
Ohmmeter method
97
Ohm meter method
• Same as measuring low resistance using ohm meter
98
Measurement of high resistance
Measurement of high resistance
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
Measurement of high
resistance
Direct deflection
method
Megger method
Loss of charge method
Mega Ohm bridge method
107
Direct deflection method
108
Measurement of insulation resistance of a cable
Direct deflection method
• 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
Direct deflection method
• 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
Direct deflection method
• 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
Measurement of high
resistance
Direct deflection method
Megger method
Loss of charge method
Mega Ohm bridge 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 high resistance
• 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
Measurement of high
resistance
Direct deflection method
Megger method
Loss of charge method
Mega Ohm bridge method
123
Loss of charge method
124
Loss of charge method
• 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
Loss of charge method
• Step 3: Time (t) taken for the potential difference to fall from V1 to V2 is noted during discharge.
• 𝑅𝑒𝑓𝑓 =𝑅𝑋𝑅𝑙𝑒𝑎𝑘
𝑅𝑥+𝑅𝑙𝑒𝑎𝑘
126
Loss of charge method
• At the time of discharge:
𝑖 = −𝑑𝑞
𝑑𝑡
𝑖 = −𝐶𝑑𝑣
𝑑𝑡
𝑖 =𝑣
𝑅𝑒𝑓𝑓
127
Loss of charge method
• −𝐶𝑑𝑣
𝑑𝑡 =
𝑣
𝑅𝑒𝑓𝑓
•𝑑𝑣
𝑣= −
𝑑𝑡
𝐶 𝑅𝑒𝑓𝑓
128
Loss of charge method
• 𝑑𝑣
𝑣= −
𝑑𝑡
𝐶𝑅𝑒𝑓𝑓
𝑡
0
𝑣2𝑣1
• 𝑙𝑛𝑣2
𝑣1= −
𝑡
𝐶𝑅𝑒𝑓𝑓
•𝑣2
𝑣1= 𝑒(−𝑡 𝐶𝑅𝑒𝑓𝑓 )
• From the above
expression Reff can be determined
129
Loss of charge method
• 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
Measurement of high resistance
131
Measurement of high
resistance
Direct deflection method
Megger method
Loss of charge method
Mega Ohm bridge method
Mega Ohm Bridge Method
132
Mega Ohm Bridge Method
• It consits of:
– Power supply
– Bridge members
– Amplifier
– Indicating instrument
133
Mega Ohm Bridge Method
• 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
Mega Ohm Bridge Method
• Dial R2 is calibrated as
1- 10 – 100 – 1000MΩ
• Dial R2 1-10 is in logarithmic scale
• Unknown resistance is
𝑅3 =𝑅1𝑅4𝑅2
• 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
Measurement of earth
resistance
Fall of potential
method
Megger earth tester
141
FALL OF POTENTIAL METHOD
142
FALL OF POTENTIAL METHOD
• Potential E is applied
• Current I circulates through the E and Q
• Voltage between E and P is noted
143
FALL OF POTENTIAL METHOD
• Pattern of current flow through earth:
144
FALL OF POTENTIAL METHOD
• 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
FALL OF POTENTIAL METHOD
• The potential V rises near E and Q due to current density
• In the middle section V remains constant
146
FALL OF POTENTIAL METHOD
• Value of earth resistance is given by:
• 𝑅𝐸 =𝑉𝐸𝑃
𝐼
147
FALL OF POTENTIAL METHOD
• 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
FALL OF POTENTIAL METHOD
• Variation of resistance with distance is shown
149
MEASUREMENT OF EARTH RESISTANCE
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
MEASUREMENT OF POWER
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
MEASUREMENT OF POWER
161
Wattmeters
Dynamometer type
Induction type
Electrostatic type
Dynamometer type wattmeter
162
Dynamometer type wattmeter
• Fixed coil – current flowing is proportional to load current
• Moving coil- current flowing is proportional to load voltage
163
Dynamometer type wattmeter
• Strength of magnetic field- proportional to currents through two coils
164
Dynamometer type wattmeter
165
• V- supply voltage
• I – load current
• R- resistance of moving
coil circuit
Dynamometer type wattmeter
• Fixed coil current: 𝑖𝑓 = 𝑖
• Moving coil current:
𝑖𝑚= 𝑣
𝑅
• Deflecting torque:
𝑇𝑑α 𝑖𝑓𝑖𝑚 =𝑖𝑣
𝑅
166
Dynamometer type wattmeter
• For dc circuit deflecting torque is proportional to power
• For ac circuit deflecting torque is proportional to voltage, current and power factor
𝑃 = 𝑉𝐼 𝑐𝑜𝑠ϕ
167
Dynamometer type wattmeter
• 𝑖1 − 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑖𝑛 𝑓𝑖𝑥𝑒𝑑 𝑐𝑜𝑖𝑙
• 𝑖2 − 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑖𝑛 𝑚𝑜𝑣𝑖𝑛𝑔 𝑐𝑜𝑖𝑙
• M- mutual inductance between
two coils
• Instantaneous torque is given by:
𝑇𝑖 = 𝑖1𝑖2𝑑𝑀
𝑑θ
168
Dynamometer type wattmeter
• Instantaneous voltage in pressure coil is:
𝑣 = 2 𝑉 𝑠𝑖𝑛ω𝑡
• Instantaneous current through pressure coil is:
𝑖 =2 𝑉 𝑠𝑖𝑛ω𝑡
𝑅𝑝 = 2 𝑖𝑝 𝑠𝑖𝑛ω𝑡
• 𝑅𝑝 - resistance of
pressure coil
169
Dynamometer type wattmeter
• Current through current coil lags voltage by an angle ϕ
𝑖𝑐 = 2 I sin ω𝑡 − ϕ
170
Dynamometer type wattmeter
• Instantaneous torque is given by:
171
Dynamometer type wattmeter
• Average deflecting torque is given by:
172
Dynamometer type wattmeter
• Control torque is 𝑇𝑐 = 𝐾θ
• K- spring constant
• Θ- final steady state deflection
• At balance position
𝑇𝐶 = (𝑇𝑑)𝑎𝑣
173
Dynamometer type wattmeter
• At balance condition:
174
Shape of scale of dynamometer wattmeter
175
Shape of scale of dynamometer wattmeter
• Deflection θ is proportional to power measured
and scale is uniform since 𝑑𝑀
𝑑θ is constant.
• Wattmeters are designed such that 𝑑𝑀
𝑑θ remains over 40 to 50 degree on each side
of zero mutual inductance position.
• M varies linearly in this zone with respect to θ
176
Shape of scale of dynamometer wattmeter
• If zero mutual inducatnce position is kept in the middle then M varies linearly for deflection upto 80 to 100 degrees
177
Shape of scale of dynamometer wattmeter
178
Dynamometer type wattmeter
• Ranges:
Current coil: 0.25A to 100A
Pressure coil : 5V to 750V
179
Dynamometer type wattmeter
Dynamometer type wattmeter
Suspended coil torsion type
Pivoted coil indicating type
180
Suspended coil torsion type dynamometer wattmeter
181
Suspended coil torsion type dynamometer wattmeter
• 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
Suspended coil torsion type dynamometer wattmeter
• 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
Pivoted coil indicating type dynamometer wattmeter
• 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
Pivoted coil indicating type dynamometer wattmeter
• 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 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
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
Error due to pressure coil inductance
192
Error due to pressure coil inductance
• Pressure coil current lagging behind voltage by an angle β
193
Error due to pressure coil inductance
• Let power factor be lagging
194
Error due to pressure coil inductance
195
Error due to pressure coil inductance
196
Error due to pressure coil inductance
197
Error due to pressure coil inductance
• If power factor is leading:
198
Error due to pressure coil inductance
199
Error due to pressure coil inductance
200
Compensation for Error due to pressure coil inductance
201
Compensation for Error due to pressure coil inductance
202
Compensation for Error due to pressure coil inductance
203
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
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 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
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
Error due to power loss in pressure coil and current coil
• There are two methods of connecting wattmeter
209
Error due to power loss in pressure coil and current coil
• 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
Error due to power loss in pressure coil and current coil
211
Error due to power loss in pressure coil and current coil
• 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
Error due to power loss in pressure coil and current coil
213
Error due to power loss in pressure coil and current coil
• 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
Compensation for Error due to power loss in pressure coil
• 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
Compensation for Error due to power loss in pressure coil
217
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
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 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
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 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
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 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
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
Low power factor electrodynamometer wattmeter
• So features incorporated in lpf meters are:
228
Low power factor electrodynamometer wattmeter
229
Low power factor electrodynamometer wattmeter
230
Low power factor electrodynamometer wattmeter
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
ELECTRODYNAMOMETER TYPE POWER FACTOR METER
• 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
ELECTRODYNAMOMETER TYPE POWER FACTOR METER
• 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
ELECTRODYNAMOMETER TYPE POWER FACTOR METER
• 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 = ωL
240
ELECTRODYNAMOMETER TYPE POWER FACTOR METER
• 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
ELECTRODYNAMOMETER TYPE POWER FACTOR METER
• 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
ELECTRODYNAMOMETER TYPE POWER FACTOR METER- working
244
ELECTRODYNAMOMETER TYPE POWER FACTOR METER- working
245
ELECTRODYNAMOMETER TYPE POWER FACTOR METER- working
• 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
ROTATING FIELD TYPE MOVING IRON POWER FACTOR METER
• 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
ROTATING FIELD TYPE MOVING IRON POWER FACTOR METER
• 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
ROTATING FIELD TYPE MOVING IRON POWER FACTOR METER
• 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
ROTATING FIELD TYPE MOVING IRON POWER FACTOR METER
• 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
ALTERNATING FIELD TYPE MOVING IRON POWER FACTOR METER
• 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
ALTERNATING FIELD TYPE MOVING IRON POWER FACTOR METER
• 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
ALTERNATING FIELD TYPE MOVING IRON POWER FACTOR METER
• 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
Working/operation of single phase energy meter
• 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
Working/operation of single phase energy meter
• Let us consider a sinusoidal flux φ (t) is acting perpendicularly to the plane of the aluminium disc, the direction of eddy current (Ie) by Lenz’s law is indicated in figure
278
Working/operation of single phase energy meter
279
β=0 since reactance of Al dsc is zero
Working/operation of single phase energy meter
• So in all induction type meters, two eddy currents are there so that resultant torque will be there
280
Working/operation of single phase energy meter
281
Working/operation of single phase energy meter
• 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
Derivation of Torque equation
284
Derivation of Torque equation
285
Derivation of Torque equation
286
Derivation of Torque equation
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
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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
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Overload compensation
• 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
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Overload compensation
• 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
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Overload compensation
• 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
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Voltage compensation
• 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
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Voltage compensation
• 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
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ADVANTAGES OF INDUCTION TYPE ENERGYMETER
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DISADVANTAGES OF INDUCTION TYPE ENERGYMETER
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THREE PHASE ENERGYMETER
Three phase system
Four wire Three element energy meter
Three wire Two element energy meter
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THREE PHASE THREE ELEMENT ENERGYMETER
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THREE PHASE THREE ELEMENT ENERGYMETER
• 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
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THREE PHASE THREE ELEMENT ENERGYMETER
• 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
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THREE PHASE THREE ELEMENT ENERGYMETER
• 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
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THREE PHASE TWO ELEMENT ENERGYMETER
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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
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ELECTRONIC ENERGY METER
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ELECTRONIC ENERGY METER
• 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
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ELECTRONIC ENERGY METER
• 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
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ELECTRONIC ENERGY METER
• 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
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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%
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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
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TRIVECTOR METER
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TRIVECTOR METER
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TRIVECTOR METER
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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.
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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
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TRIVECTOR METER VARIATION OF PERCENTAGE SPEED vs
PHASE ANGLE
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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
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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
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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
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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
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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
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TOD METER
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