MODULE 2 MEASUREMENT OF RESISTANCE, POWER,

ENERGY

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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

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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

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Measurement of medium resistance

Measurement of medium resistance

Ammeter Voltmeter method

Substitution method

Wheatstone bridge method

Carey Foster Bridge method

Ohmmeter method

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Measurement of high resistance

Measurement of high resistance

Direct deflection method

Megger method

Loss of charge method

Mega Ohm bridge method

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Direct deflection method

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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

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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

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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

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Loss of charge method

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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

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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

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Loss of charge method

• At the time of discharge:

𝑖 = −𝑑𝑞

𝑑𝑡

𝑖 = −𝐶𝑑𝑣

𝑑𝑡

𝑖 =𝑣

𝑅𝑒𝑓𝑓

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Loss of charge method

• −𝐶𝑑𝑣

𝑑𝑡 =

𝑣

𝑅𝑒𝑓𝑓

•𝑑𝑣

𝑣= −

𝑑𝑡

𝐶 𝑅𝑒𝑓𝑓

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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.

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EARTHING AND MEASUREMENT OF EARTH RESISTANCE

• What is meant by earthing?

• How will you measure earth resistance?

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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.

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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.

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MEASUREMENT OF EARTH RESISTANCE

Measurement of earth resistance

Fall of potential method

Megger earth tester

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MEASUREMENT OF EARTH RESISTANCE

Measurement of earth

resistance

Fall of potential

method

Megger earth tester

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FALL OF POTENTIAL METHOD

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FALL OF POTENTIAL METHOD

• Potential E is applied

• Current I circulates through the E and Q

• Voltage between E and P is noted

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FALL OF POTENTIAL METHOD

• Pattern of current flow through earth:

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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

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FALL OF POTENTIAL METHOD

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

• In the middle section V remains constant

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FALL OF POTENTIAL METHOD

• Value of earth resistance is given by:

• 𝑅𝐸 =𝑉𝐸𝑃

𝐼

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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

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FALL OF POTENTIAL METHOD

• Variation of resistance with distance is shown

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MEASUREMENT OF EARTH RESISTANCE

Measurement of earth

resistance

Fall of potential method

Megger earth tester

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MEGGER EARTH TESTER

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MEGGER EARTH TESTER

• It consists of

– DC generator

– Current reverser

– Rectifier

– Current coil

– Potential coil

– Electrodes E,P and Q

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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

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MEGGER EARTH TESTER

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

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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

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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

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MEGGER EARTH TESTER

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

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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)

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MEASUREMENT OF POWER

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Wattmeters

Dynamometer type

Induction type

Electrostatic type

Wattmeter

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• 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

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Wattmeters

Dynamometer type

Induction type

Electrostatic type

Dynamometer type wattmeter

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Dynamometer type wattmeter

• Fixed coil – current flowing is proportional to load current

• Moving coil- current flowing is proportional to load voltage

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Dynamometer type wattmeter

• Strength of magnetic field- proportional to currents through two coils

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Dynamometer type wattmeter

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• 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

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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

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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

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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

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Dynamometer type wattmeter

• Current through current coil lags voltage by an angle ϕ

𝑖𝑐 = 2 I sin ω𝑡 − ϕ

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Dynamometer type wattmeter

• Instantaneous torque is given by:

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Dynamometer type wattmeter

• Average deflecting torque is given by:

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Dynamometer type wattmeter

• Control torque is 𝑇𝑐 = 𝐾θ

• K- spring constant

• Θ- final steady state deflection

• At balance position

𝑇𝐶 = (𝑇𝑑)𝑎𝑣

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Dynamometer type wattmeter

• At balance condition:

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Shape of scale of dynamometer wattmeter

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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

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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

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Shape of scale of dynamometer wattmeter

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Dynamometer type wattmeter

• Ranges:

Current coil: 0.25A to 100A

Pressure coil : 5V to 750V

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Dynamometer type wattmeter

Dynamometer type wattmeter

Suspended coil torsion type

Pivoted coil indicating type

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Suspended coil torsion type dynamometer wattmeter

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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.

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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.

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Pivoted coil indicating type dynamometer wattmeter

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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.

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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.

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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.

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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.

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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

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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

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ENERGY

261

ENERGY

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ENERGY METER TYPES

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Energy meter

Single phase

Three phase

SINGLE PHASE ENERGYMETER CONSTRUCTION

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SINGLE PHASE ENERGYMETER CONSTRUCTION- PARTS

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• 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).

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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.

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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.

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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.

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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

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Working/operation of single phase energy meter

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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.

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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

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Working/operation of single phase energy meter

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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

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Working/operation of single phase energy meter

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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

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Derivation of Torque equation

Phasor Diagram

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Derivation of Torque equation

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Derivation of Torque equation

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Derivation of Torque equation

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Derivation of Torque equation

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ENERGYMETER CONSTANT

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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

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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.

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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

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

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

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

307

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

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

313

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

314

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

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

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

319

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

320

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

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

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

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