POWER MEASUREMENT

POWER MEASUREMENT

Introduction

Power may be defined as the rate at which energy is transformed and made availableIn almost all cases the power in a d.c. circuit is best measured by separately measuring quantities, V and I and by computing P=VIIn case of a.c. circuits the instantaneous power varies continuously as the current and voltage go through a cycle of valuesThe fact that the power factor is involved in the expression for the power means that a wattmeter must be used instead of merely an ammeter and voltmeter.

Dynamometer type wattmeter construction

LPF wattmeter Ordinary electro-dynamometer wattmeter is not suitable for measurement of power in low power factor circuits owing to (i) small deflecting torque on the moving system even when the current and pressure coils are fully excited and (ii) introduction of large error due to inductance of pressure coil at low power factor.

The special features incorporated in an electro-dynamometer type wattmeter to make it suitable for measurement of power in low power factor circuits are :

i) Pressure coil Circuit. The pressure coil circuit is made of low resistance in order to make the pressure coil current large resulting in increased operating torque.(ii) Compensation For Pressure Coil current (ii) Compensation For Inductance of Pressure Coil. . The error caused by inductance of pressure coil is compensated by connecting a capacitor across a part of series resistance in the pressure coil circuit, as shown in fig

Low power factor wattmeter (electro-dynamometer type)

Wattmeter

A wattmeter is essentially an inherent combination of an ammeter and a voltmeter and, therefore , consists of two coils known as current coil and pressure coil.Wattmeter connection:

Wattmeter Errors

Error due to inductance of pressure coil

Error due to pressure coil capacitance

Error due to Eddy currents : soild metal parts are removed as far away from the current coil as possible

Error due to power loss in pressure coil or current coilThere are two method of connecting wattmeters in the circuit for measurement of power, as shown in figure below (a) and (b).Fig (a) :

Fig (b) :

Measurement of Power in Single Phase A.C. Circuit

3-voltmeter method

Disadvantages : (i) Even small errors in measurement of voltages may cause serious errors in the value of power, (ii) Supply voltage higher than normal voltage is required

3-Ammeter method

The disadvantages of measurement of power by 3 voltmeters are overcome in this method

Measurement of power in conjuction with instrument transformers

This method is used when the currents and voltages of the circuits to be measured are highFigure below shows a measurement of power with wattmeter in conjunction with instrument transformers in single phase A.C. circuits

Vector diagram for inductive load

Vector diagram for capasitive load

Measurement of Power in 3-Phase Circuit

Measurement of power in 3-phase, 4-wire circuits-----------

P=W1+W2+W3

Measurement of power in 3-phase, 3-wire circuits-------------

P=W1+W2+W3

3-wattmeter method of measuring 3-phase power of delta connectedP=W1+W2+W3

1-wattmeter method of measuring balanced 3-phase power (a) star connected, (b) delta connectedP=3W

2-wattmeter method of measuring 3-phase 3-wire power : (a) star connected, P=W1+W2

(b) delta connectedP=W1+W2

Determination of P.F. from Wattmeter Reading

If load is balanced, then p.f. of the load can be determined from the wattmeter readingsVector diagram for balanced star connected inductive load -----

The watt-ratio Curve ----------

p.f. can be determined from reading of two wattmeters

Total power : w1 + w2 + w3

If neutral wire available, the common point X should be the neutral wire.Note: Total power does not depends upon whether the load is balanced or not.

Two-Wattmeter MethodCurrent coils of two wattmeter's are connected in any two lines and the potential coil of each joined to the third line

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W1W2I3I2I1

TWO-WATTER METHOD BALANCED LOAD

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300VBYVRN-VYNIRVYNIYVRYVBNIBVRNVYNVBN

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R.M.SLOAD PHASE VOLTAGESPHASE CURRENTS

Power factorSince, Total power = W1+ W2 Power Factor :(w2-w1)(w2+w1)tan = 3

Which is greater W1 or W2 ?W1=VLILCOS(300+ )W2=VLILCOS(300- )

answerSince can vary between 900 to 00 So, tan vary between 0 to 1.Therefore, whose reading is proportional to (300- ) is greater and positive(w2-w1)(w2+w1)tan = 3 PF :

Effect of load pf on wattmeter readings00600More than 600900Cos 1o.5