sign in sign up
<<
Home , Galvanometer, Wattmeter

DYNAMOMETER

 A pair of fixed coils connected in series

 When energized gives the same effect as that of the permanent magnets

 In this field there will be a moving coil which when energized acted upon by a torque by which it deflects

 F1, F2: Fixed coils (Current Coil) ; M: Moving coil (Pressure Coil); R: High resistance in series with Moving coil

 I1 : load current; I2: current through moving coil DYNAMOMETER WATTMETER

 2 fixed coils in series act as the CC and the moving coil in

series with R act as the PC

 MC is pivoted between the 2 fixed coils carries a current I2 proportional to V

 I2 is fed to M through two springs which also provides the necessary controlling torque

 Can be used on both ac and dc circuits as both the coils are

energized simultaneously by a common source due to which a

unidirectional torque is produced Electrodynamometer Wattmeter DYNAMOMETER WATTMETER

 Principle of operation is the same as that for dynamo-electric machines Working

 Td is produced by the interaction of two magnetic fluxes  One of the fluxes is produced by a fc which carries a current proportional to the load current & therefore called CC  CC is thick in cross section and has less number of turns  The other flux is created by a mc which carries a current proportional to the load and thus called PC  PC is thin in cross - section and has hundreds of turns  A high non-inductive R is connected to the PC so that its current is almost in phase with the load voltage Working

 There are two alternative methods of connection, depending on which coil is connected near the load

 In dynamometer type instrument deflecting torque is produced by magnetic effect of

 Control torque (Tc) is provided by control springs  Damping torque is provided by Air Friction

 PC carries a needle that moves over a scale to indicate the measurement  On an ac ckt the Td is proportional to the avg. instantaneous product of V and I, thus measuring true power, and possibly (depending on load characteristics) showing a different reading to that obtained by simply multiplying the readings showing on a stand-alone & a stand-alone in the same ckt Working  2 circuits of a wattmeter are likely to be damaged by excessive current

 The ammeter and voltmeter are both vulnerable to overheating - in case of an overload, their pointers will be driven off scale

 But in the wattmeter, either or even both the CC and PC circuits can overheat without the pointer approaching the end of the scale!

 This is because the position of the pointer depends on the , voltage and current

 Thus, a circuit with a LPF will give a low reading on the wattmeter, even when both of its circuits are loaded to the maximum safety limit

 Therefore, a wattmeter is rated not only in , but also in and Deflecting torque Torque expression based on energy concept

 Assume the self- of fixed and moving coils are Lf & Lm respectively  Further it is assumed that the mutual between the fixed and movable coils is M  Total energy stored in the of the coils is given by

 where if & im are the currents through the fixed and moving coils

 From above equation the expression for Td is written as

 Note Lf & Lm are not functions of θ but „M‟ is a function of the deflection θ (i.e. relative position of moving coil) Deflecting torque  Equ. L between fc & mc can be (cumulative manner)  and from this the mutual inductance,  However, M varies with the relative positions of the mc & fc

 Mmax occurs when the axes of the mc and fc are aligned with θ = 180º, as this position gives the maximum flux linkage between coils

 When θ = 0º, M = - Mmax  If the plane of the moving coil is at an angle θ with the direction of

B that produced by the fixed coil, then M = - Mmax Cos θ

 D.C operation: Taking, if = IL (dc) and im = V (dc)/ R Deflecting torque

 At steady deflection Td = Tc

 A.C operation: In dynamometer instrument Td is proportional to the mean value of the I2 or V2 (note both coils are connected in series for or ), and the scale can therefore be calibrated to read r.m.s values of or voltage

 Let im (t) = (Vmax/ R) Sin ωt (assuming L of mc is negligible) &

 if (t) = iL (t) = Im Sin (ωt φ ) where „φ‟ is the pf angle of load where + sign for leading & – sign for lagging  where V & I are the r.m.s values of load voltage & current respectively

 At steady deflection Td = Tc , therefore, θ ∝ power (average) Two Ways of Connections Two Ways of Connections  Fig. (a): PC on supply side, CC on load side

 VPC = VLoad + VCC  So the wattmeter reading includes power loss in CC i.e.,

 Fig. (b): PC on load side, CC on supply side

 ICC = ILoad + IPC  So the wattmeter reading includes power loss in PC i.e.,

 If ILoad is small, VCC small so that PC introduced is less i.e., connection in fig. (a) is preferred for small load current and high load

 If ILoad is high, IPC small so that PP introduced is less i.e., connection in fig. (b) is preferred for high load current and small load voltages

Advantages of Dynamometer  Made to give a very high degree of accuracy – used as a standard for calibration purposes

 Equally accurate on dc as well as ac measurements

 Can be used on ac for any waveform – not restricted to sine waveform

Disadvantages of Dynamometer wattmeters  At LPF, the inductance of PC causes serious error unless special precautions are taken to reduce this effect Three phase power measurement Three - Phase Power Measurement

 P is measured in 3 phase systems using 3 phase wattmeter (also called as 2 element wattmeter) or 2 or 3 single phase wattmeters

 Element means a pair of coils ( one CC & one PC)

 Andre E. Blondel’s Theorem 1893: “In a system of N conductors, N-1 meter elements, properly connected, will measure the power or energy taken”

 The connection must be such that all potential coils have a common tie to the conductor in which there is no current coil

 Cost saver in metering installation with fixed Three-Wattmeter Method

Power can be measured in a balanced or unbalanced 3-phase load of either Y or type.

Current is measured between terminals 1 and 2, Voltage across the load is measured between terminals 3 and 4 Two-Wattmeter Method

The voltage coil of each wattmeter is connected across a line voltage and the current has a line current through it. Ptot = P1 P2 Two-Wattmeter Power Measurement

cc = current coil vc = voltage coil

W1 read

PVI11AB A cos W2 read

PVI22CB C cos

For balanced load with abc phase sequence

12aa30 and 30 a is the angle between phase current and phase voltage of phase a Two-Wattmeter Power Measurement(cont.)

PPP12

2VILL cos cos30

3VILL cos To determine the power factor angle

PPVI12 LL2cos cos30

PPVI12 LL( 2sin sin30 )

PPVI12 LL2cos cos30 3

PPVI12 LL( 2sin sin30 ) tan PPPP tan 31 2 or tan1 3 1 2 PPPP1 2 1 2 Example 1 P = ?

Z 10 45

line-to-line voltage = 220Vrms

The phase voltage 220 V 30 A 3 The line current V 220 30 I A 12.7 75 and I 12.7 195 A Z 10 3 45 B

PVI11AC A cos 2698 W PPP123421 W PVI22BC B cos 723 W Three Phase Circuit In a four-wire system (3 phases and a neutral) the real power is measured using three single phase wattmeters

IA PA Phase A A W

VAN V IB PB Phase B A W

VBN V IC PC Phase C A W

VCN V

Neutral (N) Example a) Four wire system

WR IR

VR Z = 5 30o Ω ER EL = 415 R

IN

EB o VB ZY = 10 90 EY VN Ω WY

o ZB = 20 45 Ω

IY IB

WB Three-phase Load Find the three-phase total power, PT. Example b) Three wire system

WR IR

VR Z = 5 30o Ω ER EL = 415 volt R

EB o ZY = 10 90 EY VN Ω WY

o ZB = 20 45 Ω

IY IB

WB Three-phase Load Find the three-phase total power, PT. Example b) Three wire system

WR IR

VR Z = 5 30o Ω ER EL = 415 volt R

EB VB o ZY = 10 90 EY VN Ω WY

o ZB = 20 45 Ω

IY IB

WB Three-phase Load Find the three-phase total power, PT. Three Phase Circuit Three wire system, The three phase power is the sum of the two - meters reading

PAB IA Phase A A W

VAB = VA - VB V Phase B

V = V - V CB C B V Phase C A W IC PCB

PT PAB PCB Proving: PT PAB PCB The three phase power (3-wire system) is the sum of the two watt-meters reading

IA PA Phase A Instantaneous power: A W

VAN V pA = vA iA IB PB Phase B A W pB = vB iB VBN V IC PC Phase C pC = vC iC A W

VCN V

Neutral (N) pT = pA + pB + pC = vA iA + vB iB +vC iC

= vA iA + vB iB +vC iC = vA iA + vB (-iA -iC) +vCiC Proving:

The three phase power (3-wire system) is the sum of the two watt-meters reading

PAB Instantaneous power: IA Phase A A W pT = vA iA + vB (-iA –iC) +vCiC

VAB = VA - VB V Phase B = (vA – vB )iA + (vC – vB )iC

V = V - V CB C B V = vAB iA + vCBiC Phase C A W IC PCB

pT = pAB + pCB

PT PAB PCB Multi - range Wattmeter  Current ranges (0.5A and 1A) can be changed by switching two field coils from series to parallel connection

 Voltage ranges (60V, 120V and 240 V) can be made by switching different values of multiplier 1. Name the different essential torques in indicating instruments Deflecting torque, Controlling torque, Damping torque 2. Name the types of instruments used for making voltmeter and ammeter PMMC type, Moving iron type, Dynamometer type, Hot wire type, Electrostatic type, Induction type 3. State the advantages of PMMC instruments Uniform scale, No hysteresis loss, Very accurate, High efficiency 4. State the disadvantages of PMMC instruments Cannot be used for ac m/s, Some errors are caused by temperature variations 5. State the applications of PMMC instruments m/s of dc voltage and current, used in dc 6. How the range of instrument can be extended in PMMC instruments In ammeter by connecting a resister, in voltmeter by connecting a series resister 7. State the advantages of Dynamometer type instruments Can be used for both dc and ac m/s, Free from hysteresis and eddy current errors 8. State the advantages of Moving iron type instruments Less expensive, Can be used for both dc and ac, Reasonably accurate 9. State the advantages of Hot wire type instruments Can be used for both dc and ac, Unaffected by stray magnetic fields, Readings are independent of frequency and waveform. 10.What are the constructional parts of dynamometer type wattmeter? Fixed coil, Moving Coil, Current limiting resister, Helical spring, Spindle attached with pointer, Graduated scale 11. Write down the deflecting torque equation in dynamometer type wattmeter Td ∞ VI Cos θ 12. State the disadvantages of Dynamometer type wattmeter Readings may be affected by stray magnetic fields, At low power factor it causes error 13. Name the errors caused in Dynamometer type wattmeter Error due to PC inductance, Error due to PC , Error due to methods of connection, Error due to stray magnetic fields, Error due to eddy current 14. Name the methods used for power measurement in three phase circuits (i)Single wattmeter method, (ii) Two wattmeter method, (iii) Three wattmeter method 15.Name the methods used in Wattmeter calibration. By comparing with std wattmeter, By using V-A meter method, By using 1. In a 3ø power measurement by two wattmeter method, the reading of one of the wattmeters was -ve. The power factor of the load must be

(i) Greater then 0.5 (ii) less then 0.5 (iii) equal to 0.5 (iv) -ve

2. Two wattmeter method is used to measure the power taken by a 3ø induction motor on No load. The wattmeter readings are 375W and -50W. The power factor of motor at no load will be

(i) 0.404 lag (ii) 0.5 lag (iii) unity pf (iv) 0.85 lag

3. In 3ø circuit for zero power factor, the power measured by 2 watt meter is

(i) 2 watt (ii) zero (iii) 4 watt (iv) 6 watt ERRORS IN WATTMETERS Introduction

 Power may be defined as the rate at which energy is transformed or made available

 In almost all cases the power in a d.c. circuit is best measured by separately measuring quantities, V and I and by computing P=VI

 In case of a.c. circuits the instantaneous power varies continuously as the current and voltage go through a cycle of values

 The 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. 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 Cos True power Reading of wattmeter Cos θ Cos θ  Error due to pressure coil capacitance sin sin cot  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 coil

 There are two method of connecting wattmeters in the circuit for measurement of power, as shown in figure below (a) and (b).

2  Fig (a) : Wattmeter reading W I rc

V 2  Fig (b) : Wattmeterreading W R rp Measurement of Power in Single Phase A.C. Circuit

2 2 2 2 2 2 V V V V3 V1 V2  3 - Voltmeter method P 3 1 2 cos 2R 2V1V2

 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 2 2 2 R 2 2 2 I 3 I1 I 2  3 - Ammeter method P I 3 I1 I 2 cos 2 2I1I 2

 The disadvantages of measurement of power by 3 voltmeters are overcome in this method Measurement of power in conjunction with instrument transformers

 This method is used when the currents and voltages of the circuits to be measured are high

 Figure below shows a measurement of power with wattmeter in conjunction with instrument transformers in single phase A.C. circuits  Vector diagram for inductive load

cos K cos cos

 Vector diagram for capacitive load

cos K cos cos 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 connected

 P = W1+W2+W3

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

 P = 3W  2 - wattmeter method of measuring 3-phase 3-wire power :

(a) star connected

 P = W1+W2

(b) delta connected

 P = 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 readings

 Vector diagram for balanced star connected inductive load ----- 3 W W cos costan 1 1 2 W1 W2

 The watt-ratio curve ------

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