WATTMETER METHOD

Prepared By

A.JOHNY RENOALD M.E.,(Ph.D.,)

Types:

Single phase wattmeter

Electro dynamo wattmeter

Low power factor wattmeter

Three phase wattmeter 3 phase 3 wire system

2 wattmeter method

Wattmeter model

Electro dynamo wattmeter:

Low power factor:

Ir –current flowing through R phase in A

Iy- current flowing through Y phase in A

Ib- current flowing through Y phase in A

Vr-voltage across R phase of the load in V

Vy-voltage across R phase of the load in V

Vb-voltage across R phase of the load in V

Instantaneous power consumed by the load

=VRIR+VY IY+VBIB ----------------------------1

sum of Instantaneous reading of the wattmeter will be equal to

The Instantaneous power consumed by the load.

P=PR+PY+PB= VRIR+VY IY+VBIB -----------------------------2

In star connected circuit :

Instantaneous reading of wattmeter 1,

P1=iR(vR-vB) --------------1

P2=iY(VY-vB) ---------------2

Hence sum of the instantaneous reading of two

wattmeter

=P1+P2

= iR(vR - vB)+ iY (vY - vB)

P1+P2 = vR iR+vY iY – vB (iR + iY) ------------------3

As the load is star connected using KCL,

iR+ iY+ iB=0

Hence

iR + iY = - iB -------------------- 4

Equation 4 & 3 we get,

P1+P2 = vR iR + VY iY –vB (-iB)

P1+P2 = vR iR + VY iY +vB IB

Sum of the two instantaneous reading of two wattmeter

=total power consumed by the load.

This is applicable for both balanced & un balanced load.

If delta connected load total instantaneous power consumed in

the circuit is,

P1= -VBR(iRY - iBR)

P2= VYB(iYB – iRY)

p1+p2= -VBR(iRY - iBR)+VYB(iYB – iRY)

p1+p2= -VBR iRY +VBR iBR + VYB iYB –VYB iRY)

p1+p2= VBR iBR + VYB iYB – iRY (VYB + VBR)

Apply KVL, VRY+ VYB + VBR=0

VRY+ VYB = –VRY

p1+p2 = VBR iBR + VYB iYB – iRY (- VRY)

p1+p2 = VBR iBR + VYB iYB + iRY VRY)

Sum of the instantaneous reading of two wattmeter is equal to

Total power consumed by the load.

Analog Voltmeters &Ammeters: Electrostatic type of instruments, all the type of ammeters and

voltmeters work on the same operating principle i.e., The

deflecting torque is produced by the electric current

Current which is proportional to the voltage. It’s to be

measured devices.

Generally voltmeter connected in parallel with the circuit

whose voltage to be measured. Voltmeter have high electrical

resistance.

Generally ammeter connected in series with the circuit whose

current to be measured. ammeter have low electrical resistance

How its work:

Types:

PMMC:

TORQUE EQUATION

The equation for the developed torque of the PMMC can be obtained from

the basic law of electromagnetic torque. The deflecting torque is given by,

Td = NBAI

Where,

Td = deflecting torque in N-m

B = flux density in air gap, Web/m2

N = Number of turns of the coils

A = effective area of coil m2

I = current in the moving coil, amperes

Therefore, Td = GI

Where,

G = NBA = constant

The controlling torque is provided by the springs and is proportional to the

angular deflection of the pointer.

Tc = KØ

Where,

Tc = Controlling Torque

K = Spring Constant Nm / Rad or Nm / deg

Ø = angular deflection

For the final steady state position,

Td = Tc

Therefore GI = KØ

So,

Ø = (G/K)I (or) I = (K/G) Ø

Thus the deflection is directly proportional to the

current passing through the coil. The pointer deflection

can be used to measure current.

Application:

Ammeter

Voltmeter

Galvanometer

Ohm meter

Moving iron instruments:

The general principle of a M.I instrument can

be explained under;

commonly used for laboratory instruments

Advantage like low cost, high accuracy,

ruggedness.

2 types

1)Attraction type instruments

2)Repulsion type instruments

Attraction type:

Repulsion type:

radial vane type: - vanes are radial strips of

iron.

co-axial vane type:-vanes are sections of

coaxial cylinders

Repulsion Type:

Repulsion type: The deflecting torque results due to repulsion between the

similarly charged soft- iron pieces or vanes. If the two pieces

develop pole strength of m1 and m2 respectively, then;

Instantaneous deflecting torque α m1m2 α H2

If the permeability of iron is assumed constant, then ; H α i,

where, i is the coil current.

Instantaneous deflecting torque α i2

Average deflecting torque, Td α mean of i2 over a cycle.

Since the instrument is spring controlled, Tc α θ

In the steady position of deflection, Td = Tc

θ α mean of i2 over a cycle.

θ α I2

Thus, the deflection is proportional to the square of the coil

current

DC AMMETER:

The basic movement of a DC ammeter is a

PMMC d’Arsonval galvanometer. The coil of

the basic movement is very small and light and

carry very small currents.(100 mA)

DC AMMETER:

Let ,

Rm=internal resistance of basic meter in Ω

Rsh=shunt resistance in Ω

Im=full scale deflection current of basic meter in A

Ish=shunt current in A

I=current to be measured in A

Vsh=Voltage drop across the shunt resistance in V

Vm=Voltage drop across the basic meter in V

Shunt resistance connecting parallel ,

Vsh=Vm

Ish Rsh =Im Rm

Rsh = Im (Rm / Ish)---------------------------------------------1

We know that , I= Ish +Im

Ish= I -Im -----------------------------------------2

Sub equation 2 in equation no 1 we get,

Rsh = (Im Rm ) /( I-Im) ----------------------------------------3

Rm/ Rsh= (I-Im) / Im

Rm/ Rsh=( I/Im) -1

I/Im=(1+ Rm/ Rsh) = m ------------------------------------------4

Where ,m is the multiplying power of shunt and it is the ratiobetween the total current to be measured and the current in thecoil of basic meter.

Multiplying power, m= (I/Im)

Equation (3) => Rsh = Im Rm / I-Im

Rsh = Rm / (I/Im- Im / Im) = Rm / (I / Im-1)

Rsh= Rm /(m-1)

MULTI RANGE AMMETER:

UNIVERSAL (OR)AYRTON SHUNT:

DC VOLTMETER:

DC VOLTMETER:

A D’Arsonal basic meter is converted into a

voltmeter by connecting a series with it. This

series resistance is known as a multiplier.

The combination of the basic meter and the

multiplier is connected across the circuit

voltage to be measured as shown in above fig.

The voltage range as calculated as below,

Im=full scale deflection current of basic meter in A

Rm=internal resistance of basic meter in Ω

Rs=multiplier resistance in Ω

V=full range voltage of the instrument

V =voltage across the basic meter for the current Im in V

From this circuit ,V= Im Rm ------------------------------------------------1

V= Im (Rm+Rs)------------------------------------------2

Rs=(V-Im Rm)/Im =(V/Im)-Rm

Rs=(V/Im)-Rm

Where ,m is the multiplying factor of multiplier and it is theratio between the full range of voltage of the instrument and thevoltage across in the coil of basic meter.

Hence ,

m = V/v -----------------------------3

m = Im (Rm+Rs)/Im Rm = (Rm+Rs)/Rm = 1+ Rs/Rm

m = 1+Rs/Rm ------------------------------------4

Equation ---------4

=> Rs/Rm =m -1

Rs = (m-1) Rm

Hence the series multiplying resistance should be (m-1) times

the meter resistance.

Multi range voltmeter:

MULTIMETER (OR) VOLT-OHM-MILLI-

AMMETER (V.O.M)

Electrodynamometer type instrument:

DIGITAL VOLTMETER:

SERVOMETER DVM :

Successive approximation DVM :

RAMP TYPE:

LINEAR RAMP TYPE DVM :

LINEAR RAMP WAVEFORM:

STAIR CASE RAMP TYPE:

DUAL SLOP INTEGRATING DVM:

WAVEFORM OF DUAL SLOPE

DVM:

FREQUENCY METERS:

Mechanical resonance type / vibrating reed

type frequency meter.

Electrical resonance type / Ferro dynamic

type frequency meter.

Weston type frequency meter.

Mechanical resonance type / vibrating

reed type frequency meter:

OPERATION:

Magnetizing coil carries a current I and produces flux f in phase with current I. Flux f induces emf E in the moving coil lagging behind it by 90o. Emf E circulates current Im in the moving coil. Phase of current Imdepends upon inductance L of the moving coil and capacitance C.

Circuit of moving coil is inductive & therefore current Im lags behind Emf E by an angle a. The torque acting on the moving coil is,

Td a Im I cos (90o + a)

Circuit of moving coil is capacitive & therefore current Im leads emf E by an angleb. The torque acting on the moving coil is,

Td a Im I cos (90o - b)

Inductive reactance of the circuit of moving coil is equal to its capacitive reactance & therefore current Im is in phase with emf E. The torque acting on the moving coil is,

Td a Im I cos 90o = 0

DIGITAL FREQUENCY METER:

ANALOG PHASE METER:

DIGITAL PHASE METER:

Magnetic circuits:

The operating characteristics of electrical machines,apparatus and instruments are greatly influenced by theproperties of Ferro-magnetic materials used for theirconstruction.

Some magnetic measurements are ,

The measurement of magnetic force (H) & magnetic flux density (B).

The determination of B -H curve and hysteresis loop.

The determination of eddy current and hysteresis losses.

The testing of permanent magnets.

Method of reversal:

Step by step method:

Energy meter:

ENERGY= POWER Χ TIME

When Power Is Delivered At An Average Rate Of 1000 Watts

For One Hour.

Depending upon the power supply there are

2types:

1Φ ENERGY METER

3 Φ ENERGY METER

SINGLE PHASE ENERGY METER:

Pointer type ,cyclometer type register:

Poly phase energy meter:

(2 Element method)

3 element method:

(3 phase energy meter)