Wattmeter construction and derivation of torque equation is explained here

1. ELECTRICAL ENGINEERING DEPARTMENT
203144: ELECTRICAL MEASUREMENTS AND
INSTRUMENTATION
UNIT III – LECTURE 14
T.M. SARWADE

2. CONTENTS
● Measurement of Power
● Construction, working principle, torque equation of dynamometer type wattmeter

3. 3.1 POWER IN DC CIRCUITS:
Power taken by a load from a DC supply P = V*I watt.
V – Voltmeter, I – Ammeter
Ammeter and voltmeter require power for their operation
Fig. 1. Measurement of power in DC circuits

4. 3.1 POWER IN DC CIRCUITS:
Power taken by a load from a DC supply P = V*I watt.
V – Voltmeter, I – Ammeter
Ammeter and voltmeter require power for their operation
In fig 1 (a), 𝐼𝑉 = 𝑉 𝑅𝑉 and Power consumed by load = 𝑉𝐼𝐿 = 𝑉 𝐼 − 𝐼𝑉 = 𝑉 𝐼 − 𝑉 𝑅𝑉 = 𝑉𝐼 −
𝑉2
𝑅𝑉
In other words, Power indicated by instruments = Power consumed in load + power loss in
voltmeter
In Fig 1 (b) Power consumed by load = 𝑉𝐿 × 𝐼 = 𝑉 − 𝑉𝐴 × 𝐼 = 𝑉𝐼 − 𝑉𝐴𝐼

5. To obtain true power corrections must be applied for power loss.
Normally this loss is very small compared to load power.
To overcome this error it is advised to use Wattmeter instead of ammeter and
voltmeter.

6. 3.2 POWER IN AC CIRCUITS:
Instantaneous power varies through a cycle.
But we are focusing on average power 𝑃 = 𝑉𝐼 cos 𝜙
V – RMS value of voltage
I – RMS value of current
cos 𝜙 - power factor
Wattmeter is preferable over ammeter and voltmeter
i. Dynamometer Wattmeters  DC/AC
ii. Induction Wattmeters  AC
iii. Electrostatic Wattmeters  for small amt of ac and low p.f.

7. Moving Coil Instruments
Permanent magnet
type
Dynamometer type.

8. Construction of Dynamometer type
wattmeter

10.  An electrodynamometer is often used in accurate voltmeter and ammeters.
 It may also serve as a transfer instrument, because it can be calibrated on dc and then used directly on
ac thereby equating ac and dc measurements of voltage and current directly.
 A movable coil is used to provide the magnetic field in an electrodynamometer, instead of a permanent
magnet, This movable coil rotates within the magnetic field.
Dynamometer type instrument

17. WATTMETER BASICS
 The M terminal connects to the power supply.
 The L terminal connects to the load.
 The C terminal is shorted to the M terminal.
 The V terminal connects to the systems neutral.
Wattmeter Symbol
Types of connection

18. ELECTRODYNAMOMETER WATTMETERS: TORQUE EQUATION
Instantaneous torque of an electrodynamometer instruments is given by
 𝑇𝑖 = 𝑖1𝑖2 𝑑𝑀 𝑑𝜃
Let V and I be r.m.s. values of voltage and current being measured
So, Instantaneous value of voltage across pressure coil circuit is
𝒗 = 𝟐𝑽 𝒔𝒊𝒏 𝝎𝒕
If P.C. has high resistance  resistive coil
So, current in P.C. in phase with Instantaneous value of voltage is:
 𝒊𝒑= 𝒗 𝑹𝒑 = 𝟐 𝑽 𝑹𝒑 𝒔𝒊𝒏 𝝎𝒕 = 𝟐 𝑰𝒑 𝒔𝒊𝒏 𝝎𝒕 (1)

19. Here, 𝐼𝑝 = 𝑉
𝑝 𝑅𝑝  rms value of current in P.C. circuit
𝑅𝑝 = resistance of P.C. circuit
If current in C.C. lags the voltage in phase by angle 𝜙, instantaneous value of current in C.C. is:
𝑖𝑝 = 2 𝐼 sin 𝜔𝑡 − 𝜙 (2)
∴ 𝑇𝑖 = 2 𝐼𝑝 sin 𝜔𝑡 × 2 𝐼 sin 𝜔𝑡 − 𝜙 × 𝑑𝑀 𝑑𝜃
= 2 𝐼𝑝 𝐼 sin 𝜔𝑡 sin 𝜔𝑡 − 𝜙 𝑑𝑀 𝑑𝜃
= 𝑰𝒑 𝑰 𝒄𝒐𝒔 𝝓 − 𝒄𝒐𝒔 𝟐𝝎𝒕 − 𝝓 × 𝒅𝑴 𝒅𝜽 (3)

20. It is clear that there is a component of power which varies as twice the frequency of current and
voltage.
Average deflecting torque:
𝑇𝑑 =
1
𝑇
0
𝑇
𝑇𝑖 𝑑 𝜔𝑡
𝑇𝑑 =
1
𝑇
0
𝑇
𝐼𝑝 𝐼 cos 𝜙 − cos 2𝜔𝑡 − 𝜙 × 𝑑𝑀 𝑑𝜃 𝑑 𝜔𝑡
𝑇𝑑 = 𝐼𝑝 𝐼 cos 𝜙 × 𝑑𝑀 𝑑𝜃 (4)
𝑻𝒅 = 𝑽𝑰 𝑹𝒑 𝒄𝒐𝒔 𝝓 × 𝒅𝑴 𝒅𝜽 (5)
𝜃 = 𝑉𝐼 cos 𝜙 𝑅𝑝 𝐾 × 𝑑𝑀 𝑑𝜃 (7)
𝜃 = 𝐾1 𝑽𝑰 𝒄𝒐𝒔 𝝓 × 𝑑𝑀 𝑑𝜃 (8)
𝜽 = 𝑲𝟏 × 𝒅𝑴 𝒅𝜽 × 𝑷 (9)

21. Controlling torque exerted by springs 𝑻𝒄 = 𝑲𝜽
where, 𝑲= spring constant and 𝜽 = final steady deflection
Since moving system of the instrument can not follow rapid variations in torque, it will take up a
position at which average deflection torque is equal to restoring torque of the springs
∴ At balance position, 𝑻𝒄 =𝑻𝒅,−→ 𝐾𝜃 = 𝐼𝑝 𝐼 cos 𝜙 × 𝑑𝑀 𝑑𝜃
Or deflection, 𝜃 = 𝐼𝑝 𝐼 cos 𝜙 × 𝑑𝑀 𝑑𝜃 𝐾 (6)
 𝜃 = 𝑉𝐼 cos 𝜙 𝑅𝑝 𝐾 × 𝑑𝑀 𝑑𝜃 (7)
𝜃 = 𝐾1 𝑽𝑰 𝒄𝒐𝒔 𝝓 × 𝑑𝑀 𝑑𝜃 (8)
 𝜽 = 𝑲𝟏 × 𝒅𝑴 𝒅𝜽 × 𝑷 (9)

22. QUIZ
● How to connect a wattmeter in a circuit?
● How many terminals does a wattmeter have
● Which is fixed and which one is moving coil of wattmeter?

23. PREPARATION FOR NEXT SESSION
● Look through errors in wattmeter with their compensation

24. WRAP UP
• In this session we learned about wattmeter construction
• Torque equation
• Wattmeter terminals