Unit - 3

Measurement Of Power

Q1) What is the working principle of Dynamometer?

A1) Dynamometer type wattmeter works on a very simple principle which is stated as "when any current carrying conductor is placed inside a magnetic field, it experiences a mechanical force and due to this mechanical force, deflection of conductor takes place."

Q2) Explain the working of Dynamometer?

A2) When power is to be measured in a circuit, the instrument is suitably connected in the circuit. The current coil is connected in series with load so that it carries the circuit current. The potential coil is connected across the load so that it carries current proportional to the voltage. Due to the current in the coils, mechanical force exists between them. The result is that the moving coil, moves the pointer over the scale. The pointer comes to rest at a position where deflecting torque is equal to the controlling torque. Reversing the current, reverses the field due to fixed coil as well as the current in the moving coil so that the direction of the deflection torque remains unchanged. Therefore, such instruments can be used for the measurement of a.c as well as d.c power.

Q3) Derive the deflecting torque of dynamometer?

A3) Let us assume that the fixed & moving coils having self-inductances Lf & Lm respectively. Further it is assumed that mutual inductance between fixed & moving coil is M.

Total energy stored in the magnetic field of the coil is given by;

Where if  & im are the current through the fixed and magnetic coils, from the above equation it can be derived that torque developed is;

Let the applied voltage be,

Currents through moving & fixed coil are given by;

Where, is the power factor angle of load (± is leading/lagging)

Instantaneous Deflecting Torque,

The mean/average torque

Q4) Explain Low Power Factor Wattmeter?

A4) If an ordinary electrodynamometer wattmeter is used for measurement of power in low power factor circuits, (PF<0.5), then the measurements would be difficult and inaccurate since:

The deflecting torque exerted on the moving system will be very small and

Errors are introduced due to pressure coil inductance (which is large at LPF)

Thus, in a LPF wattmeter, special features are incorporated in a general electrodynamometer wattmeter circuit to make it suitable for use in LPF circuits as under:

Pressure coil current: The pressure coil circuit is designed to have a low value of resistance so that the current through the pressure coil is increased to provide an increased operating torque.

Compensation for pressure coil current: On account of low power factor, the power is small and the current is high.

Compensation for pressure coil inductance: At low power factor, the error caused by the pressure coil inductance is very large. Hence, this has to be compensated, by connecting a capacitor C across a portion of the series resistance in the pressure coil circuit.

Realizing a small control torque: Low power factor wattmeter are designed to have a very small control torque so that they can provide full scale deflection for power factor values as low as 10%.

Q5) Derive the equation for Three Wattmeter Method?

A5)  Here, it is applied to three phase four wire systems, current coil of all the three wattmeter marked as 1, 2 and 3 are connected to respective phases marked as 1, 2 and 3. Pressure coils of all the three wattmeter are connected to a common point at neutral line. Clearly each wattmeter will give reading as product of phase current and line voltage which is phase power. The resultant sum of all the readings of wattmeter will give the total power of the circuit. Mathematically we can write

Q6) Explain the working of Two Wattmeter Method for both the cases?

A6) There are two types of connection in this method

When the load is star connected, the diagram is as follows

For star connected load clearly the reading of wattmeter one is product of phase current and voltage difference (V2-V3). Similarly the reading of wattmeter two is the product of phase current and the voltage difference (V2-V3). Thus the total power of the circuit is sum of the reading of both the wattmeter. Mathematically we can write;

But we have, hence putting the value of

So,

Total Power =

When the load is delta connected, the diagram is as follows

The reading of first wattmeter can be written as;

The reading of second wattmeter can be written as;

But

Hence total power,

Q7) Explain the errors in Electrodynamometer type Wattmeter?

A7)
(i) Pressure Coil Inductance: In an ideal dynamo-meter type watt meter the current in pressure coil in phase with the applied voltage. But in practically the pressure coil of watt meter has an inductance and current in it will lag behind the applied voltage. If there is no inductance the current in pressure coil will be in phase with the applied voltage. In the absence of inductance in pressure coil of wattmeter, it will read correctly in all power factors and frequency.

(ii) Pressure Coil Capacitance: The pressure coil circuit may have capacitance in addition with inductance. This capacitance mainly due to the inter turn capacitance of the series resistance. The effect of capacitance is opposite to that due to inductance. Therefore the wattmeter will read high when the load power factor is leading

(iii)Error due to Mutual Inductance: Errors may occur due to the mutual inductance between the current and pressure coils of the watt meter. These errors are quite low at power frequencies. But they increased with increase in frequencies. The effect of mutual inductance can be avoided by arranging the coil system in such a way that they have no mutual inductance. So we can eliminate the errors due to mutual inductance.

(iv) Eddy Current Errors: Eddy currents are induced in the solid metal parts and within the thick conductors by the alternating magnetic field produced by the current coil. This eddy currents produce their own magnetic field and it will alter that produced by the main current in the current coil and thus error occurred. This error can be minimized by avoiding solid metal parts as much as possible and by using 32 stranded conductors for high current applications. 

(v) Stray Magnetic Field Errors: The electrodynamometer type wattmeter has a weak operating field and therefore it is affected by stray magnetic fields it will result in serious errors. Hence these instruments should be shielded against stray magnetic field.

(vi) Errors caused by vibration of moving system: The torque on the moving system varies with frequency which is twice that of voltage. If the parts of the moving system have a natural frequency which is resonance with the frequency of torque pulsation, the moving system would vibrate with considerable amplitude. These vibrations will cause errors. This error can be reduced by design.

(vii) Temperature Error: The change in room temperature may affect the indication of wattmeter. This is because of change in temperature will change in resistance of pressure coil and stiffness of springs which provide controlling torque. This effect are opposite in nature and cancel each other.

Q8) What are the different parts of dynamometer?

A8) It consists of 4 parts

Moving Coil

Fixed Coil

Control System

Damping System

Scale
 

Q9) Define Active, Reactive & Apparent Power?

A9) Active Power: The power which is actually consumed or utilized in an AC Circuit is called True power or Active power or Real power. It is measured in kilowatt (kW) or MW. It is the actual outcomes of the electrical system which runs the electric circuits or load.
P= V*I*cos

Reactive Power: The power which flows back and forth that means it moves in both the directions in the circuit or reacts upon itself, is called Reactive Power. The reactive power is measured in kilo volt-ampere reactive (kVAR) or MVAR.
P= V*I*sin

Apparent Power: The product of root mean square (RMS) value of voltage and current is known as Apparent Power. This power is measured in kVA or MVA.
P=V*I

Q10) Give the advantages & Disadvantages of Dynamometer?

A10) 

Advantages:

1.     These instruments are free from hysteresis losses and eddy current losses.

2.     They have a precision grade accuracy.

3.   These instruments can be used on both A.C and D.C. They are also used as a transfer instruments.

4.    Electrodynamometer voltmeters are very useful where accurate RMS values of voltage, irrespective of waveforms, are required.

Disadvantages

1.     They have a non-uniform scale.

2.     These instruments have a low sensitivity due to a low torque to weight ratio.

3.     They are more expensive than either the PMMC or the M.I type instruments.

4.    These instruments are sensitive to overloads and mechanical impacts. Therefore, they must be handled with great care.

5.       The operating current of these instruments is large due to the fact that they have a weak magnetic field.