# Errors in Dynamometer Type Wattmeter & Methods to Compensate Errors

In practice, there are some errors introduced in dynamometer type wattmeter while measuring power. Due to which the instrument indicates a value lower or higher than the actual value. Let us see various types of errors in dynamometer type wattmeter and necessary corrections to compensate for those errors.

## Errors in Dynamometer Type Wattmeter :

### Errors Due to Mutual Inductance :

The mutual inductance between the voltage coil and current coil increases the phase angle.

When the voltage coil is connected across the load and it decreases the phase angle from

When voltage coil is connected across the supply. Since the error is directly proportional to tan β, the mutual inductance between the coils affects the error.

In order to minimize the error introduced due to mutual inductance, the coils are designed and placed in such a way that the mutual inductance between them is zero at rated power frequency. So, these errors are dominant at higher frequencies than at power frequency.

### Errors Due to Connections :

There are two methods to connect a wattmeter in the circuit whose power consumption is to be measured. They are shown in the below figures.

When the voltage coil is connected across the supply as shown in figure 1, it measures the voltage drop across the series combination of current coil and load. Hence, the wattmeter reading PR ought to be the sum of power consumed by the load PL and the power loss in the current coil PC.

i.e., PR = PL + PC
= PL + IL2 RC

### Eddy Current Errors :

The alternating flux produced by the current coil when links with the conductors and metal parts of the meter, an emf is induced in them. This results in the circulation of eddy currents in those parts. This eddy current produces a magnetic flux which aids the main field flux for leading power factor loads and opposes the main field flux for lagging power factor loads.

Since the deflection torque is directly proportional to the main field flux, the meter reads high for leading loads and low for lagging loads. Also, the resultant flux is displaced from the phase angle of the current coil (or main field) flux. For leading power factor loads, the phase angle between resultant flux and the voltage coil flux is decreased and for lagging power factor loads, it is increased.

Since the deflection torque is directly proportional to the cosine of angular phase displacement between the two fluxes, the meter reads high for leading loads and low for lagging loads. Hence, the effect is similar to the effect caused due to the change in magnitude of the main field flux. In order to reduce this error, laminated metallic parts and standard conductors are employed.

### Errors Due to Stray Magnetic Fields :

The stray magnetic fields (i.e., external magnetic fields) may disturb the operating field as it is quite weak in the case of electrodynamometers. So, if the external field aids the main field then, the meter reads high and if it opposes the main field then the meter reads low. In order to reduce these errors, proper shielding is to be provided.

### Errors Due to Vibration of Moving System :

As the supply is an alternating one, the torque produced in the moving system pulsates at double the frequency of supply, f. If any part of the moving system like pointer, spindle, spring, etc., has its natural frequency of pulsating torque 2f, it comes under resonance and starts vibrating with that frequency.

These vibrations in the moving system cause the pointer to deflect at some other position thus introducing error. Also, it is not quite easy to read the position since the frequency vibration is double that of supply.

In order to avoid this error, the natural frequency of various parts of the moving system is kept far away from 2f.

### Temperature Error :

An increase in temperature causes an increase in the resistance of the voltage coil and current coil. This reduces the current through the coils and hence the operating field. Thus, the deflection on torque is reduced. Also, due to an increase in temperature, the stiffness of the spring increases thereby, the control torque reduces.

Thus, the variations in deflecting and controlling torques cancel each other's effect and so, the effect of variations in temperature are almost negligible. For this to happen, the voltage coil circuit resistance should be made up proper composition of the alloy, so as to have a low temperature coefficient.

### Errors Due to Voltage Coil Inductance :

The inductance of voltage coil makes the voltage coil current IP, to lag the applied voltage by a small angle β and β is given by,

β = tan-1 (ωL/RP)

#### Where,L = Inductance of voltage coilRP = Total resistance of voltage coil circuitThe phasor diagrams for lagging and leading power factor loads are shown below.

At lagging power factor loads, due to the effect of inductance, the voltage coil current IP will become nearly equal in phase with load current. So, the driving torque increases and makes the wattmeter read high. The correction factor to be multiplied by the wattmeter reading, to obtain the actual power consumption is,

At leading power factor loads, as the phase angle between the load current, I, and voltage coil current IP is more, the driving or deflecting torque reduces and makes the meter read low. Hence, a correction factor to be multiplied with the reading in order to obtain the actual power consumption is,

### Errors Due to Voltage Coil Capacitance :

Apart from inductance, the voltage coil also possesses the effect of capacitance which is due to the inter-turn capacitance of the series resistance. So, the wattmeter reads high at lagging power factor loads and low at leading loads.

The voltage coil capacitive reactance is very small when compared to inductive reactance. Hence, the voltage coil circuit possesses net inductive reactance. So, the wattmeter reads high on lagging power factor loads and low on leading power factor loads.

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