# Induction Type Watt Hour Meter or Energy Meter

The electromechanical type energy meter, what we use in our domestic and industrial installation is single phase induction type watt hour meter. Although nowadays, the Electric Supply Companies, are replacing the conventional electromechanical type meters by Digital one. But still, we need to know the basic function and constructional features of induction type single phase watt hour meter for our knowledge base. This type of energy meter measures electrical energy in a kilowatt hour. That is why sometimes we call this meter as kilowatt-hour meter.

## Working Principle of Watt Hour Meter

Constructionally an induction type single phase watt hour meter has many similarities to an induction type wattmeter. Moreover, the working principle of a watthour meter is more or less similar to that of an induction type wattmeter. We do not provide any control spring and pointer in an energy meter. Instead, we provide a breaking magnet.

### Construction of Watt Hour Meter

An induction type energy meter consists of an aluminum disc on a spindle in between two electromagnets. So, the disc is free to rotate. We connect one electromagnet across the supply main. So, it makes the flux of this magnet proportional to the system voltage. Hence, we call this electromagnet as shunt magnet.  The core of this electromagnet has three limbs. In an energy meter, normally the central limb of the shunt magnet holds the voltage coil. Then we connect another electromagnet in series with the supply line. Thus we call this electromagnet as a series magnet. Unlike the shunt magnet, the series magnet consists of two limbs. Each of the limbs holds half of the current coil. Since we connect it in series with the supply line, the flux produced by this coil is proportional to the supply current.

Another basic component we use in watt-hour meter is breaking magnet. This is nothing but a u-shaped permanent magnet. The edge of the aluminum disc rotates in between the poles of this permanent magnet. The flux of the magnet produces eddy current in the disc. As a result, this arrangement provides braking torque to the rotating disc.

### Rotating Torque of Induction Energy Meter

We also provide copper shading ring at the central limb of the shunt magnet. This is to maintain the phase angle between the supply voltage V and flux of shunt magnet φsh at 90°. This flux induces an emf Esh in the aluminum disc which obviously lags the flux by another 90°. Then we consider the disc does not have any inductive property. So, the EMF produces an eddy current Ish in phase with it. Hence, ultimately we can say the phase angle between the flux φsh and eddy current Ish is 90°.

Let us assume that there is a phase angle θ between the supply voltage V and the supply current I. The current I, through the series magnet produces flux φse in phase with it. Also, this flux induces an emf Ese in the disc in 90° lag with it. Since the disc is purely resistive, the emf produces eddy current Ise in phase with it.

The interaction between flux of shunt magnet φsh and eddy current Ise caused by series magnet provides a torque on the disc. Then, we can write the expression of this torque as

Similarly we can write the torque produced due to interaction of series magnetic field φse and the eddy current Ish induced by shunt magnetic field as

From the above expression of two torques, we can derive the expression of resultant torque as follows

Now the function of braking magnet comes into the picture. Since the speed of the disc is directly proportional to the rate of cutting of braking magnet flux by the disc. So, the torque produced by the braking magnet on the aluminum disc is directly proportional to the speed of the disc. Let us assume that N is the speed of the disc in RPM. So we can write,

At steady rotational condition of the disc,

From the above equity we can write,

Integrating both sides we get,

From that we can conclude,

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