EMF Equation of DC Generator

EMF Equation of DC Generator

A DC generator is used to convert mechanical energy into electrical energy. The armature is a rotating part of the DC machine. The mechanical energy gets from the prime mover or diesel engine. The electrical energy is collected from terminals of the field winding. The EMF produced in field winding is known as Generated EMF (EG).

A DC motor is used to convert electrical energy into mechanical energy. In the case of a motor, EMF of rotation is known as Back EMF (EB).

The equation for generated EMF is the same as the equation of back EMF. Let’s derive the EMF equation for DC Generator.

EMF Equation of DC Machine

Consider a DC machine with the following parameter;

P = Number of poles

Ф = Flux per pole (Wb)

A = Number of parallel paths in the armature

Z = Total number of Armature conductor

N = Speed of Rotor (RPM)

Now, ф is the flux produced by one pole. If there is P number of poles presents in the DC machine, then total flux produced by a machine is;

    \[ Total \, Flux  \quad d \phi= P \phi \]

If the actual speed of the rotor is N, then the time taken to complete one revolution is;

    \[ dt = \frac{60}{N} \]

According to faraday’s law of electromagnetic induction, the induced EMF of the armature conductor is equal to the rate of change of flux.

Hence,

    \[ E = \frac{d\phi}{dt} \]

Induced EMF in once the conductor is;

    \[ E = \frac{d\phi}{\frac{60}{N}} \]

    \[ E = P \phi \frac{N}{60} \]

So, the above equation gives the value of EMF generated by one conductor.

The total number of conductors connected in series is the ratio of total conductor and a total number of parallel paths.

Therefore,

    \[ Total \, number \, of \, conductors \, connected \, in \, series = \frac{Z}{A} \]

Total induced EMF in a machine is a multiplication of EMF of one conductor and number of conductors connected in series.

So,

Total EMF Induced in DC Machine (E) = EMF of one conductor X Number of conductors connected in series

    \[ E = P \phi \frac{N}{60} \times \frac{Z}{A} \]

The above equation is a general form of the equation of Generated EMF for DC Generator and the equation of Back EMF for DC Motor.

There are two types of connection for armature winding;

  • Wave Winding
  • Lap Winding

For Wave winding,

Total number of parallel path A = 2

Hence, Total EMF (E)

    \[ E = P \phi \frac{N}{60} \times \frac{Z}{2} \]

    \[ E =  \frac{P \phi N}{120} \]

For Lap winding,

The total number of parallel paths is equal to the number of poles of the machine.

Total number of parallel path A = P.

Therefore, Total EMF(E)

    \[ E = P \phi \frac{N}{60} \times \frac{Z}{P} \]

    \[ E =   \frac{\phi N Z}{60} \]

 

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