# Generation of 3 Phase Power in 3 Phase Circuits

## Power in 3 Phase Circuits

Power in a single phase system or circuit is given by the relation shown below.

Where,

V is the voltage of single phase, i.e. V_{ph
}I is the current of single phase, i.e. I_{ph }and

Cosϕ is the power factor of the circuit.

**Contents:**

In a 3 phase circuits (balanced load), the power is defined as the sum of various powers in a three phase system. i.e.

Power in star connections in a 3 phase circuits is given as

As phase voltage and line voltage in star connection are represented as shown below.

Therefore, the equation (1) can be written as

Power in delta connections in 3 phase circuits is given by the equation shown below.

In delta connections, relation between phase and line voltage and phase and line current is given as

Hence, equation (3) can be written as

Thus, the Total Power in a 3 Phase balanced load system, irrespective of their connections, whether the system in star connected or delta connected, the power is given by the relation

√3 V_{L}I_{L}Cosϕ. Its units are kilowatt (kW) or Watt (W).

**Apparent Power** is given as

The unit of apparent power is kilo volt ampere (kVA) or volt-ampere (VA).

Similarly, the** Reactive Power** is given by the equation.

Its units are kilovolt-ampere reactive (kVAR) or volt-ampere reactive (VAR).

## Generation of 3 Phase E.M.Fs in a 3 Phase Circuit

In a 3 phase system, there are three equal voltages or EMFs of the same frequency having a phase difference of 120 degrees. These voltages can be produced by a three-phase AC generator having three identical windings displaced apart from each other by 120 degrees electrical.

When these windings are kept stationary, and the magnetic field is rotated as shown in the figure A below or when the windings are kept stationary, and the magnetic field is rotated as shown below in figure B, an emf is induced in each winding. The magnitude and frequency of these EMFs are same but are displaced apart from one another by an angle of 120 degrees.

Consider three identical coils a_{1}a_{2}, b_{1}b_{2} and c_{1}c_{2} as shown in the above figure. In this figure a_{1}, b_{1} and c_{1} are the starting terminals, whereas a_{2}, b_{2 }and c_{2} are the finish terminals of the three coils. The phase difference of 120 degrees has to be maintained between the starts terminals a_{1}, b_{1} and c_{1}.

Now, let the three coils mounted on the same axis and they are rotated by either keeping coil stationary and moving the magnetic field or vice versa in an anticlockwise direction at (ω) radians per seconds. Three EMFs are induced in the three coils respectively.

Considering the figure C, the analysis about their magnitudes and directions are given as follows.

The emf induced in the coil a_{1}a_{2} is zero and is increasing in the positive direction as shown by the waveform in the above figure C represented as e_{a1a2}.

The coil b_{1}b_{2} is 120 degrees electrically behind the coil a_{1}a_{2}. The emf induced in this coil is negative and is becoming maximum negative as shown by the wave e_{b1b2}.

Similarly, the coil c_{1}c_{2} is 120 degrees electrically behind the coil b_{1}b_{2}, or we can also say that the coil c_{1}c_{2} is 240 degrees behind the coil a_{1}a_{2}. The emf induced in the coil is positive and is decreasing as shown in the figure C represented by the waveform e_{c1c2}.

The EMFs induced in the three coils in a 3 phase circuits are of the same magnitude and frequency and are displaced by an angle of 120 degrees from each other as shown below in the phasor diagram.

These EMFs of a 3 phase circuits can be expressed in the form of the various equations given below.