Question

What is the formula for 3-phase induction motor?

Answer 1

For a 3-phase induction motor, there are a few important formulas that relate to its performance. The key formulas are as follows:

1. Synchronous Speed (Ns)

The synchronous speed of a 3-phase induction motor is the speed at which the magnetic field rotates. It is given by:

\[
N_s = \frac{120 \times f}{P}
\]

Where:

1. \( N_s \) = Synchronous speed (in RPM)
   

1. \( f \) = Frequency of the supply (in Hz)
   

1. \( P \) = Number of poles in the motor
   

2. Slip (s)

Slip is a measure of how much the rotor speed differs from the synchronous speed. It is defined as:

\[
s = \frac{N_s - N_r}{N_s} \times 100
\]

Where:

1. \( N_s \) = Synchronous speed (in RPM)
   

1. \( N_r \) = Rotor speed (in RPM)
   

3. Motor Power Output (P_out)

The power output of the motor is given by:

\[
P_{\text{out}} = \frac{3 \times V \times I \times \cos \phi}{1000}
\]

Where:

1. \( P_{\text{out}} \) = Output power (in kW)
   

1. \( V \) = Line-to-line voltage (in Volts)
   

1. \( I \) = Line current (in Amps)
   

1. \( \cos \phi \) = Power factor (cosine of the phase angle between current and voltage)
   

4. Input Power (P_in)

The total input power to the motor is:

\[
P_{\text{in}} = \sqrt{3} \times V \times I \times \cos \phi
\]

Where:

1. \( P_{\text{in}} \) = Input power (in Watts)
   

1. \( V \) = Line-to-line voltage (in Volts)
   

1. \( I \) = Line current (in Amps)
   

1. \( \cos \phi \) = Power factor
   

5. Efficiency (η)

The efficiency of the motor is the ratio of the output power to the input power:

\[
\eta = \frac{P_{\text{out}}}{P_{\text{in}}} \times 100
\]

Where:

1. \( \eta \) = Efficiency (in percentage)
   

1. \( P_{\text{out}} \) = Output power (in Watts)
   

1. \( P_{\text{in}} \) = Input power (in Watts)
   

These formulas are fundamental for understanding and analyzing the operation of 3-phase induction motors.