Project 1

Motor power (Po) = 5 hp = 3.75 KW

Motor required voltage (V) = 230 V

Motor operating frequency (F) = 60 Hz

Stator poles (p) = 4 

Stator resistance (`r_s`) = `0.513 Omega`

Rotor resistance (`r_f`) = `0.408 Omega`

Motor inertia (J) = 0.1 `Kg-m^2`

Stator inductance (`L_1s`) = 2.52 mH

Rotor inductance (`L_1r`) = 2.52 mH

Magnetizing inductance (Lm) = 84.7 mH

Procedure:

For the given parameters, the following figures show the designed model of a 5 hp squirrel cage induction motor 

Voltage transformation subsystem:

Flux generator subsystem:

Induction motor subsystem:

Mechanical dynamics subsystem:

Load torque:

3-phase balanced supply:

1. Simulating the start-up behavior of the induction motor represented in the stationary d-q reference frame:

When initial speed =0 

`V_(qs)(t)`:

Zoomed-in:

`i_(qs)(t)` and `i_(ds)(t)`:

`i_(qr)(t)` and `i_(dr)(t)`:

Electromagnetic torque and Load torque:

The Electromagnetic torque is following the Load torque when required.

Initial speed and Rotor speed:

1. Simulating the start-up behavior of the induction motor represented in the synchronous reference frame:

When Synchronous speed Ns = Rotor speed N

We know, Ns = `(120*F)/p`

`therefore N = N_s = (120*60)/4 = 1800` rpm

Therefore, speed in rad/sed (`omega`) = `(2pi*N)/60`

`therefore omega = (2pi*1800)/60 = 188.5` rad/sed

`V_(qs)^e(t)`:

Zoomed-in:

`i_(qs)^e(t)`:

`i_(qr)^e(t)`:

Electromagnetic torque and Load torque:

When the synchronous speed and rotor speed are matched, the electromagnetic torque developed is higher than the load torque.

Initial speed and Rotor speed:

1. Simulating the start-up behavior of the induction motor represented in the rotor reference frame:

When Initial speed (`omega`) = Rotor speed (`omega_r`)

`V_(qs)^r(t)`:

Zoomed-in:

`i_(qs)^r(t)`:

`i_(qr)^r(t)`:

Electromagnetic torque and Load torque:

When the initial and rotor speeds are matched, the electromagnetic torque developed is less than the load torque.

Initial speed and Rotor speed:

1. Simulating the start-up behavior of the induction motor represented in the rotor flux reference frame:

Slip = `(omega_s-omega)/omega_s`

New rotor speed = Slip x Calculated rotor speed

`V_(qs)^(rf)(t)`:

Zoomed-in:

`i_(qs)^(rf)(t)`:

`i_(qr)^(rf)(t)`:

Electromagnetic torque and Load torque:

When the slip is added to the initial speed, the electromagnetic torque is developed when the load torque is required.

Initial speed and Rotor speed:

Conclusion:

Thus, the design and simulation of the starting behavior of a 5 hp 3-phase Induction motor has been performed satisfactorily.