Induction Motor Control Example¶

Three-phase induction motor with V/f and vector control.

Overview¶

Induction motors are the workhorse of industry: - Robust and reliable - Low cost - Self-starting - Various control methods available

Specifications¶

Parameter	Value
Rated Power	5.5 kW
Rated Voltage	400V
Rated Frequency	50 Hz
Pole Pairs	2
Rs	0.5 Ω
Rr	0.4 Ω
Ls = Lr	80 mH
Lm	75 mH

Circuit Files¶

im_vf_control.ipes - V/f (scalar) control
im_vector.ipes - Indirect field-oriented control
im_dtc.ipes - Direct torque control

Theory¶

V/f Control¶

Maintain constant flux by keeping V/f ratio: $$\frac{V}{f} = \text{constant}$$

With voltage boost at low frequency for Rs drop.

Slip Frequency¶

\[f_{slip} = f_s - f_r = \frac{n_s - n}{n_s} \cdot f_s\]

\[\omega_{slip} = \frac{R_r}{L_r} \cdot \frac{i_q}{i_d}\]

Torque Equation¶

\[\tau_e = \frac{3}{2}p\frac{L_m}{L_r}\psi_r i_q\]

Control Methods¶

Scalar (V/f)¶

Frequency Ref ──► V/f Curve ──► PWM ──► Inverter ──► Motor

Simple implementation
Open-loop (no encoder)
Limited dynamics

Indirect Field-Oriented Control (IFOC)¶

Speed Ref ──► Speed PI ──► iq* ───┬──► Current PI ──► PWM
                                  │
         ψr Ref ──► Flux PI ──► id* ──►
                                  │
         ωslip = f(iq*/id*) ──────┘

High dynamic performance
Requires motor parameters
Rotor position from encoder + slip calculation

Direct Torque Control (DTC)¶

Direct control of torque and flux
Hysteresis controllers
Variable switching frequency
Very fast torque response

Design Considerations¶

Field Weakening¶

Above base speed, reduce flux to maintain voltage limit: $$\psi_r = \psi_{rated} \cdot \frac{f_{base}}{f_s}$$

Motor Starting¶

V/f: Current limited by inverter rating
Vector: Controlled current during acceleration

Exercises¶

V/f Control: Implement open-loop V/f drive
Slip Calculation: Measure slip at different loads
IFOC: Implement indirect vector control
Speed Reversal: Four-quadrant operation