V/f Control of an Induction Motor Drive for Light EVs

The problem

Induction motors are rugged, magnet-free and cheap, which makes them attractive for some light commercial EVs, pumps and compressors. V/f control is the simplest way to drive them, but at low speed and under load it suffers from torque loss and speed droop. Simulating the drive shows these limits clearly and how simple fixes such as boost and slip compensation help.

Objectives

• Model an induction motor with a three-phase inverter in Simscape Electrical.
• Implement open-loop V/f control with a frequency ramp.
• Add low-speed voltage boost and measure its effect on starting torque.
• Add slip compensation and measure speed regulation under load.
• Map current and efficiency over the operating range.

What you need

Key concepts

Constant V/f

Air-gap flux is roughly proportional to V/f, so keeping the ratio constant up to base frequency keeps flux, and hence torque capability, nearly constant.

Slip

The rotor turns slower than the stator field: s = (ns − nr)/ns. Torque is produced only with slip, so speed falls slightly as load rises.

Low-speed boost

At low frequency the stator resistance drop is a large share of applied voltage, so flux falls; adding a fixed voltage offset restores it.

Slip compensation

Estimating slip from measured current or power and adding it to the commanded frequency reduces speed droop without a speed sensor.

Step-by-step guide

1. 1

   Set example motor parameters

   Pick a labelled example: a 4-pole, 50 Hz, low-voltage induction motor of a few kilowatts on a 96 V DC link, with per-phase equivalent-circuit parameters (stator and rotor resistance, leakage and magnetising inductance) from a textbook example or a datasheet test report. Compute synchronous speed (1500 rpm at 50 Hz), rated slip and the V/f ratio from rated line voltage and frequency.

   Checkpoint: A parameter script that prints synchronous speed, V/f ratio and expected rated slip.

2. 2

   Verify the motor model alone

   Place the Simscape Electrical induction machine block, connect it to an ideal three-phase sinusoidal source at rated voltage and frequency, and add an inertia and load torque. Run a direct-on-line start, then load it to rated torque. Plot torque against speed during the start to reproduce the classic torque–speed curve. Use a variable-step stiff solver such as ode23t. Save the curve and slip values, since they are the reference for every inverter-fed test later.

   Checkpoint: The torque–speed curve shows a breakdown torque peak and rated slip within a few per cent of the calculation.

3. 3

   Add the inverter

   Replace the sinusoidal source with a three-phase inverter fed from the DC link, starting with an average-value model driven by sine references. Scale the modulation so that full modulation gives the rated voltage at base frequency, and check the line voltage fundamental. Later you can swap in a switching bridge at an example 8 kHz to see current ripple. Compare the stator current waveforms too, because the inverter should not change the fundamental.

   Checkpoint: At 50 Hz and full modulation the motor runs at the same speed as with the ideal source.

4. 4

   Implement V/f with a ramp

   Build the controller: a frequency command passes through a Rate Limiter (for example 25 Hz/s), then a lookup table gives voltage magnitude from frequency with a straight line through the origin to base. Integrate frequency to get the angle for the three sine references. Above base frequency hold voltage at its maximum. Start the motor from standstill at no load.

   Checkpoint: The motor accelerates smoothly following the ramp with stator current staying below a chosen limit.

5. 5

   Study low-speed behaviour and add boost

   Run at 5 Hz and apply increasing load to find the maximum torque before the motor stalls. Then add a voltage boost, an offset at zero frequency that tapers to zero at a chosen frequency, and repeat. Sweep the boost value with sim() in a loop and plot available low-speed torque and no-load current against boost, since too much boost over-fluxes the motor.

   Checkpoint: Low-speed maximum torque rises with boost, and no-load current rises too, with a chosen compromise value justified.

6. 6

   Add slip compensation

   Estimate slip frequency as proportional to load, using measured active current or input power and the rated slip at rated load. Add it to the commanded frequency through a low-pass filter. Apply load steps at 25 and 50 Hz and compare steady-state speed with and without compensation. Watch for instability if the compensation gain is too high, since it creates positive feedback on frequency, and record the gain at which the speed begins to oscillate.

   Checkpoint: Speed droop under rated load falls from roughly the rated slip to a small fraction of it.

7. 7

   Map current and efficiency

   Script a grid of frequency commands and load torques, run each point to steady state, and record stator current, input power, output power and efficiency. Plot efficiency contours over the torque–speed plane. Note where V/f performs poorly, especially low speed with high torque, and explain why vector control is used in traction drives. Use a fixed settling time per point and check that it is long enough by comparing two different durations at a few points.

   Checkpoint: An efficiency map over the operating range, with poorest points identified and explained.

8. 8

   Write the report

   Summarise the motor model check, the V/f profile, the boost and slip compensation studies and the efficiency map. State limits such as no magnetic saturation, no iron loss unless modelled and ideal switches. Compare V/f with field-oriented control in a short table of what each needs and what each delivers. Include the script that regenerates each figure so that a reviewer can rerun the full study from the parameter file.

   Checkpoint: A report with reproducible figures and a justified recommendation of boost and slip compensation settings.

Testing & validation

• Direct-on-line torque–speed curve matches the equivalent-circuit calculation.
• Inverter-fed motor reaches the same speed as with an ideal source.
• Low-speed torque capability improves with boost.
• Slip compensation reduces speed droop under load.
• Efficiency map computed over the operating range.

Expected results

A V/f induction motor drive model with tested boost and slip compensation and an efficiency map, showing where scalar control is adequate and where vector control is needed.

Take it further

• Add closed-loop speed control with an encoder and compare with slip compensation.
• Implement indirect rotor-flux-oriented control and compare low-speed torque.
• Add iron loss and magnetic saturation to the motor model.
• Run the drive on a light-vehicle drive cycle and log energy.

Viva and review questions

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