V/f speed control (VFD principle)

Reference notes

Use Next → on the narrator above to step through the V/f speed-control principle and the VFD architecture that implements it.

The principle: keep V/f constant → keep Φ constant

From the transformer-EMF equation applied to the stator winding:

If V_t is fixed by the supply and f is fixed by the grid, the air-gap flux Φ is also fixed. But a VFD can vary both V_t AND f. The key insight:

And constant Φ means the machine retains its full torque capability: from T ∝ Φ · I₂, rated I₂ still gives rated T, at any frequency.

Constant-torque region (below base speed)

From 0 Hz up to rated frequency (50 Hz typical), the VFD outputs:

so V/f stays at its rated value V_rated/f_rated. The motor sees rated flux at every speed; it can produce full rated torque from 0 rpm up to base speed.

• Synchronous speed is n_s = 120·f/P, so it scales linearly with f.
• Slip behaviour is unchanged — the same torque-slip curve, just translated to a new synchronous speed.
• Power output P = T · ω scales with speed, since T is constant.

Constant-power region (above base speed)

The VFD can't exceed the supply voltage; V_t caps at V_rated. To push speed beyond base, the VFD raises f without raising V. Now V/f drops below rated → flux drops → torque capability drops.

• P = V_rated · I_rated · cos θ — the VA rating is fixed, so P at the rated current is fixed.
• P = T · ω, so T must drop as ω rises.
• This is the constant-power (field-weakening) region above base speed — typically up to 2× base before stability and bearing limits kick in.

Low-frequency boost

At very low frequencies (1–5 Hz), the stator winding's I·R drop becomes a significant fraction of the applied voltage. Less voltage available to balance the back-EMF means less flux — and the motor can't deliver full torque. To maintain rated flux at near-zero speeds, the VFD adds a voltage boost at low f:

Without boost, low-frequency torque sags — which matters for fan/pump applications starting under load. Modern drives auto-tune this boost based on motor parameters.

VFD architecture

A typical VFD has three stages:

1. Rectifier — converts the incoming 3-phase AC to a DC link voltage (~ 1.35 × V_line for a 6-pulse diode bridge).
2. DC link — a capacitor (and sometimes a small inductor) smooths the DC.
3. Inverter — IGBT-based, switches at 2–16 kHz with PWM to synthesise a 3-phase output of any chosen amplitude and frequency.

Modern drives integrate input filtering, output filtering, a microcontroller for V/f profile generation, optional braking resistor, and rich I/O for sensors and fieldbus communication.

Open-loop V/f vs vector control

• Open-loop V/f (scalar control): the drive just sets V and f from a lookup curve. Cheap, simple, good enough for pumps, fans, conveyors. No speed sensor needed. Speed regulation ~3–5 %.
• Closed-loop vector control (FOC): the drive measures or estimates rotor flux and decouples the d- and q-axis currents — I_d (flux-producing) and I_q (torque-producing) — the same Blondel trick used in synchronous machines. Achieves DC-motor-like dynamic performance. Used in CNC, robotics, electric vehicles.
• Direct torque control (DTC): alternative high-performance scheme that estimates torque directly and switches inverter states to track a torque command. Used in some industrial drives.

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