Volt/Hz control and frequency control schemes

Volt/Hz control varies the supply frequency of an induction motor to change its synchronous speed, while changing the voltage in proportion so that the air-gap flux stays constant.

Basis of V/f control

$$V \approx E_1 = 4.44\,f N_1 k_w \phi \Rightarrow \phi \propto \frac{V}{f}$$ $$T_{max} \approx \frac{3}{2\omega_s}\frac{V^2}{X} \propto \left(\frac{V}{f}\right)^2$$

• Keeping $V/f$ constant keeps $\phi$ and $T_{max}$ constant; speed–torque curves shift parallel with frequency.
• At low frequency, a voltage boost $V = V_0 + kf$ compensates the stator $IR$ drop.
• Above base frequency, voltage is held at rated value: flux and $T_{max}$ fall (constant power, field-weakening region).

 V |        _________ V rated
   |      /
   |    /   V/f const
   |  /
   |/ <- boost V0
   +------+----------> f
        f base

Frequency control schemes

1. Voltage source inverter (VSI) / PWM inverter drive

 ac -> [diode rectifier] -> C -> [PWM inverter] -> IM

• Diode rectifier and capacitor give stiff dc; PWM inverter gives variable $V$ and $f$ together. Low harmonics, wide range, many motors from one inverter. Regeneration needs an extra converter or braking chopper.

2. Variable-voltage (square-wave) inverter

• Controlled rectifier or chopper varies the dc link voltage; six-step inverter varies frequency. Simple, but harmonics at low speed and poor input power factor.

3. Current source inverter (CSI) drive

• Controlled rectifier with large dc link inductor gives a stiff current; inverter switches it to the phases. Inherent regeneration and short-circuit protection; used for single large motors (fans, pumps). Torque pulsations at low speed.

4. Cycloconverter drive

• Direct ac–ac conversion to a lower frequency (up to about 1/3 of supply). For large, low-speed drives (cement mills, ship propulsion).

Control modes

• Open-loop V/f: frequency set from speed reference, voltage from V/f function; simple, used for fans and pumps; speed drops with load.
• Closed-loop slip regulation: speed is sensed; PI controller sets slip frequency, $\omega_e = \omega_r + \omega_{sl}$; slip limit gives current/torque limit and good regulation.
• Constant flux / vector control: stator current controlled so that flux and torque components are regulated separately, giving dc-motor-like dynamic performance.