--- title: "Volt/Hz control and frequency control schemes" subject: "Utilization of Electrical Energy" chapter: 3 key: "semester_7/utilization_of_electrical_energy:v-hz-control-frequency-schemes" source: https://www.bctengineer.com/q/semester_7/utilization_of_electrical_energy/v-hz-control-frequency-schemes site: BCT Engineering --- # Volt/Hz control and frequency control schemes Utilization of Electrical Energy · Chapter 3: Control of Electric Drive - Asked in: 2070 Asar - Video: [V/Hz Control for Motor Drives (Full Lecture)](https://www.youtube.com/watch?v=cmJcuNf1-1o) — Jim Pytel - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/utilization_of_electrical_energy/v-hz-control-frequency-schemes - Whole chapter: https://www.bctengineer.com/md/semester_7/utilization_of_electrical_energy/chapter-3 ## Question Starting from Volt/Hz control of three phase induction motors. Discuss their frequency control schemes. ## Short answer V/f control keeps air-gap flux constant by varying voltage with frequency. Frequency control schemes include PWM voltage-source inverter, square-wave inverter, current-source inverter, and cycloconverter. Control modes are open-loop V/f, closed-loop slip regulation, and vector control. ## Answer **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). ```text V | _________ V rated | / | / V/f const | / |/ <- boost V0 +------+----------> f f base ``` #### Frequency control schemes **1. Voltage source inverter (VSI) / PWM inverter drive** ```text 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. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is V/f kept constant when changing the frequency of an induction motor? A. Because V is proportional to f for any torque B. Because flux is proportional to V/f, so constant V/f keeps flux and Tmax constant C. To keep the slip at 1 D. To reduce stator resistance Answer: B. From V = 4.44 f N k φ, φ is proportional to V/f; Tmax is proportional to (V/f)^2, so both stay constant. (Key point: Flux and V/f) 2. What is done above the base frequency? A. Voltage is increased further with frequency B. Voltage is held at rated value, so flux and Tmax fall (constant-power, field-weakening region) C. Frequency is held constant D. The motor is reconnected in delta Answer: B. Voltage cannot exceed its rating, so V/f decreases, weakening flux and reducing maximum torque. (Key point: Above base frequency) 3. Which statement about VSI and CSI drives is correct? A. CSI needs an extra converter for regeneration, VSI does not B. Both need a braking chopper C. CSI has inherent regeneration and short-circuit protection; a diode-rectifier VSI needs an extra converter or braking chopper D. VSI uses a large dc link inductor Answer: C. The CSI uses a controlled rectifier with a large dc inductor and can regenerate; the VSI with a diode rectifier and capacitor cannot return power. (Key point: VSI versus CSI) 4. What is the characteristic of a cycloconverter drive? A. Direct ac-ac conversion to a lower frequency (about 1/3 of supply) for large, low-speed drives B. It produces frequencies above the supply C. It needs a dc link capacitor D. It is used for small high-speed drives Answer: A. A cycloconverter converts ac to ac directly with an output limited to about one third of supply frequency, suiting cement mills and ship propulsion. 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