--- title: "Constant V/f control of induction motor" subject: "Utilization of Electrical Energy" chapter: 3 key: "semester_7/utilization_of_electrical_energy:constant-v-f-control-induction-motor" source: https://www.bctengineer.com/q/semester_7/utilization_of_electrical_energy/constant-v-f-control-induction-motor site: BCT Engineering --- # Constant V/f control of induction motor Utilization of Electrical Energy · Chapter 3: Control of Electric Drive - Asked in: 2080 Baisakh, 8 marks; 2072 Chaitra, 8 marks (asked 2 times) - 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/constant-v-f-control-induction-motor - Whole chapter: https://www.bctengineer.com/md/semester_7/utilization_of_electrical_energy/chapter-3 ## Question Draw the torque speed-characteristics of induction motor with constant V/f control for speed variation from very low up to the base speed. Describe an open loop control scheme for induction motor with constant V/f control. ## Short answer Below base speed, voltage varies proportionally with frequency to keep flux and maximum torque nearly constant, so torque-speed curves at different frequencies shift left in parallel. An open-loop V/f scheme uses a rectifier-DC link-PWM inverter, a ramp, a V/f generator with low-speed voltage boost; speed is set by frequency and drops with load by slip. ## Answer In an induction motor, the air-gap flux is $\phi \propto \dfrac{V}{f}$ (neglecting stator drop). If frequency is reduced to lower the speed while voltage is kept constant, the flux rises and the core saturates. So below base speed, **voltage is varied in proportion to frequency (constant V/f)**, keeping the flux and hence the maximum torque nearly constant. #### Torque-speed characteristics Synchronous speed $N_s = 120f/P$ falls with $f$; the slip speed at maximum torque, $s_m\omega_s \approx (R_2'/X_2')\,\omega_s$, is the same at every frequency because $X_2' \propto f$. Therefore the curves shift left parallel to each other with almost the same maximum torque. ```text T | f4 f3 f2 f1 = base | _.-. _.-. _.-. _.-. | / | / | / | / | | / |/ |/ |/ | Tmax ~ const |/ / / / | +------+-----+-----+-----+--> speed Ns4 Ns3 Ns2 Ns1 (at very low f, Tmax falls - dotted - because stator R drop is significant; add voltage boost) ``` - From base speed down to about 10 to 15 % of base frequency, $T_{max}$ is nearly constant: **constant torque region**. - At very low frequencies the stator resistance drop becomes comparable to $V$, so flux and $T_{max}$ fall; a **voltage boost** (offset $V_0$) is added: $V = V_0 + kf$. - Above base speed, $V$ is held at rated and $f$ increased: field weakening (constant power). #### Open-loop constant V/f control scheme ```text 3-ph AC ->[Diode rect]--+--[L]--+--[PWM inverter]--> IM | C ^ DC link | gate pulses w* (speed ref) ->[Ramp]->[f*]->[V/f ]-->[PWM generator] | [block] V* and f* +--------->(with low-speed boost) ``` 1. **Rectifier and DC link**: three-phase diode rectifier with LC filter gives a constant DC voltage. 2. **Speed reference** $\omega^*$ sets the frequency command $f^*$ (since $N \approx N_s$ at small slip). 3. **Ramp (soft start) block** limits the rate of change of $f^*$ so that slip and current stay within limits during acceleration and deceleration. 4. **V/f function generator** gives $V^* = V_0 + kf^*$ (boost at low frequency), saturating at rated voltage above base frequency. 5. **PWM generator and voltage source inverter** produce three-phase output with amplitude $V^*$ and frequency $f^*$. 6. The motor runs near synchronous speed for that frequency; speed drops slightly with load (equal to slip speed), as no speed feedback is used. Slip compensation can be added using measured current. **Features** - Simple, cheap, no speed sensor; several motors can be run from one inverter (textile mills). - Speed accuracy limited by slip; poor dynamic response; current limit needed for protection. - Widely used for fans, pumps, conveyors and other general-purpose drives. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is V varied in proportion to f below base speed? A. To keep air-gap flux (and Tmax) nearly constant, avoiding saturation B. To raise slip C. To raise frequency D. To reduce Ns Answer: A. Flux ~ V/f; constant V with lower f would saturate the core. (Key point: Why V/f) 2. With constant V/f, the torque-speed curves for different f: A. Shift parallel with almost same Tmax B. Have increasing Tmax C. Have zero Tmax D. Overlap Answer: A. Slip speed at Tmax is the same, so curves shift left. (Key point: Curves) 3. Why add voltage boost at very low frequency? A. Stator resistance drop is comparable to V, lowering flux and Tmax B. To raise speed above base C. To reduce losses D. For power factor Answer: A. V = V0 + kf compensates the stator drop. (Key point: Low-frequency boost) 4. In the open-loop scheme, speed drops slightly with load because: A. Speed feedback is used B. No speed feedback; speed = sync speed minus slip C. DC link voltage falls D. The ramp block Answer: B. Without a sensor, slip speed causes the drop. 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