--- title: "Induction generator and excitation capacitor" subject: "Electrical Machines" chapter: 5 key: "semester_4/electrical_machines:induction-generator-excitation-capacitor" source: https://www.bctengineer.com/q/semester_4/electrical_machines/induction-generator-excitation-capacitor site: BCT Engineering --- # Induction generator and excitation capacitor Electrical Machines · Chapter 5: Three Phase Induction Machines - Asked in: 2073 Bhadra (old course), 8 marks - Video: [Induction Generator](https://www.youtube.com/watch?v=2htEfpcAvSo) — Engineering College Banswara - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machines/induction-generator-excitation-capacitor - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-5 ## Question Explain how an induction motor can be used as induction generator. Explain the procedure to determine the value of excitation capacitor required for voltage build up in the generator. ## Short answer Drive the induction motor above synchronous speed; negative slip reverses rotor current and torque, delivering power. For self-excitation, measure the magnetisation curve, then choose capacitor current line intersecting it. For required voltage, C = Im/(2 pi f V0); minimum C = 1/(omega Xm). ## Answer #### Induction motor as induction generator If a three-phase induction motor connected to the supply is driven by a prime mover above synchronous speed, the slip becomes negative ($s<0$). The rotor conductors now cut the rotating field faster than the field itself rotates, so the rotor emf and current reverse. The torque opposes the driving torque, and the machine converts mechanical power into electrical power, which it delivers to the supply. It still draws lagging reactive power from the supply (or from capacitors) for magnetisation. For an isolated (stand-alone) system the reactive power is supplied by capacitors connected across the stator terminals. This is the **self-excited induction generator**. #### Procedure to find the excitation capacitor 1. Run the machine as a motor at the supply frequency and no load. Measure terminal (phase) voltage $V$ against magnetising current $I_m$ to get the **no-load magnetisation curve** (V against $I_m$). It is linear at first and then saturates. 2. A capacitor of capacitance $C$ per phase draws a current $I_c = \frac{V}{X_c}$, with $X_c = \frac{1}{2\pi f C}$. In the V-I plane it is a **straight line through the origin** with slope $X_c$. 3. For stable voltage, the capacitor line must cut the magnetisation curve. The intersection point gives the generated voltage. 4. **For a required voltage $V_0$:** read $I_m$ at $V_0$ from the curve. Then $$ X_c = \frac{V_0}{I_m}, \qquad C = \frac{I_m}{2\pi f V_0} $$ 5. **Minimum (critical) capacitance:** the line tangent to the linear part of the curve has slope $X_m$ (unsaturated magnetising reactance), so $$ C_{min} = \frac{1}{\omega X_m} = \frac{1}{\omega^2 L_m}, \quad \omega = 2\pi f $$ If $C < C_{min}$, the line does not meet the curve and the voltage does not build up. ```text V | / Xc line (larger C: flatter) | _.-*---- saturation curve | .-' / | .' / | / / +------------------> Im V0 found at crossing ``` The generated frequency depends on speed: $f \approx \frac{P N_r}{120}$ less the small slip, so frequency is a little different from that used in the test. Use the frequency of operation in $X_c$. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In the V-I plane, the capacitor of reactance X_c appears as: A. A curve that saturates B. A horizontal line at the rated voltage C. A straight line through the origin with slope X_c D. A vertical line at the critical current Answer: C. I_c = V/X_c so V = I_c X_c, a straight line through the origin. (Key point: Capacitor line) 2. To get a required voltage V0, how is the capacitor found? A. Read I_m at V0 from the magnetisation curve, then C = I_m/(2 pi f V0) B. Read the short-circuit current and divide by V0 C. Use C = 2 pi f V0 / I_m D. Take C equal to the critical value always Answer: A. X_c = V0/I_m, so C = I_m/(2 pi f V0). (Key point: Required capacitance) 3. What is the minimum (critical) capacitance for voltage build-up? A. Line tangent to the saturated part, C = X_m B. Line tangent to the linear part with slope X_m, C_min = 1/(omega X_m) C. Any C gives build-up if speed is high D. C_min = omega X_m Answer: B. The line must be flatter than the unsaturated magnetisation line, so C > 1/(omega X_m). (Key point: Critical capacitance) 4. Which frequency should be used in X_c = 1/(2 pi f C)? A. Always the test supply frequency B. Always 50 Hz C. The frequency of operation, which depends on speed D. Zero, since it is stand-alone Answer: C. The generated frequency depends on rotor speed, so use the actual operating frequency. (Key point: Frequency in Xc) ## Related in Electrical Machines - [Induction generator excitation capacitor value](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ainduction-generator-excitation-capacitor) — Electrical Machines I, chapter 5 - [Voltage build-up in isolated induction generator](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ainduction-generator-isolated-buildup) — Electrical Machines I, chapter 5 - [Voltage build-up in induction generator](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Ainduction-generator-voltage-buildup) — Electrical Machines, chapter 5 - [Shunt generator voltage build-up, critical resistance and speed](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ashunt-buildup-critical-define) — Electrical Machines I, chapter 3, asked 9× - [Starting shunt generator on no load and voltage build-up](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ashunt-generator-no-load-buildup) — Electrical Machines I, chapter 3 - [Voltage build-up; series generator at no load](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Avoltage-buildup-series-generator-no-load) — Electrical Machines, chapter 3 ## Related in other subjects - [Voltage build-up at line–cable junction](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Aline-cable-junction-voltage) — High Voltage Engineering, chapter 3 - [Capacitor bank for 340 kW induction motor](https://www.bctengineer.com/question.md?key=semester_7%2Futilization_of_electrical_energy%3Acapacitor-bank-340kw-induction-motor) — Utilization of Electrical Energy, chapter 6, asked 2×