--- title: "Induction generator excitation capacitor value" subject: "Electrical Machines I" chapter: 5 key: "semester_4/electrical_machines_i:induction-generator-excitation-capacitor" source: https://www.bctengineer.com/q/semester_4/electrical_machines_i/induction-generator-excitation-capacitor site: BCT Engineering --- # Induction generator excitation capacitor value Electrical Machines I · Chapter 5: Three-Phase Induction Machines - Asked in: 2073 Bhadra, 8 marks - Video: [induction generator working principle | induction generator in hindi | animation | construction](https://www.youtube.com/watch?v=2eTLpzuozLA) — Mind of Engineer - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machines_i/induction-generator-excitation-capacitor - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines_i/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 rotor above synchronous speed to get negative slip and generate power. In isolated mode, a capacitor bank supplies lagging excitation. Determine capacitance: obtain magnetisation curve at desired voltage, find magnetising current Im; then Xc = Vph/Im; capacitance per phase (star) C = 1/(2πf Xc) (delta C = C/3). ## Answer An induction motor works as an **induction generator** when its rotor is driven by a prime mover above synchronous speed ($N > N_s$), so that slip is negative and mechanical power is converted into electrical power. #### Motor to generator action - With $N < N_s$ ($s > 0$) the machine motors. - Driven at $N > N_s$ ($s < 0$), the rotor cuts the field in the opposite sense; rotor emf, current and torque reverse. Air-gap power $3I_2^2R_2/s$ becomes negative: power flows from shaft to stator terminals. - The machine still needs **lagging reactive power** to magnetize its core. On a grid it takes this from the grid. In **isolated mode** a 3-phase **capacitor bank** across the stator supplies it, and voltage builds up by self-excitation from residual magnetism. ```text Prime mover +------+ (N > Ns) ====| IG |===+======> Load +------+ | === C per phase ``` Voltage settles where the magnetization curve meets the capacitor line $V = I_c X_c = I_c/(\omega C)$. #### Procedure to find the excitation capacitance 1. **Obtain the magnetization curve.** Run the machine as a motor on no load (speed $\approx N_s$) from a variable-voltage supply, or drive it at synchronous speed. Vary the applied phase voltage $V$ from about 120% of rated downwards and record the no-load (magnetizing) current $I_m$. Plot $V$ against $I_m$. ```text V | _.---- magnetization | .-' curve Vr|---.* <- required point | /| capacitor line | / | slope = Xc |/__|_____________ Im Im,r ``` 2. **Choose the operating voltage** $V_r$ (rated phase voltage) and read the corresponding magnetizing current $I_{m,r}$ from the curve. 3. **Capacitive reactance per phase** — the capacitor line must pass through this point: $$ X_c = \frac{V_r}{I_{m,r}} $$ 4. **Capacitance per phase (star-connected bank):** $$ C_Y = \frac{1}{2\pi f X_c} = \frac{I_{m,r}}{2\pi f V_r} $$ For a **delta-connected bank** (each capacitor at line voltage): $C_\Delta = C_Y/3$. 5. **Minimum capacitance:** the capacitor line must be less steep than the linear (air-gap) part of the curve; otherwise voltage will not build up. The slope of the air-gap line gives $X_{c,max}$ and so $C_{min}$. 6. **Allowance for load:** for a lagging load, extra capacitance is added to supply the load VAr, $Q_L = 3V^2\omega\, \Delta C$, so that voltage does not collapse. Also, because the slip is negative, the generated frequency is slightly below the speed-equivalent value $PN/120$, so the calculation should use this expected (slightly lower) operating frequency, not $PN/120$ itself. **Example:** 400 V, 50 Hz machine; at rated phase voltage 230.94 V the curve gives $I_m = 4$ A. $$ \begin{aligned} X_c &= \frac{230.94}{4} = 57.74\ \Omega \\ C_Y &= \frac{1}{2\pi \times 50 \times 57.74} = 55.1\ \mu\text{F per phase} \\ C_\Delta &= \frac{55.1}{3} = 18.4\ \mu\text{F per phase} \end{aligned} $$ ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why does an induction machine need a capacitor bank in isolated generation? A. To supply the lagging reactive power needed to magnetize the core, building up voltage from residual magnetism B. To increase the prime mover speed C. To supply active power D. To reduce slip to zero Answer: A. With no grid, capacitors provide the magnetizing VAr and the voltage builds up by self-excitation. (Key point: Motor to generator action) 2. How is the magnetization curve obtained? A. By blocking the rotor and measuring current B. By measuring open-circuit rotor voltage at standstill C. By running as a motor on no load near Ns at varying voltage and recording magnetizing current D. By measuring winding resistance Answer: C. No-load voltage versus magnetizing current gives the V-Im curve. (Key point: Magnetization curve) 3. How is Xc and the star-connected capacitance found at rated voltage Vr and magnetizing current Im,r? A. Xc = Im,r/Vr; C = Xc/(2 pi f) B. Xc = Vr/Im,r; C = 1/(2 pi f Xc) C. Xc = Vr x Im,r; C = 2 pi f Xc D. Xc = Vr/Im,r; C = 2 pi f Xc Answer: B. The capacitor line V = Im Xc passes through the required point, so Xc = Vr/Im,r and C = 1/(2 pi f Xc). (Key point: Capacitor value) 4. Which statement is correct? A. A delta bank needs 3 times the star capacitance per phase B. Capacitor line must be steeper than the air-gap line C. C_delta = C_Y/3, and the capacitor line must be less steep than the linear part of the curve for voltage to build up D. Capacitance does not affect build-up Answer: C. Each delta capacitor sees line voltage, so it needs one third the star value; build-up needs the line to intersect the curve above the linear part. (Key point: Delta bank and minimum C) ## Related in Electrical Machines I - [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 - [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 - [Excitation capacitors in isolated and grid-connected induction generator](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ainduction-generator-capacitor-isolated-grid) — Electrical Machines I, chapter 5 - [Shunt generator build-up conditions, critical speed and resistance](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ashunt-buildup-conditions-critical) — Electrical Machines I, chapter 3 - [Induction motor as generator in grid-connected mode](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ainduction-generator-grid-connected) — Electrical Machines I, chapter 5, asked 5× ## Related in other subjects - [Induction generator and excitation capacitor](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Ainduction-generator-excitation-capacitor) — Electrical Machines, 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 - [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 - [Voltage build-up, critical resistance and speed](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Avoltage-buildup-critical-resistance-speed) — Electrical Machines, chapter 3, asked 3×