--- title: "Power capability curve of alternator" subject: "Electric Machines II" chapter: 1 key: "semester_5/electric_machines_ii:power-capability-curve" source: https://www.bctengineer.com/q/semester_5/electric_machines_ii/power-capability-curve site: BCT Engineering --- # Power capability curve of alternator Electric Machines II · Chapter 1: Three Phase Synchronous Generator - Asked in: 2083 Baisakh (new course), 3 marks - Video: [GENERATOR CAPABILITY CURVE : simplest way to derive](https://www.youtube.com/watch?v=KsG6qERjvC0) — Electrocean - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/electric_machines_ii/power-capability-curve - Whole chapter: https://www.bctengineer.com/md/semester_5/electric_machines_ii/chapter-1 ## Question Explain the power capability curve of a synchronous alternator. What are its main components? ## Short answer The power capability curve defines the safe operating region of a synchronous generator in the P–Q plane at rated voltage. Main limits: armature current limit (circle), field current limit (arc on lagging side), prime mover limit (horizontal line), steady-state stability limit (line on leading side), and under-excitation limit. ## Answer The **power capability curve** (capability chart or P–Q diagram) of an alternator shows the region of active power $P$ and reactive power $Q$ in which the machine can run continuously without exceeding any thermal or stability limit, at rated voltage. ```text P (MW) | prime mover limit | ______________________ | | \ field current limit | | armature current \ (arc, lagging side) | | limit (circle) \ | | rated point | | stability | | limit | --+-----+----------O--------------+----> Q lead -3V^2/Xs origin lag (absorb) (supply) ``` #### Main components (limits) 1. **Armature (stator) current limit**: a circle centred at the origin with radius = rated MVA ($S = 3VI_{rated}$). Exceeding it overheats the stator winding. 2. **Field (rotor) current limit**: an arc centred at $(-3V^2/X_s, 0)$ on the Q-axis, with radius $3EV/X_s$ for maximum field current. It limits operation at lagging pf (over-excitation) to protect the rotor winding. 3. **Prime mover (turbine) limit**: a horizontal line at the maximum mechanical power of the turbine. 4. **Steady-state stability limit**: a line at $\delta = 90^\circ$ (in practice with a margin, about 70°) on the leading side, limiting under-excited operation. 5. **Minimum excitation / under-excitation limit** and stator end-core heating limit on the leading side. The rated operating point (rated MVA at rated pf, e.g. 0.85 lag) lies where the armature and field current limits meet. The safe operating area is the region enclosed by all these limits. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What does the power capability (P-Q) curve show? A. Efficiency vs load B. Safe region of P and Q for continuous operation at rated voltage C. Voltage vs current D. Frequency vs speed Answer: B. It shows the area of active and reactive power where thermal and stability limits are not exceeded. (Key point: What the curve shows) 2. What is the armature current limit on the chart? A. A horizontal line B. An arc centred at (-3V^2/Xs, 0) C. A circle at the origin with radius equal to rated MVA D. A vertical line at Q = 0 Answer: C. S = 3V I_rated is constant, so the stator limit is a circle centred at the origin with radius rated MVA. (Key point: Armature current limit) 3. What does the field current limit protect, and where does it apply? A. Stator winding, at leading pf B. Prime mover, at all pf C. Stator core ends, at unity pf D. Rotor winding, at lagging pf (over-excitation) Answer: D. The arc of radius 3EV/Xs for maximum field current limits over-excited, lagging operation to protect the rotor. 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