--- title: "V-curve and inverted V-curve" subject: "Electrical Machine" chapter: 6 key: "semester_4/electrical_machine:v-curve-inverted-v-curve" source: https://www.bctengineer.com/q/semester_4/electrical_machine/v-curve-inverted-v-curve site: BCT Engineering --- # V-curve and inverted V-curve Electrical Machine · Chapter 6: Three Phase Synchronous Machines - Asked in: 2071 Magh, 6 marks - Video: [V and inverted V curves of synchronous motors](https://www.youtube.com/watch?v=7sYV3KypcKY) — Mahesh - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machine/v-curve-inverted-v-curve - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machine/chapter-6 ## Question What do you mean by V-curve and inverted V-curve for a synchronous motor? Explain with a neat diagram. ## Short answer V-curve plots armature current against field current at constant load; its V shape has minimum current at unity power factor. Inverted V-curve plots power factor against field current, peaking at unity, lagging on left (under-excitation) and leading on right (over-excitation). ## Answer For a synchronous motor connected to a supply of constant voltage and frequency and driving a constant load, the **V-curve** is the plot of armature current I_a against field current I_f. It is called a V-curve because of its V-like shape. The **inverted V-curve** is the plot of power factor against field current under the same conditions. It has an inverted V (arch) shape. #### Curves ```text V-curves (Ia against If) Ia | \ \ \ / / / | \ \ \ / / / | \ \ \ / / / | \ \ \ / / / full load | \ \ o / / | \ \ / / | \ \ / / half load | \ \ / / | \ o / | \ / | \ / no load | \ / | o +--------------------------------------> If under-excited over-excited (lagging pf) (leading pf) o = minimum Ia (unity pf); the line through the o's is the unity-pf compounding curve, sloping to the right. Inverted V-curve (pf against If, one load) pf | unity | * | * * | * * | * * +---------------------> If lagging | leading ``` - The lowest point of every V-curve is where I_a is minimum and the power factor is unity. The line joining these minima (the compounding curve) slopes to the right as the load rises, since more excitation is needed to keep unity pf at a higher load. - Left of the minimum: the motor is under-excited, I_a lags V (lagging pf), and the current rises as I_f falls. - Right of the minimum: the motor is over-excited, I_a leads V (leading pf), and the current rises as I_f rises. - A higher load gives a curve higher up (larger I_a for every I_f), because the in-phase component I_a cos φ is larger. The no-load curve has its minimum close to the I_f axis: the minimum current is only the small current needed to supply the no-load losses. #### Reason At constant load, the power input 3 V I_a cos φ is constant, so I_a cos φ is constant. Changing I_f only changes the reactive component I_a sin φ. At minimum I_a, sin φ = 0 and I_a = I_a cos φ, so the pf is unity. On either side, the extra reactive component makes I_a larger, which gives the V shape. The pf is lagging on the left, rises to unity at the V minimum, and then falls again (now leading) on the right, giving an inverted V. For a higher load the pf curve is flatter and its peak moves to the right. #### Use The curves show how the motor can be used for power-factor correction (on the over-excited side) and let the operator find the excitation needed for a required pf. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What does the V-curve plot? A. Power factor against Ia B. Armature current Ia against field current If at constant load C. Torque against speed D. Eb against load angle Answer: B. It is Ia versus If at constant voltage, frequency and load. (Key point: V-curve definition) 2. What does the inverted V-curve plot? A. Power factor against field current B. Voltage against current C. Ia against load D. Speed against torque Answer: A. pf rises to unity at the minimum of the V and falls on either side. (Key point: Inverted V-curve) 3. Why does Ia rise on both sides of the minimum? A. The in-phase component grows B. The reactive component grows while Ia cos(phi) is constant C. Power input changes D. Speed changes Answer: B. Ia cos(phi) is fixed at constant load; changing If changes Ia sin(phi). 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