--- title: "V-curve and inverted V-curve" subject: "Electrical Machines" chapter: 6 key: "semester_4/electrical_machines:v-curve-inverted-v-curve" source: https://www.bctengineer.com/q/semester_4/electrical_machines/v-curve-inverted-v-curve site: BCT Engineering --- # V-curve and inverted V-curve Electrical Machines · Chapter 6: Three Phase Synchronous Machines - Asked in: 2071 Magh, 6 marks - Video: [V curve and Inverted V Curve for synchronous MotorI 5th sem I Engineers Group I Diploma semester](https://www.youtube.com/watch?v=svn_ahuyR4o) — ENGINEERS GROUP : SEMESTER (POLYTECHNIC) - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machines/v-curve-inverted-v-curve - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/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 A V-curve plots armature current versus field current at constant load, minimum at unity pf. An inverted V-curve plots power factor versus field current, peaking at unity pf, showing how excitation controls reactive power. ## Answer #### V-curve A V-curve of a synchronous motor is the graph of **armature current $I_a$ against field current $I_f$**, at constant supply voltage and constant load (mechanical output). The curve has the shape of the letter V. - The lowest point of each curve is at **unity power factor**, where the armature current is minimum. - To the left (under-excited) the current **lags** the voltage; the pf is lagging, and $I_a$ increases as $I_f$ is reduced. - To the right (over-excited) the current **leads**; the pf is leading, and $I_a$ increases as $I_f$ is increased. - Curves are drawn for no load, half load, full load, etc. A higher load gives a curve higher up, and its minimum point moves to a larger field current. - The dotted line joining the minima is the **unity power factor line**; the region to its left is lagging pf and the region to its right is leading pf. ```text Ia |\ / | \ full load / | \ / | \ half load / | \ \ / / | \ \ no / / | \ \ load/ / +-------\----*---/------> If lagging unity pf leading (under) (min Ia) (over) ``` #### Inverted V-curve The inverted V-curve is the plot of **power factor against field current** at constant load. The power factor rises as the field current increases from the under-excited region, reaches its maximum value of unity at the same field current at which the V-curve is at its minimum, and then falls again (now leading) as the field current is raised further. The shape is like an inverted V. ```text pf 1.0| /\ | / \ | / \ | / \ +-----------------> If lag unity lead ``` These curves show that a synchronous motor can be operated at any power factor by changing its excitation, so it is used for power factor correction (as a synchronous condenser). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What does a V-curve plot? A. Armature current against field current at constant load B. Voltage against speed C. Power factor against load D. Torque against slip Answer: A. It shows Ia versus If at constant supply voltage and load. (Key point: V-curve axes) 2. What does the bottom of the V represent? A. Zero load B. Unity power factor with minimum armature current C. Pull-out D. Maximum lag Answer: B. Minimum Ia occurs at unity pf. (Key point: Minimum point) 3. What happens to the curves for higher load? A. Move lower B. Move higher and the minimum shifts to larger If C. Same D. Become flat Answer: B. More load needs more active current, so curves are higher. (Key point: Higher load) 4. What is the inverted V-curve? A. Ia against If B. Power factor against field current, peaking at unity C. Torque against angle D. V against I Answer: B. pf rises to 1 at the same If where Ia is minimum, then falls to leading. 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