--- title: "Synchronous generator load characteristics, capacitive load" subject: "Electrical Machines" chapter: 6 key: "semester_4/electrical_machines:sync-gen-load-characteristics-capacitive" source: https://www.bctengineer.com/q/semester_4/electrical_machines/sync-gen-load-characteristics-capacitive site: BCT Engineering --- # Synchronous generator load characteristics, capacitive load Electrical Machines · Chapter 6: Three Phase Synchronous Machines - Asked in: 2078 Poush, 2+3+3 marks - Video: [Capacitive load characteristics of synchronous generator ](https://www.youtube.com/watch?v=wXAqpYjtis4) — Joyonti Bristy - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machines/sync-gen-load-characteristics-capacitive - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-6 ## Question Explain load characteristics of synchronous generator. Why terminal voltage of a synchronous generator is greater than internal generated emf (E) in case of capacitive load? Explain with the help of armature reaction and phasor diagram. ## Short answer With capacitive load, armature reaction is magnetising, aiding the main field flux. The phasor drop jIXs has a component opposing V, so E = V + jIXs yields E < V, making terminal voltage greater than internal emf. ## Answer #### Load characteristics of a synchronous generator The load characteristic (external characteristic) is the plot of terminal voltage $V$ against load current $I$ at constant speed, constant field current and constant power factor. ```text V | leading pf (rises) | _.-' | ______----- unity pf (small fall) | `-._ | `-._ lagging pf (falls) +----------------------> I ``` - **Lagging pf (inductive):** the armature reaction is demagnetising, and the synchronous impedance drop also reduces the voltage, so $V$ falls considerably with load. - **Unity pf:** the armature reaction is mainly cross-magnetising; $V$ falls slightly. - **Leading pf (capacitive):** the armature reaction is magnetising, so $V$ rises with load. #### Why $V > E$ with capacitive load The phasor equation for a generator is $\vec E = \vec V + \vec I(R_a + jX_s)$, where $X_s$ includes the armature reaction reactance ($X_s = X_{ar} + X_l$). - With leading current, the armature flux **aids** the main field flux (magnetising armature reaction). In the phasor diagram this appears as a reactance drop $jIX_s$ that acts in the opposite sense to the lagging case. - The drop $j\vec I X_s$ leads $\vec I$ by $90^\circ$, and $\vec I$ itself leads $\vec V$, so $j\vec I X_s$ has a component directed **opposite** to $\vec V$. In $\vec E = \vec V + j\vec I X_s$ the second term therefore **reduces** the magnitude, so $E < V$. ```text * tip of E .-' \ .-' \ jIXs (leads I by 90 deg) .-' E \ .-' \ O------------------------> V I leads V by phi; E = V + jIXs is shorter than V ``` Neglecting $R_a$, with $I$ leading $V$ by angle $\phi$ (and $IX_s$ small compared with $V$): $$ E \approx V - I X_s \sin\phi \quad\Rightarrow\quad V \approx E + IX_s\sin\phi > E $$ The same result is seen physically: the capacitive load current produces a field that adds to the main field, so the net flux (and the terminal voltage) is greater than that due to the field current alone. This is a Ferranti-like voltage rise, and it is why the voltage regulation is negative for leading pf. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is plotted in the load characteristic of an alternator? A. Terminal voltage against load current at constant speed, field current and power factor B. E against If C. Current against speed D. Efficiency against load Answer: A. It is V against I with speed, field current and pf held constant. (Key point: Load characteristic definition) 2. What happens to V with load at lagging pf? A. Rises B. Falls considerably because armature reaction is demagnetising C. Stays constant D. Is zero Answer: B. Lagging current weakens the field and adds to the drop, so V falls. (Key point: Lagging pf behaviour) 3. What is the armature reaction for leading current? A. Demagnetising B. Cross-magnetising C. Magnetising D. None Answer: C. Leading current produces armature flux that aids the main flux. (Key point: Capacitive armature reaction) 4. In E = V + jIXs with leading I, why is V > E? A. Because R is negative B. The jIXs term points opposite to V and reduces the magnitude of E, so E < V C. The emf is increased D. Frequency rises Answer: B. The reactance drop for a leading current opposes V, so E is smaller than V (negative regulation). (Key point: V greater than E) ## Related in Electrical Machines - [Armature reaction in synchronous generator](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Aarmature-reaction-sync-gen-loads) — Electrical Machines, chapter 6 - [Synchronous generator working; armature reaction](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Async-gen-working-armature-reaction) — Electrical Machines, chapter 6 - [EMF of short shunt compound generator (0.5 Ω armature)](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ashort-shunt-compound-50a-200v-0p5ohm) — Electrical Machines I, chapter 3, asked 2× - [Short shunt vs long shunt generated voltage (150 A, 230 V)](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ashort-shunt-150a-230v-long-shunt) — Electrical Machines I, chapter 3 - [30 kW shunt generator: emf, copper loss, efficiency](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Agen-shunt-30kw-loss-1000w) — Electrical Machines, chapter 3, asked 2× - [30 kW shunt generator: emf, copper loss, efficiency (100 W)](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Agen-shunt-30kw-loss-100w) — Electrical Machines, chapter 3, asked 2× ## Related in other subjects - [Why terminal voltage exceeds emf on capacitive load](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Aterminal-voltage-greater-capacitive) — Electric Machines II, chapter 1, asked 3× - [Terminal voltage above emf and armature reaction](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Aterminal-voltage-greater-ar-effect) — Electric Machines II, chapter 1 - [Load characteristics and capacitive load voltage rise](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Aload-characteristics-capacitive-load) — Electric Machines II, chapter 1, asked 3× - [When terminal voltage is less or more than emf](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Aterminal-voltage-less-or-more) — Electric Machines II, chapter 1