--- title: "Non-salient power angle relation for salient machines" subject: "Electric Machines II" chapter: 1 key: "semester_5/electric_machines_ii:non-salient-power-angle-salient" source: https://www.bctengineer.com/q/semester_5/electric_machines_ii/non-salient-power-angle-salient site: BCT Engineering --- # Non-salient power angle relation for salient machines Electric Machines II · Chapter 1: Three Phase Synchronous Generator - Asked in: 2072 Kartik, 4 marks - Video: [SM29 Power Angle Characteristics of Synchronous Machine](https://www.youtube.com/watch?v=VZMixA7E3o8) — Lectures in Electrical Engineering - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/electric_machines_ii/non-salient-power-angle-salient - Whole chapter: https://www.bctengineer.com/md/semester_5/electric_machines_ii/chapter-1 ## Question "Power angle characteristics of non salient pole synchronous machine is not valid for salient pole synchronous machine". Justify the statement. ## Short answer Non-salient pole machines have uniform air gap, so power is P = (3EV/X_s) sinδ. Salient-pole machines have non-uniform air gap (Xd > Xq), requiring two-reaction theory and an additional reluctance power term (3V²/2)(1/Xq - 1/Xd) sin2δ, making the cylindrical-rotor formula invalid. ## Answer The statement is **true**. The power-angle equation of a non-salient (cylindrical-rotor) machine is $$ P = \frac{3EV}{X_s}\sin\delta $$ It assumes a **uniform air gap**, so the same reactance $X_s$ acts on the armature mmf in every direction. #### Why it fails for salient-pole machines 1. A salient-pole rotor has a **non-uniform air gap**: small under the pole (direct axis, d-axis) and large between poles (quadrature axis, q-axis). 2. Reluctance along the d-axis is low, so $X_d$ is large; along the q-axis reluctance is high, so $X_q$ is smaller ($X_d > X_q$). A single $X_s$ cannot represent the machine. 3. The armature current must be split into $I_d$ and $I_q$ (two-reaction theory), and the power becomes $$ P = \frac{3EV}{X_d}\sin\delta + \frac{3V^2}{2}\left(\frac{1}{X_q} - \frac{1}{X_d}\right)\sin2\delta $$ 4. The second term is the **reluctance power**; it exists even with zero excitation ($E = 0$), because the rotor tends to align with the stator field along its minimum-reluctance path. A cylindrical rotor has no such term ($X_d = X_q$). #### Effect on the curve ```text P | resultant (salient) | .-"-. | .' .--'-. excitation term | .' .' '. |.' .-'-. '. reluctance term (sin 2d) +--------'----------'----> delta 0 45 70 90 180 ``` - Maximum power occurs at $\delta < 90^\circ$ (typically 60°–75°), not at 90°. - $P_{max}$ is larger than for a cylindrical machine with the same $E$ and $X_d$; the curve is steeper at small $\delta$ (higher synchronising power). Hence the cylindrical-rotor formula would give a wrong $P_{max}$ and wrong stability limit for salient-pole machines. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What assumption makes P = 3EV sin(delta)/Xs valid for a non-salient machine? A. Zero armature resistance only B. Uniform air gap, so a single reactance Xs acts in all directions C. A very high speed D. A delta connected stator Answer: B. A uniform air gap lets one reactance represent the armature reaction in every direction. (Key point: Assumption of uniform air gap) 2. In a salient-pole machine, how do Xd and Xq compare, and why? A. Xd < Xq because the d-axis gap is large B. Xd = Xq C. Xd > Xq because the d-axis gap is small, so reluctance is low D. Xd > Xq because the q-axis gap is small Answer: C. The d-axis has a small gap and low reluctance, giving a larger reactance than the q-axis. (Key point: Xd vs Xq) 3. What is the reluctance power term? A. A term proportional to sin(delta) that needs excitation B. A term in sin(2 delta) that exists even when E = 0 C. A loss term D. A term that vanishes for salient poles Answer: B. The term (3V^2/2)(1/Xq - 1/Xd) sin 2delta arises because the rotor tends to align along minimum reluctance, even with zero excitation. (Key point: Reluctance power) 4. At what load angle does a salient-pole machine reach maximum power? A. Exactly 90 degrees B. Exactly 45 degrees C. Below 90 degrees, typically 60 to 75 degrees D. At 180 degrees Answer: C. The reluctance term shifts the peak to below 90 degrees, unlike the cylindrical rotor. (Key point: Maximum power angle) ## Related in Electric Machines II - [Power angle characteristics of salient pole machine](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Asalient-power-angle-derivation) — Electric Machines II, chapter 2 - [Internal emf and load angle of salient pole motor](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Asalient-motor-200kw-load-angle) — Electric Machines II, chapter 2 - [25 MVA salient pole motor maximum power](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Asalient-motor-25mva-max-power) — Electric Machines II, chapter 2, asked 3× - [30 MVA salient pole motor maximum power](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Asalient-motor-30mva-max-power) — Electric Machines II, chapter 2, asked 3× - [20 MVA salient pole motor maximum power](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Asalient-motor-20mva-max-power) — Electric Machines II, chapter 2, asked 3× - [Power angle characteristics of cylindrical rotor machine](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Apower-angle-cylindrical-rotor) — Electric Machines II, chapter 1, asked 2× ## Related in other subjects - [Power of salient pole machine, power angle curve](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Asalient-pole-power-angle-characteristics) — Electrical Machines, chapter 6 - [Two reaction model of salient pole machine](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Atwo-reaction-model-salient-pole) — Electrical Machines, chapter 6 - [Salient pole vs cylindrical rotor alternators](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Asalient-vs-cylindrical-alternator-justify) — Electrical Machines, chapter 6 - [Reversible HVDC power flow: firing angle relation](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Ahvdc-reversible-firing-angle-relation) — Power Electronics, chapter 7