--- title: "Two reaction model of salient pole machine" subject: "Electrical Machines" chapter: 6 key: "semester_4/electrical_machines:two-reaction-model-salient-pole" source: https://www.bctengineer.com/q/semester_4/electrical_machines/two-reaction-model-salient-pole site: BCT Engineering --- # Two reaction model of salient pole machine Electrical Machines · Chapter 6: Three Phase Synchronous Machines - Asked in: 2071 Magh (old course), 8 marks - Video: [18 Two Reaction Theory of Salient Pole Machine Blondel's Theory Alternator](https://www.youtube.com/watch?v=whVQQHllvWo) — SP Engg. ACADEMY - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machines/two-reaction-model-salient-pole - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-6 ## Question Explain two reaction model of salient pole synchronous machine. ## Short answer In salient-pole machines the non-uniform air gap requires resolving armature mmf into direct-axis (d-axis) and quadrature-axis (q-axis) components. The reactances differ, Xd > Xq. The phasor equation is E = V + I Ra + j Id Xd + j Iq Xq, yielding a power expression with excitation and reluctance terms. ## Answer #### Two-reaction model In a salient-pole machine the air gap is not uniform: it is small along the pole axis (**direct axis, d-axis**) and large between the poles (**quadrature axis, q-axis**). So the same mmf produces different flux along the two axes, and the single synchronous reactance of a cylindrical rotor cannot be used. Blondel's **two-reaction theory** resolves the armature mmf (and the current) into two components, one along each axis, and treats each separately. - $I_d = I\sin\psi$: **direct-axis component**, in quadrature with the emf $E$, and acting along the pole axis (magnetising or demagnetising). - $I_q = I\cos\psi$: **quadrature-axis component**, in phase with $E$, acting along the inter-polar axis (cross-magnetising). Here $\psi$ is the angle between $I$ and $E$. Each component produces an armature reaction flux, and so a reactance: $$ X_d = X_{ad} + X_l, \qquad X_q = X_{aq} + X_l $$ with $X_d > X_q$ because the d-axis has the lower reluctance (typically $X_q \approx 0.6\text{--}0.7X_d$). #### Phasor equation (generator) $$ \vec E = \vec V + \vec I R_a + j\vec I_d X_d + j\vec I_q X_q $$ ```text E /| jIdXd/ | V at angle delta from E / | / |jIqXq ---+----+-----> V Iq in phase with E Id 90 deg behind/ahead ``` #### Load angle and components From the phasor diagram (neglecting $R_a$), with $\delta$ the angle between $E$ and $V$: $$ I_q = \frac{V\sin\delta}{X_q}, \qquad I_d = \frac{E - V\cos\delta}{X_d} $$ These are used to find the power developed: $$ P = \frac{VE}{X_d}\sin\delta + \frac{V^2}{2}\left(\frac{1}{X_q}-\frac{1}{X_d}\right)\sin2\delta $$ The second term is the **reluctance power**; it exists even without excitation. For a cylindrical rotor, $X_d = X_q = X_s$, and the model reduces to the simple synchronous reactance model. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is the cylindrical-rotor model not used for salient pole machines? A. Air gap is non-uniform so the same mmf gives different flux along d and q axes B. Salient poles have no armature C. Frequency differs D. Voltage is DC Answer: A. Reluctance differs between pole axis and inter-polar axis. (Key point: Why two reactions) 2. How are Id and Iq defined? A. Id = I sin(psi) in quadrature with E; Iq = I cos(psi) in phase with E B. Id = I cos(psi); Iq = I sin(psi) C. Both in phase with E D. Both in quadrature Answer: A. psi is the angle between I and E. (Key point: Current components) 3. What is the relation between Xd and Xq? A. Xd < Xq B. Xd = Xq C. Xd > Xq because the d-axis has lower reluctance D. Both zero Answer: C. Typically Xq is about 0.6-0.7 Xd. (Key point: Reactances) 4. What is the reluctance power term? A. Term in sin(2 delta) that exists even without excitation B. Term in sin(delta) only C. Friction loss D. Copper loss Answer: A. (V^2/2)(1/Xq - 1/Xd) sin 2 delta arises from saliency. 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