--- title: "Potier method of voltage regulation" subject: "Electric Machines II" chapter: 1 key: "semester_5/electric_machines_ii:potier-method-regulation" source: https://www.bctengineer.com/q/semester_5/electric_machines_ii/potier-method-regulation site: BCT Engineering --- # Potier method of voltage regulation Electric Machines II · Chapter 1: Three Phase Synchronous Generator - Asked in: 2082 Bhadra (new course), 4 marks - Video: [SM25 ZPF or Potier Method](https://www.youtube.com/watch?v=CxozfJuCcnk) — 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/potier-method-regulation - Whole chapter: https://www.bctengineer.com/md/semester_5/electric_machines_ii/chapter-1 ## Question With the help of relevant curves and diagram, explain the Potier method for determining the voltage regulation of a synchronous generator. ## Short answer The Potier (ZPF) method uses OCC, ZPFC and Ra. A Potier triangle is constructed from ZPFC at full-load to separate leakage reactance drop (XL = RS/I) and armature reaction mmf (SP). Regulation is found by phasor addition of V and I(Ra+jXL) to get Eg, then adding field current for Eg and armature-reaction mmf, obtaining E0 from OCC, and computing (E0-V)/V×100%. ## Answer The **Potier (zero power factor, ZPF) method** finds regulation by separating the **leakage reactance drop** and the **armature reaction mmf**, and it allows for saturation. It is more accurate than the EMF and MMF methods. #### Tests and curves needed 1. **Open-circuit characteristic (OCC)**: $E$ vs field current $I_f$. 2. **Zero power factor characteristic (ZPFC)**: terminal voltage vs $I_f$ with full-load current at zero pf lagging (purely inductive load). Two points are enough: the short-circuit point A (V = 0) and one point P at rated voltage. 3. Armature resistance $R_a$. #### Potier triangle ```text V OCC | __.--'' | .-' | .' R | .' /| ZPFC | .' / | __.-' | .' / | _.-' | / Q----S-----P (rated V, | / rated I) +----A---------------------> If O (short-circuit point) QP = OA, QR parallel to air-gap line ``` - From P draw PQ horizontally to the left, equal to OA. - From Q draw a line parallel to the air-gap (linear) part of the OCC, meeting the OCC at R. - Drop a perpendicular RS onto PQ. Triangle **PRS** is the **Potier triangle**: - $RS$ = leakage reactance drop $IX_L$, so $X_L = RS/I$ (Potier reactance); - $SP$ = field current equivalent to **armature reaction** mmf ($F_a$). #### Finding regulation (phasor steps) 1. Take $V$ as reference, current $I$ at the given pf. 2. Air-gap emf: $\bar E_g = \bar V + \bar I(R_a + jX_L)$. 3. From the OCC read the field current $F_g$ needed for $E_g$; it leads $E_g$ by 90°. 4. Add the armature-reaction field current $F_a$ (from the triangle), drawn opposite to $I$ (to cancel the armature mmf), to $F_g$: the resultant field current is $\bar F_r = \bar F_g + \bar F_a$, i.e. $$ F_r = \sqrt{F_g^2 + F_a^2 + 2F_gF_a\cos(90^\circ - \theta)} $$ where $\theta$ is the angle between $E_g$ and $I$ (lagging pf). 5. From the OCC read $E_0$ for $F_r$. Then $$ \%\text{Reg} = \frac{E_0 - V}{V}\times100 $$ ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What does the Potier method separate, and why is it more accurate? A. Iron and copper loss; it ignores saturation B. Leakage reactance drop and armature reaction mmf; it allows for saturation C. Friction and windage; it uses the OCC only D. Eddy and hysteresis loss; it uses SCC only Answer: B. Using the OCC and zero power factor characteristic, it finds XL and the armature reaction field current while accounting for saturation. (Key point: Purpose of Potier method) 2. Which tests are needed? A. Only the short-circuit test B. OCC, ZPF characteristic and armature resistance C. Load test and no-load loss test D. Blocked rotor test only Answer: B. The OCC, ZPFC (short-circuit point and one rated-voltage point) and Ra are used. (Key point: Tests required) 3. In the Potier triangle PRS, what does RS represent? A. Armature reaction mmf B. Leakage reactance drop I XL C. Armature resistance drop D. No-load emf Answer: B. RS equals the leakage reactance drop I XL, while SP gives the field current equivalent to armature reaction. (Key point: Potier triangle) 4. How is the resultant field current found? A. Fr = Fg - Fa B. Fr = Fg + Fa as phasors, Fa drawn opposite to I C. Fr = Fa only D. Fr = Fg x Fa Answer: B. Fg (leading Eg by 90 degrees) is added phasorially to Fa; E0 is read from the OCC at Fr. 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