---
title: "Emf and regulation of 1500 kVA 13 kV alternator"
subject: "Electric Machines II"
chapter: 1
key: "semester_5/electric_machines_ii:emf-regulation-1500kva-13kv"
source: https://www.bctengineer.com/q/semester_5/electric_machines_ii/emf-regulation-1500kva-13kv
site: BCT Engineering
---

# Emf and regulation of 1500 kVA 13 kV alternator

Electric Machines II · Chapter 1: Three Phase Synchronous Generator

- Asked in: 2076 Asoj, 8 marks
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/electric_machines_ii/emf-regulation-1500kva-13kv
- Whole chapter: https://www.bctengineer.com/md/semester_5/electric_machines_ii/chapter-1

## Question

A three phase, star connected 1500 kVA, 13 kV alternator has armature resistance of 0.9 ohm per phase and synchronous reactance of 8 ohm per phase. In each of the following cases the alternator is supplying rated full load current at rated terminal voltage. Calculate emf generated and voltage regulation in each following cases: i) unity P.F. ii) 0.8 P.F. lagging

## Short answer

Rated Vph=7505.6 V, I=66.62 A. Unity pf: E=√((V+IRa)²+(IXs)²) = 7584.3 V/phase, regulation 1.05%. 0.8 pf lagging: E=√((Vcosφ+IRa)²+(Vsinφ+IXs)²) = 7883.0 V/phase, regulation 5.03%.

## Answer

**Given:** star, 1500 kVA, 13 kV, $R_a = 0.9\ \Omega$, $X_s = 8\ \Omega$ per phase; rated current at rated voltage.
$$
\begin{aligned}
V_{ph} &= \frac{13000}{\sqrt3} = 7505.55\ \text{V} \\
I &= \frac{1500\times10^3}{\sqrt3\times13000} = 66.62\ \text{A} \\
IR_a &= 66.62\times0.9 = 59.96\ \text{V},\quad IX_s = 66.62\times8 = 532.94\ \text{V}
\end{aligned}
$$

#### (i) Unity power factor
$$
\begin{aligned}
E &= \sqrt{(V + IR_a)^2 + (IX_s)^2} = \sqrt{7565.51^2 + 532.94^2} \\
&= 7584.26\ \text{V per phase}\quad (E_L = 13136\ \text{V}) \\
\%\text{Reg} &= \frac{7584.26 - 7505.55}{7505.55}\times100 = 1.05\%
\end{aligned}
$$

#### (ii) 0.8 pf lagging
$$
\begin{aligned}
V\cos\phi + IR_a &= 6004.44 + 59.96 = 6064.40\ \text{V} \\
V\sin\phi + IX_s &= 4503.33 + 532.94 = 5036.27\ \text{V} \\
E &= \sqrt{6064.40^2 + 5036.27^2} = 7882.95\ \text{V per phase}\quad (E_L = 13654\ \text{V}) \\
\%\text{Reg} &= \frac{7882.95 - 7505.55}{7505.55}\times100 = 5.03\%
\end{aligned}
$$

| Case | E per phase (V) | E line (V) | Regulation |
|---|---|---|---|
| Unity pf | 7584.26 | 13136 | 1.05% |
| 0.8 pf lagging | 7882.95 | 13654 | 5.03% |

**Answer: unity pf: E = 7584.3 V/phase, regulation 1.05%; 0.8 lag: E = 7883.0 V/phase, regulation 5.03%.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Rated current of 1500 kVA, 13 kV is
   A. 115.4 A
   B. 66.62 A
   C. 200 A
   D. 38.5 A
   Answer: B. I = 1500e3/(sqrt3 x 13000). (Key point: Current)

2. At unity pf, E is
   A. V + IRa + IXs
   B. V - IXs
   C. sqrt((V+IRa)^2 + (IXs)^2) = 7584 V
   D. V
   Answer: C. Reactive drop is perpendicular to V. (Key point: Unity pf)

3. At 0.8 lagging the regulation is
   A. 1.05 %
   B. -5.03 %
   C. 22 %
   D. 5.03 %
   Answer: D. E = 7883 V vs 7505.6 V. (Key point: Lagging)

## Related in Electric Machines II

- [Emf and regulation of 1500 kVA alternator](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Aregulation-1500kva-12000v) — Electric Machines II, chapter 1, asked 2×
- [Regulation of delta connected 1600 kVA alternator](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Aregulation-delta-1600kva) — Electric Machines II, chapter 1
- [Emf, regulation and loading with given load impedance](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Aemf-regulation-load-impedance) — Electric Machines II, chapter 1
- [Synchronous reactance and regulation from test data](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Aregulation-1500kva-2300v-test) — Electric Machines II, chapter 1
- [Internal emf, no-load emf and regulation](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Ainternal-noload-emf-50kva) — Electric Machines II, chapter 1
- [Internal emf and armature reaction reactance](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Ainternal-emf-armature-reactance) — Electric Machines II, chapter 1

## Related in other subjects

- [1600 kVA alternator: emf, regulation, power angle](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Aalt-1600kva-regulation-power-angle) — Electrical Machines, chapter 6
- [1500 kVA alternator: excitation emf, voltage at leading pf](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Aalt-1500kva-6600v-excitation-emf) — Electrical Machines, chapter 6
- [Star alternator supplying delta load (8+j6)](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Astar-alternator-delta-load-8j6) — Basic Electrical Engineering, chapter 8
- [5 MVA alternator: regulation and pf for zero regulation](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Aalt-5mva-11kv-regulation-zero) — Electrical Machines, chapter 6