Almost every unit of electricity in Bangladesh — from gas, coal, oil and hydro (Kaptai) power plants — is produced by a synchronous generator (alternator). Questions on its construction, speed formula, EMF equation, armature reaction and synchronisation are among the most common in PGCB, BPDB, NWPGCL, EGCB, APSCL, RPCL, BCS (EEE) written exams and power-plant vivas. This post explains the alternator with an animation, worked problems and MCQs.
- A DC-excited rotor (field) is turned by a prime mover; its rotating flux induces three-phase EMFs in the stationary armature (stator) windings.
- It always runs at synchronous speed Ns = 120f/P — 3000 rpm for a 2-pole, 50 Hz machine.
- EMF per phase: E = 4.44 f Φ T Kp Kd.
- Rotor types: salient-pole (low-speed hydro) and cylindrical / non-salient (high-speed steam/gas turbines).
- Synchronising conditions: equal voltage, equal frequency, same phase sequence, phase angle matched.
- On an infinite bus: prime-mover input controls active power; excitation controls reactive power.
- Construction
- Working principle (animation)
- Synchronous speed and frequency
- EMF equation, pitch and distribution factors
- Armature reaction
- Synchronous impedance and voltage regulation
- Parallel operation and synchronisation
- Power–angle relation and control
- Solved problems
- Practice MCQs
- বাংলায় দ্রুত রিভিশন
1. Construction
Stator (armature): laminated silicon-steel core with slots carrying a three-phase, star-connected distributed winding. Rotor (field): carries a DC field winding supplied through slip rings or a brushless exciter.
| Feature | Salient-pole rotor | Cylindrical (non-salient) rotor |
|---|---|---|
| Shape | Projecting poles, large diameter, short length | Smooth cylinder, small diameter, long length |
| Poles | Many (e.g. 12–60+) | 2 or 4 |
| Speed | Low (e.g. 100–600 rpm) | High (3000 / 1500 rpm at 50 Hz) |
| Prime mover | Hydraulic turbines, diesel engines | Steam and gas turbines (turbo-alternators) |
| Air gap | Non-uniform | Uniform |
| Damper winding | Usually provided on pole faces | Rotor body acts as damper |
Excitation systems: DC exciter (older), brushless exciter (AC exciter + rotating diodes), and static excitation (thyristor rectifier fed from generator terminals). The AVR controls field current to hold terminal voltage.
2. Working Principle (Animation)
The field winding, excited by DC, makes the rotor an electromagnet with N and S poles. When the prime mover rotates it, the rotor flux sweeps past the three stator coils A, B and C, which are displaced 120° in space. By Faraday’s law, each coil gets a sinusoidal EMF; because the rotor reaches each coil one-third of a revolution later than the previous one, the three EMFs are 120° apart in time — a balanced three-phase supply.
3. Synchronous Speed and Frequency
f = P Ns / 120 ⇒ Ns = 120 f / P| Poles | 2 | 4 | 6 | 12 | 40 |
|---|---|---|---|---|---|
| Ns at 50 Hz (rpm) | 3000 | 1500 | 1000 | 500 | 150 |
Grid frequency is held at 50 Hz by turbine governors; if the total generation is less than load, all machines slow and frequency falls.
4. EMF Equation, Pitch and Distribution Factors
Eph = 4.44 f Φ Tph Kp Kd volts (RMS per phase)- Φ = flux per pole (Wb), Tph = turns in series per phase.
- Pitch (coil-span) factor Kp = cos(α/2), where α = angle by which the coil span is short of a full pole pitch. Short-pitched coils reduce harmonics and save copper.
- Distribution (breadth) factor Kd = sin(mβ/2) / [m sin(β/2)], where m = slots per pole per phase and β = slot angle (electrical). Distributing the winding gives a more sinusoidal waveform.
- Line voltage of a star-connected alternator = √3 Eph.
5. Armature Reaction
When the alternator supplies load, armature current produces its own flux that affects the main field. The effect depends on load power factor:
| Load power factor | Effect of armature flux | Result |
|---|---|---|
| Unity | Cross-magnetising (distorts field) | Small voltage drop |
| Zero lagging (inductive) | Demagnetising (opposes main flux) | Terminal voltage falls — needs more excitation |
| Zero leading (capacitive) | Magnetising (aids main flux) | Terminal voltage rises |
6. Synchronous Impedance and Voltage Regulation
Armature reaction is represented by a fictitious reactance Xa; together with leakage reactance Xl it forms the synchronous reactance Xs = Xl + Xa, and Zs = Ra + jXs. Per phase: E = V + I Zs.
% Regulation = (E0 − V) / V × 100Regulation is positive for lagging and unity pf, and may be negative for leading pf. It is found by the synchronous impedance (EMF) method, MMF method, Potier (ZPF) method, or ASA method using open-circuit and short-circuit tests.
7. Parallel Operation and Synchronisation
Generators are connected in parallel to the grid (or to each other) for reliability, economy and to meet changing demand. Before closing the breaker, the incoming machine must match the bus:
- Equal terminal voltage (adjust excitation),
- Equal frequency (adjust prime-mover speed),
- Same phase sequence (checked once, e.g. with a phase-sequence indicator),
- Phase angle in coincidence (zero phase difference at the instant of closing).
Methods: dark-lamp or bright-lamp (three-lamp) method, synchroscope, or automatic synchronisers. Closing out of phase produces heavy current surges and mechanical shocks.
8. Power–Angle Relation and Control
P = (E V / Xs) sin δ (per phase, Ra neglected)- δ = load (power) angle between E and V. Maximum (steady-state stability limit) power occurs at δ = 90°.
- On an infinite bus (constant V and f): increasing steam/water input increases δ and active power P; changing excitation changes E and therefore reactive power Q (over-excited → supplies lagging VARs; under-excited → absorbs VARs).
- If the machine is pushed beyond δ = 90°, it loses synchronism (pole slipping) and must be tripped.
9. Solved Problems
Problem 1. Find the number of poles of a 50 Hz hydro generator running at 375 rpm. P = 120f/Ns = 6000/375 = 16 poles.
Problem 2. A 3-phase, 50 Hz, star-connected alternator has Φ = 0.03 Wb, 200 turns per phase, Kp = 0.96 and Kd = 0.96. Find phase and line EMF.
- Eph = 4.44 × 50 × 0.03 × 200 × 0.96 × 0.96 ≈ 1228 V
- EL = √3 × 1228 ≈ 2127 V
Problem 3. A generator with E = 1.2 pu, connected to an infinite bus V = 1.0 pu through Xs = 1.0 pu, operates at δ = 30°. Find P and the maximum power.
P = (1.2 × 1.0/1.0) sin 30° = 0.6 pu; Pmax = 1.2 pu at δ = 90°.
10. Practice MCQs (click to see answer)
1. Synchronous speed of a 4-pole, 50 Hz alternator is: (a) 3000 rpm (b) 1500 rpm (c) 1000 rpm (d) 750 rpm
2. Hydro-electric generators usually have: (a) Cylindrical rotors with 2 poles (b) Salient-pole rotors with many poles (c) No field winding (d) Squirrel-cage rotors
3. In large alternators the armature is placed on the stator because: (a) It is cheaper to make the rotor heavy (b) High-voltage winding is easier to insulate and cool when stationary (c) It increases frequency (d) It eliminates the field
4. Armature reaction at zero lagging power factor is: (a) Cross-magnetising (b) Demagnetising (c) Magnetising (d) Zero
5. Which is NOT a condition for synchronising an alternator? (a) Equal voltage (b) Equal frequency (c) Same phase sequence (d) Equal kVA rating
6. Reactive power output of an alternator on an infinite bus is controlled by: (a) Prime-mover input (b) Field excitation (c) Frequency (d) Number of poles
7. The pitch factor for a coil short-pitched by 30° electrical is: (a) 0.866 (b) 0.966 (c) 0.5 (d) 1
8. Steady-state stability limit occurs at load angle: (a) 0° (b) 45° (c) 90° (d) 180°
9. Voltage regulation of an alternator can be negative for: (a) Lagging pf (b) Unity pf (c) Leading pf (d) Never
10. The instrument used to show the phase difference between an incoming alternator and the bus is a: (a) Wattmeter (b) Synchroscope (c) Megger (d) Frequency meter
11. বাংলায় দ্রুত রিভিশন
- সিনক্রোনাস জেনারেটর (অল্টারনেটর): DC-উত্তেজিত রোটর ঘুরে স্টেটরের তিনটি কয়েলে ১২০° পার্থক্যে তিন-ফেজ EMF তৈরি করে।
- গতি Ns = 120f/P (২-পোল ৫০ Hz → ৩০০০ rpm)। EMF/ফেজ = 4.44 f Φ T Kp Kd।
- স্যালিয়েন্ট-পোল রোটর: কম গতি, অনেক পোল (হাইড্রো); সিলিন্ড্রিক্যাল রোটর: উচ্চ গতি, ২/৪ পোল (স্টিম/গ্যাস টারবাইন)।
- আর্মেচার রিঅ্যাকশন: ল্যাগিং pf-এ ডিম্যাগনেটাইজিং, লিডিং pf-এ ম্যাগনেটাইজিং, ইউনিটি pf-এ ক্রস-ম্যাগনেটাইজিং।
- সিনক্রোনাইজেশনের শর্ত: সমান ভোল্টেজ, সমান কম্পাঙ্ক, একই ফেজ সিকোয়েন্স, ফেজ কোণ মিল।
- ইনফিনিট বাসে: টারবাইনের ইনপুট সক্রিয় শক্তি (P) এবং এক্সাইটেশন প্রতিক্রিয়াশীল শক্তি (Q) নিয়ন্ত্রণ করে। P = (EV/Xs) sin δ।
Related Posts
- 220 Most Repeated Power Sector MCQs
- Rooftop Solar in Bangladesh: Net Metering Rules
- EEE Job Viva Voce Preparation
- BREB/PBS Job Exam Preparation Guide
References: B. L. Theraja, Electrical Technology Vol. II; M. G. Say, Alternating Current Machines; P. Kundur, Power System Stability and Control. Images and animations: original work by Totalecer.
Thank you for visiting my blog.