Synchronous Machines for SSC JE Electrical: Alternator, EMF Equation, Voltage Regulation, Parallel Operation and Synchronous Motor

Synchronous machines (alternators and synchronous motors) generate most of the world’s electricity, and they are a regular topic in SSC JE Electrical. This guide on synchronous machines for SSC JE covers the construction, the speed and EMF formulas, the voltage regulation, the parallel operation of alternators and the synchronous motor, with solved examples, practice questions and FAQs.

Alternator (Synchronous Generator)

• An alternator converts mechanical energy into AC electrical energy; it works on Faraday’s law of electromagnetic induction.
• The field winding (rotor) carries a DC current through slip rings, and the armature winding (stator) is stationary and carries the load current; this reduces insulation problems at high voltages (up to 33 kV).
• Synchronous speed N_s = 120 f / P (rpm), where f is the frequency and P is the number of poles.
• Frequency f = P N / 120.
• For a 50 Hz supply: 2 poles → 3000 rpm; 4 poles → 1500 rpm; 6 poles → 1000 rpm; 8 poles → 750 rpm; 10 poles → 600 rpm.

Types of Rotors

EMF Equation

E_ph = 4.44 K_p K_d f φ T_ph (rms EMF per phase), where K_p is the pitch (coil span) factor, K_d is the distribution factor, φ is the flux per pole and T_ph is the number of turns per phase. For a full-pitch concentrated winding the EMF per phase is 4.44 f φ T_ph.

• Pitch factor K_p = cos(α/2), where α is the angle by which the coil is short pitched.
• Distribution factor K_d = sin(mγ/2) / (m sin(γ/2)), where m is the number of slots per pole per phase.
• Short pitching and distribution reduce the harmonics and improve the waveform but slightly reduce the EMF.
• Three-phase windings are star connected to avoid the third harmonics in the line voltage and to allow a neutral.

Armature Reaction in an Alternator

Voltage Regulation

• Voltage regulation = (E₀ − V) / V × 100%, where E₀ is the no-load EMF and V is the full-load terminal voltage.
• The regulation is positive for lagging and unity power factors, and may be negative for a leading power factor.
• Synchronous impedance Z_s = √(R_a² + X_s²); the EMF (synchronous impedance) method overestimates the regulation, so it is called the pessimistic method.
• Methods to find the regulation: EMF method (synchronous impedance), MMF method (optimistic) and Potier triangle method (zero power factor, the most accurate), and the ASA method.
• The short circuit ratio (SCR) is the field current for the rated open-circuit voltage divided by the field current for the rated short-circuit current; it is the reciprocal of the synchronous reactance in per unit.

Parallel Operation of Alternators

The conditions for connecting an alternator to the bus bars (synchronisation):

1. The terminal voltage of the incoming machine must equal the bus bar voltage.
2. The frequency must be the same.
3. The phase sequence must be the same.
4. The phase angle must be the same (the voltages must be in phase).

• Synchronisation is checked by the synchronous lamps (dark lamp or bright lamp method) or by a synchroscope.
• The share of the active power is adjusted by the governor of the prime mover; the reactive power share is adjusted by the excitation.
• Increasing the excitation of an alternator on infinite bus bars changes its reactive power, not the real power.
• Advantages of parallel operation: continuity of supply, better efficiency, maintenance without a shutdown and more flexibility for the load growth.

Synchronous Motor

• A synchronous motor runs at the constant synchronous speed N_s = 120f/P at all loads; if the load is excessive, it falls out of step and stops.
• It is not self-starting; the starting methods are: (1) damper (amortisseur) winding in the pole faces (it runs as an induction motor), (2) a small pony motor or an auxiliary induction motor, (3) a variable frequency supply.
• The field winding is excited by a DC source (excitation) once the motor reaches a speed close to the synchronous speed.
• The power factor can be controlled by changing the excitation: under-excited gives lagging pf and over-excited gives leading pf.
• V-curves show the armature current against the field current at constant load; the lowest point of each curve is at unity power factor; the inverted V-curves show the power factor against the field current.
• Hunting is the oscillation of the rotor about its mean position because of sudden load changes; it is reduced by damper windings.
• Torque angle (load angle) δ is the angle between the rotor and the stator field; the maximum power occurs at δ = 90° (for a cylindrical rotor).

Synchronous Condenser

A synchronous motor that is over-excited and runs without a mechanical load is called a synchronous condenser (synchronous capacitor). It acts as a capacitor and supplies the reactive power to improve the power factor and the voltage regulation of the transmission lines.

Comparison: Synchronous and Induction Motors

Solved Examples

Example 1. Find the synchronous speed of a 6-pole machine on a 50 Hz supply.
N_s = 120 × 50 / 6 = 1,000 rpm.

Example 2. At what speed should a 4-pole alternator run to give 50 Hz?
N = 120 × 50 / 4 = 1,500 rpm.

Example 3. An alternator has a no-load EMF of 250 V and a full-load terminal voltage of 230 V. Find the voltage regulation.
(250 − 230)/230 × 100 = 8.7%.

Example 4. Which machine is used as a synchronous condenser?
An over-excited synchronous motor running at no load.

Quick Tips

• Memorise N_s = 120f/P and the speeds for 50 Hz.
• Remember that a salient pole rotor is for hydro plants and a cylindrical rotor for thermal plants.
• Remember the four conditions of synchronisation.
• Remember that an over-excited synchronous motor draws a leading current.

Quick Revision Points

• N_s = 120f/P.
• E = 4.44 K_pK_d f φ T_ph.
• Voltage regulation = (E₀ − V)/V.
• A synchronous motor is not self-starting.
• A synchronous condenser improves the power factor.

Practice Questions With Answers

1. What is the synchronous speed of a 4-pole machine at 50 Hz?
   Answer: 1,500 rpm
2. Which rotor is used in hydro-electric alternators?
   Answer: Salient pole rotor
3. Which rotor is used in turbo-alternators?
   Answer: Cylindrical rotor
4. Is a synchronous motor self-starting?
   Answer: No
5. What is hunting?
   Answer: Oscillation of the rotor about its mean position
6. What is the name of the over-excited no-load synchronous motor?
   Answer: Synchronous condenser
7. What are the conditions for parallel operation?
   Answer: Same voltage, frequency, phase sequence and phase angle
8. Which instrument is used to check synchronism?
   Answer: Synchroscope
9. Which method of finding regulation is the most accurate?
   Answer: Potier triangle method
10. What is the winding in the pole faces that starts a synchronous motor called?
    Answer: Damper (amortisseur) winding

How to Practise This Chapter

Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Electrical Engineering notes page, read the previous topic DC Machines and the next topic Power Systems: Transmission and Distribution.

Frequently Asked Questions

What is an alternator?

A synchronous generator that converts mechanical energy into AC electrical energy.

What is synchronous speed?

The speed of the rotating magnetic field, N_s = 120f/P.

Why is the armature of an alternator stationary?

To avoid the sliding contacts for the high voltage and large currents.

What is a salient pole rotor?

A rotor with projecting poles, used in low-speed machines.

What is the pitch factor?

The ratio of the EMF of a short-pitch coil to that of a full-pitch coil.

What is voltage regulation of an alternator?

The rise in the terminal voltage when the full load is removed, as a percentage of the rated voltage.

How is a synchronous motor started?

By a damper winding or a pony motor, as it is not self-starting.

What is a V-curve?

A graph of the armature current against the field current of a synchronous motor.

What is a synchronous condenser?

An over-excited synchronous motor running without load to supply the reactive power.

Is this topic asked in SSC JE?

Yes. Synchronous machines are asked in SSC JE Electrical.

What is hunting in a synchronous machine?

The oscillation of the rotor about the synchronous speed.

What is a synchroscope?

An instrument that shows the phase and the frequency difference for the synchronisation.