AEE Electrical Engineering Core · Chapter 6

Synchronous Machines: Alternators and Synchronous Motors

What to remember

Speed and frequency are locked: f = P N / 120. The generated EMF per phase is E = 4.44 f Φ T Kp Kd (T = turns per phase), where Kp is the pitch factor and Kd is the distribution factor.
Alternator regulation depends on power factor: it is highest for lagging, small or negative for leading loads. Armature reaction is demagnetising for lagging loads, magnetising for leading loads and cross-magnetising for unity power factor.
A synchronous motor runs only at synchronous speed and has no starting torque. Overexcited, it takes leading current and works as a power-factor corrector (synchronous condenser).

1. Construction

Stator (armature): a laminated core with a three-phase winding. Rotor (field): carries DC-excited field poles. DC comes from slip rings and brushes (static excitation) or a brushless exciter with a rotating rectifier.

Feature	Cylindrical (round-rotor)	Salient-pole
Speed	High (1500 or 3000 rpm)	Low to medium (below about 1000 rpm)
Poles	2 or 4	Many
Rotor shape	Long and slim	Short, large diameter
Air gap	Uniform	Non-uniform
Prime mover	Steam or gas turbine (turbo-alternator)	Hydro turbine, diesel engine
Damper winding	Not common	Provided

A hydro alternator runs slowly and so needs many poles. For example, at 50 Hz and 100 rpm: P = 120 × 50/100 = 60 poles.

2. EMF equation and winding factors

Frequency f = P N/120, where N is in rpm.

EMF per phase E = 4.44 f Φ T Kw, where Kw = Kp × Kd.

Pitch factor (coil span factor): Kp = cos(α/2), where α is the angle by which the coil is short-pitched (electrical degrees). For a full-pitch coil Kp = 1. A coil spanning 5/6 of a pole pitch has α = 30° and Kp = cos 15° = 0.966.

Distribution factor: Kd = sin(mγ/2) / (m sin(γ/2)), where m = slots per pole per phase and γ = slot angle = 180°/(slots per pole) electrical degrees. For m = 3 and γ = 20°, Kd = 0.96.

Short pitching and distributing the winding reduce harmonics and make the EMF waveform nearly sinusoidal. They slightly reduce the fundamental EMF. Three-phase windings are star-connected to remove third-harmonic voltage from the line voltage.

3. Armature reaction and synchronous impedance

Armature reaction depends on the load power factor:

Unity pf: cross-magnetising; distorts the field.
Zero pf lagging: fully demagnetising; the terminal voltage falls.
Zero pf leading: fully magnetising; the terminal voltage rises.

Armature reaction is represented by a reactance Xa; adding the leakage reactance XL gives the synchronous reactance Xs = Xa + XL. The synchronous impedance Zs = Ra + jXs, and |Zs| = √(Ra² + Xs²). Ra is small, so Zs ≈ Xs.

Per-phase equation for a cylindrical-rotor alternator: E0 = V + I Zs (phasor sum).

Open-circuit characteristic (OCC): E0 against If at rated speed. Short-circuit characteristic (SCC): Isc against If; a straight line because the machine stays unsaturated during short circuit (armature reaction is demagnetising). Zs = (open-circuit voltage per phase)/(short-circuit current), both at the same field current.

Short-circuit ratio (SCR) = field current for rated open-circuit voltage / field current for rated short-circuit current = 1/Xs (per unit, unsaturated). A low SCR means a higher Xs, so the machine is cheaper but has poorer regulation and lower stability limit.

4. Voltage regulation

Regulation = (E0 − V)/V × 100 percent for an alternator.

Method	Principle	Result
Synchronous impedance (EMF) method	Uses Zs from OCC and SCC	Gives higher regulation than actual (pessimistic)
MMF (Ampere-turn) method	Adds MMFs	Gives lower regulation than actual (optimistic)
Zero power factor (Potier) method	Uses the ZPF characteristic to separate leakage reactance and armature reaction	Most accurate
ASA method	Combination for accuracy	Between the two

The EMF method is simple but ignores saturation, which is why it overestimates regulation.

5. Parallel operation (synchronising)

Conditions to connect an alternator to the bus-bars:

1. Equal terminal voltage (rms).
2. Same frequency.
3. Same phase sequence.
4. In phase (zero phase angle between the voltages).

Methods: three dark lamps (lamps connected straight across each pole of the switch; all dark means synchronism), two bright one dark lamp (to also show the sequence) and a synchroscope (pointer shows speed difference and direction).

After synchronising, the governor setting (prime-mover input) controls active power sharing. The excitation (field current) controls the reactive power sharing and terminal voltage. Increasing excitation of one machine makes it supply more lagging reactive current.

An alternator connected to an infinite bus has fixed voltage and frequency. Changing its excitation changes only the power factor, not the real power. Changing steam or water input changes the real power only.

6. Power-angle characteristic

For a cylindrical-rotor machine (Ra neglected), per-phase power P = (E V / Xs) sin δ, where δ is the load (power) angle between E and V. Maximum power at δ = 90° (steady-state stability limit). Operating below this keeps the machine stable.

For a salient-pole machine, with direct-axis reactance Xd and quadrature-axis reactance Xq (Xd > Xq):

P = (E V / Xd) sin δ + (V²/2)(1/Xq − 1/Xd) sin 2δ.

The second term is reluctance power; it exists even without excitation. Maximum power occurs at a δ less than 90°. (Two-reaction theory.)

7. Synchronous motor

A synchronous motor runs at constant synchronous speed Ns = 120 f/P for all loads. With rotor poles locked to the stator rotating field, the motor develops torque only at Ns. At standstill, the rotor poles are alternately attracted and repelled, so there is no starting torque.

Starting methods: (a) damper (amortisseur) winding on pole faces, which makes the motor start as a cage induction motor with the field winding short-circuited through a resistor (never left open, as a dangerously high voltage would be induced in it); (b) a small pony motor; (c) a variable-frequency supply from a converter. The DC field is applied near synchronous speed.

Effect of changing excitation (constant load, constant supply voltage):

Underexcited: lagging power factor, motor draws lagging current.
Normal excitation: unity power factor, minimum armature current.
Overexcited: leading power factor; the motor delivers reactive power to the supply.

V-curves: armature current against field current at constant load; the minimum of each V is at unity power factor. Higher load shifts the curve upward. Inverted V-curves: power factor against field current.

Synchronous condenser: an overexcited synchronous motor running without mechanical load, used at the receiving end of a long line to improve power factor and regulate voltage. Its power factor correction is smooth, but its cost is high.

Hunting: oscillation of the rotor about its mean synchronous position, due to sudden load changes. It is reduced by damper windings.

Back EMF and torque angle: In the motor, the equation is V = E + I Zs and E lags V. Pull-out torque occurs at δ = 90° for a cylindrical rotor. Torque = P/ωs.

Merits: constant speed, improves power factor, efficient at large sizes. Demerits: needs DC excitation, no self-starting, hunting. Uses: large compressors, pumps, rolling mills, synchronous condensers and constant-speed drives.

8. Efficiency and losses

Losses: copper (armature and field), iron (hysteresis and eddy), friction and windage, stray load. Cooling for large machines is by hydrogen or water, as hydrogen has low density and reduces windage and gives better heat removal. Efficiency = output/(output + losses). Ratings of alternators are in kVA or MVA.

Worked example (power angle): A round-rotor machine has E = 1.2 pu, V = 1 pu, Xs = 0.6 pu. Pmax = 1.2 × 1/0.6 = 2 pu at δ = 90°. At δ = 30°, P = 2 × 0.5 = 1 pu. At a rated load of 1 pu, the machine therefore has a safe margin to the stability limit.

Worked example (synchronous impedance): At a field current of 2 A, the open-circuit EMF is 1000 V per phase and the short-circuit current is 100 A. Zs = 1000/100 = 10 Ω. If Ra = 1 Ω, then Xs = √(100 − 1) = 9.95 Ω, nearly equal to Zs because Ra is small.

Exam traps

1. Alternator regulation is (E0 − V)/V; transformer regulation is (V0 − V)/V0. Do not mix them.
2. Lagging load: demagnetising armature reaction; leading load: magnetising.
3. EMF method overestimates regulation; MMF method underestimates. Potier is most accurate.
4. Speed of a synchronous motor never changes with load; only the torque angle changes.
5. Overexcited synchronous motor takes leading current; overexcited alternator supplies lagging current.
6. Real power is controlled by the prime mover; reactive power by the excitation.
7. The SCC is a straight line, while the OCC is not.
8. Reluctance power exists only in salient-pole machines (Xd ≠ Xq).

One-liners

1. f = P N/120.
2. Turbo-alternators are cylindrical rotors; hydro-alternators are salient-pole.
3. Three-phase windings are connected in star.
4. Zs = open-circuit voltage / short-circuit current at the same field current.
5. SCR = 1/Xs (per unit).
6. Damper windings help starting and reduce hunting.
7. Synchronous condenser = overexcited, no-load synchronous motor.
8. Pull-out torque at δ = 90° for a round rotor.
9. Hydrogen cooling reduces windage loss.
10. Maximum power of a salient-pole machine occurs below 90°.
11. Parallel operation needs equal voltage, frequency, phase sequence and phase.
12. V-curve minimum point corresponds to unity power factor.

Practice questions

The frequency of the EMF of a 4-pole alternator running at 1500 rpm is
1. 25 Hz
2. 100 Hz
3. 50 Hz
4. 60 Hz
Answer
C. 50 Hz
f = PN/120 = 4×1500/120 = 50 Hz.
The speed of a 10-pole alternator generating 50 Hz is
1. 1000 rpm
2. 300 rpm
3. 500 rpm
4. 600 rpm
Answer
D. 600 rpm
N = 120f/P = 6000/10 = 600 rpm.
A hydro alternator runs at 100 rpm and generates 50 Hz. The number of poles is
1. 60
2. 120
3. 30
4. 50
Answer
A. 60
P = 120×50/100 = 60.
A 2-pole alternator must run at what speed to give 50 Hz?
1. 3000 rpm
2. 1000 rpm
3. 1500 rpm
4. 6000 rpm
Answer
A. 3000 rpm
N = 120×50/2 = 3000 rpm.
Turbo-alternators are built with
1. slip-ring induction rotors
2. permanent magnets
3. salient-pole rotors with many poles
4. cylindrical (non-salient) rotors
Answer
D. cylindrical (non-salient) rotors
High speed needs a slim round rotor for mechanical strength.
Hydro-alternators have salient-pole rotors because they
1. run at very high speed
2. run at low speed and need many poles
3. have no field winding
4. need a uniform air gap
Answer
B. run at low speed and need many poles
Low speed demands many poles; large diameter and short length.
The EMF per phase of an alternator with f = 50 Hz, Φ = 0.1 Wb, T = 100 turns and Kw = 1 is
1. 222 V
2. 1110 V
3. 2220 V
4. 4440 V
Answer
C. 2220 V
E = 4.44×50×0.1×100 = 2220 V.
The pitch factor of a full-pitch coil is
1. 0.5
2. 1
3. 0.966
4. 0.866
Answer
B. 1
Kp = cos(α/2) with α = 0.
A coil short-pitched by 30 electrical degrees has a pitch factor of about
1. 0.966
2. 0.5
3. 0.866
4. 0.707
Answer
A. 0.966
Kp = cos(30°/2) = cos 15° = 0.966.
A winding has 3 slots per pole per phase and a slot angle of 20°. The distribution factor is about
1. 1.0
2. 0.5
3. 0.96
4. 0.87
Answer
C. 0.96
Kd = sin(30°)/(3 sin 10°) = 0.5/0.521 = 0.96.
A 36-slot, 4-pole, three-phase stator has slots per pole per phase equal to
1. 3
2. 9
3. 12
4. 6
Answer
A. 3
36/(4×3) = 3.
Short pitching a winding is done mainly to
1. increase the fundamental EMF greatly
2. increase the rotor speed
3. reduce harmonics in the induced EMF
4. reduce stator size only
Answer
C. reduce harmonics in the induced EMF
It cancels certain harmonics and shortens end connections.
Armature reaction in an alternator at zero lagging power factor is
1. purely cross-magnetising
2. fully magnetising
3. zero
4. fully demagnetising
Answer
D. fully demagnetising
Lagging current produces armature flux opposing the field.
Armature reaction at unity power factor in an alternator is
1. demagnetising
2. cross-magnetising
3. magnetising
4. absent
Answer
B. cross-magnetising
Armature mmf is at 90° to the field axis.
An alternator supplying a leading load has an armature reaction effect which is
1. demagnetising, raising voltage
2. demagnetising, lowering voltage
3. cross-magnetising only
4. magnetising, raising the terminal voltage
Answer
D. magnetising, raising the terminal voltage
Leading current strengthens the main field.
The synchronous impedance of an alternator is found from
1. a no-load test on the stator only
2. the open-circuit and short-circuit characteristics
3. insulation resistance test
4. the load test at unity pf only
Answer
B. the open-circuit and short-circuit characteristics
Zs = OC voltage/SC current at the same field current.
An alternator gives 1000 V per phase on open circuit and 100 A on short circuit at the same field current. Its synchronous impedance is
1. 10 Ω
2. 0.1 Ω
3. 1 Ω
4. 100 Ω
Answer
A. 10 Ω
Zs = 1000/100 = 10 Ω.
An alternator has Zs = 5 Ω and Ra = 3 Ω per phase. Its synchronous reactance is
1. 8 Ω
2. 34 Ω
3. 4 Ω
4. 2 Ω
Answer
C. 4 Ω
Xs = √(5² − 3²) = 4 Ω.
The no-load voltage of an alternator is 11 kV and the full-load terminal voltage is 10 kV. The regulation is
1. 1%
2. 11%
3. 9.1%
4. 10%
Answer
D. 10%
(E0 − V)/V = 1/10 = 10%.
The short-circuit characteristic of an alternator is a straight line because
1. the field current is constant
2. the machine stays unsaturated, as armature reaction is strongly demagnetising
3. the speed varies linearly
4. the load is unity power factor
Answer
B. the machine stays unsaturated, as armature reaction is strongly demagnetising
Net flux is small, so the iron does not saturate.
A machine has Xs = 0.8 per unit (unsaturated). Its short-circuit ratio is
1. 0.8
2. 1.6
3. 0.64
4. 1.25
Answer
D. 1.25
SCR = 1/Xs = 1.25.
Which method of finding regulation is the most accurate?
1. Zero power factor (Potier) method
2. Direct impedance method without OCC
3. Synchronous impedance method
4. MMF method used alone
Answer
A. Zero power factor (Potier) method
It separates leakage reactance and armature reaction.
Statements about regulation methods: 1. The EMF method gives a regulation higher than the actual value. 2. The MMF method gives a regulation higher than the actual value.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
The EMF method is pessimistic; the MMF method is optimistic (lower).
Which is NOT a condition for synchronising an alternator to the bus-bars?
1. Same frequency
2. Equal voltage
3. Equal kVA rating
4. Same phase sequence
Answer
C. Equal kVA rating
Ratings may differ.
In the three-dark-lamp method of synchronising, lamps going dark together at the same instant indicates
1. wrong phase sequence
2. the voltages are in phase and the phase sequence is correct
3. voltage mismatch only
4. machine overload
Answer
B. the voltages are in phase and the phase sequence is correct
Each lamp sees zero voltage difference, so all go dark.
After an alternator is synchronised to an infinite bus, its real power output is changed by changing
1. the bus voltage
2. the number of poles
3. the field excitation
4. the prime-mover input
Answer
D. the prime-mover input
Excitation changes only the power factor and reactive power.
Increasing excitation of an alternator connected to an infinite bus (prime-mover input constant) changes
1. its power factor and reactive power only
2. its real power only
3. its frequency
4. its speed
Answer
A. its power factor and reactive power only
Real power depends on the torque from the prime mover.
For a cylindrical-rotor alternator, per-phase power is P = EV sinδ / Xs. With E = V = 1 pu, Xs = 1 pu, and δ = 30°, power is
1. 0.866 pu
2. 1 pu
3. 0.5 pu
4. 0.25 pu
Answer
C. 0.5 pu
sin 30° = 0.5.
With E = 1.2 pu, V = 1 pu and Xs = 0.6 pu, the maximum power transferable (cylindrical rotor) is
1. 0.72 pu
2. 1 pu
3. 1.2 pu
4. 2 pu
Answer
D. 2 pu
Pmax = EV/Xs = 1.2/0.6 = 2 pu at δ = 90°.
In a salient-pole machine, reluctance power arises because
1. the air gap is uniform
2. Xd differs from Xq
3. the rotor has no excitation
4. the speed is low
Answer
B. Xd differs from Xq
The second term of the power equation depends on (1/Xq − 1/Xd).
In a salient-pole machine,
1. Xd equals Xq
2. Xq is greater than Xd
3. Xd is greater than Xq
4. Xd is zero
Answer
C. Xd is greater than Xq
The direct-axis air gap is shorter, so its reluctance is lower, but its reactance is higher.
A synchronous motor has
1. slip proportional to load
2. high starting torque
3. no starting torque
4. variable speed with load
Answer
C. no starting torque
The rotor cannot lock to a rapidly rotating field from rest.
The speed of a 4-pole synchronous motor on a 25 Hz supply is
1. 1500 rpm
2. 750 rpm
3. 1000 rpm
4. 375 rpm
Answer
B. 750 rpm
Ns = 120×25/4 = 750 rpm.
A synchronous motor is started as an induction motor using
1. a commutator
2. the field winding with DC at standstill
3. a permanent magnet only
4. its damper (amortisseur) winding
Answer
D. its damper (amortisseur) winding
The cage-like damper winding gives starting torque.
An overexcited synchronous motor operates at
1. leading power factor
2. unity power factor always
3. lagging power factor
4. zero power factor lagging
Answer
A. leading power factor
It delivers reactive power to the system.
A synchronous condenser is
1. an overexcited synchronous motor running on no load
2. an underexcited alternator
3. a capacitor bank
4. a transformer tap changer
Answer
A. an overexcited synchronous motor running on no load
It supplies lagging reactive power to improve power factor.
Statements about synchronous motors: 1. An overexcited motor takes a leading current. 2. The speed varies with load.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
Speed is constant at Ns.
In a V-curve of a synchronous motor, the minimum armature current corresponds to
1. zero power factor leading
2. unity power factor
3. maximum torque angle
4. zero power factor lagging
Answer
B. unity power factor
Current is least when it is entirely in phase with voltage.
Hunting in a synchronous motor is reduced by
1. reducing supply voltage
2. removing the shaft load
3. a higher field current
4. damper windings
Answer
D. damper windings
Dampers oppose oscillation with induced currents.
For a cylindrical-rotor synchronous motor the pull-out torque occurs at a torque angle of
1. 45°
2. 30°
3. 90°
4. 180°
Answer
C. 90°
Power ∝ sin δ is maximum at 90°.
Hydrogen cooling in large turbo-alternators is used because hydrogen
1. is a good insulator of electricity
2. has low density, reducing windage loss, and good heat transfer
3. is cheaper than air
4. burns inside the machine
Answer
B. has low density, reducing windage loss, and good heat transfer
Low density cuts friction and windage; it cools well.
Alternators are rated in
1. kW only
2. hp only
3. kVAR only
4. kVA or MVA
Answer
D. kVA or MVA
Losses depend on current and voltage, not on power factor.
Match item with feature: (a) Damper winding (b) Synchronous condenser (c) Potier method 1. Power factor correction 2. Reducing hunting 3. Regulation by ZPF
1. a-3, b-1, c-2
2. a-1, b-2, c-3
3. a-2, b-1, c-3
4. a-2, b-3, c-1
Answer
C. a-2, b-1, c-3
Dampers reduce hunting; condenser corrects pf; Potier uses ZPF.
The terminal voltage of an alternator falls with increased load at lagging power factor mainly because of
1. a fall in speed of rotor only
2. reduced field resistance
3. armature reaction and synchronous impedance drop
4. increase in iron loss only
Answer
C. armature reaction and synchronous impedance drop
Demagnetising reaction and Zs drop reduce V for a given E0.
Three-phase alternator windings are usually star-connected because
1. star needs no insulation
2. star has higher resistance
3. delta cannot carry current
4. third-harmonic voltages do not appear in the line voltage
Answer
D. third-harmonic voltages do not appear in the line voltage
Triplen harmonics cancel in line-to-line voltage.

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1.The work done by the motor per unit time is called ________.
2.Practically, the work output of a machine is _______ the work input due to the effect of friction.
3.PSLV-C37 successfully carried and deployed a record _____ satellite in sun-synchronous orbits. (RRB NTPC CBT-I (01/04/2021) Shift 2)
4.Kidney failure is treated periodically on a kidney machine. The process is known as ________.
5.Why does a mechanic apply grease between the moving parts of a bicycle or a motor?
6.Which of the following devices does NOT use an electric motor? Electric fan, Electric mixer, Galvanometer, Computer
7.Which of the following rules is used to determine the direction of the force on a currentcarrying conductor in an electric motor?
8.Which of the following quantities determine the rate of work performed by a machine?
9.Which of the following statements are true regarding general safety in the workshop? Statement 1: Use any available tool for the job, even if it is not the correct one. Statement 2: Keep the tools in their proper place after use. Statement 3: Clean the machine while it is still running. Statement 4: Replace worn-out or damaged tools immediately.
10.What placed between moving parts of a machine can reduce friction?

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