Synchronous machines

In short

A synchronous machine is an AC machine whose rotor runs in exact step with the rotating field of the stator, at the synchronous speed Ns = 120f/P. As a generator (alternator) it produces most of India's electricity - every thermal, hydro and nuclear set at NTPC, NHPC, NPCIL, Tata Power and the captive stations is a synchronous generator; as a motor it drives large constant-speed compressors and mills and corrects power factor as a synchronous condenser. It is the heaviest-weighted topic in electrical machines for GATE, ESE, state PSU and PSU recruitment (NTPC, PGCIL, BHEL, SAIL, DVC, state electricity boards), and the base for all power-system stability study. Examination focuses on voltage regulation methods, the power-angle relation, parallel operation and the salient-pole two-reaction theory.

Explained

Construction, types and ratings

• Stator (armature): three-phase double-layer winding in slots of a laminated CRGO/silicon-steel core; it carries the load current and is where the EMF is induced. Stationary armature allows high-voltage insulation (11 kV, 15.75 kV, 21 kV), heavy current take-off through fixed terminals, and only low-voltage DC on the moving part.
• Rotor (field): carries DC field winding fed through slip rings and brushes, or through a brushless rotating rectifier. Two forms:
  • Cylindrical (non-salient, turbo) rotor: small diameter, long axial length, 2 or 4 poles, 3000/1500 rpm at 50 Hz; used with steam and gas turbines. Mechanically robust, uniform air gap, low windage, so Xd ≈ Xq.
  • Salient-pole rotor: projecting poles with laminated pole shoes and damper bars, large diameter, short length, many poles (6 to 80), 75-1000 rpm; used with hydro turbines and diesel/engine sets. Air gap is non-uniform, so Xd > Xq.
• Damper (squirrel-cage) winding in the pole faces damps oscillations, helps starting of synchronous motors and carries negative-sequence currents during unbalance.
• Cooling: air for small sets, hydrogen for 200-500 MW turbo sets (low density, high conductivity), direct water cooling of stator bars in 500-800 MW units. Indian practice: 210/250 MW hydrogen-cooled, 500/660/800 MW water-cooled stator.
• Standards: IS/IEC 60034 series (rotating electrical machines - ratings, performance, tests, degrees of protection), IS 4722 for rotating machines, IEC 60034-4 for determining synchronous machine quantities from tests, and CEA (Technical Standards for Connectivity to the Grid) Regulations with the IEGC for grid-connected generators.

EMF equation, winding factors and the air-gap field

• The rotating DC field sweeps the stator conductors; each phase sees a sinusoidal flux linkage, giving the generated EMF E = 4.44 Kc Kd f φ T per phase (T = turns per phase = Z/2).
• Pitch (coil-span) factor Kc = cos(α/2), where α is the short-pitch angle - short pitching suppresses harmonics and saves copper.
• Distribution (breadth) factor Kd = sin(mβ/2)/(m sin(β/2)), m = slots per pole per phase, β = slot angle - distributing the winding makes the waveform more sinusoidal.
• Harmonics: eliminated or reduced by short pitching, skewed/fractional-slot windings, star connection (no third harmonic line voltage) and sinusoidal pole-face shaping.

Armature reaction and the equivalent circuit

• Armature reaction is the effect of the stator MMF on the main field; its nature depends on the power factor of the load:
  • Unity pf: armature MMF at 90° to field MMF - purely cross-magnetising (distorts, slight reduction by saturation).
  • Zero pf lagging: armature MMF directly opposes field - purely demagnetising, terminal voltage falls.
  • Zero pf leading: armature MMF aids the field - magnetising, terminal voltage rises.
• Armature reaction is represented as a reactance Xa; adding leakage reactance XL gives synchronous reactance Xs = Xa + XL, and synchronous impedance Zs = Ra + jXs (Ra is usually small, Xs/Ra ≈ 10-100).
• Phasor relation (cylindrical rotor): E = V + I(Ra + jXs), with + for a generator and E = V − I(Ra + jXs) for a motor.
• Per unit: Xs is typically 1.0-2.0 pu for turbo-alternators and 0.6-1.2 pu for salient-pole machines; this large value is why fault current settles to a modest steady value while the sub-transient current is much higher.

Voltage regulation and its determination

• Voltage regulation = (E − V)/V × 100 at constant speed and field current; it is positive for lagging, may be zero or negative for leading power factors.
• Direct loading: only for small machines; load the alternator, record V at full load and on no load.
• EMF (synchronous impedance) method: run open-circuit test (OCC: Voc vs If) and short-circuit test (SCC: Isc vs If). Zs = Voc/Isc at the same field current, Ra by DC test (×1.2-1.5 for skin/AC effects). Because Zs is taken on the unsaturated (air-line) part, it over-estimates regulation - pessimistic method.
• MMF (ampere-turn) method: add field MMFs - the MMF for rated voltage on OCC plus the MMF to circulate rated current on short circuit - vectorially at (90° + φ). Uses the saturated curve and ignores leakage reactance drop, so it under-estimates - optimistic method.
• Potier (ZPF / zero power factor) method: needs OCC plus a zero-power-factor full-load curve (machine over-excited into a purely inductive load, or run as an under-excited synchronous motor at zero pf). Construct the Potier triangle to split the total reactance into leakage reactance XL and armature-reaction MMF, so saturation is handled properly - the most accurate of the three for cylindrical-rotor machines.
• ASA method is a refinement of the MMF method that adds a saturation correction.
• Short circuit ratio (SCR) = field current for rated voltage on OCC / field current for rated current on SCC ≈ 1/Xd (pu, unsaturated). Low SCR (0.5-0.7, turbo sets) means cheaper machine but poorer steady-state stability and larger voltage dip; high SCR (1.0-1.5, hydro) gives better stability and voltage regulation.

Two-reaction (Blondel) theory for salient-pole machines

• The non-uniform air gap makes reluctance along the pole axis (direct axis) lower than between poles (quadrature axis), so Xd > Xq (typically Xq ≈ 0.6-0.7 Xd).
• Armature current is resolved into Id (along d-axis, magnetising/demagnetising) and Iq (along q-axis, cross-magnetising): E = V + Ra I + j Xd Id + j Xq Iq.
• Load angle δ is found from tan(δ + φ) = (V sinφ + I Xq)/(V cosφ + I Ra) for a generator; then Id = I sin(δ + φ), Iq = I cos(δ + φ) and E = V cosδ + Id Xd (neglecting Ra).
• Slip test: drive the rotor at slightly less than synchronous speed with the field open and a reduced balanced voltage applied to the stator; Xd = Vmax/Imin, Xq = Vmin/Imax from the slowly varying envelopes.
• A salient-pole machine develops reluctance power even with zero excitation - the second-harmonic term in the power-angle equation - so its maximum power occurs at δ < 90°.

Power-angle relation, operating limits and the synchronous motor

• Neglecting Ra, generator power per phase P = (E V/Xs) sinδ, and for a salient-pole machine P = (E V/Xd) sinδ + V²(Xd − Xq) sin2δ/(2 Xd Xq).
• δ (load/torque angle) is the electrical angle between E and V - it increases with load; the machine is statically stable while dP/dδ > 0 (δ < 90° for cylindrical rotor). Synchronising power per electrical radian = (EV/Xs) cosδ.
• Reactive power Q = (E V cosδ − V²)/Xs: over-excited (E cosδ > V) delivers lagging reactive power to the grid; under-excited absorbs it.
• The capability (operating-chart) curve of a generator is bounded by the stator (armature) current limit, the field (rotor heating) limit, the prime-mover/turbine MW limit and the under-excitation stability/end-core heating limit.
• Synchronous motor: the stator field and rotor poles lock magnetically; speed is rigidly Ns regardless of load (until pull-out). Load increase is absorbed by an increase in δ, not a fall in speed.
  • Not self-starting: at standstill the rotating field alternately pulls and pushes the poles, giving zero average torque. Started as an induction motor using the damper winding (field shorted through a resistance), then DC excitation applied near synchronous speed to pull into step; small machines may be started by a pony motor or VFD.
  • V curves: at constant load, a plot of armature current versus field current is V-shaped - minimum current at unity pf; under-excitation gives lagging pf, over-excitation gives leading pf. Inverted V curves plot power factor versus field current.
  • Synchronous condenser: an over-excited synchronous motor on no load supplying leading reactive power for power-factor correction and voltage support; continuously variable, unlike switched capacitor banks.
  • Hunting (phase swinging): oscillation of the rotor about its steady δ after a sudden load or excitation change; damped by damper windings and, on the grid, by power system stabilisers.
  • Pull-out (maximum) torque occurs at δ = 90° (cylindrical rotor); loss of synchronism trips the machine or triggers pole-slip protection.

Parallel operation and synchronisation

• Conditions for synchronising: same phase sequence, equal voltage magnitude, equal frequency, and the incoming machine's phase matched (zero phase difference) at the instant of closing.
• Methods: three dark lamp, two bright one dark lamp method, and in practice a synchroscope or automatic synchroniser with check-sync relay.
• Load sharing: real power sharing is set by prime-mover governor droop (speed-load characteristic); reactive power sharing is set by excitation (voltage droop). Changing excitation alone on an infinite bus changes only Q and pf, not P.
• On an infinite bus, V and f are fixed; the machine's operating point is set by the turbine input (P) and excitation (E). For constant excitation, the locus of E's tip as load varies is a circular arc of radius |E|; for constant power it is a straight line parallel to V - standard exam figures.
• Indian grid practice: the IEGC requires generators to operate within 49.90-50.05 Hz band targets, to follow free governor (restricted governor) action, and to maintain declared reactive support; synchronisation and AVR/PSS performance are governed by CEA and CERC/Grid-India (formerly POSOCO) procedures.

Key points

• Synchronous speed - Ns = 120f/P rpm; at 50 Hz, 2 poles = 3000 rpm, 4 poles = 1500 rpm, 24 poles = 250 rpm.
• Stationary armature - allows high-voltage, high-current output; only the low-power DC field rotates.
• EMF equation - E = 4.44 Kc Kd f φ T per phase; Kc = cos(α/2), Kd = sin(mβ/2)/(m sin(β/2)).
• Armature reaction - cross-magnetising at unity pf, demagnetising at lagging pf, magnetising at leading pf.
• Synchronous reactance - Xs = leakage + armature-reaction reactance; typically 1-2 pu for turbo-alternators.
• Regulation methods - EMF pessimistic, MMF optimistic, Potier (ZPF) accurate; ASA is a corrected MMF method.
• SCR ≈ 1/Xd pu; low SCR means a cheaper, less stable machine with larger voltage dip.
• Two-reaction theory - Xd > Xq for salient poles; adds a reluctance term V²(Xd − Xq)sin2δ/(2XdXq) to power.
• Slip test - Xd = Vmax/Imin and Xq = Vmin/Imax, run just off synchronous speed with the field open.
• Power-angle equation - P = (EV/Xs) sinδ; stable while δ < 90°; synchronising power = (EV/Xs) cosδ per rad.
• Excitation and reactive power - over-excited generator supplies lagging Q; over-excited motor draws leading current.
• V curves - armature current versus field current at constant load; minimum at unity power factor.
• Synchronous motor - constant speed at any load, not self-starting, started on its damper winding.
• Synchronous condenser - over-excited idle synchronous motor for continuously variable leading VAR support.
• Hunting - rotor oscillation about δ; damped by damper bars and power system stabilisers.
• Synchronising conditions - same phase sequence, voltage, frequency and phase angle.
• Load sharing - P by governor droop, Q by excitation; excitation alone cannot shift kW on an infinite bus.
• Capability curve limits - armature heating, field heating, turbine MW and under-excitation stability/end-core heating.

Formulas and examples

Example 1 - Speed, poles and EMF constants. A 50 Hz, 3-phase alternator is directly coupled to a hydro turbine running at 375 rpm. Its stator has 180 slots, the winding is short-pitched by one slot.

• Poles: P = 120 f / Ns = 120 × 50 / 375 = 16 poles.
• Slots per pole = 180/16 = 11.25; slots per pole per phase m = 180/(16 × 3) = 3.75 (fractional-slot winding).
• Slot angle β = 180° (electrical per pole) / 11.25 slots = 16°; short-pitch angle α = 16°.
• Kc = cos(16/2) = cos 8° = 0.990; Kd = sin(3.75 × 8°)/(3.75 × sin 8°) = sin 30°/(3.75 × 0.13917) = 0.5/0.52189 = 0.958.
• If φ = 0.12 Wb and T = 120 turns/phase: E = 4.44 × 0.990 × 0.958 × 50 × 0.12 × 120 = 3,032 V per phase (≈ 5.25 kV line, star).

Example 2 - Regulation by the EMF method. A 3-phase, star-connected, 11 kV, 10 MVA alternator has Ra = 0.4 Ω/phase and Xs = 6 Ω/phase. Find the regulation at full load, 0.8 pf lagging and 0.8 pf leading.

• V per phase = 11,000/√3 = 6,351 V; I = 10 × 10⁶/(√3 × 11,000) = 525 A.
• cosφ = 0.8, sinφ = 0.6. Lagging: E = √[(6,351 × 0.8 + 525 × 0.4)² + (6,351 × 0.6 + 525 × 6)²] = √[(5,081 + 210)² + (3,811 + 3,150)²] = √[5,291² + 6,961²] = √(27.99 M + 48.46 M) = 8,744 V.
• Regulation (lagging) = (8,744 − 6,351)/6,351 × 100 = +37.7 %.
• Leading: E = √[5,291² + (3,811 − 3,150)²] = √[27.99 M + 0.437 M] = 5,332 V → regulation = (5,332 − 6,351)/6,351 × 100 = −16.0 % (terminal voltage rises on load, magnetising armature reaction).

Example 3 - Power angle, synchronising power and pull-out. The same machine (Xs = 6 Ω, Ra neglected) delivers 6 MW to an 11 kV infinite bus with E = 8,744 V/phase.

• P = 3 E V sinδ / Xs → 6 × 10⁶ = 3 × 8,744 × 6,351 × sinδ / 6 = 27.77 × 10⁶ sinδ → sinδ = 0.216 → δ = 12.5°.
• Pmax (steady-state stability limit) = 27.77 × 10⁶ W = 27.8 MW at δ = 90° - far above the 10 MVA rating, so the machine is limited by heating, not stability.
• Synchronising power = (3EV/Xs) cosδ = 27.77 × 10⁶ × cos 12.5° = 27.1 MW per electrical radian = 0.473 MW per electrical degree.

Example 4 - Salient-pole machine, two-reaction theory. A 3-phase star-connected salient-pole alternator, 1 kV line, Xd = 4 Ω, Xq = 2 Ω per phase, Ra ≈ 0, delivers 100 A at 0.8 pf lagging. Find δ, E and the regulation.

• V = 1,000/√3 = 577.4 V/phase; cosφ = 0.8, sinφ = 0.6.
• tan(δ + φ) = (V sinφ + I Xq)/(V cosφ) = (346.4 + 200)/461.9 = 546.4/461.9 = 1.183 → (δ + φ) = 49.8°.
• φ = cos⁻¹0.8 = 36.87° → δ = 12.9°.
• Id = I sin(δ + φ) = 100 × sin 49.8° = 76.4 A; Iq = 100 × cos 49.8° = 64.6 A.
• E = V cosδ + Id Xd = 577.4 × cos 12.9° + 76.4 × 4 = 562.9 + 305.6 = 868.5 V/phase.
• Regulation = (868.5 − 577.4)/577.4 × 100 = +50.4 %. (Using Xd for the whole current would have given a larger, wrong answer - hence the two-reaction theory.)

Example 5 - Synchronous condenser for power-factor correction. A plant draws 1,200 kW at 0.7 pf lagging. A synchronous motor is added that itself takes 200 kW (assume unity-pf mechanical load inside it) and the combined pf must be 0.9 lagging. Find the leading kVAR the motor must supply.

• Plant Q = 1,200 × tan(cos⁻¹0.7) = 1,200 × 1.0202 = 1,224 kVAR lagging.
• New total P = 1,200 + 200 = 1,400 kW; permitted Q = 1,400 × tan(cos⁻¹0.9) = 1,400 × 0.4843 = 678 kVAR lagging.
• Motor must supply 1,224 − 678 = 546 kVAR leading; its kVA = √(200² + 546²) = 581 kVA at pf = 200/581 = 0.344 leading.

Where it is used

• Thermal, hydro, nuclear and gas power stations: every NTPC, NHPC, NPCIL, SJVN and state-board unit is a synchronous generator - 210/250/500/660/800 MW turbo sets at 15.75-21 kV, and salient-pole hydro sets at Bhakra, Tehri, Koyna and Nathpa Jhakri.
• Generator engineering roles: BHEL, Siemens Energy, GE Vernova, Andritz and Voith design, test and commission synchronous machines; shop tests follow IS/IEC 60034 (OCC, SCC, ZPF, slip test, temperature rise, sudden short-circuit for reactances).
• Operations and grid control: Grid-India/NLDC-RLDC and SLDC/station control-room engineers manage synchronising, excitation (AVR), free governor action, reactive dispatch and pole-slip/loss-of-field protection under the IEGC and CEA regulations.
• Industrial drives and power factor: synchronous motors on large cement-mill, blower, chipper and compressor drives in cement, steel and paper plants; synchronous condensers for VAR support, including in substations supporting grids with heavy renewable penetration (also for inertia and short-circuit strength).
• Captive and distributed generation: diesel and gas-engine alternators (Kirloskar, Cummins, Stamford/AvK) in hospitals, data centres, malls and industry, run in island or grid-parallel mode.
• Renewables and traction: wound-field and permanent-magnet synchronous generators in wind turbines (full-converter), and PMSMs in EVs and modern traction - the same synchronous principle with electronic commutation.

Interview questions

• Q: Why is the armature of a synchronous machine kept stationary? A: The armature carries high voltage and large current, so keeping it fixed simplifies insulation, bracing and terminal connections; only the low-voltage, low-power DC field needs slip rings.
• Q: Why is a synchronous motor not self-starting? A: At standstill the stator's rotating field passes the rotor poles too fast to pull them along, giving alternating positive and negative torque with zero average; it must be run up close to synchronous speed first.
• Q: What happens to the speed of a synchronous motor as load increases? A: It stays exactly at Ns; the load angle δ increases instead, until load exceeds the pull-out torque and the motor loses synchronism.
• Q: What are V curves? A: Plots of armature current against field current at constant load - current is minimum at unity pf, rises on under-excitation (lagging) and on over-excitation (leading).
• Q: Why does the EMF method over-estimate regulation while the MMF method under-estimates it? A: The EMF method takes Zs from the unsaturated air-line, giving too large a drop; the MMF method uses the saturated OCC and ignores leakage reactance, giving too small a value.
• Q: What does the Potier method give that the others do not? A: It separates the leakage reactance drop from the armature-reaction MMF using the zero-power-factor curve, so saturation is correctly accounted for.
• Q: Why is Xd greater than Xq in a salient-pole machine? A: The direct axis passes through the iron pole, a low-reluctance path, so the same MMF produces more flux than along the inter-polar quadrature axis.
• Q: What is the significance of the short-circuit ratio? A: SCR ≈ 1/Xd(pu); a higher SCR means lower synchronous reactance, better voltage regulation and steady-state stability, but a larger, costlier machine.
• Q: If you increase the excitation of a generator on an infinite bus, what changes? A: Only the reactive power and power factor change - the real power is set by the turbine input; the machine moves towards supplying more lagging VARs.
• Q: What is hunting and how is it suppressed? A: Oscillation of the rotor about its equilibrium load angle after a disturbance; damper windings and power system stabilisers on the excitation system damp it.
• Q: What is a synchronous condenser and why prefer it to a capacitor bank? A: An over-excited, unloaded synchronous motor supplying leading VARs; its output is continuously and smoothly variable, it adds inertia and short-circuit strength, and it does not resonate with the network.
• Q: Why do damper windings matter in a generator rather than only in a motor? A: Besides damping rotor swings, they carry negative-sequence and harmonic currents during unbalanced faults, protecting the rotor surface from localised heating.

Common mistakes

• Using line voltage instead of phase (line-to-neutral) voltage in E = V + I(Ra + jXs) and in the regulation formula.
• Treating Zs = Voc/Isc with Voc as line voltage, or forgetting to take both readings at the same field current.
• Applying Xd to the whole armature current in a salient-pole machine instead of resolving into Id and Iq, and so overstating E and regulation.
• Assuming a leading power factor always gives negative regulation - it depends on how large I·Xs is compared with V sinφ.
• Believing excitation changes the kW output of a machine on an infinite bus; it changes only Q and power factor.
• Confusing the load angle δ (between E and V) with the power-factor angle φ (between V and I), or using degrees where radians are needed for synchronising power.
• Taking maximum power at δ = 90° for a salient-pole machine - the reluctance term shifts the peak to below 90°.

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