Synchronous Motor

How a synchronous motor differs from an induction motor

Both a synchronous motor and an induction motor have a stator that produces a rotating magnetic field — three coils 120° apart fed three-phase AC. Both rely on torque between the rotating field and a magnetic structure inside the rotor. The difference is what the rotor is.

In an induction motor, the rotor is a passive squirrel cage. The rotating field induces currents in the cage (Faraday's law), the cage's currents make a magnetic field of their own, and torque arises from the interaction. But this only works when there's a difference in speed — the rotor must slip below synchronous speed for the field to look like it's moving across the cage and inducing voltage. Equilibrium is a small slip (1–5 %) at whatever value gives just enough torque to balance the load.

In a synchronous motor, the rotor has its own permanent magnetic field — from rare-earth magnets, a DC-excited field winding, or rotor saliency. Once the rotor is up to speed, its field locks onto the stator's rotating field, and the two spin together at exactly the same speed. There is no slip. The torque comes from the angular displacement δ between the rotor's field and the stator's field — a small lag (a few degrees) under light load, growing toward 90° as load increases. Past 90°, the magnetic coupling weakens and the rotor "falls out of sync."

     stator (3 windings, 120° apart)
        ╲   |   ╱
         ╲  |  ╱
   ───────┐│┌───────       rotating field at n_s = 120 f / p
          │││         ──→  field rotates this way
   ╔══════╪╪═══════╗
   ║  rotor with    ║       rotor turns at EXACTLY n_s (no slip)
   ║  N/S poles —   ║
   ║  PM, wound,    ║       rotor's own field locks onto stator's
   ║  or reluctance ║       lag angle δ < 90° in normal operation
   ╚════════════════╝

The synchronous speed equation

         120 · f
   n_s = ────────         (rpm; f in Hz, p = number of magnetic poles)
            p

This relationship is fixed by physics and mains frequency. It is independent of load, supply voltage, or motor size. A 4-pole synchronous motor on 60 Hz mains runs at exactly 1800 rpm. Period.

Pole count p	n_s at 50 Hz	n_s at 60 Hz	Typical application
2	3000 rpm	3600 rpm	Steam-turbine generators, high-speed compressors
4	1500 rpm	1800 rpm	Industrial drives, machine tools, gas-turbine generators
6	1000 rpm	1200 rpm	Medium-speed pumps, large fans
8	750 rpm	900 rpm	Hydro generators, slow-speed industrial
12	500 rpm	600 rpm	Pelton wheel hydro
32	187.5 rpm	225 rpm	Slow-speed direct-drive hydro
96 (low-head Kaplan)	62.5 rpm	75 rpm	Run-of-river hydro turbines

The largest synchronous generators in any country share the same nameplate speed: 3000 or 3600 rpm for steam and gas turbines (2-pole, set by thermodynamic cycle requirements), 1500 or 1800 rpm for combined-cycle gas turbines (4-pole), 75–250 rpm for hydro turbines (12 to 96+ poles, set by water-head physics). All synchronous, all spinning at exactly the rate the grid frequency demands.

Three rotor architectures

• Permanent-magnet synchronous motor (PMSM). The rotor carries rare-earth permanent magnets — usually neodymium-iron-boron (NdFeB), sometimes samarium-cobalt (SmCo) for high-temperature service. Two sub-variants: surface-mounted PM (magnets glued onto the rotor) and interior PM (magnets buried inside laminations, adding reluctance torque to magnetic torque). PMSMs are the dominant high-efficiency motor architecture in modern EVs, HVAC compressors, drone propulsion, industrial servo drives, and high-end spindle motors. Efficiency reaches 95–97 % at rated load.
• Wound-field synchronous motor. The rotor carries a DC-excited field winding. Direct current flows through slip rings (older designs) or a brushless rotating exciter (modern). The DC field current can be varied independently, giving precise control of the back-EMF and reactive power flow. This is the architecture of every large grid generator — every steam turbine alternator, gas turbine alternator, and hydro alternator above ~100 MVA. Field current adjustment is how grid operators dispatch reactive power.
• Synchronous reluctance motor (SynRM). No magnets, no field winding — the rotor has only laminated steel arranged with high anisotropy (one axis low-reluctance, the perpendicular axis high-reluctance). Torque arises from the rotor's preference to align its low-reluctance axis with the stator field. SynRM efficiency is competitive with PMSM (94–96 %) at lower cost — no rare-earth dependence — but power factor is poor (0.5–0.7) and torque density is lower. ABB's SynRM industrial drives have grown the segment substantially since 2014.
• Permanent-magnet assisted synchronous reluctance (PMa-SynRM). A hybrid combining a reluctance rotor with small auxiliary ferrite or NdFeB magnets to boost power factor without rare-earth dependence. Common in mid-2020s EV traction motors as the industry tries to reduce rare-earth content.

Worked example: a 4-pole 1800 rpm PMSM for an industrial drive

Design parameters: 60 Hz mains, 4-pole IPM-rotor PMSM, 90 kW rated output, full-load efficiency 96 %, breakdown torque ratio 2.2.

Synchronous speed. n_s = 120 · 60 / 4 = 1800 rpm — exactly. No load-dependent variation.

Synchronous angular velocity. ω_s = 2π · 1800 / 60 = 188.5 rad/s.

Rated torque. T_rated = P / ω = 90 000 / 188.5 = 477 N·m. (For comparison, a similar-rated induction motor would deliver this at ~1730 rpm and slightly higher torque, since power = torque × angular velocity and induction-motor speed is slip-reduced.)

Breakdown (pull-out) torque. T_max = 2.2 × 477 = 1050 N·m. The motor can momentarily handle 220 % rated torque without falling out of sync — useful for handling start-up shocks of pumps or compressor surge.

Operating load angle. At rated torque, δ ≈ arcsin(1 / 2.2) ≈ 27°. Plenty of margin to 90°.

Input current. At 96 % efficiency, P_in = 93.75 kW. At a typical 400 V three-phase supply with 0.95 leading power factor: I = 93 750 / (√3 · 400 · 0.95) ≈ 142 A.

Rotor field. An IPM rotor with NdFeB N48UH-grade magnets (B_r ≈ 1.35 T at 80 °C). Effective air-gap flux density ~0.9 T after iron and air-gap factors.

Drive. Modern PMSM applications always pair the motor with an inverter drive — there's no practical way to start an unmodified PMSM directly from the line without a damper cage. The inverter ramps frequency from 0 to 60 Hz at startup, dragging the rotor up with the field; once at speed, it can hold synchronous speed precisely or modulate to any desired speed (variable-frequency operation).

Synchronous vs induction vs BLDC compared

Property	PMSM	Induction	BLDC (six-step)	Synchronous reluctance
Rotor field source	Permanent magnets	Induced currents	Permanent magnets	Rotor saliency
Slip	0	1–5 %	0	0
Speed accuracy	Exact	Load-dependent	Exact	Exact
Efficiency at rated load	95–97 %	85–95 %	85–93 %	94–96 %
Efficiency at 25 % load	92–94 %	72–82 %	78–88 %	89–92 %
Power factor	0.95–1.0	0.80–0.92	0.95+	0.5–0.7
Torque ripple	Low (sinusoidal FOC)	Low	Moderate (6-step)	Higher
Rare-earth dependence	Heavy (NdFeB)	None	Heavy (NdFeB)	None or light
Cost ($/kW)	1.4–1.8×	1.0× (reference)	1.2–1.5×	0.9–1.2×
Self-starts from line?	No (needs damper or inverter)	Yes	No (needs inverter)	No (needs inverter)
Typical use	EV, HVAC, servo, high-end pumps	Pumps, fans, conveyors	Drones, computer fans, e-bikes	Industrial drives, pumps

PMSMs win on efficiency, especially at partial load — the metric that matters most for energy-conscious applications. Induction wins on cost and simplicity. SynRM is the rare-earth-free alternative and is gaining ground rapidly in regulated efficiency tiers.

Where synchronous motors show up

• Every grid generator on Earth. Every steam turbine, gas turbine, hydro turbine, and large diesel generator that feeds a national grid is a wound-field synchronous machine. The grid frequency is locked, and the only way to share dispatch among generators is to run them all in lockstep at exact synchronous speed. The largest single units are 1.6 GVA turbo-alternators (4-pole, 1500/1800 rpm) in nuclear and coal plants; the largest hydro alternators are 800+ MVA, often 90+ pole at 75–125 rpm.
• EV traction motors. Tesla Model 3 (Long Range, Performance), BMW i3 and i4, Hyundai Ioniq 5/6, Kia EV6, Mercedes EQS, Volvo XC40 Recharge — every modern EV that targets long range uses a PMSM (often interior-magnet IPM) traction motor. The PMSM's high partial-load efficiency translates directly to driving range. Earlier Tesla Model S used induction; the Model 3 switched to PMSM and got ~10 % more range on the same battery.
• High-efficiency HVAC compressors. Variable-speed scroll compressors in modern air conditioning units (Mitsubishi Hyper-Heating, Daikin Inverter, Carrier Greenspeed) use PMSM motors paired with three-phase inverter drives. The efficiency at 25 % load drives SEER (Seasonal Energy Efficiency Ratio) above 20, vs. ~13 for single-speed induction compressors.
• Industrial machine-tool spindles. CNC milling and turning spindle motors are PMSMs above 5 kW (or wound-field synchronous in very large machining centres) — the zero-slip behaviour is essential for precise surface-cutting speeds.
• Large industrial drives (compressors, pumps, fans). Above ~1 MW, wound-field synchronous motors compete with induction motors on the basis of higher efficiency and adjustable power factor (synchronous machines can absorb or supply reactive power by adjusting the field, useful for plant power-factor correction).
• Quartz clock and turntable motors (small scale). A typical wall clock or vinyl turntable uses a small synchronous motor (with magnet-stator and a magnetic rotor) running directly from mains — accuracy is exactly grid frequency, locked to within ppm of the grid's nominal value over 24 hours.
• Drones, e-bikes, robotics, high-end RC. The "BLDC" motors marketed for these applications are technically PMSMs with trapezoidal back-EMF; modern controllers run them with sinusoidal field-oriented control (FOC) for smoother torque.

The breakdown torque cliff

The torque-vs-load-angle relation is approximately:

T(δ) ≈ T_max · sin(δ)        for a non-salient (round-rotor) machine

δ is the load angle: the angular displacement between the rotor's field axis and the stator's rotating field axis. Under no load, δ ≈ 0. Increase the mechanical load and δ grows, generating more torque to balance it. Maximum torque occurs at δ = 90°; that maximum is the breakdown or pull-out torque, typically 1.5–2.5 × rated torque.

Past 90°, the sine function decreases — but the load is still pulling, so the rotor slows down, δ keeps growing past 90°, torque keeps falling, and the motor decelerates rapidly. The stator field "slips past" the rotor: it now sees alternating positive and negative torque cycles, oscillates, and eventually stalls or trips. Recovery requires reducing the load and restarting; a synchronous motor cannot "reaccelerate from sub-sync speed" the way an induction motor can.

For salient-pole machines (most large wound-field synchronous generators), there's an additional reluctance torque component that increases the breakdown torque to ~2.5–3 × rated. Modern interior-PM (IPM) machines also exploit reluctance for similar benefit.

Where the 3–5 % efficiency loss comes from

• Stator copper. I²R loss in the three-phase winding — dominates total loss at high load. Reduced by using bigger conductors and higher voltage (lower current for the same power).
• Stator iron. Hysteresis and eddy currents in the laminated stator core. Roughly constant with load; reduced by thinner laminations and higher grade silicon-steel (M19, M27 grades).
• Rotor losses. PMSM: very small (no rotor copper loss; only eddy-current loss in the magnets, which is why high-end PMs are segmented). Wound-field: DC field winding I²R loss, plus brush wear if slip-ring excited. SynRM: minimal rotor loss (laminated steel only).
• Mechanical: bearings + windage. Friction in the bearings + air resistance of the rotor. Constant with load; reduced by high-speed bearings (ceramic or oil-mist) and aerodynamic rotor shaping.
• Inverter losses (when applicable). Modern PMSM systems are almost always inverter-fed; the inverter adds 2–5 % of its own losses on top of the motor's losses. System efficiency = motor × inverter = typically 91–94 %.
• Magnet temperature derating. NdFeB magnets lose flux at 0.12 %/°C up to ~150 °C, then permanent loss above 180 °C. PMSMs must include thermal management of the magnets themselves — the cost of a missed temperature limit is a permanent torque reduction.

Common design and operation pitfalls

• Demagnetisation under fault. A short-circuit on the stator can drive large currents that, depending on rotor angle, partially demagnetise the rotor magnets. The motor's torque capability drops permanently. Modern designs use high-coercivity (UH or SH grade) magnets and fast inverter trip protection to avoid this.
• Pull-out from a torque transient. A pump or compressor surge that briefly exceeds breakdown torque pulls the motor out of sync. Even a single such event requires shutdown and restart — application engineers must size breakdown margin generously (2.0× minimum) for variable loads.
• Starting without inverter or damper. Connecting a PMSM directly to mains without a soft start or damper winding causes large transient currents and rotor vibration without acceleration. Some early hobbyist EV conversions made this mistake; the result is FET destruction and no motion.
• Cogging torque on light-load operation. The interaction of permanent magnets with stator slot openings creates a pulsating reluctance torque even with no stator current. Skewing the rotor magnets (or stator slots) by one slot-pitch suppresses cogging; high-end servo PMSMs use fractional-slot windings for minimum cogging.
• Field-current loss in wound-field machines. Loss of DC excitation current means the rotor field collapses; the motor sees zero torque and stalls. Modern brushless exciters use a small auxiliary generator on the same shaft, eliminating slip-ring failure as a cause.
• Iron saturation at low frequency. Running an inverter-fed PMSM at very low speed with constant V_supply causes the stator flux to climb (V/f relationship). Iron saturation creates extra losses and harmonics; standard practice is to maintain V/f constant (down to a minimum frequency, below which V is held constant and flux is allowed to fall).
• Bearing currents from inverter dV/dt. Common-mode voltage from the inverter induces shaft currents that pit bearing races (electrical-discharge machining damage). Mitigated by shaft-grounding rings, insulated bearings, or output dV/dt filters. Same problem as in inverter-fed induction motors but exacerbated by PMSM's higher di/dt for the same torque.

Historical context

The synchronous motor predates the induction motor. The first practical synchronous generators were Werner von Siemens' dynamo machines of the 1860s, refined into the modern wound-field synchronous alternator by Westinghouse and General Electric in the 1890s. The 1900s established the synchronous generator as the only practical architecture for grid power — every electrical generator of any significant size built since 1900 has been synchronous.

Permanent-magnet synchronous motors waited for high-energy-product magnets. Samarium-cobalt (SmCo) magnets, available from the late 1960s, enabled the first commercial PMSMs in industrial servo drives in the 1970s. Neodymium-iron-boron (NdFeB) magnets, discovered by Sumitomo Special Metals and General Motors in 1983, dropped the cost per joule of magnetic energy by an order of magnitude and made PMSMs the obvious choice for high-efficiency variable-speed applications. By the mid-2010s, PMSMs had become the default EV traction motor; by the late 2020s, they dominate any new motor application above 5 kW where energy efficiency matters.

Synchronous reluctance motors (SynRM) — known in textbook form since the 1920s but commercially unviable until inverter drives matured — entered the industrial drive market in 2014 with ABB's IE5 SynRM line. With rare-earth supply chain risks and rising NdFeB prices, SynRM and PMa-SynRM (PM-assisted) are projected to take significant market share in mid-power industrial drives through the 2030s.