Synchronous Motors

Motors that lock exactly to the supply frequency. Learn the power-angle equation, excitation and V-curves, power-factor correction with over-excited machines, starting, hunting, and why permanent-magnet synchronous motors dominate EVs.

A synchronous motor's rotor is a magnet — either a DC-excited field winding or permanent magnets — that locks onto the stator's rotating field and turns at exactly synchronous speed, whatever the load (up to its limit).

Because its excitation can be adjusted, a synchronous motor can draw leading current and correct the power factor of a whole plant. Permanent-magnet versions (PMSM) power most electric vehicles, servo drives and wind turbines.

An analogy

A synchronous motor is like a dog on a stiff leash following a walker exactly. Pull harder (more load) and the leash angle increases, but the dog keeps the same pace. Pull too hard and the leash snaps — the motor 'pulls out of step'.

Locked to the grid

The rotor field locks to the stator field, so speed = 120f/P exactly: 1500 rpm for 4 poles at 50 Hz, with no slip. That makes synchronous motors ideal for timing-critical drives, compressors running at constant speed, and clocks.

Load angle δ

As mechanical load increases, the rotor falls slightly behind the stator field by an angle δ, and power transferred grows as sin δ. At δ = 90° power peaks; any more load and the rotor slips poles and loses synchronism (pull-out).

Excitation and V-curves

For a fixed load, changing field current changes the motor's power factor. Under-excited: it draws lagging (inductive) current. Normally excited: unity pf, minimum current. Over-excited: it draws leading current and supplies reactive power to the grid, acting as a 'synchronous condenser'. Plotting armature current against field current gives the characteristic V-shaped curves.

Starting and hunting

A synchronous motor has zero average torque at standstill, so it isn't self-starting. It is started as an induction motor using damper (amortisseur) bars in the rotor, then the DC field is applied near synchronous speed. The same damper bars suppress 'hunting' — oscillations of δ after load changes.

PMSM and field-oriented control

Permanent-magnet synchronous motors need no field current, so they have no rotor copper loss and very high efficiency and power density. Driven by an inverter with rotor-position feedback and field-oriented control, they give precise torque from zero speed — the standard for EV traction, robotics and servo systems.

Formulas

• Speed: N = N_s = 120 f / P (exactly)
• Power–angle equation (3-phase): P = 3 · V·E·sin δ / X_s
• Pull-out power: P_max = 3·V·E / X_s (δ = 90°)
• Torque: T = P / ω_s

Worked example: Power at a given load angle

Given: V_LL = 400 V → V_ph = 231 V; E = 250 V/phase; X_s = 5 Ω; δ = 20°

Find: Power delivered and the pull-out power.

• P = 3 × 231 × 250 × sin 20° / 5
• = 3 × 11 550 × 0.342 = 11.85 kW
• P_max = 3 × 231 × 250 / 5 = 34.65 kW

Answer: 11.9 kW at δ = 20°, pull-out at 34.7 kW

Worked example: Synchronous speed

Given: 6 poles; f = 50 Hz

Find: Running speed.

• N = 120 × 50 / 6 = 1000 rpm (exactly, at any load below pull-out)

Answer: 1000 rpm

Common mistakes

• Wrong: Applying DC field current at standstill to start the motor. — Right: Start it asynchronously (damper bars or a VFD) and apply excitation close to synchronous speed.
• Wrong: Operating near δ = 90° to get the most power. — Right: Keep δ around 20–35° to leave margin for transient load and voltage dips.

Applications

• Power-factor correction: Large plants run over-excited synchronous motors on compressors so they also cancel the reactive power of induction motors.
• EV traction: Interior-permanent-magnet synchronous motors deliver high torque density and efficiency above 95 % across a wide speed range.
• Grid support: Synchronous condensers (motors with no mechanical load) are being installed again to supply inertia and short-circuit strength to renewable-heavy grids.

Key takeaways

• Speed = 120f/P exactly; no slip.
• P = 3VE sin δ / X_s; pull-out at δ = 90°.
• Excitation controls power factor (V-curves); over-excited = leading.
• Not self-starting; PMSMs with FOC dominate EVs and servos.

Going further

• Salient-pole machines: With non-uniform air gaps (salient poles), a reluctance torque term adds to the excitation torque: P = VE sin δ/X_d + V²(1/X_q − 1/X_d) sin 2δ/2. Interior-PM EV motors exploit this reluctance torque for extra torque and field weakening.
• Transient stability: After a fault, the rotor angle swings. The equal-area criterion decides whether the machine regains synchronism: the accelerating area during the fault must be matched by a decelerating area before δ reaches its unstable limit.
• Synchronous reluctance motors: SynRM rotors have no magnets and no windings, only shaped iron flux barriers. Paired with a VFD they reach IE4/IE5 efficiency without rare earths.