Synchronous motor V-curves

Reference notes

Use Next → on the narrator above to step through six configurations: from synchronous-motor concept, to the V-curves, to PF correction.

Synchronous motor in one paragraph

A synchronous motor has the same construction as a synchronous alternator. The stator is supplied with three-phase AC, producing a rotating field at synchronous speed n_s. The rotor is DC-excited, producing a constant magnetic field. The rotor's poles lock onto the stator's rotating field and rotate at exactly n_s regardless of load (until you exceed the pull-out limit). This rigid coupling is what makes them so useful in process drives, large compressors, and clocks.

What makes synchronous motors interesting: the field-current knob

At constant shaft load, varying the rotor's DC field current I_f changes |E_f| in the per-phase equivalent circuit. Three things happen as you sweep I_f:

• Under-excited (low I_f, small |E_f|): the motor draws current that lags V_t. It looks like an inductive load to the supply.
• Normal excitation (just right): I_a is in phase with V_t — unity PF. |I_a| is at its minimum for that load.
• Over-excited (high I_f, large |E_f|): the motor draws current that leads V_t. It supplies reactive power to the grid — looks like a capacitor.

This is unique to synchronous machines. Induction motors can't do this — they always consume lagging reactive.

V-curves: I_a vs I_f at constant load

Plot armature current magnitude vs field current at constant shaft load and you get a U-shaped curve — hence "V-curve" (or sometimes more accurately "U-curve"):

• Goes high on the left (under-excited, lagging PF, large |I_a|).
• Bottoms out at the minimum (unity PF point).
• Rises again on the right (over-excited, leading PF, large |I_a|).

For higher shaft loads the entire V-curve shifts up and to the right. The locus of the minimum points forms the "unity power factor" line.

Synchronous condenser: PF correction in big metal

An over-excited synchronous motor running at no shaft load draws almost pure leading reactive current — it's a giant rotating capacitor. Utilities and large factories deploy "synchronous condensers" (no-load synchronous motors) at substations to correct power factor on heavy lagging industrial loads. Modern static VAR compensators have taken over this role at the smaller end, but synchronous condensers are still installed where dynamic control of reactive power is needed.

Why this matters

• An over-excited synchronous motor driving a real industrial load is the only common machine that simultaneously delivers mechanical power AND supplies reactive power back to the grid. Two-for-one.
• The V-curve gives the operator a single chart for choosing the right field-current setting for any operating mode: "drive the load AND fix the plant's PF" → over-excite.
• The horizontal axis (I_f) is the operator's control. The vertical axis (|I_a|) is what the supply sees. The PF is implicit in which "side" of the V you're on.

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