Motor-Generator Duality

Part of Generators and Motors

How the same machine can operate as either a motor or a generator depending on which form of energy is supplied.

Why This Matters

One of the most practical and empowering insights in electrical engineering is that motors and generators are the same machine operating in different modes. Supply mechanical energy to the shaft, and a machine delivers electrical energy — it is a generator. Supply electrical energy to the terminals, and the same machine delivers mechanical energy — it is a motor. The underlying electromagnetic principles are identical; only the direction of energy flow differs.

For a rebuilding civilization, this duality has concrete value. A single machine design serves double duty. A generator can serve as a motor to test its winding integrity. A motor can serve as a generator for emergency power. Motor-generator sets (one machine driving another) convert between electrical specifications — voltage, frequency, phase count — that cannot be easily done otherwise without solid-state electronics.

Understanding the duality also prevents dangerous mistakes. A generator connected backwards to a source becomes a motor drawing enormous current. A motor connected to an overrunning load becomes a generator, and if the circuit is not prepared for this, the regenerated energy can damage equipment.

The Electromagnetic Basis

In any electrical machine, torque arises from the interaction of two magnetic fields: one from the stator and one from the rotor. When these fields are not aligned, they exert a force on each other trying to align. This force manifests as torque on the rotor.

In generator mode: an external mechanical torque rotates the rotor faster than the stator field (or rotates it when the stator field is stationary). The rotor conductors cut flux, generating an EMF. If a load is connected, current flows. This current in the rotor interacts with the field to create a braking torque opposing rotation (Lenz’s law) — the “load torque” that the prime mover must overcome.

In motor mode: an external electrical source drives current through the stator (and in some designs the rotor). The resulting fields interact to create a torque that rotates the rotor. As the rotor speeds up, it generates a back-EMF opposing the supply voltage. The difference between supply voltage and back-EMF drives the current. The machine settles at the speed where electromagnetic torque balances mechanical load torque.

The machine does not “know” which mode it is in. The physics is continuous. The mode is determined purely by the relative magnitudes of applied voltage and back-EMF (for DC machines) or by the relative speeds of rotating field and rotor (for AC induction machines).

DC Machine Duality in Practice

A DC machine is the clearest example of the duality. The same machine can operate as either motor or generator with only a change in operating condition — no rewiring required.

Test it directly: take a small DC motor (from a salvaged appliance). Connect its terminals to a voltmeter and spin the shaft by hand. It generates a voltage. Stop spinning and connect it to a battery (correct polarity): it runs as a motor. The same machine, the same terminals.

In generator mode: terminal voltage V = E − I×R, where E is the internal EMF (proportional to speed and field), I is the output current, and R is winding resistance. Under no load, terminal voltage equals internal EMF. Under load, the voltage drops due to resistive loss in the windings. A well-designed generator has low winding resistance so the voltage drop is small.

In motor mode: terminal voltage V = E + I×R, where E is now the back-EMF (opposing the supply). The supply must exceed the back-EMF to drive current through the resistance. At starting (zero back-EMF), all the supply voltage drives current through just the resistance — hence the very high starting current. As the motor accelerates, back-EMF grows and current falls.

The reversibility means that to change a DC machine from motor to generator, you just need to change which source you connect: electrical source for motor, mechanical source for generator. The connections are the same.

AC Machine Duality: Synchronous Machines

A synchronous generator (alternator) consists of DC field windings on the rotor and AC armature windings on the stator. Driven by a prime mover, it generates AC power at a frequency determined by speed and pole count. It supplies power to the grid.

The same synchronous machine, connected to the AC grid and with its DC field excited appropriately, operates as a synchronous motor — drawing AC power from the grid and delivering mechanical power. The machine is identical; the energy direction reverses.

Synchronous machines have a third mode exploited in large power systems: the synchronous condenser. Running as a motor with no mechanical load, it draws or supplies reactive power only (leading or lagging current from the grid), acting as a large variable capacitor or inductor. This stabilizes transmission line voltage. A rebuilding grid would use this mode to compensate for the reactive load of induction motors.

The transition from generator to motor mode in a synchronous machine is smooth and can happen during operation. If a generator’s prime mover suddenly loses power, the machine can transition to motoring mode, drawing power from the grid to keep spinning. This is called motoring and can damage the prime mover (a steam turbine, for example, can be damaged by reverse torque). Protection relays monitor for this condition and open the circuit breaker to isolate the machine.

Induction Machine Duality

Induction machines are also reversible. An induction motor driven above synchronous speed by an external mechanical force generates power back into the supply — this is induction generator mode. The slip becomes negative (rotor faster than synchronous speed), rotor currents reverse direction, and the machine exports power.

This mode is used in wind turbines and small hydroelectric generators connected to an existing AC grid. The grid provides the reactive magnetizing current the induction machine needs; the machine returns real power. It is a simpler and cheaper generator than a synchronous machine because no DC excitation or synchronizing equipment is needed.

If the grid fails while an induction generator is running, the machine cannot sustain generation — it loses its reactive current source and collapses. This is actually a safety feature: induction generators do not “island” and continue energizing a dead grid. But it means they cannot serve as standalone off-grid generators without additional capacitor banks to supply reactive current.

Motor-Generator Sets

A motor-generator (MG) set is simply one motor mechanically coupled to one generator on a common shaft. Electrical energy enters the motor, becomes mechanical energy on the shaft, and becomes electrical energy again from the generator — at different voltage, frequency, or phase count.

Why would you do this? For energy conversion that is otherwise impossible without sophisticated electronics:

Frequency conversion: a 50 Hz motor driving a generator at the right speed for 60 Hz output, converting between two different grid standards.

Voltage isolation and transformation: the motor and generator have no electrical connection, only mechanical. This provides complete galvanic isolation between source and output — useful for powering sensitive instruments from a dirty power source.

Phase conversion: a single-phase motor driving a three-phase generator, supplying three-phase loads from a single-phase source (or vice versa). This is practical for workshops that have only single-phase supply but need three-phase motors.

DC to AC conversion: a DC motor driving an AC generator, converting battery or photovoltaic power to AC. Before solid-state inverters became cheap and reliable, MG sets were the standard method for this conversion.

MG sets have low efficiency (typically 85–90% for each machine, so 72–81% combined) compared to a solid-state transformer or inverter (95%+). But they are made from repairable mechanical components, require no semiconductors, and can handle overloads and faults gracefully. For a civilization without electronics manufacturing capability, MG sets may be the only practical way to convert between electrical specifications.

Building a Motor-Generator Set

The key requirements are mechanical: a rigid base, accurate alignment between the motor and generator shafts, and a coupling that handles any residual misalignment without transmitting vibration.

Use a rigid coupling if shaft alignment is within 0.1 mm and angular misalignment is below 0.05°. Use a flexible coupling (jaw coupling with elastomer spider, or disk coupling) if alignment is less perfect. Never use a rigid coupling with misalignment — it will destroy bearings.

Align the shafts by placing a straightedge across the coupling halves in four positions (top, bottom, both sides) and shim the machine feet until the straightedge contacts both halves evenly. Then check with a dial indicator on the coupling to verify runout below 0.05 mm. Good alignment extends bearing life by a factor of 5 or more.

Size the motor and generator for the intended load, with 20–30% margin. The motor must supply the generator’s rated output plus both machines’ losses. Total input = (generator rated output) / (motor efficiency × generator efficiency). For a 10 kW generator output with 85% efficiency machines: input = 10 / (0.85 × 0.85) = 13.8 kW.