Introduction
Electrical motors are reversible machines; they can function as motors or as generators. A motor receives electrical power from a battery and transforms it in torque developing a Counter Electromotive Force CEMF, which opposes the battery. A generator receives mechanical power from a mechanical actuator and transforms
it in electrical power developing a Counter Torque, which opposes the actuator.
A motor behaves as motor and as generator at the same time. In fact while a motor is 'motoring', that is doing mechanical work, it generates CEMF acting as generator, although the CEMF is lower than the battery voltage so the motor acts as a load and absorbs current.
In certain situations the CEMF may overcome the battery, in which case the generator component becomes dominant; the motor acts as a generator inverting the direction of its current and forcing it into the battery.
The typical situation is the one of a heavy vehicle rolling on a sharp downhill slope and forcing the motor to turn fast enough that the CEMF becomes larger than the battery voltage. As soon as the motor overcomes the battery it inverts the current direction and starts feeding current into the battery, while developing a counter torque that acts as a brake. This phase is called regeneration (recharging of the battery).
The Voltage/Current plane
Two wire DC electrical devices have one of the two poles marked as positive. By convention this is the pole where the positive voltage applied or generated is located.
These devices are divided into two categories:
- Generators: Batteries, dynamos, fuel cells etc.
- Users: Resistors, ovens, motors etc.
The current is defined as positive if it enters the positive pole of a user, or exits the positive pole of a generator. See figure 1.

FIGURE 1.
Obviously it is possible to force a negative current on the positive pole.
As an example, a common car battery (generator) sources a positive current (exiting the positive pole) when starting the car and sinks a negative current (entering the positive pole) while being recharged.
Similarly current can be made to exit from the positive pole of a resistor (user) inverting the voltage across it. By representing positive and negative voltage/current in a plane as a VI axis, we distinguish four quadrants.
As an example let's look at a car battery (figure 2); Q1 and Q 3 are the quadrants where the battery acts as a generator, since the current exits the positive pole. In Q1 the generator maintains a positive power rail while in Q3 the battery maintains a negative power rail.

FIGURE 2.
Q2 and Q4 are the user quadrants, where the battery acts as a load to a battery charger that pushes current into the battery recharging it. In Q2 the battery charger output maintains a positive power rail, where in Q4 the charger maintains a negative power rail.
We will see shortly that a permanent magnet DC motor is also a four-quadrant device, acting as a user in Q1 and Q3, and as a generator in Q2 and Q4.
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