First of all, a DOL controlled motor may run in Fwd only, or in Fwd and Rev, depending upon the load and process (quad 1 or quad1 & quad 3 operation) - you simply switch it on/off via a contactor and it accelerates/decelerates between 0 and full speed, through its designed torque/slip curve. There will be no generation in these quads, the contactor is open, therefore the electrical supply to the motor windings is OFF and the motor will simply slow and stop in a load defined time (instantaneously or over a few seconds if the load is direct shaft connected, e.g. no fluid couplings or clutches).
When the motor is controlled by a variable frequency drive (VFD), it is the VFD that controls quadrant operation, the motor simply reacts to how it is being controlled (fwd accel / rev accel / forward decel / reverse decel).
When the motor is being decelerated by a VFD, the VFD output reduces. If the motor load is overhauling, the rotor can be driven at a faster rate than the VFD speed set point, therefore the motor begins to generate active power back towards the VFD. This is quadrant 2 where speed is -ve but torque (braking) is still +ve.
If we consider both directions of motor operation (forward/reverse or CW and CCW) and both modes (acceleration and deceleration), there are four distinct areas, or quadrants, of operation.
Quadrants 1 and 3 represent the motor applying torque in the direction of motion, while quadrants 2 and 4 represent applying torque opposite the direction of the motion. In quadrants 1 and 3 the flow of energy is from electrical to mechanical. The motor is converting electrical power from the VFD into motion in the system. In quadrants 2 and 4, the motor is actually acting as a generator. The motion of the system is being converted into electrical power, which is then absorbed by the VFD or fed back into the supply.
Quadrant 1 Driving or motoring, forward accelerating quadrant with positive speed and torque
Quadrant 2 Generating or braking, forward braking-decelerating quadrant with positive speed and negative torque
Quadrant 3 Driving or motoring, reverse accelerating quadrant with negative speed and torque
Quadrant 4 Generating or braking, reverse braking-decelerating quadrant with negative speed and positive torque.