The four quadrants

Plot torque horizontally and speed vertically. The sign of the power decides everything:

P = T \cdot \omega

Torque and speed with the same sign: $P > 0$ , the motor is motoring, taking energy from the grid.
Torque and speed with opposite signs: $P < 0$ , the load drives the machine and it is generating.

A conveyor or a fan lives in quadrant I only. A hoist, an elevator or a rolling mill needs all four.

Try it: the four quadrants

Motoring: the grid supplies energy

Quadrant I. Torque and speed both positive: the motor pushes the way it turns, lifting a heavy car.

Quadrant: I
Torque (p.u.): 0.60
Speed (p.u.): 0.70
Power T·ω (p.u.): 0.42

P = T · ω ( P > 0 : grid → load, P < 0 : load → grid / resistor )

Predict first

An empty elevator car goes down. The counterweight (car + half the rated load) is heavier than the empty car. Which quadrant is the drive in?

Quadrant IV: generating, because the car is going downQuadrant III: motoring, pulling the light car downQuadrant II: generating

FoundationStart here if this is new to you

Ask one question: who is doing the pushing? If the motor pushes and the load resists, the motor is working (motoring). If the load pushes and the motor holds it back, like brakes on a car going downhill, the motor is braking and turns that energy into electricity (generating).

ExplorerGo deeper: derivations and open questions

Energy per trip. Integrate $P(t)$ over a trip to get the energy drawn or returned. With the Lab III elevator, a full-load-down trip returns about 11 kW during its 4.8 s at constant speed, with a 16 kW peak as it starts to brake. Is a braking resistor or an active front end the better choice for a busy office building? What changes for a lift used twice a day?