Image: Experimental electric scooter capable of progressive regenerative braking
using Roboteq Brushless motor controller
Motor and generator at the same time
The simplified model of a motor is a resistor in series with an inductor and a voltage generator. The resistor and inductor are simply the resistance and inductance of the electromagnets inside the motor. The voltage generator represents the voltage that is created by the motor while it is turning and is referred as Back EMF, or BEMF. The BEMF voltage is a fixed ratio of Volts per RPM.
Fig1. Model for electrical motors
When the motor is locked mechanically and a voltage is applied, the model is essentially a resistor across the battery and the current is measured as I=VBat/Rm. The inductance only affects the current the instant the voltage is applied and its effect disappears if the voltage remains constant.
Fig 2: Equivalent circuit when motor is stopped or stalled
If the motor is allowed to spin, then it will generate a BEMF voltage proportional to its rotation speed. The model therefore is now a resistor with generators on both sides. The resulting voltage at the resistor is now the battery voltage minus the BEMF, and the current is I = (VBat - VBemf) / Rm. Practically, this means that as the motor accelerates, the current decreases.
Fig 3: Acceleration condition
If the motor could spins fast enough for the backEMF to equal the battery voltage, the two voltage sources would cancel each other and the equivalent voltage at the resistor would be 0. Therefore no current would flow from the battery. In practice, this cannot happen because this would mean that the motor would have no torque at all, while some is needed to overcome the friction.
Fig 4: Stable speed without load or friction
In practice, the motor speed will stabilize when the BEMF is such that the current from the battery, which in turn