Braking of DC Motors

When a DC motor must be decelerated quickly, simply removing the supply is insufficient because the mechanical inertia keeps the rotor spinning and the load may demand precise stopping position or time. Braking of DC motors refers to controlled methods of converting the kinetic energy of the rotating system into electrical or thermal energy to bring the motor to rest or reverse direction rapidly. Three distinct braking methods are used in industrial drives: regenerative braking, dynamic braking, and plugging.

Core Concept Explanation

All three braking methods exploit the generator action of the DC motor. When a motor rotates, the armature conductors cut magnetic flux and generate a back EMF Eb = k x phi x N in the direction opposing the applied voltage. Braking occurs when this generated EMF drives a current that produces a torque opposing the direction of rotation. The difference between the three methods lies in how the armature circuit is arranged and where the energy goes.

In regenerative braking, the motor speed is increased (by the load, as in a descending hoist or an electric vehicle going downhill) until back EMF Eb exceeds the supply voltage Vs. The armature current then reverses direction (Ia = (Eb - Vs) / Ra, which is negative in the motoring convention). The machine acts as a generator feeding real power back to the supply. This is the most energy-efficient method and is standard in modern electric vehicle and traction drives.

In dynamic braking (also called rheostatic braking), the supply is disconnected and the armature is connected across an external resistance Rb. The spinning motor acts as a self-excited generator with Eb driving current through Ra + Rb. The braking torque decelerates the motor and all kinetic energy is dissipated as heat in Rb. The braking torque decreases as speed drops (since Eb = k x phi x N decreases) so the deceleration is not uniform.

In plugging (counter-current braking), the armature supply polarity is reversed while the motor is still running. The armature now has both the supply voltage Va and back EMF Eb acting in the same direction to drive current. The resulting current is extremely high: Ia = (Va + Eb) / Ra which can be 10 to 20 times rated current. A series resistance Rs is always inserted to limit this current to a safe value. Plugging gives the fastest deceleration but wastes the most energy and creates high mechanical stress.

Mathematical Expression

The braking torque in each method is:

Tb = k x phi x Ia_brake

For regenerative braking: Ia_brake = (Eb - Vs) / Ra. This is positive in generating convention, creating negative torque in motoring convention.

For dynamic braking: Ia_brake = Eb / (Ra + Rb) = k x phi x N / (Ra + Rb). Braking torque at speed N is Tb = (k x phi)^2 x N / (Ra + Rb).

For plugging: Ia_brake = (Va + Eb) / (Ra + Rs). At initial speed N0, this is the maximum current. The limiting resistance Rs must satisfy Rs = (Va + Eb_0) / Ia_max - Ra where Ia_max is the allowed peak current (typically 1.5 to 2 times rated current).

Practical Understanding

Regenerative braking requires the converter to be capable of handling reverse power flow. A single fully controlled thyristor rectifier can provide regenerative braking in one rotation direction (two-quadrant operation) because the current direction is fixed by the thyristors but the voltage polarity can be reversed by increasing alpha beyond 90 degrees. For four-quadrant operation enabling motoring and regenerative braking in both directions, a dual converter (two anti-parallel thyristor bridges) or a four-quadrant chopper is required.

Dynamic braking is widely used as a failsafe method because it is entirely passive once the armature switch is thrown. The braking resistor value is chosen as a compromise: too high means weak initial braking torque and too low means excessive current at the start. Variable resistance banks can be switched in steps to maintain roughly constant braking torque throughout deceleration.

Plugging is used in applications requiring the fastest possible stop, such as emergency stops in machine tools and cranes. After the motor reaches zero speed the supply must be disconnected immediately, otherwise the motor will accelerate in the reverse direction. This is typically detected by a zero speed switch or a back-EMF sensing circuit.

Given:
DC motor, Ra = 1 ohm, k x phi = 1.5 V/(rad/s), running at N = 100 rad/s
Dynamic braking with Rb = 9 ohm

Why this formula applies:
Motor acts as generator, Eb drives current through Ra + Rb

Formula:
Eb = k x phi x N
Ia = Eb / (Ra + Rb)
Tb = k x phi x Ia

Substitution:
Eb = 1.5 x 100 = 150 V
Ia = 150 / (1 + 9) = 150 / 10
Tb = 1.5 x 15

Calculation:
Ia = 15 A
Tb = 22.5 N-m

Final Answer:
Initial braking current = 15 A, Initial braking torque = 22.5 N-m

Exam Tip: In plugging problems, GATE commonly asks for the value of limiting resistance. Use Rs = (Va + Eb_initial) / Ia_max - Ra. Note that Va and Eb add in plugging (both oppose rotation) unlike in motoring where they oppose each other. Also remember: after reaching zero speed in plugging, motor will reverse if supply is not cut.

Mechanism: Speed-Torque Curve During Braking

• Regenerative braking: Motor speed exceeds synchronous or no-load speed. Eb greater than Vs, armature current reverses, torque opposes motion. Energy flows back to supply grid. Requires bidirectional converter.
• Dynamic braking: Supply disconnected, armature closed on Rb. Braking torque proportional to speed (since Eb proportional to N). Deceleration curve is exponential. All kinetic energy converts to heat in Rb.
• Plugging: Armature supply polarity reversed. Both Va and Eb drive current in same direction. Braking torque is maximum at all speeds but current is extremely high without limiting resistance Rs.
• Plugging stopping sequence: Insert Rs, reverse Va, wait for N to reach zero (monitor back-EMF), disconnect supply immediately to prevent reverse running.
• Four-quadrant operation summary: Quadrant 1 is forward motoring, Quadrant 2 is forward regenerative braking, Quadrant 3 is reverse motoring, Quadrant 4 is reverse regenerative braking.

Quick Revision

• Regenerative: Eb greater than Vs, Ia reverses, energy to supply. Most efficient. Requires bidirectional converter.
• Dynamic: Supply off, armature on Rb. Ia = Eb / (Ra + Rb). Energy wasted in Rb.
• Plugging: Va reversed. Ia = (Va + Eb) / (Ra + Rs). Highest current, fastest stop.
• Plugging limiting resistance: Rs = (Va + Eb0) / Ia_max - Ra.
• Dynamic braking torque: Tb = (k x phi)^2 x N / (Ra + Rb). Decreases with speed.
• Exam trap: In plugging, Va and Eb add (do not subtract) because supply polarity is reversed against a still-rotating motor.
• Always disconnect supply at zero speed during plugging, otherwise motor reverses direction.