Q2Electric Drives and Their Control

Dynamic Braking of DC Separately Excited Motor with Speed-Torque Characteristics

In dynamic braking of a DC separately excited motor, the armature is disconnected from the DC supply and instead connected across a braking resistor, while the field winding remains separately excited and energized as before. Since the motor's rotor continues to rotate by inertia immediately after disconnection, it continues to generate a back-EMF proportional to its speed and field flux, and this back-EMF now drives current through the braking resistor (rather than in the normal motoring direction), producing a retarding torque proportional to the armature current, which decelerates the motor.

The braking torque is given by T = (Kphi)^2*omega/(Ra+Rb), where Kphi is the motor's torque constant, omega is the angular speed, Ra is the armature resistance, and Rb is the external braking resistance - this shows the braking torque is directly proportional to speed, producing a straight-line speed-torque characteristic passing through the origin (zero torque at zero speed) in the second quadrant (negative torque, since the torque now opposes the direction of rotation, while speed remains initially positive as the motor continues rotating in its original direction while decelerating).

As the motor decelerates, the back-EMF and hence the braking torque both progressively decrease toward zero, meaning the braking effect naturally weakens as speed decreases, resulting in the motor asymptotically approaching zero speed rather than stopping abruptly - this exponentially-decaying-toward-zero speed-torque behavior is characteristic of dynamic braking, and the resistance value Rb is typically chosen to limit the initial peak braking current (and hence peak braking torque) to a safe value while still providing an acceptably fast overall deceleration time.

Power Limitations in Armature Voltage Control

In armature voltage control of a DC motor (with field flux held constant at its rated value), the motor's torque capability remains constant (equal to rated torque) throughout the entire armature-voltage-controlled speed range, since torque T = Kphi*Ia depends only on armature current, which can be maintained at its rated value regardless of speed. However, since power is the product of torque and speed, the maximum available power increases linearly with speed as armature voltage (and hence speed) is increased from zero toward base speed, meaning only a small fraction of the motor's rated power capability is actually utilized at low speeds within this control range, even though full rated torque remains available - this is the fundamental power limitation of pure armature voltage control, requiring either accepting reduced power availability at low speed, or combining armature voltage control with field-weakening control above base speed to achieve full utilization of the motor's power rating across a wider overall speed range.

Beyond the specific dynamic braking mechanism and power-limitation analysis discussed above, it is worth situating both topics within the broader context of DC drive design: dynamic braking represents one of the simplest and most cost-effective methods of achieving controlled deceleration in a DC drive, requiring only a resistor and a switching contactor rather than any bidirectional power-electronic converter capability, while the armature-voltage-control power limitation directly motivates the widespread combined use of armature voltage control below base speed and field weakening above base speed in virtually all practical variable-speed DC drive installations requiring a wide operating speed range.

A further important practical consideration for dynamic braking system design is the sizing of the braking resistor itself, which must be rated to safely dissipate the peak instantaneous braking power (occurring at the highest initial speed, where back-EMF and hence braking current are greatest) as well as the total cumulative braking energy expected over repeated braking cycles, since an undersized braking resistor risks thermal damage during a single severe braking event, while a resistor sized purely for peak instantaneous power without adequate consideration of cumulative thermal capacity risks overheating during frequent, repeated braking cycles in applications such as elevator or crane drives that brake many times per operating shift.

The power limitations in armature voltage control arise fundamentally because this method operates below the base (rated) speed of the motor while holding the field current at its rated value, which means the maximum available torque (proportional to armature current times constant flux) can be maintained at its rated value throughout the controlled speed range, but because power equals torque times speed, the maximum available power decreases proportionally as speed is reduced below base speed - this speed range is therefore described as the constant-torque region. To extend the operating range above base speed, field weakening (reducing field current below rated value) is used instead, which allows speed to increase above base speed while holding armature voltage at its rated maximum, but now the maximum torque available decreases in inverse proportion to speed (since flux has decreased) while the maximum power remains approximately constant at its rated value - this is described as the constant-power region. The overall practical limitation is therefore that no single control method (armature voltage control or field weakening alone) can deliver both rated torque and rated power simultaneously across the full desired speed range from zero to well above base speed; achieving wide speed range operation in practice requires combining armature voltage control for the constant-torque region below base speed with field weakening for the constant-power region above base speed, and the crossover point between the two regions is set at the base speed where both armature voltage and field current simultaneously reach their rated values.

Field weakening as a means of extending speed range above base speed also introduces its own set of practical limitations that must be considered in drive design: as flux is reduced to raise speed above base speed, commutation conditions in a DC machine become progressively more difficult (since weaker main field makes the machine more susceptible to armature reaction distorting the flux distribution near the brush neutral axis), and at sufficiently high field-weakened speeds, mechanical considerations such as centrifugal stress on the rotor windings and bearing limitations may impose an absolute upper speed limit regardless of the electrical field-weakening capability available. Additionally, since developed torque is proportional to the product of flux and armature current, the maximum torque available in the field-weakened region falls in inverse proportion to the field weakening ratio, meaning applications requiring high torque at high speed (rather than merely high power) cannot be well served by field weakening alone, and typically require an increase in motor voltage rating or a different drive architecture (such as a higher base-speed motor with a mechanical gearbox) instead.