How to calculate brake resistor size?

To effectively calculate brake resistor size, you need to determine its optimal resistance value (in Ohms) and its required power rating (in Watts). These two parameters are crucial for safely and efficiently decelerating loads controlled by Variable Frequency Drives (VFDs) or other motor control systems. The sizing process fundamentally relies on understanding the energy that needs to be dissipated during braking and the frequency of these braking events.

Understanding Dynamic Braking Resistors

A dynamic braking resistor is an essential component in many motor control applications. When a motor connected to a VFD decelerates, it acts as a generator, feeding electrical energy back into the VFD's DC bus. If this energy is not dissipated, the DC bus voltage will rise, potentially tripping the VFD and causing an uncontrolled stop. The brake resistor converts this excess electrical energy into heat, safely dissipating it to allow for controlled deceleration.

Key Parameters for Brake Resistor Sizing

To specify a dynamic braking resistor, three critical pieces of information are needed: the energy dissipated per stop, the duty cycle of the braking events, and the appropriate resistance value. The first two are typically combined to determine the resistor's power rating.

1. Resistance Value (Ohms)

The resistance value (R) dictates the peak braking current and, consequently, the braking torque. It's a balance between preventing VFD overcurrent faults and achieving effective deceleration.

• VFD Compatibility: Most VFD manufacturers specify a minimum allowable resistance value for their drive. Using a resistance lower than this minimum can cause excessive current flow, damaging the VFD's braking transistor.

• DC Bus Voltage (V_dc): This is the voltage across the VFD's DC bus during braking. For a 3-phase AC input, it's typically around 1.414 * RMS_AC_Input_Voltage. For example, a 480V AC input might have a 678V DC bus.

• Peak Braking Current (I_peak): This is the maximum current the VFD's internal braking transistor can handle without damage.

• Formula for Minimum Resistance:
  The minimum resistance value (R_min) can be estimated using Ohm's Law:
  R_min = V_dc_max / I_peak_max
  Where:

  • V_dc_max is the maximum DC bus voltage allowed before the VFD trips.
  • I_peak_max is the maximum instantaneous current the VFD's braking circuit can safely handle.

  Impact of Resistance:

  • Too Low: Can overload the VFD's braking transistor, leading to damage or immediate fault trips.
  • Too High: Results in insufficient braking current, causing slower deceleration, potential overvoltage trips, or an inability to stop the load effectively.

2. Energy Per Stop (Joules)

This is the amount of kinetic (and sometimes potential) energy that the resistor must dissipate during each braking event.

• Kinetic Energy (E_k): This energy depends on the mass and velocity of the load.

  • For Linear Motion: E_k = 0.5 * m * v^2
    Where:
    • m = mass of the load (kg)
    • v = maximum velocity of the load (m/s)
  • For Rotational Motion: E_k = 0.5 * J * ω^2
    Where:
    • J = total moment of inertia of the motor and load (kg·m²)
    • ω = maximum angular velocity of the motor/load (rad/s)

• Potential Energy (E_p): For vertical loads (e.g., hoists), potential energy released during lowering must also be considered:
  E_p = m * g * h
  Where:

  • m = mass of the load (kg)
  • g = acceleration due to gravity (9.81 m/s²)
  • h = height of descent (m)

  The total energy to be dissipated per stop is E_total = E_k + E_p (if applicable).

3. Duty Cycle and Power Rating (Watts)

The duty cycle describes how frequently braking occurs and for how long. This, combined with the energy per stop, determines the average power the resistor needs to handle, which directly relates to its continuous power rating (wattage).

• Braking Time (t_b): The duration of a single braking event (seconds).

• Total Cycle Time (T_cycle): The total time from the beginning of one braking event to the beginning of the next (seconds). This includes run time, braking time, and dwell time.

• Duty Cycle (%): (t_b / T_cycle) * 100%

• Average Power (P_avg): This is the continuous power rating the resistor must safely dissipate over time without overheating.
  P_avg = E_total / T_cycle
  Alternatively, if the braking frequency (f_b in stops per second) is known:
  P_avg = E_total * f_b

  The resistor's power rating must meet or exceed this P_avg, often with an additional safety factor to account for ambient temperature, enclosure, and application variations.

Step-by-Step Calculation Guide

Follow these steps to size a brake resistor:

1. Determine DC Bus Voltage (V_dc):

   • Consult your VFD's manual for its nominal DC bus voltage and its maximum allowable DC bus voltage before an overvoltage trip. A common approximation for 3-phase input is V_dc ≈ 1.414 * V_AC_input.

2. Calculate Minimum Resistance (R_min):

   • Refer to your VFD's manual for the manufacturer's recommended minimum braking resistance. This is usually the primary factor.
   • As a check, calculate R_min = V_dc_max / I_peak_max_VFD, where I_peak_max_VFD is the maximum instantaneous current the VFD's braking transistor can handle (also found in the VFD manual).
   • Select a resistor with a resistance value slightly above R_min to ensure safe operation, e.g., 10-20% higher.

3. Calculate Energy Per Stop (E_total):

   • Determine the kinetic energy of your load (E_k) using the appropriate linear or rotational formula.
   • If applicable, calculate the potential energy (E_p) for vertical loads.
   • Sum them to get E_total = E_k + E_p.

4. Define Braking Time (t_b) and Total Cycle Time (T_cycle):

   • Estimate t_b based on your application's required deceleration time.
   • Determine T_cycle by considering the run time, braking time, and any dwell time between cycles.

5. Calculate Average Power (P_avg):

   • Use the formula: P_avg = E_total / T_cycle.
   • This is the continuous power rating the resistor must be capable of handling.

6. Select the Resistor:

   • Choose a brake resistor with:
     • Resistance (Ohms): Equal to or greater than your calculated R_min and compatible with your VFD's specifications.
     • Power Rating (Watts): Equal to or greater than your calculated P_avg, preferably with a safety factor (e.g., 1.25 to 1.5 times P_avg). Ensure the resistor can also momentarily handle the peak instantaneous power (V_dc^2 / R).

Summary Table of Parameters

Parameter	Description	Formula / Derivation
DC Bus Voltage	Internal DC voltage of the VFD during braking.	V_dc ≈ 1.414 * V_AC_input (for 3-phase) or VFD spec.
Minimum Resistance	Lowest safe ohmic value to prevent VFD damage.	R_min_VFD_spec (from manual) or V_dc_max / I_peak_max_VFD
Kinetic Energy	Energy of motion to be dissipated per stop.	0.5 * m * v^2 (linear) or 0.5 * J * ω^2 (rotational)
Potential Energy	Energy of height to be dissipated per stop (for vertical loads).	m * g * h
Total Energy per Stop	Sum of kinetic and potential energy to be dissipated.	E_total = E_k + E_p
Braking Time	Duration of the active braking event.	t_b (seconds, determined by application)
Total Cycle Time	Complete time of one operational cycle (run, brake, dwell).	T_cycle (seconds)
Duty Cycle	Percentage of time the resistor is active during a cycle.	(t_b / T_cycle) * 100%
Average Power Rating	Continuous power the resistor must dissipate without overheating (Wattage).	P_avg = E_total / T_cycle or E_total * f_b (braking frequency)

Practical Considerations

• Safety Factor: Always apply a safety factor to your calculated average power. Resistors generate heat, and their performance can be affected by ambient temperature and enclosure.
• Thermal Management: Ensure adequate airflow around the resistor. If enclosed, the enclosure must be properly ventilated or sized to dissipate the heat.
• Mounting and Wiring: Follow manufacturer guidelines for mounting and ensure proper wiring practices using appropriately sized cables and fusing.
• VFD Braking Logic: Configure the VFD's braking parameters (e.g., braking chopper activation voltage, deceleration ramps) to work in conjunction with the selected resistor.

By carefully calculating these parameters, you can select a brake resistor that provides reliable and safe operation for your application.