# Dimensioning a Shunt Resistor for Regenerative Braking

# Online calculation tool:

Source: https://jscalc.io/calc/dtIKlDgHxyhE3FKJ

If needed this could also be used with the excel tool that can be downloaded here: http://goo.gl/jPmhm4. Note that the excel tool could not be up to date. Preferably refer to the online calculation tool.

# Shunt resistor calculation basics

Motor power flow

In normal operation the servo drive receives uncontrolled electrical power from a DC bus and outputs a controlled electrical power through the phases of the motor. Then the motor converts this electrical power to a mechanical power that moves the load:

But in regenerative mode the inertia of the load is driving the movement of the motor, not the servo drive, and thus the motor acts as a generator which load is the servo drive and, ultimately, the DC bus. The same way the DC bus voltage is stepped-down in normal operation, the generated voltage is stepped-up in regenerative mode, which causes the DC bus voltage to increase. As this is typically not wanted, the servo drive can connect a shunt braking resistor to dissipate this excess of regenerated energy, preventing it to reach te DC bus.

Typical application circuit:

## Quick guide for shunt braking resistor choice (1/3)

The following steps provide a safe, conservative approach to dimension the shunt resistor for most systems (we will consider that 100% of deceleration energy goes to the shunt resistor). In case of doubt it is better to include the shunt braking option and, if finally not needed, remove it.

- Determine your system max. kinetic energy (E
_{k}) at max. speed and/or max. potential energy (E_{p}) at max. height. Calculate the mechanical energy E_{m}:**E**_{m}= E_{k}+ E_{p}

Include here motor, gearing and load inertia. - Determine the min. deceleration time ( t
_{dec}) and max. number of decelerations per second (D_{b}). - Determine the resistor Ω value with the following formula:
**R ≈ V**_{max}(supply) * 1.1 / i(shunt)

where:

V_{supply}(max) (V) is the power supply max voltage including tolerances.

i(shunt) (A) is the deceleration current (if unknown, use driver peak RMS current, available in the driver datasheet).**Choose a standard resistor with value close to R.** - Determine resistor average power P
_{av}by:**P**_{av}= E_{m}* D_{b}

Consider power-temperature derating on the resistor datasheet. - Determine the resistor peak (overload) power P
_{pk }by:**P**_{pk}= E_{m}/ t_{dec}

always being P_{pk}:**P**_{pk}≤ V_{max}(supply)^{2}/ R

to ensure the integrity of the chosen resistor. The peak power depends on peak time, check the resistor datasheet. The P_{pk}(5 s) is typically:**P**_{pk}(typ.) = P_{av}* 10

for wire-wound resistors. - Connect the shunt resistor according to the installation manual. Provide generous dissipation to the resistor if P
_{av}is close to the resistor nominal power.

### Example 1/3

JUP-30/130 driver with a 30 kg vertical load on a 100 mm diameter pulley and 1 m height.Power supply is a 4.5 kW, 130 V_{DC} with 14000 µF total capacitance (Jupiter + supply). Maximum speed is 1000 rpm.Maximum deceleration length is 6 revolutions, 1 cycle every 3 seconds.

- Calculate
**kinetic energy**at 1000 rpm

ω_{0}=**104.7 rad/s**

Rotor and pulley moment of inertia: 100 * 10^{-4}kg·m^{2}→ E_{k}(rotor) = ½ * 100 * 10^{-4}* 104.7^{2}=**54.8 J**

Load: 1000 rpm at 100 mm diameter pulley → (1000 / 60 ) * π * 0.1 = 5.2 m/s → E_{k}(load) = ½ * 30 * 5.2^{2}=**405.6 J**

E_{k}= 54.8 + 405.6 =**460.4 J**

Calculate maximum**potential energy**at height = 1 m

E_{p}= m * g * h = 30 * 9.8 * 1 =**294 J**

Total**mechanical energy**: E_{m}= E_{k}+ E_{p}=**754.4 J** **Braking time**calculation (considering constant deceleration α and total angle of Θ = 6 rev =**37.7 rad**):

Θ = ω_{0}* t + ½ * α * t^{2}and α = - ω_{0}/ t → Θ = ω_{0}* t + ½ * (- ω_{0}/ t ) * t^{2}= ω_{0}* t - ½ * ω_{0}* t = ½ ω_{0}· t

→ 37.7 = 0.5 * 104.7 * t → t_{dec}=**0.72 s**;**D**= 1 / 3_{b}**= 0.333****Resistor value**:

R ≈ V_{max}(supply) * 1.1 / i(shunt). For Jupiter R = 130 * 1.1 / 30 =**4.7 Ω**- Resistor
**average power**:

P_{av}= E_{m}* D_{b}= 754.4 * 0.333 =**252 W** - Resistor
**peak power**:

P_{pk}= E_{m}/ t_{dec}=**1047 W**

P_{pk}≤ V_{max}(supply)^{2}/ R → 1047 ≤ 143^{2}/ 4.7 → 1047 ≤ 4350 W →**OK!**

4.7 Ω is a standard value →**perfect!**

## Quick guide for shunt braking resistor choice (2/3)

Steps for choosing the resistor part number:

**Technology:** wirewound aluminium resistors are preferred due to their high peak capacity.

**Packaging:** for high power systems (> 1 kW) it is recommended to use dynamic braking resistors packs with their heatsink and housing to prevent potential burns.

**Environmental:** Take into account heatsink or air temperature for the average power rating.

**Power overload:** For peak power use the graphs or ratings specified on the manual. Sometimes even the peak energy is specified.

### Example 2/3

Choosing the resistor part number. Calculated specs are: R = 4.7 Ω, P_{av} ≥ 251 W, P_{pk} ≥ 1047 W. Filtering on Digi-Key. Seems that the best option is **HSC3004R7J**.

**Technology:** Wirewound aluminum resistor

**Packaging:** Compared to Ohmite alternative, it includes screws for fastening.

**Environmental:** Air temperature is unknown, choosing the 250 W could not be enough, 300 W is chosen.

**Power overload:** 25 x 300 = 7500 W → 1047 ≤ 7500 → OK!

## Quick guide for shunt braking resistor choice (3/3)

Ingenia driver configuration:

- Set max user bus voltage (i.e. shunt activation voltage) (0x2101:0x02) to the voltage you want the shunt transistor to be activated at.
- In the actuator window, set Shunt Available to Yes and write the change to the driver.
Click on Configure and set the duty used and the hysteresis. The duty used is the duty cycle of the modulation performed in the shunt transistor and it can be changed during testing. However, it is recommended to set the value to 2048 (100%) when the engineering stage is finished.

Set hysteresis (see picture below). A value of 1% is recommended.

Remember to write all the changes made to the driver.

Start testing with small accelerations and monitor DC link circuit voltage (mV) on the scope.

Some of the Ingenia drivers have an orange shunt activation LED. This should turn on during braking.

Shunt control frequencies

PWM signal for driving the shunt braking resistor is 20 kHz in most of the Ingenia Servo Drives.

DC bus voltage is sampled under a rate of 1 kHz in most of the Ingenia Servo Drives.

See more in the product manual.

Note on control loops

Control loops play an important role on the braking dynamics.

Make them less aggressive to minimise regeneration.

Minimise deceleration ramps as much as possible.

### 3/3 Example

For Jupiter, according to the results obtained previously:

- Select the available shunt resistor checkbox.
- Set Duty used to 2047.
- Set max user bus voltage (i.e. shunt activation voltage) (0x2101:0x02) to 130 * 1.1 =
**143 V** - Set Hysteresis to 1 (1%). Shunt will turn on at
**144.4 V**and off at**141.6 V** - Start testing with small accelerations and monitor DC link circuit voltage (mV) on the scope.
- Monitor shunt braking resistor temperature

# Extra information

## Moment of inertia for various shapes

Moment of inertia for rotational loads can be calculated as:

I = η * M * R^{2}

where:

- η is a form factor
- M is the system mass in kg
- R is the maximum radius of the system from your axis of rotation in m

With this, kinetic energy can be calculated as:

K = ½ * I * ω^{2}

where:

- ω is the angular speed in rad/s

## Quick worst case calculation

“I don’t want to calculate the exact moment of inertia, I just want a worst case assumption to know if I need a shunt braking resistor”

Use:

I = M * R^{2}

Where the simplification η = 1 is applied.

## Using PWM modulation for driving the shunt braking resistor

Modulate PWM might be equivalent to “changing the effective value of resistor”, but:

Increases EMI

Increases power losses

**should be avoided on the production stage**by using a well chosen shunt braking resistor.

## Energy that can be stored on the DC bus capacitor

Using a DC bus capacitor can be sometimes a cheap alternative to using a shunt braking resistor to avoid an uncontrolled increase of the DC bus voltage in case of re-injection. However, this method has serious disadvantages:

Large voltage swing from nominal to max is needed to be effective. Watch out the power supply Overvoltage disconnection!

Huge capacitors are needed

Capacitors are typically dimensioned for EMI rather than energy storage in low voltage DC drives