Scope:
When a moving motor and load are required to decelerate rapidly, the kinetic energy of the load drives the motor's shaft to generate energy back to the servo drive. This is called “regenerative energy”.
In most cases, regenerative energy is stored by the motor's internal resistance, servo drive and power supply, but in some cases, when high speed and inertia are involved, the energy becomes too great and causes the voltage on the bus (Vbus) to rise. A shunt resistor and a control provide a simple and effective solution to protect the power supply and servo drive by sinking energy though the shunt resistor.
This application note describes methods to calculate the resistance and power of the shunt resistor.

System diagram
The shunt resistor is placed between the VP+ and PR terminals of the servo drive using a special control circuit, as shown below:
When the control circuit detects the presence of a voltage rise above a given threshold level, it connects the shunt resistor, and the energy sinks from the VP+ terminal to the PR terminals and dissipates as heat.
The resistor should have a low enough resistance to enable it to absorb the regenerative energy. It should also have a sufficient power rating.

Shunt Resistor value calculations
For a given application, the maximum resistance of the shunt resistor is derived from the motor's characteristics, the value of Vbus, the braking torque and the maximum speed.
The mechanical power to be dissipated is given by the following formula:
The mechanical power to be dissipated is: 

Where: 


Torque in Nm 

Angular Velocity in rad/sec 

The braking torque can be derived from the motor's torque constant (Kt) and by measuring the value of the current on deceleration.
The mechanical power is dissipated on the motor itself and the shunt resistor. It is also partially absorbed by the capacitance on the bus.
For the purposes of this Application Note, we will neglect the bus capacitance absorption and concentrate on the shunt resistance.
The power dissipation on the motor itself is actually the copper loss and can be calculated from the formula:

Where: 

is the phasetophase resistance of the motor, 

is the current at brake time. 

The additional power 

needs to be dissipated on the shunt resistor. Otherwise, the bus voltage Vbus will rise and may cause damage to 
the bus components that cannot withstand the high voltage level.
Normally, we allow a voltage rise up to 90% of the drive's maximum voltage rating before engaging the shunt resistor (unless there are other voltagesensitive components on the bus). When the shunt resistor is engaged, current flows through the resistor, causingto be dissipated as heat. For good practice, we recommend using a maximum of 70% pulsewidth modulation (PWM) to the Rshunt switching transistor.
The shunt resistance is therefore calculated at the maximum allowable voltage from the formula
Where:
is the maximum level of (the voltage level at which the shunt resistor is engaged). 
Shunt Resistor Power calculations
The shunt resistor should dissipate a maximum peak power when the motor is at its maximum speed and its maximum deceleration torque T:
Assuming that the deceleration torque is constant, we may assume that the current is also constant. Since the speed is constantly decreasing, the power that needs to be dissipated is also decreasing.
At certain speed ,the shunt resistor's power will be zero:
The power on the shunt resistor actually dissipates within a very short period of time.
Below is a typical motion diagram that shows the power dissipation on the shunt resistor.
The resistor's average power is derived from the value of calculated above and from ,
which is influenced by the value of the deceleration .
For a given deceleration and , the shunt resistor's average power is:
Example:
In this example, we assume the following motor data:
V shunt = 0.9 x 200 V = 180 V
Speed = 2000Rpm
Braking current = 5A
R = 10Ω
Ke = 40v/Krpm
Therefore,
Thus
The dissipated mechanical power is:
The copper loss on the motor:
Leaving to be dissipated by the shunt resistor.
The maximal shunt resistance is:
Therefore, the final resistance is
Now, let us assume the following deceleration:
Then we have:
Therefore the power of the shunt resistor is:
