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# Four Quadrant Operation of DC Motor – Motoring and Breaking Operation

A DC motor operates in two modes – *motoring*
*and breaking*.

- In motoring operation, it converts electrical energy into the mechanical energy, which assists its motion.
- In breaking operation, it converts mechanical energy into electrical energy, thus works as a generator and opposes its motion.

The motor can provide motoring and breaking operations in both forward and reverse directions. Therefore, a DC motor can operate in both directions of rotation and of producing both motoring and breaking, hence it is known as four quadrant operation of DC motor.

The power developed by the motor is given by the product of angular speed and the torque. If the developed power by motor is positive, then the mode of operation is called *motoring* and when the developed power is negative, the mode of operation is called *breaking*.

For the four quadrant operation of the motor, the sign conventions about the signs of speed and torque are given as follows −

- The speed of the motor is considered positive, when it is rotating in forward direction.
- In motor drives involving up and down motions, the speed of the motor in upward direction is considered to be forward motion.
- The torque is considered positive, when it produces acceleration.
- The torque is assigned negative sign, if it produces retardation.

## Four Quadrant Operation

The four quadrant operation of the motor can be described as follows −

### Quadrant I

In the first quadrant, the developed power by the motor is positive, thus the motor operates in *motoring mode* and converts electrical energy into mechanical energy. Therefore, the operation of the motor in first quadrant is called *forward motoring*.

### Quadrant II

In the second quadrant, the direction of the rotation is positive i.e. speed is positive and the torque is negative. Hence, the developed power is negative and the machine operates as a generator which opposes its motion. The kinetic energy of the moving parts of the machines is converted into electrical energy. Therefore, the operation of motor in second quadrant is called *forward breaking*.

### Quadrant III

In the third quadrant, the motor speed and torque both are negative, hence the power is positive. Therefore, the operation of the motor in the third quadrant is known as *reverse motoring*.

### Quadrant IV

In the fourth quadrant, the motor speed is negative and the developed torque is positive, hence the motor power is negative which is corresponding to the breaking operation. Therefore, the operating in fourth quadrant is known as reverse breaking.

The four quadrant operation of the motor can be summarised in the figure shown below.

.

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