This document discusses the fundamentals of electrical drives. It begins by presenting the fundamental torque equation that relates the motor torque, load torque, moment of inertia, and angular velocity. It then discusses multi-quadrant operation of drives, defining sign conventions for speed and torque and describing the four quadrants of operation - forward motoring, forward braking, reverse motoring, and reverse braking. An example is given of a hoist system and how it operates in the different quadrants depending on the load and direction of motion. References for further reading are also provided.
2. FUNDAMENTAL TORQUE EQUATION
J- Polar moment of inertia of motor load
system, kg-๐2
๐ค๐ - Angular velocity of motor, rad/sec
T- Developed Motor electromagnetic torque,
N-m
๐๐ - Load torque, N-m
3. FUNDAMENTAL TORQUE EQUATION
Fundamental torque equation of above motor load system is given as-
๐ โ ๐๐ =
๐
๐๐ก
๐ฝ๐ค๐ = ๐ฝ
๐๐ค๐
๐๐ก
+ ๐ค๐
๐๐ฝ
๐๐ก
โฆ.(1)
For most of the drives inertia is constant.
i.e.
๐๐ฝ
๐๐ก
= 0
โดEquation (1) becomes,
๐ โ ๐๐ = ๐ฝ
๐๐ค๐
๐๐ก
โด ๐ = ๐๐ + ๐ฝ
๐๐ค๐
๐๐ก
โฆโฆ(2)
i.e. Motor developed torque has to supply load torque and dynamic
torque present during transient operations (starting, acceleration,
deceleration).
4. MULTI-QUADRANT OPERATION OF
DRIVES
Sign Convention
๏ถSpeed : Motor Speed is considered to be positive, if it is rotating in
forward direction. If we consider a particular direction of rotation as
forward (or +ve), then rotation in opposite direction will be Reverse
direction (-ve). In applications involving up and down motion, the
direction of rotation of motor causing upward motion will be the
forward.
๏ถTorque : In case of forward motion, if the motor torque causes it to
accelerate, then it will be positive torque. The load torque operates in
opposite direction that of the motor torque.
5. MULTI-QUADRANT OPERATION OF
DRIVES
Modes of Operation
๏ถMotoring- Electrical energy is converted into mechanical energy. i.e.
power flows from supply to motor.
๏ถBraking- Motor works as generator converting mechanical energy
into electrical energy. i.e. power flows from motor to supply.
6. MULTI-QUADRANT OPERATION OF
DRIVES
Power developed by motor is given by product torque and speed.
i.e. ๐ = ๐ ร ๐ค๐
๏ถQuadrant I (Forward Motoring)- Speed is +ve and Power is +ve
๏ถQuadrant II (Forward Braking)- Speed is +ve and Power is โve
๏ถQuadrant III (Reverse Motoring)- Speed is โve and Power is +ve
๏ถQuadrant IV (Reverse Braking)- Speed is โve and Power is -ve
https://circuitglobe.com/four-quadrant-operation-
of-dc-motor.html
7. MULTI-QUADRANT OPERATION OF
DRIVES
Example of Hoist
๐ค๐๐๐โ๐ก ๐๐ ๐๐๐๐ก๐ฆ ๐๐๐๐ < ๐ค๐๐๐โ๐ก ๐๐ ๐๐๐ข๐๐ก๐๐ ๐ค๐๐๐โ๐ก
๐ค๐๐๐โ๐ก ๐๐ ๐๐๐๐๐๐ ๐๐๐๐ > ๐ค๐๐๐โ๐ก ๐๐ ๐๐๐ข๐๐ก๐๐ ๐ค๐๐๐โ๐ก
๏ถForward direction will be the one causing upward
motion of hoist.
๏ถQuadrant I (Forward Motoring)- To move the loaded
cage upward, motor has to rotate in anticlockwise
direction. So it is the forward direction. The motor
torque should act in the same direction to lift the cage
against gravity.
๏ถQuadrant II (Forward Braking)- The empty cage is
moved upward due to counter weight itself. For safe
operation, motor torque should act in opposite
direction of rotation.
https://sciamble.com/Resources/pe-drives-lab/basic-
drives/dc-four-quadrant
8. MULTI-QUADRANT OPERATION OF
DRIVES
Example of Hoist
๏ถQuadrant III (Reverse Motoring)- To move the empty
cage in downward direction, motor has to rotate in
clockwise direction. The motor torque also has to act
in clockwise direction against the gravity due to
counter weight.
๏ถQuadrant IV (Reverse Braking)- To move fully loaded
cage in downward direction, motor will rotate in
clockwise direction due to gravity of its weight. For
safe operation, motor torque will act in anticlockwise
direction.
9. REFERENCES
๏ถ G. K. Dubey, โFundamentals of Electrical Drivesโ, Second Edition,
Narosa Publishing House