JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II ELECTRICAL MACHINES - I Previous Question Paper (September - 2021 - R15)

In a magnetic field system with a non-linear magnetic material, the co-energy is defined as the area between the flux linkage axis and the magnetization curve. While the energy stored in the magnetic field is represented by the integral of current with respect to flux linkage, co-energy is a mathematical quantity that simplifies the calculation of force and torque in systems where the relationship between flux and current is non-linear.

The expression for co-energy (W'_f) is given by:

where λ is the flux linkage, i is the current, and x is the displacement. For a linear magnetic system, the co-energy is numerically equal to the stored magnetic energy.

Electromechanical energy conversion is the process of transferring energy between an electrical system and a mechanical system through a magnetic field coupling medium. This process is reversible, allowing for both motor action (electrical to mechanical) and generator action (mechanical to electrical).

To derive the force (f_f) in a singly excited magnetic system, we consider the energy balance equation: Electrical energy input = Change in stored magnetic energy + Mechanical work done. For a differential displacement dx at constant current, the mechanical work done is:

Using the co-energy concept, the force is expressed as the partial derivative of co-energy with respect to displacement at constant current:

For rotational systems, the torque (T_e) is derived similarly by replacing displacement x with angular position θ:

In a linear system where inductance L(θ) is a function of position, the torque becomes: