Question

In a doubly excited magnetic system with salient pole type stator and rotor, if the rotor is not allowed to move, then the equation for magnetic field stored energy in establishing the currents from zero to is and ir is __________

(a) Wfld=1/2 is^2Ls+1/2 ir^2Lr

(b) Wfld=1/2 is^2Ls+Mrs is ir

(c) Wfld=1/2 is^2Ls+1/2 ir^2Lr+Mrs is ir

(d) Wfld=1/2 ir^2Lr+Mrs is ir

I had been asked this question during a job interview.

I want to ask this question from Doubly Excited Magnetic Systems in chapter Basic Concepts in Rotating Machines of Electrical Machines

Answer 1

The correct option is (c) Wfld=1/2 is^2Ls+1/2 ir^2Lr+Mrs is ir

The best explanation: As the rotor is not allowed to move, dWmech=0, thus dWelec=0+dWfld=isdΨs+irdΨr, if in this equation, we introduce the self and mutual inductance terms, (Ψs=Lsis) and integrate the resulting equation from 0 to is, 0 to ir and 0 to iris, the respective terms, finally we get  Wfld=1/2 is^2Ls+1/2 ir^2Lr+Mrs is ir.