Question

The self and mutual inductances of a doubly excited magnetic system are Ls=0.6+0.20cos2θr H and Lr=0.75+0.30cos2θr H and Msr=0.8cosθr H. For a stationary rotor at an angular position of θr=60°,what is the magnitude of torque when the currents is=20A DC and ir=10A DC?

(a) -233.88N-m

(b) +233.88N-m

(c) -467.76N-m

(d) +467.76N-m

I had been asked this question during an interview for a job.

My question is from Elementary Synchronous Machines topic in portion Basic Concepts in Rotating Machines of Electrical Machines

Answer 1

The correct option is (a) -233.88N-m

Best explanation: For θr=60°; Ls, Lr, Msr and their derivatives with respect to θr have the following values:

Ls=0.50H, Lr=0.60H, Msr=0.40H, dLs/dθr=-0.3464, dLr/dθr=-0.52, dMsr/dθr=-0.693

Substituting the numerical values in Te = 1/2is^2dLs/dθr+1/2ir^2dLr/dθr+isrdMsr/dθr = -233.88N-m.