Test: Doubly Excited Magnetic System - Electrical Engineering (EE) MCQ

All of the above applications require two independent sources of excitation.

As the rotor is not allowed to move, dW_mech = 0, thus dW_elec = 0 + dW_fld = i_sdΨ_s + i_rdΨ_r, if in this equation, we introduce the self and mutual inductance terms, (Ψ_s = L_si_s) and integrate the resulting equation from 0 to is, 0 to ir and 0 to iris, the respective terms, finally we get W_fld = 1/2 i_s²L_s+ 1/2 i_r²L_r + M_rs i_s i_r.

T_e = ∂W_fld(i_s,i_r,θ_r)/∂θ_r = ∂W_fld¹(i_s,i_r,θ_r)/∂θ_r
f_e = ∂W_fld(i_s,i_r,x)/∂x = ∂W_fld¹(i_s,i_r,x)/∂x
The positive sign in the formula indicates that force/torque acts in a direction as to tend to increase both field energy and co-energy.

The torque developed by the interaction of stator and rotor magnetic fields is the electromagnetic torque or interaction torque.

Reluctance torque:
1/2i_s²dL_s/dθ_r and 1/2i_r²dL_r/dθ_r
Positive or negative value of current doesn’t affect the torque direction. The interaction/electromagnetic torque = i_si_rdM_sr/dθ_r, here the direction of i_s and i_r changes the torque.

Widely used motor/generators such as synchronous and induction machines belong to doubly excited systems, and many other practical applications require multiply excited magnetic systems.

T_e = 1/2 i_s ²dL_s/dθ_r + 1/2i_r²dL_r/dθ_r + i_si_rdM_sr/dθ_r.

Equation for magnetic torque is T_e = 1/2i_s²dL_s/dθ_r+1/2i_r²dL_r/dθ_r+i_si_rdM_sr/dθ_r, if i_r = 0, T_e = 1/2i_s²dL_s/dθr and if i_s = 0, then T_e = 1/2i_r²dL_r/dθ_r, and these equations for torque are called reluctance torques.

Because the change of reluctance (Rl_s or Rl_r) are responsible for the production of these torques.

Reluctance motors can work on single excitation, and synchronous motors require double excitation.