Equivalent Circuit of a DC Machine

A review of the material presented with regard to elementary direct-current machines can be helpful at this stage to recall the principles of operation for dc machines. The circuit representations of a dc generator and a dc motor are shown in Figure. Under steady-state conditions the interrelationships between voltage and current are given by

where the plus sign signifies a motor and the minus sign a generator. V_f is the voltage applied to the field circuit, If is the field current, and Rf is the field-winding resistance. V_t is the terminal voltage, E_a is the generated emf, Ia is the armature current, and Ra is the armature resistance. The generated emf E_a is given by Equation as

E_a = K_aφω_m

which is the speed (motional) voltage induced in the armature circuit due to the flux of the stator-field current. The electromagnetic torque T_e is given by Equation as

T_e = K_aφI_a

where K_a is the design constant. The product E_aI_a, known as the electromagnetic power being converted, is related to the electromagnetic torque by the relation

P_em = E_aI_a = T_eω_m

For amotor, the terminal voltage is always greater than the generated emf, and the electromagnetic torque produces rotation against a load. For a generator, the terminal voltage is less than the generated emf, and the electromagnetic torque opposes that applied to the shaft by the prime mover.