Circuit Model of DC Machine

DC MACHINE CIRCUIT MODEL

The parallel paths of dc machine armature are symmetrical and each has an induced emf E_a and a resistance R. The armature can be represented by the DC Machine Circuit Model with voltage E_a and a series resistance:

R_a = R_p / A

as shown in Figure 2.18. The armature resistance is quite small so as to limit the copper- loss to an acceptable value.

Figure 2.18 also shows the field circuit of the machine and the field coil axis is placed at 90° to the brush axis as per the actual arrangement in the machine. From circuit point of view it is not necessary to rigidly follow this scheme. Since most of the time steady-state dc behavior of the machine will be considered, the inductances of field and of armature (this is negligible any way) circuits are of no consequence and are not shown in the circuit model.

The voltage drop at brush-commutator contact is fixed (1-2 V), independent of armature current as the conduct on process is mainly through numerous short arcs. However, this voltage being small is modeled as linear resistance and lumped with R_a. From now onwards it will be assumed that R_a includes the effect of brush voltage drop.

Generating Mode

The machine operates in generating mode (puts out electrical power) when I_a is in the direction of induced emf E_a as in Figure 2.19(a). For the armature circuit:

V (terminal voltage) = E_a – I_a R_a ; E_a > V

The mechanical power converted to electrical form is :

P_mech (in)|_net = E_a I_a = P_elect (out)|_gross

The net electrical power output is:

P₀ = VI_a

In actual machine this angle is 90° elect.

Also E_a I_a – VI_a = I_a² R_a = armature copper-loss

And P_mech (in)|_gross = shaft power = P_mech (in)|_net + rotational loss

 In this mode torque of electromagnetic origin is opposite to the direction of rotation of armature i.e., mechanical power is absorbed and a prime-mover is needed to run the machine.

The conductor emf and current are also in the same direction for generating mode as shown in the cross-sectional view of Figure 2.19(c).

Motoring Mode

In this mode, I_a flows in opposition to induced emf E_a as in Figure 2.19(b). E_a is now known as the back emf to stress the fact that it opposes the armature emf. For the armature circuit:

In this mode torque of electromagnetic origin is in the direction of armature rotation, i.e., mechanical power is put out and is absorbed by load (mechanical). Conductor emf and current are also in opposite directions for motoring mode as shown in Figure 2.19(c).