The separately excited dc generator, the field winding is connected to a separate source of dc power. This source may be another dc generator, a controlled rectifier, or a diode rectifier, or a battery. The steady-state model of the separately excited dc generator is shown in Fig. 1. In this model
Rfw is the resistance of the field winding.
Rfc is the resistance of the control rheostat used in the field circuit.
Rf = Rfw + Rfc is the total field circuit resistance.
Ra is the resistance of the armature circuit, including the effects of the brushes. Sometimes Ra is shown as the resistance of the armature winding alone; the brush-contact voltage drop is considered separately and is usually assumed to be about 2 V.
RL is the resistance of the load.
In the steady-state model, the inductances of the field winding and armature winding are not considered.
The defining equations are the following:
Vf = Rf If …(1)
Ea = Vt + Ia Ra …(2)
Ea = Ka F wm …(3)
Vt = It RL …(4)
Ia = It …(5)
Equation 2 defines the terminal or external characteristic of the separately excited dc generator; the characteristic is shown in Fig.2. As the terminal (i.e., load) current It increases, the terminal voltage Vt decreases linearly (assuming Ea remains constant) because of the voltage drop across Ra. This voltage drop Ia Ra is small, because the resistance of the armature circuit Ra is small. A separately excited dc generator maintains an essentially constant terminal voltage.
At high values of the armature current, a further voltage drop (D VAR) occurs in the terminal voltage; that is known as armature reaction (or the demagnetization effect) and causes a divergence from the linear relationship. This effect can be neglected for armature currents below the rated current. It will be discussed in the next section.
The load characteristic, defined by Eq. 4, is also shown in Fig. 2. The point of intersection between the generator external characteristic and the load characteristic determines the operating point, that is, the operating values of the terminal voltage Vt and the terminal current It.
Fig. 1: Steady state model of a separately excited dc generator.
Fig. 2: Terminal characteristics of a separately excited dc generator.
Armature Reaction (AR)
With no current flowing in the armature, the flux in the machine is established by the mmf produced by the field current, as shown in Fig-3a. However, if the current flows in the armature circuit, it produces its own mmf (hence flux) acting along the q-axis. Therefore, the original flux distribution in the machine due to the field current is disturbed. The flux produced by the armature mmf opposes flux in the pole under one half of the pole and aids under the other half of the pole, as shown in Fig. 3b. Consequently, flux density under the pole increases in one half of the pole and decreases under the other half of the pole. If the increased flux density causes magnetic saturation, the net effect is a reduction of flux per pole. This is illustrated in Fig. 3c.
Fig. 3: Armature reaction effects.
To have a better appreciation of the mmf and flux density distribution in a dc machine, consider the developed diagram of Fig.4a. The armature mmf has a saw tooth wave form as shown in Fig. 4b. For the path shown by the dashed line, the net mmf produced by the armature current is zero because it encloses equal numbers of dot and cross currents. The armature mmf distribution is obtained by moving this dashed path and considering the dot and cross currents enclosed by the path. The flux density distribution produced by the armature mmf is also shown in Fig. 4b by a solid curve. Note that in the interpolar region (i.e., near the q-axis), this curve shows a dip. This is due to the large magnetic reluctance in this region. In Fig.4c the flux density distributions caused by the field mmf, the armature mmf, and their resultant mmf are shown. Note that
· Near one tip of a pole, the net flux density shows saturation effects (dashed portion).
· The zero flux density region moves from the q-axis when armature current flows.
· If saturation occurs, the flux per pole decreases. This demagnetizing effect of armature current increases as the armature current increases.
At no load (Ia = It = 0) the terminal voltage is the same as the generated voltage (Vt0 = Ea0). As the load current flows, if the flux decreases because of armature reaction, the generated voltage will decrease (Eq. 3). The terminal voltage will further decrease because of the Ia Ra drop .
In Fig.5, the generated voltage for an actual field current If(actual) is Ea0. When the load current Ia flows the generated voltage is Ea = Vt + Ia Ra. If Ea < Ea0, the flux has decreased (assuming the speed remains unchanged) because of armature reaction, although the actual field current If(actual) in the field winding remains unchanged. In Fig. 5, the generated voltage Ea is produced by an effective field current If(eff). The net effect of armature reaction can therefore be considered as a reduction in the field current. The difference between the actual field current and effective field current can be considered as armature reaction in equivalent field current. Hence,
If(eff) = If(actual) – If(AR) …(6)
where If(AR) is the armature reaction in equivalent field current
Fig. 4: MMF and flux density distribution.
Fig.5: Effect of armature reaction.
The armature mmf distorts the flux density distribution and also produces the demagnetizing effect known as armature reaction. The zero flux density region shifts from the q-axis because of armature mmf (Fig.4), and this causes poor commutation leading to sparking. Much of the rotor mmf can be neutralized by using a compensation winding, which is fitted in slots cut on the main pole faces. These pole face windings are so arranged that the mmf produced by currents flowing in these windings opposes the armature mmf. This is shown in the developed diagram of Fig. 6a. The compensating winding is connected in series with the armature winding so that its mmf is proportional to the armature mmf. Figure 6b shows a schematic diagram and Fig 6c shows the stator of a dc machine having compensating windings. These pole face windings are expensive. Therefore they are used only in large machines or in machines that are subjected to abrupt changes of armature current. The dc motors used in steel rolling mills are large as well as subjected to rapid changes in speed and current. Such dc machines are always provided with compensating windings.