SEPARATELY EXCITED DC GENERATOR

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

            R_fw is the resistance of the field winding.

            R_fc is the resistance of the control rheostat used in the field circuit.

            R_f = R_fw + R_fc is the total field circuit resistance.

R_a is the resistance of the armature circuit, including the effects of the brushes. Sometimes R_a 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.

R_L 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:

V_f = R_f I_f                                                         …(1)

E_a = V_t + I_a R_a                                                 …(2)

E_a = K_a F w_m                                                  …(3)

V_t = I_t R_L                                                         …(4)

I_a = I_t                                                               …(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 I_t increases, the terminal voltage V_t decreases linearly (assuming E_a remains constant) because of the voltage drop across R_a. This voltage drop I_a R_a is small, because the resistance of the armature circuit R_a 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 V_AR) 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 V_t and the terminal current I_t. 

 

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 (I_a = I_t = 0) the terminal voltage is the same as the generated voltage (V_t0 = E_a0). 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 I_a R_a drop .

In Fig.5, the generated voltage for an actual field current I_f(actual) is E_a0. When the load current I_a flows the generated voltage is E_a = V_t + I_a R_a. If E_a < E_a0, the flux has decreased (assuming the speed remains unchanged) because of armature reaction, although the actual field current I_f(actual) in the field winding remains unchanged. In Fig. 5, the generated voltage E_a is produced by an effective field current I_f(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,

I_f(eff) = I_f(actual) – I_f(AR)                                         …(6)

where I_f(AR) is the armature reaction in equivalent field current

Fig. 4: MMF and flux density distribution.

 

Fig.5: Effect of armature reaction.

 

Compensating Winding

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.

 

SHUNT (SELF-EXCITED) GENERATOR

In the shunt or self-excited generator, the field is connected across the armature so that the armature voltage can supply the field current. Under certain conditions, to be discussed here, this generator will build up a desired terminal voltage.

The circuit for the shunt generator under no-load conditions is shown in Fig. 1. If the machine is to operate as a self-excited generator, some residual magnetism must exits in the magnetic circuit of the generator. Figure 2. shows the magnetization curve of the dc machine. Also shown in this figure is the field resistance line, which is a plot of R_fI_f versus I_f. A simplistic explanation of the voltage buildup process in the self-excited dc generator is as follows: 

Fig. 1: Schematic of a shunt (self-excited) dc machine. 

 

Fig. 2: Voltage build-up in a self-excited dc generator. 

Assume that the field circuit is initially disconnected from the armature circuit and the armature is driven at a certain speed. A small voltage, E_ar, will appear across the armature terminals because of the residual magnetism in the machine. If the switch SW is now closed (Fig. 1), the field circuit is connected to the armature circuit and hence a current will flow in the field winding. If the mmf of this field current aids the residual magnetism, eventually a current I_fl will flow in the field circuit. The buildup of this current will depend on the time constant of the field circuit. With I_fl flowing in the field circuit, the generated voltage is E_al – from the magnetization curve – but the terminal voltage, V_t = I_flR_f < E_al. The increased armature voltage E_al will eventually increase the field current to the value I_f2, which in turn will build up the armature voltage to E_a2. This process of voltage buildup continues. If the voltage drop across R_a is neglected (i.e., R_a << R_f), the voltage builds up to the value given by the crossing point (P in Fig. 2) of the magnetization curve and the field resistance line. At this point, E_a = I_fR_f = V_t (assume R_a is neglected), and no excess voltage is available to further increase the field current. In the actual case, the changes in I_f and E_a take place simultaneously and the voltage buildup follows approximately the magnetization curve, instead of climbing the flight of stairs. 

Fig. 3: Effect of field resistance.

 

Figure 3 shows the voltage buildup in the self-excited dc generator for various field circuit resistances. At some resistance value R_f3, the resistance line is almost coincident with the linear portion of the magnetization curve. This coincidence condition results in an unstable voltage situation. This resistance is known as the critical field circuit resistance. If the resistance is greater than this value, such as R_f4, buildup (V_t4) will be insignificant. On the other hand, if the resistance is smaller than this value, such as R_f1 or R_f2, the generator will build up higher voltages (V_t1, V_t2). To sum up, three conditions are to be satisfied for voltage buildup in a self-excited dc generator:

1.      Residual magnetism must be present in the magnetic system.

2.      Field winding mmf should aid the residual magnetism.

3.      Field circuit resistance should be less than the critical field circuit resistance.

Voltage – Current Characteristics

The circuit of the dc shunt generator on load is shown in Fig. 4. The equations that describe the steady-state operation on load are

E_a = V_t + I_aR_a       …(1)

E_a = K_a F w_m = function of I_f    …(2)

è magnetization curve (or open-circuit saturation curve)

V_t = I_fR_f = I_f (R_fw + R_fc)     …(3)

V_t = I_tR_L     …(4)

I_a = I_f + I_t    …(5)

The terminal voltage (V_t) will change as the load draws current from the machine. This change in the terminal voltage with current (also known as voltage regulation) is due to the internal voltage drop I_aR_a (Eq. 1.25a) and the change in the generated voltage caused by armature reaction (Eq. 1.25b). The typical terminal characteristic is shown in Fig. 6. It is apparent that the terminal voltage drops faster with the armature current in the self- excited generator. The reason is that, as the terminal voltage decreases with load in the self-excited generator, the field current also decreases, resulting in less generating voltage, whereas in the separately excited generator, the field current and hence the generated voltage remain unaffected.

 

Fig. 5: Dc shunt generator with load. 

 

Fig .6: Terminal characteristic of a dc shunt generator.