Generator D.C. characterteristics

If we are given O.C.C. of a generator at a constant speed N₁ then we can easily draw the O.C.C. at any other constant speed N_2.Fig (3.11) illustrates the procedure. Here we are given O.C.C. at a constant speed N1.It is desired to find the O.C.C. at constant speed N₂ (it is assumed that n₁ < N₂₎For constant
excitation,E α N

E₂/E₁=N₂/N₁

As shown in Fig. (3.11), forI_f = OH, E₁ = HC. Therefore, the new value of e.m.f. (E₂) for the same I_f but at N₂i.

E₂=HC ×( N₂/N₁) =HD

This locates the point D on the new O.C.C. at N₂. Similarly, other points can be
located taking different values of I_f . The locus of these points will be the O.C.C. at N₂.

Critical Speed (N_C )
The critical speed of a shunt generator is the minimum speed below which it fails to excite. Clearly, it is the speed for which the given shunt field resistance represents the critical resistance. In Fig. (3.12), curve 2 corresponds to critical speed because the shunt field resistance (R_sh) line is tangential to it. If the generator runs at full speed N, thenew O.C.C. moves upward and the R’_shline represents critical resistance for this speed.

Therefore , Speed α Critical resistance

In order to find critical speed, take any convenient point C on excitation
axis and erect a perpendicular so as to cut R_sh and R’_sh lines at points B and
A respectively. Then,

BC/AC =N_C/N

or N_C = N ×(BC/AC)

Conditions for Voltage Build-Up of a Shunt Generator

The necessary conditions for voltage build-up in a shunt generator are:
(i) There must be some residual magnetism in generator poles.
(ii) The connections of the field winding should be such that the field current strengthens the residual magnetism.
(iii) The resistance of the field circuit should be less than the critical resistance. In other words, the speed of the generator should be higher than the critical speed.

Fig (3.9) (i) shows the connections of a shunt wound generator. The armature current I_a splits up into two parts; a small fraction I_sh flowing through shunt field winding while the major part I_Lgoes to the external load.

(i) O.C.C.
The O.C.C. of a shunt generator is similar in shape to that of a series generator as shown in Fig. (3.9) (ii). The line OA represents the shunt field circuit resistance. When the generator is run at normal speed, it will build up a voltage OM. At no-load, the terminal voltage of the generator will be constant (= OM) represented by the horizontal dotted line MC.

(ii) Internal characteristic
When the generator is loaded, flux per pole is reduced due to armature reaction. Therefore, e.m.f. E generated on load is less than the e.m.f. generated at no load.As a result, the internal characteristic (E/I_a) drops down slightly as shown in Fig.(3.9) (ii).

(iii) External characteristic
Curve 2 shows the external characteristic of a shunt generator. It gives the
relation between terminal voltage V and load current I_L.

V = E – IaRa = E -(I_L +I_sh)R_a

Therefore, external characteristic curve will lie below the internal characteristic curve by an amount equal to drop in the armature circuit [i.e., (I_L +I_sh)R_a ] as shown in Fig. (3.9) (ii).

Note. It may be seen from the external characteristic that change in terminal
voltage from no-load to full load is small. The terminal voltage can always be
maintained constant by adjusting the field rheostat R automatically

Critical External Resistance for Shunt Generator

If the load resistance across the terminals of a shunt generator is decreased, then load current increase? However, there is a limit to the increase in load current with the decrease of load resistance. Any decrease of load resistance beyond this point, instead of increasing the current, ultimately results in reduced current. Consequently, the external characteristic turns back (dotted curve) as shown in Fig. (3.10). The tangent OA to the curve represents the minimum external resistance required to excite the shunt generator on load and is called critical external resistance. If the resistance of the external circuit is less than the critical external resistance (represented by tangent OA in Fig. 3.10), the machine will refuse to excite or will de-excite if already running This means that external resistance is so low as virtually to short circuit the machine and so doing away with its excitation.

Note. There are two critical resistances for a shunt generator viz., (i) critical field resistance (ii) critical external resistance. For the shunt generator to build up voltage, the former should not be exceeded and the latter must not be gone below.

Fig. (3.7) (i) shows the connections of a series wound generator. Since there is only one current (that which flows through the whole machine), the load currentis the same as the exciting current.

(i) O.C.C.
Curve 1 shows the open circuit characteristic (O.C.C.) of a series generator. It can be obtained experimentally by disconnecting the field winding from the machine and exciting it from a separate d.c. source as discussed in Sec. (3.2).
(ii) Internal characteristic

Curve 2 shows the total or internal characteristic of a series generator. It gives the relation between the generated e.m.f. E. on load and armature current. Due to armature reaction, the flux in the machine will be less than the flux at no load. Hence, e.m.f. E generated under load conditions will be less than the e.m.f.  E_Ogenerated under no load conditions. Consequently, internal characteristic curve generated under no load conditions. Consequently, internal characteristic curve lies below the O.C.C. curve; the difference between them representing the effect of armature reaction [See Fig. 3.7 (ii)].

(iii) External characteristic
Curve 3 shows the external characteristic of a series generator. It gives the relation between terminal voltage and load current I_L.

V= E-I_a(R_a+R_se)

Therefore, external characteristic curve will lie below internal characteristic
curve by an amount equal to ohmic drop[i.e., I_a(R_a+R_se)] in the machine as
shown in Fig. (3.7) (ii).

The internal and external characteristics of a d.c. series generator can be plotted from one another as shown in Fig. (3.8). Suppose we are given the internal characteristic of the generator. Let the line OC represent the resistance of the whole machine i.e. R_a+R_se.If the load current is OB, drop in the machine is AB i.e.
AB = Ohmic drop in the machine = OB(R_a+R_se)

Now raise a perpendicular from point B and mark a point b on this line such that ab = AB. Then point b will lie on the external characteristic of the generator. Following similar procedure, other points of external characteristic can be located. It is easy to see that we can also plot internal characteristic from the external characteristic.

Critical Field Resistance for a Shunt Generator

We have seen above that voltage build up in a shunt generator depends upon field circuit resistance. If the field circuit resistance is R1 (line OA), then generator will build up a voltage OM as shown in Fig. (3.5). If the field circuit resistance is increased to R2 (tine OB), the generator will build up a voltage OL, slightly less than OM. As the field circuit resistance is increased, the slope of resistance line also increases. When the field resistance line becomes tangent (line OC) to O.C.C., the generator would just excite. If the field circuit resistance is increased beyond this point (say line OD), the generator will fail to excite. The field circuit resistance represented by line OC (tangent to O.C.C.) is called critical field resistance RC for the shunt generator. It may be defined as under: The maximum field circuit resistance (for a given speed) with which the shunt generator would just excite is known as its critical field resistance. It should be noted that shunt generator will build up voltage only if field circuit resistance is less than critical field resistance.

Critical Resistance for a Series Generator

Fig. (3.6) shows the voltage build up in a series generator. HereR₁,R₂ etc. represent the total circuit resistance (load resistance and field winding resistance). If the total circuit resistance is R₁, then series generator will build up a voltage OL. The line OC is tangent to O.C.C. and represents the critical resistance RC for a series generator. If the total resistance of the circuit is more than R_c (say line OD), the generator will fail to build up voltage. Note that Fig. (3.6) is similar to Fig. (3.5) with the following differences:

(i) In Fig. (3.5), R₁,R₂ etc. represent the total field circuit resistance. However, R₁,R₂ etc. in Fig. (3.6) represent the total circuit resistance (load resistance and series field winding resistance etc.).

(ii) In Fig (3.5), field current alone is represented along X-axis. However, in Fig. (3.6) load current I_Lis represented along Y-axis. Note that in a series generator, field current = load current I_L.