D.C. Generator Characteristics

The speed of a d.c. machine operated as a generator is fixed by the prime mover. For general-purpose operation, the prime mover is equipped with a speed governor so that the speed of the generator is practically constant. Under such condition, the generator performance deals primarily with the relation between excitation, terminal voltage and load. These relations can be best exhibited graphically by means of curves known as generator characteristics. These characteristics show at a glance the behaviour of the generator under different load conditions.

D.C. Generator Characteristics
The following are the three most important characteristics of a d.c. generator:
1. Open Circuit Characteristic (O.C.C.)
This curve shows the relation between the generated e.m.f. at no-load (E0) and the field current (If) at constant speed. It is also known as magnetic characteristic or no-load saturation curve. Its shape is practically the same for all generators whether separately or self-excited. The data for O.C.C. curve are obtained experimentally by operating the generator at no load and constant speed and recording the change in terminal voltage as the field current is varied.
2. Internal or Total characteristic (E/Ia)
This curve shows the relation between the generated e.m.f. on load (E) and the armature current (Ia). The e.m.f. E is less than E0 due to the demagnetizing effect of armature reaction. Therefore, this curve will lie below the open circuit characteristic (O.C.C.). The internal characteristic is of interest chiefly to the designer. It cannot be obtained directly by experiment. It is because a voltmeter cannot read the e.m.f. generated on load due to the voltage drop in armature resistance. The internal characteristic can be obtained from external characteristic if winding resistances are known because armature reaction effect is included in both characteristics

3. External characteristic (V/IL)
This curve shows the relation between the terminal voltage (V) and load current (IL). The terminal voltage V will be less than E due to voltage drop in the armature circuit. Therefore, this curve will lie below the internal characteristic. This characteristic is very important in determining the suitability of a generator for a given purpose. It can be obtained by making simultaneous measurements of terminal voltage and load current (with voltmeter and ammeter) of a loaded generator.

Open Circuit Characteristic of a D.C. Generator

The O.C.C. for a d.c. generator is determined as follows. The field winding of the d.c. generator (series or shunt) is disconnected from the machine and is separately excited from an external d.c. source as shown in Fig. (3.1) (ii). The generator is run at fixed speed (i.e., normal speed). The field current ( I_f) is increased from zero in steps and the corresponding values of generated e.m.f.(E _o) read off on a voltmeter connected across the armature terminals. On plotting the relation between Eo and I_f, we get the open circuit characteristic as shown in Fig. (3.1) (i)

The following points may be noted from O.C.C.:
(i) When the field current is zero, there is some generated e.m.f. OA. This is due to the residual magnetism in the field poles.
(ii) Over a fairly wide range of field current (upto point B in the curve), the curve is linear. It is because in this range, reluctance of iron is negligible as compared with that of air gap. The air gap reluctance is constant and hence linear relationship.

(iii) After point B on the curve, the reluctance of iron also comes into picture. It is because at higher flux densities, μ_r for iron decreases and reluctance of iron is no longer negligible. Consequently, the curve deviates from linear relationship.
(iv) After point C on the curve, the magnetic saturation of poles begins and E_o tends to level off.The reader may note that the O.C.C. of even self-excited generator is obtained by running it as a separately excited generator.

Characteristics of a Separately Excited D.C. Generator

The obvious disadvantage of a separately excited d.c. generator is that we require an external d.c. source for excitation. But since the output voltage may be controlled more easily and over a wide range (from zero to a maximum), this type of excitation finds many applications.

(i) Open circuit characteristic.
The O.C.C. of a separately excited generator is determined in a manner described in Sec. (3.2). Fig. (3.2) shows the variation of generated e.m f. on no load with field current for various fixed speeds. Note that if the value of constant speed is increased, the steepness of the curve also increases. When the field current is zero, the residual magnetism in the poles will give rise to the small initial e.m.f. as shown.

(ii) Internal and External Characteristics
The external characteristic of a separately excited generator is the curve between the terminal voltage (V) and the load current 

I_L (which is the same as armature current in this case). In order to determine the external characteristic, the circuit set up is as shown in Fig. (3.3) (i). As the load current increases, the terminal voltage falls due to two reasons:
(a) The armature reaction weakens the main flux so that actual e.m.f. generated E on load is less than that generated (E _o) on no load.

(b) There is voltage drop across armature resistance (= I_LR_a = I_aR_a). Due to these reasons, the external characteristic is a drooping curve [curve 3 in Fig. 3.3 (ii)]. Note that in the absence of armature reaction and armature drop, the generated e.m.f. would have been E _o (curve 1). The internal characteristic can be determined from external characteristic by adding I_LR_a drop to the external characteristic. It is because armature reaction drop is included in the external characteristic. Curve 2 is the internal characteristic of the generator and should obviously lie above the external characteristic.

Voltage Build-Up in a Self-Excited Generator

Let us see how voltage builds up in a self-excited generator.
(i) Shunt generator
Consider a shunt generator. If the generator is run at a constant speed, some e.m.f. will be generated due to residual magnetism in the main poles. This small e.m.f. circulates a field current which in turn produces additional flux to reinforce the original residual flux (provided field winding connections are correct). This process continues and the generator builds up the normal generated voltage following the O.C.C. shown in Fig. (3.4) (i).

The field resistance R_f can be represented by a straight line passing through the origin as shown in Fig. (3.4) (ii). The two curves can be shown on the same diagram as they have the same ordinate [See Fig. 3.4 (iii)]. Since the field circuit is inductive, there is a delay in the increase in current upon closing the field circuit switch The rate at which the current increases depends upon the voltage available for increasing it. Suppose at any instant, the field current is i (= OA) and is increasing at the rate di/dt. Then,

E_{O =} IR_f + L di/dt

R_f = total field circuit resistance

L = inductance of field circuit

R_fand the remainder part BC is available to overcome L di/dt. Since this surplus voltage is available, it is possible for the field current to increase above the value OA. However, at point D, the available voltage is OM and is all absorbed by i R_fdrop. Consequently, the field current cannot increase further and the generator build up stops.

We arrive at a very important conclusion that the voltage build up of the generator is given by the point of intersection of O.C.C. and field resistance line. Thus in Fig. (3.4) (iii), D is point of intersection of the two curves. Hence the generator will build up a voltage OM.
(ii) Series generator
During initial operation, with no current yet flowing, a residual voltage will be generated exactly as in the case of a shunt generator. The residual voltage will cause a current to flow through the whole series circuit when the circuit is
closed. There will then be voltage build up to an equilibrium point exactly analogous to the build up of a shunt generator. The voltage build up graph will be similar to that of shunt generator except that now load current (instead of field current for shunt generator) will be taken along x-axis.

(iii) Compound generator
When a compound generator has its series field flux aiding its shunt field flux, the machine is said to be cumulative compound. When the series field is connected in reverse so that its field flux opposes the shunt field flux, the generator is then differential compound. The easiest way to build up voltage in a compound generator is to start under no load conditions. At no load, only the shunt field is effective. When no-load voltage build up is achieved, the generator is loaded. If under load, the voltage rises, the series field connection is cumulative. If the voltage drops significantly, the connection is differential compound.

Critical Resistance

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. Here R₁,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.

Characteristics of Series Generator

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_O generated 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.

Characteristics of a Shunt Generator

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_L goes 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.

How to Draw O.C.C. at Different Speeds?

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), for I_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’_sh line 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. 

Compound Generator Characteristics

In a compound generator, both series and shunt excitation are combined as shown in Fig. (3.13). The shunt winding can be connected either across the armature only (short-shunt connection S) or across armature plus series field (long-shunt connection G). The compound generator can be cumulatively compounded or differentially compounded generator. The latter is rarely used in practice. Therefore, we shall discuss the characteristics of cumulatively compounded generator. It may be noted that external characteristics of long and short shunt compound generators are almost identical.
External characteristic
Fig. (3.14) shows the external characteristics of a cumulatively compounded
generator. The series excitation aids the shunt excitation. The degree of compounding depends upon the increase in series excitation with the increase in load current.

(i) If series winding turns are so adjusted that with the increase in load current the terminal voltage increases, it is called over-compounded generator. In such a case, as the load current increases, the series field m.m.f. increases and tends to increase the flux and hence the generated voltage. The increase in generated voltage is greater than the  I_aR_a drop so that instead of decreasing, the terminal voltage increases as shown by curve A in Fig. (3.14).
(ii) If series winding turns are so adjusted that with the increase in load
current, the terminal voltage substantially remains constant, it is called flat-compounded generator. The series winding of such a machine has lesser number of turns than the one in over-compounded machine and, therefore, does not increase the flux as much for a given load current. Consequently, the full-load voltage is nearly equal to the no-load voltage
as indicated by curve B in Fig (3.14).
(iii) If series field winding has lesser number of turns than for a flat compounded machine, the terminal voltage falls with increase in load
current as indicated by curve C m Fig. (3.14). Such a machine is called under-compounded generator.

Voltage Regulation

The change in terminal voltage of a generator between full and no load (at constant speed) is called the voltage regulation, usually expressed as a percentage of the voltage at full-load.

% Voltage regulation= [ (V_NL-V_FL)/V_FL ] × 100

where V_NL = Terminal voltage of generator at no load

V_{FL =} Terminal voltage of generator at full load
Note that voltage regulation of a generator is determined with field circuit and speed held constant. If the voltage regulation of a generator is 10%, it means that terminal voltage increases 10% as the load is changed from full load to no load