When we studied electric motors we saw that when applying a DC voltage to the motor terminals, it develops
a torque giving rise to rotational motion. It then transforms electrical energy into mechanical energy. In case
generators, the process is exactly the opposite, that is, we apply a torque on the generator shaft, for some
mechanical means, obtaining an electrical voltage at its terminals. As with motors, generators
we must also apply a voltage to the field winding to produce a magnetic field. So when the generator
starts to rotate, the turns that are housed in the rotor will develop a magnetomotive force
(fmm) induced, which obeys Faraday's law, and we will call it EA. This induced voltage, to appear at the output terminals of the generator, must overcome the voltage drop in the resistance RA of the armature. In this way, we will obtain a DC voltage at the output of the generator, which we will call
Vg. So, the equation that governs the operation of an electric generator
is expressed by the eq. 104-01.
eq. 104-01
This equation tells us that the magnetomotive force (fmm), or EA minus the voltage
drop across the resistance of the armature winding must be equal to the voltage Vg that appears
at the output terminals of the generator. From this equation, we can derive two more, or:
eq. 104-02
This equation allows us to calculate the magnetomotive force (fmm) induced in the armature when we know the other variables.
eq. 104-03
This equation allows us to calculate the armature current. Note that all these equations are easy to
understanding if we look at Figure 104-01, where we present the equivalent circuit of a DC generator
in a configuration with independent excitation.
Figure 104-01
Note that compared to the equivalent circuit of a motor, in the case of the generator, the armature current
IA is leaving through the positive terminal going to feed the load connected to the ends of the output terminals
from the generator. In the field winding circuit we have the same configuration as a motor. It should be noted that for the case of the engine electric we must have two voltage sources. One for powering the field winding circuit and the other for
feed the armor. In the case of the generator, we should have only one voltage source for the field winding circuit.
The generator armature behaves as a voltage source.
It should be noted that in DC machines, as we have the brushes in contact with the commutator, which lead to
armature current, this causes an additional voltage drop in the armature circuit. This voltage drop, symbolized by
VB, must be subtracted in eq. 104-01, as explained in eq. 104-04. Then,
depending on the author, some problems will mention the voltage VB. In general, unless otherwise specified,
the voltage drop across the brushes is of the order of 1 V to 2 V when we have two brushes operating in series
and we can consider it independent of the armature current.
eq. 104-04
All DC electric motor theory is applicable to generators. So now let's study the various ways
to connect a DC generator, as we did in the chapter referring to motors.
The four basic types of DC generators are the so-called Independent Excitation, Shunt, Series and
Compound. The differences among the types of generators are due to the way in which the excitation of the polar
field winding is produced. As well as the purpose of the generator is to produce a DC voltage by converting mechanical energy into electrical energy, a portion of this DC voltage is used to power the stationary magnetic field winding. Let's study each case separately.
3.1 DC Generator with Independent Excitation
A independent excitation DC generator is a generator whose field current is supplied by an external DC voltage source
separate. The equivalent circuit of this machine is shown in Figure 104-01. In this circuit, the voltage
Vg represents the actual voltage measured at the generator terminals and the current IL represents the current circulating in the load connected to the output terminals. The internal generated voltage is EA and the armature current
is IA. It is clear that in an independently excited generator the line current is equal to the armature current,
according to eq. 104-05.
eq. 104-05
Important Note
"It is interesting to note that both generators and motors manage to maintain a minimum of magnetism in their fields
polar, usually known as residual magnetism. This is due to the magnetism that remained in the polar fields of the
machine when the shutdown thereof. This characteristic is very important in generators, because with a minimum of field
the generator can present a voltage at the output terminals. As we will study later, this is fundamental for some types of
generators to are able to function satisfactorily even without excitation in the field winding."
The output voltage of an independently excited DC generator can be controlled by changing the internal voltage generated by the machine, that is, EA. By Kirchhoff's voltage law, we have the eq. 104-01, where Vg = EA - RA IA. Thus, if EA increases, then Vg will increase, and if EA decreases,
Vg will decrease. Since the generated internal voltage EA is given by eq. 103-11 where EA = KΦ ω there are two possible ways to control the voltage of this generator:
1 - Change rotation speed - If ω increases, then EA will increase accordingly
eq. 103-11, so Vg will also increase.
2 - Changing field current - Increasing field current by decreasing field resistance
RF, machine flow grows. When that happens, EA must also grow, so
Vg grows.
As the internal generated voltage EA is independent of IA, the output characteristic of the
independent excitation generator is a straight line, as represented by the red line in Figure 104-02.
This happens when the generator has no load (no load) or it is very small.
What happens in such a generator when the load is increased? When
the load supplied by the generator is increased, IL (and therefore IA) increases. as
the armature current rises, the drop RA IA grows, so the output voltage
generator falls, as indicated by the blue line in Figure 104-02.
In many applications, the speed range of the prime mover is very limited, so it is more common to control
the output voltage by changing the field current.
Figure 104-02
This output characteristic is not always entirely accurate. in generators
without compensating windings, an increase in IA causes an increase in the reaction of
armature, which leads to flux weakening. This causes a decrease in
EA, which further decreases the output voltage of the generator. in all charts
future, we will assume generators have compensating windings unless
to express the contrary. However, it is important to bear in mind that if the compensation windings are not present,
armature reaction may change characteristics.
Since the generated internal voltage of a generator is a non-linear function of its force
magnetomotive, it is not possible to simply calculate the expected value of EA
for a given field current. The magnetization curve of the generator must be
used to accurately calculate its output voltage for a given input voltage.
Furthermore, if a machine has armature reaction, then its flux will be
reduced with each load increment, causing EA to decrease. The only way to
accurately determine the output voltage in an armature reaction machine
is by the use of graphical analysis.
Figure 104-03
In Figure 104-03 we see a graph where we have a pure resistance as load, ZL. the intersection point
between the Vg line and the ZL line, determines the load current value.
The total magnetomotive force (fmm) of an independent excitation generator is the force
magnetomotive force of the field circuit minus the magnetomotive force due to the reaction
of armature, according to eq. 104-06.
eq. 104-06
As with DC motors, it is customary to define an equivalent field current, represented by IFeq,
as the current that would produce the
same output voltage as a result of the combination of all magnetomotive forces present in the machine. The tension
The resulting EA0 can be determined by locating the equivalent field current over the magnetization curve. The
equivalent field current of an independently excited DC generator is given by:
eq. 104-07
Not forgetting that the difference between the speed in the magnetization curve and the actual speed of the generator
must be taken into account consideration using the eq. 103-21, repeated below.
When we feed the field winding through all (or almost all) of the line voltage produced between the brushes
of the armature, the DC generator is called Shunt Generator. Figure 104-04 shows the complete diagram of a shunt generator.
Figure 104-04
The rotor, where the armature winding is located, is represented by the following components: an induced voltage source
EA, which has a value according to eq. 104-02; a resistance
RA of the armature winding; and a resistor RB (not shown in the figure) representing the
contact resistance between the brushes and the commutator. In this way, the complete armature circuit consists of the winding of
armature (which is the moving part) and two optional windings, namely the compensation winding LC and the winding of the Li interpoles, both located on the stator and fixed. The compensation winding LC features
a resistance that we will call RC and the winding of the interpoles Li presents a
resistance that we will call Ri. The equivalent circuit shown in Figure 104-04 can be
simplified if we add the values of the four resistances in series by a single one, which we will call RAS.
Therefore, RAS = RA + RB + RC + Ri .
Remembering that the inductances LC and Li do not interfere, because for direct current they
represent a short circuit, that is, null resistance.
See Figure 104-05 for this new representation.
Figure 104-05
From Figure 104-05 we clearly see that the three circuits, here represented by the armature circuit, the circuit
field and the load are in parallel. In this circuit, the machine armature current feeds both the field circuit and the load
connected to the machine. Therefore, from the circuit we conclude that, for a shunt generator, the relation
shown in eq. 104-08.
eq. 104-08
We should also point out that because the three circuits are in parallel, the voltages on each one are the same, or
let VA = Vg = VL. Then the currents in the circuit are easily calculated
according to eq. 104-03, eq. 104-09 and eq. 104-10. Below, we show these three equations.
eq. 104-03
eq. 104-09
eq. 104-10
Keep in mind that in eq. 104-10, the load ZL can be a purely resistive load or, a load
complex. And for this type of generator, the eq. 104-01 is valid, that is:
eq. 104-01
This type of generator has a clear advantage over the independent excitation DC generator because there is no need for a source external power supply for the field loop.
However, this leaves an important question unanswered:
when the starter is given, how does he get the initial field flow to generate EA, if he himself supplies the
field current?
Let's consider the initial case where the generator does not have a load connected to the output terminals. Assume that the axis of generator is coupled to a driving machine, such as an electric motor or diesel engine, and this sets the generator shaft in rotation.
The question is: how is the initial voltage generated at the output terminals of the generator?
The initial production of a voltage in a DC generator depends on the presence of
a residual flux in the generator poles. Initially, when a generator starts to
rotate, an internal voltage will be induced, being given by eq. 103-11, shown below for clarity.
eq. 103-11
In this case, we are considering Φ as a residual flux that exists in the polar fields of the generator,
as already mentioned previously explained ( to see click here!)
In this way, voltage EA appears at the generator terminals (it can be just one or two volts).
However, when this occurs, this voltage circulates a current in the field coil of the generator, given by eq. 104-09. That
field current produces a magnetomotive force at the poles, increasing the flux in them. The flow increment causes an increase
across EA, which increases the terminal voltage Vg. When Vg goes up,
IF grows even more, increasing Φ flow, which increases EA, generating
a chain reaction process that only ends when the output voltage reaches the nominal value stipulated according to the saturation curve
magnetic of the polar faces.
It is this effect of the magnetic saturation of the polar faces that prevents the continuous growth of the output voltage of the generator.
At startup, what happens if a shunt generator starts and no voltage
is initial produced? What could be wrong? There are several possible causes why
the initial voltage is not produced during starting. We will enunciate three possible causes. Be them:
1 - There may be no residual magnetic flux in the generator. This will prevent the priming process
get started. If the residual flux is null, then
we will have EA = 0 and the voltage will never start to be produced. If this occurs
problem, turn off the armature circuit field and connect it directly
to an external DC source, such as a battery. The current flow from this source
External DC will leave a residual flux in the poles, thus allowing a normal start. Therefore, this procedure consists of
apply directly to field a DC current for a brief period of time.
2 - There may have been a reversal of the direction of rotation of the generator or it may have
there has been a reversal in the field connections. In both cases, the residual flux still generates an internal voltage
EA. This voltage produces a current of
field which, in turn, induces a flow such that, instead of adding to it, it opposes the
residual flow. Under these circumstances, the resulting flux will decrease in intensity, actually being below the flux
residual without inducing any voltage.
If this problem occurs, it can be corrected by reversing the direction of
rotation, reversing the connections, or even briefly applying to the field a
DC current such as to reverse the magnetic polarity.
3 - The field resistance value can be set to a value greater than
than that of critical resistance. To understand this problem, refer to Figure
104-06. Normally, the starting voltage of the shunt generator will rise to the point
where the magnetization curve intersects the field resistance line. if this
field resistance has the R2 value in the figure, its line will be approximately parallel to the magnetization curve.
In this case, the generator voltage may
fluctuate widely with only minor changes from RF or IA. This value of
resistance is called critical resistance. If RF exceeds critical strength
(as in R3 in the figure), the steady-state operating voltage will occur
basically at residual level and will never go up. The solution to this problem
is in reducing RF.
As the voltage of the magnetization curve varies as a function of the speed of the
axis, the critical resistance will also vary with speed. In general, the smaller
the speed of the shaft, the smaller the critical resistance.
Figure 104-06
To understand the graphical analysis of shunt generators, it is essential to remember Kirchhoff's voltage law (LKT) already studied and
represented by equations eq. 104-01 and eq. 104-02, repeated below for clarity.
The output characteristic of a shunt DC generator is different from that of a
independent excitation generator, because the field current of the machine depends
of its output voltage. To understand the output characteristic of a shunt generator, let's start a narrative
considering that the machine starts with no load (empty) and we gradually add load to it.
As the generator load increases, IL grows and therefore IA
also grows. A rise of IA increases the voltage drop IA RA across resistance of
armature, making Vg decrease, according to eq. 104-01. This behavior is precisely
the same observed in an independent excitation generator. However, when
Vg decreases, the field current IF of the machine decreases with it. This makes the flow
machine to decrease, also reducing EA. The fall in EA causes a further decrease in
terminal voltage Vg. The resulting output characteristic is shown in Figure 8-52. Note that the fall of
voltage is steeper than simply the IA RA drop of the independent excitation generator.
In other words, the voltage regulation of this generator is worse than that of the same type of equipment in
that the excitation is connected separately.
As with the independently excited generator, there are two ways to control the voltage
of a DC generator in shunt, namely:
1 - Change the ω speed of the generator shaft.
2 - Change the RF field resistance of the generator, thus varying the field current.
The field resistance variation RF is the main method used to control
the output voltage of real shunt generators. If the field resistance RF
is decreased, then the field current IF will increase. When IF increases,
the machine's flux also rises, causing the generated internal voltage EA to increase.
The increase in EA makes the output voltage Vg of the generator also increase.
The analysis of a DC shunt (or shunt) generator is more complex than the analysis of a
independent excitation generator, because the field current of the machine depends
directly from the machine's own output voltage. So, first let's do an analysis for
machines without armature reaction, and after, we incorporated the effects of armature reaction.
No Armature Reaction
Figure 104-07 shows a magnetization curve for a shunt dc generator plotted for the actual speed of
machine operation. The field resistance RF, which is simply equal to Vg /IF, is the straight line superimposed on the curve of
magnetization. A blank, we can write that Vg = EA and the generator operates at the voltage where the voltage curve magnetization intersects the field resistance line.
Figure 104-07
To understand the graphical analysis of shunt generators, it is essential to remember Kirchhoff's voltage law (LKT)
already studied and represented by equations eq. 104-01 and eq. 104-02. Let's repeat them below for better understanding.
eq. 104-01
eq. 104-02
The difference between the generated internal voltage EA and the output voltage Vg is simply the
RA IA falls from the machine. The line with all possible values of EA is the curve of
magnetization and the line with all possible output voltages Vg is the resistance line. So to find
the output voltage for a given load,
simply determine the drop RA IA and locate on the graph the place where this drop
fits exactly between the curve EA and the line Vg. There are at most two places in the
curve where the drop RA IA will fit exactly. If there are two possible locations, the
whichever is closest to the no-load voltage represents a normal operating point.
With Armature Reaction
If armature reaction is present in a shunt dc generator, this
process will become a bit more complicated. The armature reaction produces a
demagnetizing magnetomotive force on the generator at the same time that a
RA IA falls on the machine.
To analyze an armature reaction generator, assume that its current
of armor is known. Then the resistive voltage drop RA IA will be known. THE
output voltage of this generator must be high enough to supply the flow
of the generator after the demagnetizing effect of the armature reaction has been subtracted.
To meet this requirement, the armature reaction magnetomotive force and RA IA drop must match
fit between the curve EA and the line Vg. To determine the voltage of
output corresponding to a given magnetomotive force, simply locate the place
below the magnetization curve where the triangle formed by the effects of the
armature and RA IA fit exactly between the line of possible values of Vg and
the curve of possible values of EA. See Figure 104-07.
When the excitation is produced by a field winding connected in series with the armature, so that the flux
produced is a function of the armature current and the load, the DC generator is called a series generator. The Figure 104-08
shows the complete diagram of a series generator. The series field is excited only when the load is turned on, completing the
circuit. As the field winding must carry the entire armature current, it is constructed with few turns of wire with a
gauge that supports this current, that is, a thick wire (large diameter). So how does the current
of full load circulates through the field, this field must be designed in series to have
as little resistance as possible.
Figure 104-08
Note that the armature current, field current, and line current all have the same value,
that is:
eq. 104-11
On the other hand, Kirchhoff's voltage law for the series generator is:
eq. 104-12
As in the previous case, the compensation winding, Rc, located between the poles,
and the interpole winding, Ri, are included in series with the armature winding. That
total resistance, when dealing with a series configuration, we call it Ras. The other variables already
are known.
The magnetization curve of a series dc generator closely resembles the magnetization curve
magnetization of any other generator. At no-load, however, there is no field current, so Vg
reduces to a very low level due to the residual flow present
in the machine. As the charge grows, the field current rises, so that
EA rises quickly. The voltage drop IA (RA + Ras )
also increases, but initially the increase in EA results more quickly than the increase in the fall
IA (RA + Ras ) and, consequently, Vg goes up. After one
time, the machine approaches saturation and EA becomes almost constant. At that point, the resistive drop
becomes the predominant effect and Vg starts to fall.
This type of feature is shown in Figure 104-09. It is obvious that such a machine would prove to be a
very bad constant voltage supply. In fact, your voltage regulation is a large negative number.
Figure 104-09
Series generators are only used in a few specialized applications where the characteristic of
sharp drop in device voltage
can be explored. One such application is electric arc welding. The generators
series used in arc welding are intentionally designed to have a
high armature reaction.
Thus, when the welding electrodes make contact
each other before the actual welding starts, a very high current
circulates. When the welder moves the electrodes away, there is a very sharp rise in the
generator voltage, while the current remains high. This voltage ensures
that a welding arc is maintained through the air between the electrodes.
When field winding excitation is produced by a combination of the two configurations studied above, i.e.
shunt field winding excited by armature voltage (item 3.2) and series field winding excited
by the armature current or line current (item 3.3), the DC generator is called a composite generator.
In the case of the compound generator, it is possible to establish two types of connections, usually called
cumulative compound and differential compound. A cumulative composite dc generator is a dc generator
that has the fields in series LS and in derivation LF connected in such a way that the magnetomotive
forces of the two add up.
The Figure 104-10 shows the equivalent circuit of a compound cumulative dc generator in the long lead connection.
The dots or marks that appear on the two field coils have the same meaning as the dots on a transformer: the current
entering the dotted end of the coil produces a positive magnetomotive force.
Figure 104-10
Note that the armature current enters the dotted end of the series field coil and that the current
IF of shunt enters the dotted end of the shunt field coil. Therefore,
the total magnetomotive force in this machine is given by
eq. 104-13
Where the variables involved in eq. 104-13 mean:
Fliq - total magnetomotive force present in the machine;
Fsh - shunt field magnetomotive force;
Fse - series field magnetomotive force;
FRA - magnetomotive force of machine armature reaction.
Note that the magnetomotive forces of the series field and the shunt field are added, while the
armature reaction is subtracted, agreeing with the statement that this reaction is demagnetizing.
From eq. 104-13 we can find the effective equivalent current of the shunt field,
or IF eq, knowing that F= N I. Thus, substituting in eq. 104-13 and, after
algebraically, we find:
eq. 104-14
Where do we have the variables:
NSE - number of turns of the series field;
NF - number of turns of the field (of magnetization).
Looking at the equivalent circuit shown in Figure 104-10, we can infer the following equations for the currents involved in the circuit.
The Figure 104-11 shows the circuit of a short shunt composite generator. Note that unlike the long shunt, the shunt
short has the field winding situated between the armature winding and the series field winding.
Figure 104-11
This causes the shunt field winding to be in parallel with the armature circuit and the series field circuit is
connected in series with the load. The equation eq. 104-15 is also valid for this configuration.
To understand the terminal characteristic of a cumulative composite dc generator, it is necessary to understand the simultaneous effects that occur within the machine.
Suppose the generator load is increased. So, as the load
goes up, the load current IL goes up. In this case, the armature current also increases.
Therefore, at this point, two effects occur in the generator:
When IA increases, the voltage drop IA (RA + RS ) also increases.
This tends to cause a decrease in the output voltage Vg, depending on the eq. 104-12.
As IA increases, the magnetomotive force of the series field
Fse = Nse IA
also increases. This increases the total magnetomotive force
Fliq = NF IF + Nse IA
which increases the flow in the generator. This increased flow in the generator
makes EA rise, which in turn tends to raise the output voltage Vg.
These two effects are opposite to each other, with one tending to raise Vg and the other
tending to download Vg. Which effect will be predominant on a given machine? All
will depend on how many turns in series are placed on the poles of the machine. This situation gives rise to three possible alternatives that
get their own name. Let's study each situation separately.
Few turns in series (Nif small). If there are only a few turns, the
effect of resistive voltage drop easily prevails. The voltage drops just like on a shunt generator, but not as sharply. See Figure 104-12, where we show this effect. This type of configuration, in which the output voltage at full load is lower than the output voltage at no load, is called hypocomposite. This generator has a
better voltage regulation than the equivalent composite generator.
The hypocomposite generator has a slightly "dipping" characteristic, similar to that of a shunt generator, but with a
improved regulation. If we short-circuit the terminals of the series field (Rd = 0, see Figure 104-14) of a hypercomposite cumulative generator, it will act as a shunt generator. If the resistance of the drain resistor is
increased a little so that a small current flows through the series field, any cumulative compound generator will act as
hypocompound. It is for this reason that manufacturers supply only hypercomposite generators and expect the
consumers adjust the degree of compensation using a drain resistor. drain resistor(See here!) means an adjustable resistor added in parallel with the field winding with
which you want to change the characteristics of the generator.
More turns in series (Nse bigger). When there are a few extra turns at the poles, initially the effect
of the flux booster prevails and the terminal voltage
increases with load. However, as the load continues to increase,
magnetic saturation begins and the resistive voltage drop overcomes the effect of the
flow increase. In this machine, initially the terminal voltage rises and
then drops as the load increases. If Vg empty is equal to Vg full
load, then the generator will be named normal. This generator has a zero percent regulation feature.
A normal composite generator finds an application similar to the hypercomposite one, when the voltage drop in the transmission line is negligible and the load is located in the immediate vicinity of the generator. Thus, we obtain a constant voltage across the load, although this voltage is not necessarily constant, but has negative regulation at the half load point and regulation zero at full load.
Even more turns in series are added (Nse big). If even more
turns are added to the series field winding of the generator, then the booster effect
flux will prevail over an even wider range before the resistive voltage drop takes over. The result is a
characteristic in which the
full load output voltage is actually higher than the voltage
empty output. If the voltage Vg at full load exceeds Vg at no load, then the
generator will be named hypercomposite. That is, the regulation characteristic of this generator is always
negative.
The hypercomposite generator is most suitable for transmitting DC electrical power when the load is remotely
located relative to the generator. The voltage rise characteristic of this generator is more than enough to compensate for the voltage drop in the transmission line. A drain resistor is used to control and produce a sufficient voltage rise
on the generator, to compensate for voltage drops in the lines at full load. Like line voltage drop and voltage rise
adjusted, produced by the series field, are both proportional to the load current, the voltage at a remote load will be substantially
constant from no load to full load, making it unnecessary to use voltage regulators.
See in the graphs of Figure 104-12 all the studied possibilities.
Figure 104-12
Important Note
It is also possible to have all these voltage characteristics in a single
generator if a shunt resistor is used. The Figure 104-13 shows a DC generator
cumulative compound with a relatively large number of turns in series Nse.
A current diverting resistor, called a drain resistor, is connected across
parallel to the series field. If the drain resistor Rd is set to a
high value, most of the armature current will flow through the coil of the
field in series and the generator will be hypercomposed. On the other hand, if the resistor Rd is
set to a small value, then most of the current will flow through
Rd, parallel to the series field, and the generator will be hypocomposed. The resistor can
be continuously adjusted, allowing to obtain any desired combination.
Techniques available for controlling the terminal voltage of a DC generator
cumulative compound are exactly the same techniques used for the control of the
voltage of a DC generator in shunt, that is:
Vary the speed of rotation - An increase in ω causes EA to increase,
which raises the voltage about to load (Vg).
Varying the field current - A decrease in RF causes IF to increase,
which raises the total magnetomotive force of the generator. When Fliq rises, the flow
of the machine increases, which increases EA. Finally, an increase in EA
makes Vg go up.
The equations eq. 104-16 and eq. 104-17 are the key to the description of the output characteristic of
a cumulative composite dc generator. The equivalent field current in shunt
Ieq, due to the effects of the series field and the armature reaction, is given by
eq. 104-16
Therefore, the total effective shunt field current of the machine is
eq. 104-17
This equivalent current Ieq corresponds to a horizontal distance to the left
or to the right of the field resistance line (RF) along the axes of the curve
of magnetization, as can be seen in Figure 104-14.
Figure 104-14
The resistive drop of the generator is given by IA (RA + RS), which is a length
on the vertical axis of the magnetization curve. Both the equivalent current Ieq and the resistive voltage drop
IA (RA + RS) depend on the value of the armature current IA.
Therefore, they form the two sides of a triangle whose values are a function
from IA. To obtain the output voltage for a given load, determine the size of the
triangle and find the place where it fits exactly between the current line of
field and the magnetization curve.
The no-load voltage will be the point at which the resistance line and the magnetization curve intersect, as before.
When a load is added to the generator, the magnetomotive force of the field in
series increases, increasing the equivalent current of the shunt field Ieq and the drop of
resistive voltage IA (RA + RS) of the machine. To find the new output voltage of this
generator, move the left most vertex of the triangle along the line of the
shunt field current until the upper vertex of the triangle touches the curve
of magnetization. This upper vertex will represent the generated internal voltage of the machine, while the lower line represents the
machine output voltage.
A differential compound dc generator is a generator that contains both the shunt and series fields, but this time their forces
magnetomotives subtract between them. The equivalent circuit of a compound differential dc generator is shown in Figure 104-15. Note that now the armature current is flowing out of
a dotted coil termination, while the shunt field current is flowing into a dotted coil termination.
Figure 104-15
In this machine, the net magnetomotive force is
eq. 104-18
And the equivalent current of the shunt field due to the series field and the reaction
of armature is given by
eq. 104-19
The total effective current of the shunt field of this machine is given by the equation already studied, the eq. 104-17,
repeated below for clarity.
eq. 104-17
In the same way as the cumulative compound DC generator, the differential compound generator can be connected in long derivation
or in short lderivation.
In the differential compound dc generator, the same two effects occur that were
present in the cumulative composite dc generator. This time, however, both effects act in the same direction. They are:
When IA increases, the voltage drop IA (RA + R S ) also increases.
This increase tends to decrease the output voltage Vg.
When IA increases, the magnetomotive force of the series field Fse = Nse
IA also increases. This reduces the net magnetomotive force of the Fse generator,
which in turn reduces the flux generator liquid. This flow reduced decreases EA, which in turn decreases Vg.
As both effects tend to reduce Vg, the voltage drops drastically
when the load is increased on the generator.
Even when the voltage drop characteristics of a composite dc generator
differential are very bad, it is still possible to adjust the terminal voltage for any given value of load.
Techniques available for adjusting the terminal voltage are
exactly the same as those used for shunt compound dc generators
and cumulative:
Vary the speed of rotation - An increase in ω causes EA to increase, which raises
the voltage output Vg
Varying the field current - A decrease in RF causes IF to increase,
which raises the total magnetomotive force of the generator. When Fliq rises, the flow
of the machine increases, which increases EA. Finally, an increase in EA
makes Vg go up.
Observation
Both shunt and compound dc generators depend on the non-linearity of
its magnetization curves to produce a stable output voltage. If the curve of
magnetization of a dc machine were a straight line, then the magnetization curve
and the generator line voltage line would never intersect. Consequently, empty
there would be no stable voltage at the output of the generator. As the non-linear effects are in the
center of generator operation, the output voltages of DC generators can be
determined only graphically or numerically using a computer.
