Before Studying what are
capability curves of synchronous generator, let us first discuss about
rating of generators and its compounding curves. The heating is a key
factor in deciding the rating of alternators, transformers etc. The
heating is caused by losses so ultimately rating of machine depends on
losses. These losses are independent of load p.f. as I2 R
losses depend on current while core losses are dependent on voltage.
Thus the rating of a.c. equipments is decided by the volt-amperes of the
load it can supply and not on load power only. In case of turbines and
boilers in hydroelectric and thermal stations, their sizes, water and
fuel requirement depend on output power.
The rating of synchronous generators is specified interms of
maximum apparent power in KVA and MVA load at a specified power factor
(normally 80, 85 or 90 percent lagging) and voltage for which they are
designed to operate under steady state conditions. This load is carried
by the alternators continuously without overheating. With the help of
automatic voltage regulators the terminal voltage of the alternator is
kept constant (normally within ±5% of rated voltage).
The power factor is also important factor that must be specified.
This is because the alternator that is designed to operate at 0.95 p.f.
lagging at rated load will require more field current when operate at
0.85 p.f. lagging at rated load. More field current results in
overheating of the field system which is undesirable. For this
compounding curves of the alternators can be drawn.
If synchronous generator is supplying power at constant frequency
to a load whose power factor is constant then curve showing variation
of field current versus armature current when constant power factor load
is varied is called compounding curve for alternator. It is shown in
Fig. 1
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| Fig. 1 Compounding curve for alternator |
To maintain the terminal voltage constant the lagging power
factors require more field excitation that that required for leading
power factors. Hence there is limitation on output given by exciter and
current flowing in field coils because of lagging power factors.
The ability of prime mover decides the active power output of the
alternator which is limited to a value within the apparent power
rating. The capability curve for synchronous generator specifies the
bounds within which it can operate safely. The loading on generator
should not exceed the generator rating as it may lead to heating of
stator. The turbine rating is the limiting factor for MW loading. The
operation of generator should be away from steady state stability limit
(δ = 90o). The field current should not exceed its limiting
value as it may cause rotor heating. All these considerations provides
performance curves which are important in practical applications. A set
of capability curves for an alternator is shown in Fig. 2. The effect of
increased Hydrogen pressure is shown which increases the cooling.
 |
| Fig. 2 Capability curve for an alternator with hydrogen cooling |
When the active power and voltage are fixed the allowable
reactive power loading is limited by either armature or field winding
heating. From the capability curve shown in Fig. 2, the maximum reactive
power loadings can be obtained for different power loadings with the
operation at rated voltage. From unity p.f. to rated p.f. (0.8 as shown
in Fig. 2), the limiting factor is armature heating while for lower
power factors field heating is limiting factor.
This fact can be derived as follows :
If the alternator is operating is constant terminal voltage and
armature current which the limiting value corresponding to heating then
the operation of alternator is at constant value of apparent power as
the apparent power is product of terminal voltage and current, both of
which are constant.
If P is per unit active power and Q is per unit reactive power then per unit apparent power is given by,
Thus we have,
The above equation represents a circle with center at origin and radius equal to Vt .Ia.
Similarly, considering the alternator to be operating at constant
terminal voltage and field current (hence E) is limited to a maximum
value obtained by heating limits.
Thus induced voltage E is given by,
If Ra is assumed to be zero then
The apparent power can be written as,
Substituting value of Īa obtained from (1) in equation (2),
Taking magnitudes,
This equation also represents a circle with centre at (0, -Vt2/Xs).
These two circles are represents in the Fig. 3 (see next post as Fig.
1). The field heating and armature heating limitation on machine
operation can be seen from this Fig. 3 (see next post as Fig.1).
The rating of machine which consists of apparent power and power
factor is specified as the point of intersection of these circles as
shown in the Fig. 4. So that the machine operates safely.
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