Download Capability Curve for a Turbo Generator with 0.9 Power Factor and

Capability Curve for a Turbo Generator with 0.9 Power Factor and an xd of 1.2 p.u.
It is quite easy to design turbo generator capability curves as there are only two
generator technical data required:

Generator power factor (over excited)

Direct axis synchronous reactance xd (unsaturated)
The synchronous reactance for a cylindrical rotor synchronous generator (i.e. turbo
generator) can be assumed as identical for the direct axis and the quadrature axis,
i.e. xq = xd (in reality the value of xq is about 5% less than xd but this small difference
can be neglected).
A turbo generator capability curve has been worked out as an example (see
attachment). This chart uses the p.u. (per unit) system, i.e. every rated dimension
shown in the chart has a value of 1.0 p.u. (1.0 p.u. is equal to 100%). This power
chart is valid for turbo generators with a power factor of 0.9 (over excited) and a
synchronous reactance (unsaturated) of xd = 1.2 p.u.
The advantage of using the p.u. system is that one can multiply p.u. figures with
each other and still obtain correct and meaningful data. Such calculations are not
possible when using percentage figures. Another advantage of this chart is that it is
valid for various output figures, regardless whether the generator rated output is
500 MVA or 142.8 MVA, or any other output, as long as the unit has a power factor of
0.9 (over excited) and a synchronous reactance (unsaturated) of x d = 1.2 p.u.
1. We first draw a half circle with a radius of 100 mm. This radius is equivalent to
1.0 p.u. or 100% generator power output (rated apparent power output in kVA
or MVA).
2. Then we determine the point of (maximum) reactive power (under excited) by
dividing rated voltage U (1.0 p.u) by synchronous reactance xd (1.2 p.u). This
results in 0.833 p.u. reactive power (under excited). This point is plotted as
point “A”. The vertical line above this point can be named “theoretical
stability limit”. There is no stable generator operation possible left of this
vertical line.
3. We then define the “rated power point” of the generator by drawing a
horizontal line through the ordinate at 0.9 p.u. This horizontal line represents
the active power limit (in p.u. or kW or MW) of the turbine. The point of
intersection with the half circle on the right hand side of the chart can be
named “rated power point P”. By connecting point “P” with point “C” we
obtain phase angle φ.
4. Assuming that the horizontal distance U/xd between points “A” and “C” is
equivalent to the no-load excitation current, required to excite the generator to
rated voltage 1.0 p.u., then the distance between point “A” and point “P”
represents the “rated full load excitation current” E/xd (E is the internally
generated voltage). We use a pair of dividers and connect point “P” with the
abscissa. The resulting point “D” shows the maximum permissible value of
“reactive power over excited” at zero active power. As already mentioned
above, this point is realized for an excitation current at rated full load and
power factor 0.9 (over excited).
5. We now return to the left of the diagram to complete the under excitation
section. The “theoretical stability limit” line does not permit fast (surge) load
changes. We therefore have to define a certain surge load value for safe
operation. For the determination of a “practical stability limit” curve, a safety
figure of 0.1 p.u. rated active power is assumed, named “S” in the chart (for
power factor 0.9 this is equivalent to 0.09 p.u. of rated apparent power). The
design procedure for the “practical stability limit” in the attached power chart
is self-explanatory. Fast responding excitation equipment requires less safety
margin for designing the “practical stability limit” curve.
The power chart shows that in the under excited operation mode a certain amount
of excitation has to be maintained by the excitation equipment to achieve stable
performance (no hunting) in this operating region. Generator operation in the under
excitation mode can be even limited to figures to the right of the “practical stability
limit” depicted on the chart, in case the generator stator core end sections are not
designed for coping with leakage flux concentrations. It is assumed for our case
that suitable precautions are provided to the core end zones by the generator
designer. Otherwise various load tests in the under excitation mode have to be
performed at site to determine permissible load parameters. In such cases it is also
strongly recommended to contact the generator manufacturer.
In the “D” to “P” operating region, the generator capability is limited by the field
winding temperature, i.e. we cannot increase the field excitation beyond a certain
limiting value.
In the “P” to “F” operating region, the generator capability is limited by the stator
winding temperature, i.e. we cannot increase the stator current beyond a certain
limiting value.
In the “F” to “B” operating region, the generator capability is limited by stability
considerations, i.e. we cannot decrease the field excitation beyond a certain
minimum value.