The short-circuit ratio (SCR) of a generator is the inverse
ratio of saturated direct axis reactance in per unit (P.U.):
SCR = 1/ Xd (sat)
The SCR has a direct impact on the static stability and on
the leading (absorbed) reactive power capability of the SG. A larger SCR means
a smaller xd(sat) and, almost inevitably, a larger airgap.
In turn, this requires more ampere-turns (magnetomotive
force [mmf]) in the field winding to produce the same apparent power.
As the permissible temperature rise is limited by the SG
insulation class (class B, in general, ΔT = 130°), more excitation mmf means a
larger rotor volume and, thus, a larger SG.
Also, the SCR has an impact on SG efficiency. An increase of
SCR from 0.4 to 0.5 tends to produce a 0.02 to 0.04% reduction in efficiency,
while it increases the machine volume by 5 to 10%.
The impact of SCR on SG static stability may be illustrated
by the expression of electromagnetic torque te P.U. in a lossless SG connected
to a infinite power bus:
te = SCR x E0 x Vg x 1sin δ
The larger the SCR, the larger the torque for given no-load
voltage (E0), terminal voltage V1, and power angle δ (between E0 and ΔV1 per
phase). If the terminal voltage decreases, a larger SCR would lead to a smaller
power angle δ increase for given torque (active power) and given field current.
If the transmission line reactance — including the generator
step-up transformer — is xe, and V1 is now replaced by the infinite grid
voltage Vg behind xe, the generator torque te′ is as follows:
te' = SCR x E0 x Vg x 1sin δ'/(1 + Xe/Xd)
The power angle δ′ is the angle between E0 of the generator
and Vg of the infinite power grid. The impact of improvement of a larger SCR on
maximum output is diminished as xe/xd increases.
Increasing SCR from 0.4 to 0.5 produces the same maximum
output if the transmission line reactance ratio xe/xd increases from 0.17 to
0.345 at a leading power factor of 0.95 and 85% rated megawatt (MW) output.
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