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.

Historically, the trend has been toward lower SCRs, from 0.8 to 1.0, 70 years ago, to 0.58 to 0.65 in the 1960s, and to 0.5 to 0.4 today. Modern — fast response — excitation systems compensate for the apparent loss of static stability grounds. The lower SCRs mean lower generator volumes, losses, and costs.

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