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# Saturated and unsaturated synchronous reactance

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The following readings are taken from the results of an open- and a short-circuit test on a 9375-kVA three-phase Y-connected 13,800- V (line-to-line) two-pole 60-Hz turbine generator driven at synchronous speed:

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Field current, A 169 192
Armature current, short-circuit test, A 392 446
Line voltage, open-circuit characteristic,V 13,000 13,800
Line voltage, air-gap line, V 15,400 17,500

The armature resistance is 0.064 Ohms/phase. The armature leakage reactance is 0.10 per unit on the generator rating as a base. Find (a) the unsaturated value of the synchronous reactance in Ohms per phase and per unit, (b) the short-circuit ratio, and (c) the saturated synchronous reactance in per unit and Ohms per phase.

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#### Solution Preview

(a) Unsaturated Synchronous Reactance:

Air- gap Voltage (L-L) OCC = 15,400 V

Air- gap Voltage (Phase) OCC = 15,400/sqrt(3) = 8891.2 V

Short-circuit Armature Current = 446 A

Hence, unsaturated synch. reactance = 8891.2/446 = 19.94 Ohms

Rated Voltage (L-L) = 13,800 and ...

#### Solution Summary

The solution examines saturated and unsaturated synchronous reactance for an open and short circuit test.

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