My comment above about keeping KVAR's constant was only to demonstrate that it is permissible to operate a generator at low power factor.
If the exciter/generator/field can produce 17 kVAr at 0.8 power factor they can certainly do the same at low power factors. Actually, the generator reactive capability goes up as the kW loading goes down. I just was holding it constant to prove the point that low power factor operation is possible and that the 0.8 pf on the nameplate is not a power factor limit, just a rating point.
Most generator capability curves graph kW on the horizontal axis and kVAr on the vertical axis. The fictional 12.5 kVA ,0.8 pf generator's curve will be a circle arc of constant radius starting at 12.5 kW, 0 kVAR and going up to 10 kW, 7.5 kVAR, the full load 0.8 power factor point. The circle radius gets shortened from that point over to the vertical axis (0 kW). It is not a straight horizontal line = to constant kVAR's as my example may have implied. The curve goes up, indicating the generator can produce more KVAR's at lighter loads. The limit is the rotor field current heating limit or exciter heating.
(I don't have time to upload a curve. Do a search and look at some of the fine examples on the internet. If the curve is drawn by someone in the IEC world, lagging power factor KVARS out of generator, is drawn as negative below the axis, instead of on top as we do in ANSI land. Don't get confused.)