As the field current goes up, the reactive power of a synchronous machine goes from lagging (inductive) pf, through unity pf and minimum line current, up to leading (capacitive) power factor. I had the chance to try this out one idle day at the steel plant, turning the big knob that regulated field current to a 30 MVAR synchronous condensor used in the arc furnace circuit to compensate for lagging power factor. You can plot line current vs. field current and come up with a "V-curve" so-called because of the shape - the minimum of the V corresponds to unity power factor. For loaded machines the "V" isn't very sharp, and I found that on the machine I had access to, the ammeters weren't terribly well calibrated for the low-current end of the range so it was hard to accurately plot a V-curve.
Bill