Allow me to post from a transmission operator's perspective...
Within the more robust portions of my utility, our LT/MV capacitors [ 14, 28 & 44 kV ], being nominally rated at 20, 25 and 30 MX and located at our substations, do indeed have profound effects on the HV transmission system; our Independent Electrical System Operator does in fact in large part dispatch our LT capacitors to control the 115, 230 and 500 kV system voltages. Incidentally we do have 115 and 230 kV cap banks as well, typically with a nominal rating [ meaning at rated voltage ] of 100, 200, 300 and 400 MX, generally near or within major load centres, or at major transmission nexi.
There are some more remote and weaker portions of our system that have lengthy 115 kV lines and therefore significant impedance; at substations connected to these circuits even an 11 MX cap bank can cause major voltage perturbations, necessitating considerable prudence in dispatching same.
Certainly the HV caps do deliver great gouting amounts of reactive power, and have their place; but it is the LT caps that can often be tweaked to a relative nicety, maximizing the real power capability of the HV circuits and the substation transformers in question, something of great importance during both winter and summer peaks as well as during maintenance outages in the shoulder seasons.
It's just gone midnight here, and for us it is now Christmas Eve; I'm expecting the IESO to be calling fairly soon to request a bunch of said LT caps removed from service...
CR
"As iron sharpens iron, so one person sharpens another." [Proverbs 27:17, NIV]