How do I connect up a replacement run capacitor
It looks like you bought a 3 phase PFC cap for a single phase motor.

There must be a neutral connection (lower terminals) to 3 separate caps with 1 for each phase (upper terminals).

Datasheet says "aluminum can capacitors are three-phase capacitors for power factor correction (PFC). KEMET C9T 415 / 440VAC rated voltage capacitors feature polypropylene metallized film and include an overpressure safety device. C9T PFC capacitors are also available with delta connections"


The Run cap is chosen to shift the phase of the coil to maximize torque and minimize conduction heat losses from excess current during operation.







simulate this circuit &ndash; Schematic created using CircuitLab

Unfortunately between any 2 pins of a 3 phase delta cap is the equivalent circuit of 3 caps = 1.5x C.  If two pins were shorted then it would be 2xC.

You really want a single cap equivalent to ~ 130uF within 20% or so, but perhaps the 3 phase 92.2uF cap (138uF) is close enough and is Amp rated to exceed your needs.  KEMET C9TS5MD5920AARX