ir2153 problem
It looks like a simple decoupling / reservoir capacitor.
Thr cap has to have enough "hang time" to supply
VCC during periods where the "rectified AC line" is in
the valley, below whatrver voltage the internal shunt
regulator clips it at against RVCC (or where Vline/RVCC
is less than VCC current at regulation point).
I=CdV/dt; t is the time duration of the "valley", dV
is how much droop you think you can tolerate (PSRR,
ripple related misbehaviors, etc.). I is max rated supply
current including switching load. That leaves you C.
I would want a C value at least 10X the external
MOSFETs' combined Cgg. But higher wouldn't hurt.
I would bet that IR has app notes showing sensible values.