High current, low voltage capacitors
First make a rough spec for ripple from C and ESR.

For \$C=I_C*dt/dV\$
with Vc=5V and let ripple=5%  or dV=250mV(pp) and dt= 10ms ( 100Hz) with Ic=200A   

\$C=200A*10ms/250V=8mF\$
let dV=2% 100mV from cap
  ESR=V/ESR=0.1V/200A=500 μΩ   

For a total ripple of 250mV+100mV=350mVpp

ESR*C=T= 500 μΩ * 8mF = 4 μs

Now check  Electric Double Layer Capacitors (EDLC), Supercapacitors specs. anything close rated for >5V


8.2uF 50mΩ  TOO HIGH by 100x even at $16

Now you know this concept is going to be more expensive than a 1kW PC SMPS PSU.