In Problem64 of Chapter 2, a three-phase ac/dc converter that supplies dc to a battery charging system (Graovac, 2001) was introduced. Each phase had an ac filter represented by the equivalent circuit of Figure P2.38. You were asked to show that the following equation gives the s domain relationship between the inductor current, I_acF(s), and two active sources: a current source, I_acR(s), representing a phase of the ac/dc converter, and the supply phase voltage, V_a(s):

a. Derive an s-domain equation for Vc(s).

b. Given that R = 1Ω; L = 1 mH, and C = 20 μF, i_acR(t) = 10 u(t)amps, v_a(t) = 20 t u(t) volts,10 and assuming zero initial conditions, use Simulink to model this system and plot the inductor current, i_acF (t), and the capacitor voltage, v_c(t), over a period from 0 to 15 ms.

IacF(s) = I acF1(s) + IacF2(s) 1+ RCs LCs? + RCs + 1 Tack(s) Cs -Va(s) LCs? + RCs + 1