During steady state, the average current throw he capacitor is zero, and then the derivative is also zero, if you are doing a steady state analysis, you must set the derivative of voltage in capacitors equal zero, but if you are doing a dynamic model, don´t ignore the current in a capacitor, because the current is not zero during transients, it actually can be very large.

Normally, one state model gives both transient and steady state responses. Two state models may be used in case of singularly perturbed or time-scale systems to study slow and fast dynamics.

You only need one model, for example the state space, and then you can set the derivative of the space equal zero, and the result is the steady state operation point. Best regards...