PG,
I can't look at your circuit files, but I can respond about your rechargeable battery model. You can use a capacitor to model a battery, if you don't need great accuracy. You should add at least a series resistor to the capacitor. Also, you should limit the range of the capacitor voltage. For example. if you have a capacitor model, you might say that state of charge (SOC) of zero corresponds with 3.0 VDC and SOC=1 corresponds to 4.1 VDC. Then add a series resistor with value that agrees with the voltage drop data of your battery. Use whatever voltages for SOC=1 and SOC=0 that best match the voltage curves. Also, keep in mind that batteries are highly temperature dependent, so your parameters would depend on temperature, if you care about temperature effects.
You can extend the model by making a voltage dependent voltage source. The capacitor voltage would provide the input to the dependent voltage source, and a capacitor voltage range of 0 to 1 V, would get mapped to the proper battery voltage, via a function. Implementing this is standard circuit simulators may or may not be easy, but it's trivial in a Simulink model.
I often do battery models in Simulink, and generally make a voltage source with resistance in series. Then the open circuit voltage and source resistance, I allow to be functions of state of charge (SOC) and cell temperature (T). Hence Voc(SOC, T) and R(SOC, T) are the only two elements in the circuit, but the complexity of the battery is included in functions that allow Voc and R to change based on SOC and T. Even this is only approximate and real batteries are notoriously difficult to model accurately under all operating conditions. Typicall Voc(SOC, T) and R(SOC,T) need to be measured under conditions similar to your application in order to have a useful model.
I could give more details, but I think for a school project a simple model should suffice. Make it a simple as possible. If the straight capacitor with limited voltage range, with a series resistance works for you, that's the best.