Electronic – How a battery is being charged and used as the same time

I think that a very good option is to take advantage of the PIC uC that you already have in your design and its analog (ADC) input ports for monitoring the batteries voltage and to drive the switching between those batteries using MOSFETs instead of BJT transistors. Using the uC you should not need the two comparators that you show in the picture and you will have a more intelligent charging/monitoring battery circuit that could lead to improve the batteries duration. This uC could stay in sleep mode (or low power mode as second option) all the time using interrupts to read the ADC channels. You should run the uC from its internal RC oscillator operating at the lowest frequency as possible to decrease the power consumption.

I also recommend you using Schottky diodes instead of 1N4148 and to put a small bulk capacitor at the output of the power selector circuit (or switching circuit). Those Schottky diodes will drop less voltage than the 4148.

If you decide to use the uC for the battery voltage level monitoring, try to use the internal fixed voltage thresholds that the uC provides for the internal comparators, because if you don't do that you could have some problems reading wrong analog values because those batteries are used to power the uC too (you will have ratiometric voltages).

I hope this help.

First of all you need to be very careful when designing with Lithium-ion batteries. If you exceed their specified charge or discharge rates they can leak or explode, and nobody wants that! You definitely need a charge controller. This will regulate the battery charging to safe levels, and follow a recommended charge profile, which is typically to charge first at a constant current until the cells reach a certain voltage, and then to top off at a constant voltage. This is called "CCCV" charging. You also need something to limit the discharge rate of the batteries. This can be a very simple circuit, but for safety you need something. Your buck converter can supply both the load and the charger. Any excess capacity of the solar panels will just not be used. The panel output voltage will probably rise above 48V at lower loads. For 7 cells, a linear charge controller is not good as at low battery voltages the power dissipated will cause overheating. You probably need a switcher there too, either buck or SEPIC. If you can design a pcb for this, so much the better. I appreciate that your school would probably not really appreciate it if you went and bought this on Amazon!