I`d like to know how to measure the impedances of my source(solar panel) and load(battery).
If you are hell bent on measuring the "impedance", just use a variable load resistance and measure the voltage and current as the load resistance varies.
Draw a graph of volts/current, the slope of the graph will give you the "impedance" (resistance actually as this is just a DC situation).
The reality is that you dont match impedances in power transmission. While a matched impedance will give maximum power transfer, it is also only 50% efficient - do the maths on a few examples and you will see.
For best EFFICIENCY, the source impedance should be low compared with the load impedance.
Again, do some maths and you will see that for a matched load and source, for every watt supplied to the load, there is one watt dissipated in the source.
Should I use Smith chart or something else ?
Rio FUN, I will give you a job any day, as my entertainments manager!
Thanks for the laugh, it made a good day even better!
All joking aside, a Smith Chart is used for RF, not DC.
Unless your solar cells and batteries work at RF and are connected by a nice long transmission line, the Smith chart wont do much for you.
JimB