Have you modeled a Synchronous condenser in HOMER before?
HOMER does not model power factor or voltage, so it cannot recognize the value of the power factor correction and voltage support that the synchronous condenser provides to the system. That’s why HOMER does not explicitly model synchronous condensers, nor tell you when you need one.
To HOMER, a synchronous condenser would simply represent an additional electric load. So you can model your synchronous condenser by adding a second primary load that is a constant 20 kW.
I have not modeled AGM batteries, but HOMER should have no problem modeling such a battery. You will need to find performance data for that battery on the web and create a new battery type in HOMER by clicking the New button in the Battery Inputs window.