In a simple model of a renewable energy system, I have a residential inverer and Lithium ion battery system with a round-trip efficiency (for inverter and battery, i.e. ac to ac) of 89% (at 25 degrees and a given charge / discharge power). The model needs to calculate the SOC of the battery (to determine when it's fully charged, etc.) which requires me to distinguish between charging and discharging efficiencies. Some studies assume the inefficiency is in charging, so SOC = 89% of charging energy, but this seems unlikely. Is it reasonable to assume that the losses for charging and discharging are approximately equal, so the charge and discharge efficiencies would both be approximately 94.3% (square root of 89%) or is there some other rule of thumb?
To clarify: this is a techno-economic model and is only concerned with energy flows in the system. If n(charge) is the charging efficiency and n(discharge) the discharge efficiency, all I know (from the manufacturer) is n(cycle) = n(charge) * n(discharge) = 0.89
For example, in time period t1, energy delta(E) is sent to the battery-inverter system and - if the battery has unused capacity - increases the energy stored in the battery by delta(E) * n(charge). The change in the state of charge is then:
delta(SOC) = delta(E) * n(charge) / usable capacity
I need to estimate SOC to know whether the battery has capacity to take delta(E).