## HOMER Energy Support

### Battery maximum charge rate - sample calculation

Last Updated: Jul 25, 2016 03:21PM MDT

I also don’t understand the numbers I get for the maximum charge power of the battery.

HOMER uses the lowest of the following to determine the maximum allowable battery charge power for the current time step:
1) maximum charge current (if selected in the battery definition)
2) maximum charge rate (if selected in the battery definition)
3) maximum charge power defined by the kinetic battery model (if using kinetic battery model)
4) charge power that will fill the battery by the end of the time step ("headroom constraint")

Here is a sample calculation with:
--10 minute time steps
--1 kWh battery with "idealized" model (not kinetic)
--no max charge current
--"maximum charge rate of 3 A/Ah selected
--battery is at minimum state of charge (40%) currently

max_charge_kwh = (battery_max_kwh - Q) * battery_max_charge_fraction
where:
battery_max_charge_fraction = 1 - e^(-max_charge_rate * timestep_size_in_hours)
battery_max_kwh = 1 kWh (the battery has 1 kWh capacity)
Q = 0.4 (kWh current state of charge)
The result is in kWh per 10 minute time step -- multiply by 6 to get max power in kW.

The maximum charge rate (defined in A/Ah) only applies to battery charging. It does not apply for discharging. Using the formulae above:

battery_max_charge_fraction = 1 - e^(-3*10/60) = 0.393 (10 minute time step divided by 60 minutes in an hour)
max_charge_kwh = (1 kWh - 0.4 kWh) * 0.393 = 0.236 (this is kWh per 10 minute time step)
max_charge_kwh_after_losses = max_charge_kwh / sqrt(efficiency) = 0.236 / sqrt(0.8) = 0.264 kWh (input power)

so max charge power = 0.264 / (10/60) = 1.58 kW (kWh per hour)

In the plot below, the maximum charge power (blue line) is 1.58 kW, as we calculated. This is for a 1 kWh battery, 10 minute time steps, and a 3 C maximum charge rate:

support@homerenergy.com
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