PV Array Size (without back-up generator)
In order to determine the PV Array size we will work backwards from the battery.
We have already determined the output from the battery taking discharging losses (and other losses along the way) into account.
We will now calculate the input necessary for the battery, similarly this will take into account
- Charging losses
- Charge Controller losses
The input of battery energy is subject to charging and charge controller losses. We begin by taking the input of 3.05 kWh and apply charging and charge controller losses, selected to be 85% and 95% respectively. It should be noted that batteries have a complicated operating regime and are not nearly as simple as this analysis implies. See the notes on Batteries.
Daily energy requirement from the pv array = 3.05/(0.85*0.95) = 3.78 kWh.
At this point we refer to the irradiance data and the PV module datasheet (Sharp ND-R250A5) for your chosen PV module.
Having made note of the lowest monthly irradiance of the year and the power rating of the PV module we can make an approximation of how many modules are required to charge the battery during the worst month.
It should be noted that this size represents the size for the average irradiance of the worst month. It is possible and very likely that the variance of irradiance over the winter months may deplete the battery for 1 day or 2. By increasing the battery bank for additional days of autonomy we can mitigate the possibility for loss of power, and reduce the size and cost of the PV array.
Also note that a larger battery bank does not imply a larger pv system, on the contrary; as the batteries are mostly charged through summer surplus (and topped over the sunny winter days) then a larger battery bank can minimize the PV array that is needed for the worst months. The relationship between Days of Autonomy (DOA) and PV array size is complicated and beyond the scope of this case study. See notes on Days of Autonomy and Loss of Load Probability.
For more accuracy, it is prudent to turn our attention to modelling software such as PVSyst, PV*Sol or PVGIS. A simulated analysis will be presented in a later section. See PVSyst Analysis section.
Daily energy requirement from the pv array = 3.05/(0.85*0.95) = 3.78 kWh.
At this point we refer to the irradiance data and the PV module datasheet (Sharp ND-R250A5) for your chosen PV module.
Having made note of the lowest monthly irradiance of the year and the power rating of the PV module we can make an approximation of how many modules are required to charge the battery during the worst month.
| Daily energy requirement | 2.41 | kWh | |
| Daily energy storage from battery (incl discharge losses) | 3.05 | kWh | 85% discharging loss, 93% inverter loss |
| Daily battery input (requirement from PV array) | 3.78 | kWh | 85% charging loss, 95% charge controller loss |
| December average daily irradiance | 0.68 | kWh/m^2.day | aka. 0.68 PSH |
| (Simplified) Output for 1 module under these conditions. | 170 | Wh | kWp*PSH ie. 250*0.68 |
| 0.17 | kWh | ||
| Number of modules required | 22.2 | Round up to 23 | |
| Nominal rated power of this system | 5.75 | kWp system | |
It should be noted that this size represents the size for the average irradiance of the worst month. It is possible and very likely that the variance of irradiance over the winter months may deplete the battery for 1 day or 2. By increasing the battery bank for additional days of autonomy we can mitigate the possibility for loss of power, and reduce the size and cost of the PV array.
Also note that a larger battery bank does not imply a larger pv system, on the contrary; as the batteries are mostly charged through summer surplus (and topped over the sunny winter days) then a larger battery bank can minimize the PV array that is needed for the worst months. The relationship between Days of Autonomy (DOA) and PV array size is complicated and beyond the scope of this case study. See notes on Days of Autonomy and Loss of Load Probability.
For more accuracy, it is prudent to turn our attention to modelling software such as PVSyst, PV*Sol or PVGIS. A simulated analysis will be presented in a later section. See PVSyst Analysis section.
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