System Sizing Overview and Partial State of Charge (PSOC)

Morningstar controllers and inverters are often used in autonomous off-grid systems; telecom, oil and gas, lighting, etc… Therefore, this article primarily focuses on off-grid PV systems that have predictable load usage over the lifetime of the system. 

There are three basic calculations required for sizing an off-grid PV system.

  • Average daily load energy usage (Ah / kWh)
  • Energy input from solar and other charging sources (Ah / kWh)
  • Energy storage capacity (Ah / kWh)

Estimating any of these components incorrectly can have devastating effects, including frequent loss of loads and/or shortened battery life. There are many off-grid system sizing tools available for this purpose. 

Off grid system sizing starts with the load evaluation. The purpose of this evaluation is to determine the total average daily load usage in Amp hours (Ah’s) or kilowatt hours (kWh’s). Load energy usage is based on the size of each load in the system and the estimate of the average number of hours a day that each load will be operating. Power conversion efficiency of inverters and DC-DC converters if used, self-consumption and other losses also need to be accounted for. It is crucial not to underestimate load energy usage or add loads at a later time without reevaluating the solar PV and battery sizing requirements. 

Typically the solar PV array is sized next. The solar PV array’s daily average energy production (Array Watt-hours/ Amp-hours (Wh/ Ah)) must be able to keep up with the daily load usage throughout the year in addition to being able to fully charge the battery on a regular basis. Note that in order to provide enough energy throughout the year the array must be sized for the month with the lowest solar energy and/or highest load usage. This is referred to as the critical month (typically during the winter or rainy season). 

Estimating solar production is calculated using historical monthly solar irradiation data (kWh/m2 per day) and basic algebraic equations, taking into account array size, tilt and other losses (shading, voltage drop, efficiency losses, etc…). This can be challenging since solar energy production can be very inconsistent depending on the season. In some climates it may be impractical to use solar alone without another source of energy. Adding additional solar panels to an array can improve system uptime and keep the battery fully charged on a more consistent basis. 

Once the PV array size (Watts and number of PV modules required) is determined, it is possible to select the solar controller(s), and then determine the PV array string sizing. Morningstar’s online string sizing calculator is available if needed for this. 

The battery bank is usually the last step in sizing the system. Like the solar array sizing, the Ah/kWh capacity of the battery bank requirements are calculated based on several system variables.

  • Battery chemistry
  • Battery efficiency
  • Average depth of discharge (DOD)
  • Maximum DOD
  • Average daily DOD can increase the # of cycles of the battery and life expectancy
  • High charge and discharge rates and lower temperatures reduces both the efficiency and capacity of the battery
  • Days of Autonomy (# of days of operation with no charging: Typically 3-7 days) 
  • More Autonomy (battery capacity) will reduce the LOLP for critical loads
  • Systems which include a generator can reduce the # of days of autonomy requirements 

Lithium-ion batteries have a significantly higher cycle life than lead acid batteries and therefore can be sized for a higher DOD. Increasing the size of the battery bank provides more autonomy to reduce the LOLP and the average DOD for a longer cycle life. Compromising to avoid the high upfront cost of the battery bank can come at the cost of the life of the battery.  

Loss of Load Probability (LOLP)

Some advanced off-grid PV system sizing software tools include a Loss of Load Probability (LOLP) calculation. The LOLP takes into account not only the average daily solar radiation data for the site, but also historic weather pattern variations in the daily levels of available solar radiation. While the system may be sized adequately based on the monthly daily average solar radiation (kWh/m2 per day), there will be extended periods of cloudy weather when the average solar radiation is much lower than the monthly average. The monthly LOLP is the likelihood that the battery will be discharged to the point that there will be a Low Voltage Disconnect (LVD) in a given month. The annual LOLP is the sum of the 12 monthly LOLP values. 

Please note that the LOLP calculations are less predictable and less accurate than the average solar energy per day calculations. Also, both of these calculations do not take into account potential snow cover of the solar array. In addition, the amount of loss of load for a given year will vary annually along with annual weather anomalies. For example, during a year when there is a major hurricane there could be a significant load outage, but no loss of load the following year when there are no hurricanes.  

Increasing the size of the PV array and/or battery bank will reduce the LOLP. These off-grid PV system sizing calculators can be a very useful tool in evaluating this important aspect of the system design and determining what choices will be the most cost effective in preventing loss of load.

 

Partial State of Charge (PSOC)

Systems with larger battery banks sized for many days of autonomy can spend extended periods of time with a partial state of charge (PSOC). This is because it could take a long time to fully recharge the battery when there is a very low state of charge (SOC). Not being able to recover from a very low SOC in a reasonable amount of time can cause irreversible degradation of lead-acid batteries. The risk of PSOC is much more significant in climates that have rainy seasons or winters with short days and/or snow.  

Some lead-acid battery manufacturers have indicated that PSOC is one of the most common causes of reduced lifetime for lead-acid batteries with off-grid solar systems. Some types of batteries such as lithium and other energy storage products don’t have issues with PSOC. For most lead-acid batteries, having over two weeks with a PSOC should be avoided. Reducing the number of days of autonomy by installing a smaller battery bank or using a higher LVD setting is one option, but it will likely lead to  more frequent loss of load. Increasing the size of the  solar array is a more optimal solution that will fully charge the battery more consistently and help speed up the charging process to recover from a low SOC more quickly. 

Generators can be used to prevent extended periods with a PSOC and avoid letting the battery reach a low state of charge (SOC) and loss of load. The generator should be sized large enough to recharge the battery bank relatively quickly. Note that it is best to size diesel generators so it will operate at 50-80% capacity for continuous loads. This is because when a diesel generator is under-loaded most of the time it will be less fuel efficient and cause carbon build-up, and over time produce smoke and start choking up. On the other hand, operating generators continuously at full capacity can cause the generator to overheat.   

Grid uninterruptible backup systems (UPS’s)often include solar to keep the battery charged during an outage. Usually the battery is not sized as large as for off grid systems since the grid will keep the batteries from getting discharged most of the time. A generator can also be installed with the PV/ battery backup system for longer outages. 

There is a Solar Controller Integration with AC Rectifiers white paper available on the Morningstar website that provides helpful information about Utility and AC generator applications. https://www.morningstarcorp.com/wp-content/uploads/2020/11/Solar-Controller-Integration-with-AC-Rectifiers-whitepaper.pdf