Backup Duration - Calculations

Aurora’s calculation of estimated backup duration uses a few inputs:

• The project’s hourly consumption load profile
• The design’s hourly production profile
• The storage design’s consumption configuration (what percent of a load profile is backed up)
• The storage design’s battery usable capacity
• The storage design’s calculated round trip efficiency

Aurora’s calculation takes the given design configuration and estimates how long the battery would back up the house for each day in the year. The calculation steps are as follows:

1. Start with the last hour in the day in which the battery is full charged
2. For each hour afterwards:
   1. Calculate the net load in the house (hourly consumption - hourly production)
   2. Calculate how much energy is removed from the battery to meet that load, accounting for battery discharge efficiency and inverter efficiency.
      1. If the PV system produces more energy than the load, the battery is charged with excess energy instead.
   3. Check to see if the battery still has capacity left: if so, continue to the next hour
   4. End if the battery reaches its minimum state of charge (if the battery uses up its defined usable capacity) 
3. The output of this calculation is the backup duration for a given day
4. We repeat this process for every day in the year. The reported backup duration is the P90 - effectively, 90% of days will last longer than this value  - you can confidently report that given the customers’ current load and estimated production, the battery will last at least as long as the provided backup duration. 

For example, let’s take the production and consumption profile for an example house given below. 

1. We assume that the power will go out on Monday afternoon - 5pm in this example
2. We then use the consumption and production profile to discharge or charge the battery, until the battery hits its minimum state of charge or the simulation goes past 1 week.
3. In this given example, the battery lasts into Wednesday - about 41 hours in total.

We repeat this calculation for every day in the year. After that is completed, we report the P90 value - how long the battery will last in 90% of cases. This is equivalent to the “10th percentile worst case scenario”. In the histogram below, even though in many cases the system lasts for 2, 3, or even 7 days, the P90 value is 24 hours; 90% of the time the battery system will last longer than 24 hours if an outage were to occur.