How many hours or days of Autonomy?

In our previous two blogs, we answered the questions of how many solar panels will fit on my roof, how much power can those panels produce, and will it be enough to power XYZ.

But the sun isn't always constant and doesn't shine at night and may have reduced efficiency for days at a time due to rain, storms, or other weather.

So it becomes crucial to know at least how much energy storage you would need to keep things powered at night and the next while also needing to charge the batteries back up.

This frequently referred to as hours/days of autonomy.

So, here is the definition and then lets look at a practical example of the minisplit from the forum:

To calculate the hours or days of autonomy for a solar system, you divide the total energy storage capacity of your battery bank by the average daily energy consumption of your system, taking into account factors like battery depth of discharge (DoD), system inefficiencies, and seasonal variations in solar production; essentially, it represents how long your battery bank can power your load without any additional solar input. 

• Formula:
  Days of Autonomy = (Battery Capacity in Wh) / (Daily Energy Consumption in Wh) 

• Battery Capacity:
  This is usually measured in Ampere-hours (Ah), which needs to be converted to Watt-hours by multiplying by the battery voltage. 

• Daily Energy Consumption:
  This is the total energy used by your appliances in a 24-hour period, calculated by summing up the power consumption of each appliance and multiplying by the time used. 

• Depth of Discharge (DoD):
  To ensure battery longevity, you should not fully discharge your batteries; always consider the DoD percentage when calculating capacity. 

Steps to calculate days of autonomy:

• 1. Estimate daily energy consumption:
  Add up the power consumption of all your appliances and calculate the total watt-hours used per day. 

• 2. Determine desired autonomy:
  Decide how many days of backup power you need (e.g., 2 days). 

• 3. Calculate required battery capacity:
  Multiply your daily energy consumption by the desired number of days of autonomy. 

• 4. Adjust for DoD:
  Multiply the calculated battery capacity by a factor based on your chosen DoD percentage (e.g., 0.5 for a 50% DoD). 

• 5. Consider system inefficiencies:
  Factor in potential losses due to inverter efficiency and other system components. 

Example

Production:

So building on our previous example, we have any where from 7kw-24kw in energy output produced. 

Important factors to consider:

• Location and solar radiation:
  The amount of sunlight received in your area significantly impacts the size of solar panels needed to charge your batteries. 

• Seasonal variations:
  Solar production varies throughout the year, so consider the lowest solar production period when calculating your battery capacity. 

The average "peak sun hours" of solar radiation per day in the continental United States is typically between 3.5 and 5.5 hours, with the most intense sunlight occurring around midday, but this can vary significantly depending on location and weather conditions; areas like the Southwest generally receive more peak sun hours than the Northeast. 

So that means we will have between 7kw*3.5 = 24.5 kwh per day on the low end and 24kw*5.5 = 134.75 kwh per day on the high end.

Consumption:

In terms of energy consumption, let's assume we run out minisplit 24 hours a day, so that means any where from 1.6kw*24hr = 38.4 kwh and 3.1*24 hrs = 74.4 kwh of energy consumption.

Production vs. Consumption

So on the lowend, we are not even producing enough power to run the mini split for 24 hrs, because there is a deficit:

24.5 kwh (production) - 38.4 kwh (consumption) = -13.9 kwh

At the top end of our range we have:

134.75 kwh (production) - 74.4 kwh (consumption)  = + 60.35 kwh

That excess capacity can be stored in a battery. Now remember from above that battery capacity is usually measured in Ampere-hours (Ah), which needs to be converted to Watt-hours by multiplying by the battery voltage.  So if we use a system with a nominal voltage of 48V and watt-hours = amp-hours x volts. Or amp-hours = watt-hours/volts. So we have 60.35kwh/48 V = 1,257.29 amp-hours. If you consider a typical home battery of 48V at 280 Ah for   14.3kWh LiFePO4 that comes out to 60.35 kwh / 14.3 kwh = 4.49 batteries, which we'd probably round down to 4. That's a lot of weight, but not unusually so. Seeing as for an EG4 PowerPro WallMount AllWeather Lithium Battery weighs in at a whopping 345 pounds, for four of them you are looking at 1,380 pounds of battery storage.

Days of Autonomy

Now back to the original question of how to compute the day of autonomy of our system.

Days of Autonomy = (Battery Capacity in Wh) / (Daily Energy Consumption in Wh) 

Days of Autonomy = 57.2 kwh / 38.4 kwh = 1.5 days on the low end of consumption and

Days of Autonomy = 57.2 kwh / 134.75 kwh = 0.43 days on the high end of our consumption scale.

And if we lower it to only two batteries, we'll have a range of days of autonomy of between 0.75 days and 0.215 days.

Summary

These are all ball park figures and we've looked at a couple of edge cases to get an idea about maximum and minimum.

In reality, if we were to implement a system as described for the house boat that we originally started width, we could probably do an installation with only two batteries, because your not going to be running that minisplit all out 24 hours a day.