PowerHouse Texas Energy Academy: Battery Backup Duration Exercise
A tutorial for setting up assumptions, inputs and performing calculations for whole-home backup batteries for the PowerHouse Texas Energy Academy - 2024.
Battery Capacity (Power x Duration) is a product specification of how much electricity is stored in the system. This is the capacity of the system, but it is specifically the deliverable energy capacity, the Power Rating x the total time in hours that this full power rating can be continueously provided. The Battery Capacity number will be a 'kWh"‘ number. For example, a 10kW battery with a 2-hour system duration is a 10kW x 2 hr system, having a total capacity of 20kWh.
State of Charge (SOC) is a percentage reflecting an assumption made about how much of the total battery capacity is actually available “in the tank.” As a percentage it will be a decimal between 0 and 1. In our example series, there will be two assumed fill-levels: 90% which is typical for the size of battery in question, and 50%, which is the amount with a lot of evening load at the home. The SOC percentages thus used are 0.5 and 0.9.
Available Energy is therefore a rate of consumption of power available in the battery, derated by 1-SOC%. It is expressed in kWh and becomes the numerator of the formula.
The denominator is now calculated to reflect the load actually interfacing with the battery in the state that we find it in, to figure out how many hours of home backup that system can provided.
A home’s energy usage is total kWh in a day (power load in the home x 24 hours). In the examples we will use below, a Texas home without efficient heat pumps is a home that consumes on average a daily 34 kWh This is derived from public data/EIA numbers. Every state has a different standard average daily home load.
A home can of course make changes to reduce its home load per hour - turning things off, making things more efficient, and so forth. This drags out the hours “in the tank” that a battery could provide. So, the denominator is subject to a potential derate of 1 - Usage % (a percentage reduction in total hourly load in the home). An assumed derate associated with “judicious usage” will be used below: a 50% “lights off” approach reducing hourly home load to half of normal hourly home load.
Total available battery energy hours divided by the total energy needs of the home results in a number of hours that the battery can cater to this need. This is the total hours of outage backup available.
This image shows the assumptions that will be made for inputs into the formula. These assumptions will remain standard to run the above-formula for a use case of 50% “in the tank” and 90% “in the tank”, showing differences in total hours of outage protection available for standard and upgraded homes using public data for households in Texas. There are the outcomes of using the calculated formula under these various scenarios.
The above diagram shows that the same battery in various states of charge can last anywhere from ~ 7 hours (specifically, 6.89 for 50% SOC, 35kWh 24-hour load) to well over that amount in a day. The circumstances of how the customer has utilized the battery and choices made to conserve loads powering the battery in constrained conditions, can significantly increase the “ride out” time of the system.
A customer can therefore double all of these values, in all scenarios, by adding more Power at the outset (two batteries intead of one in this example would mean 20 kW times 2 hours, a total of 40 kWs at 100% SOC to run against the same home loads, which results in surpassing 24 outage protection hours. A customer could also keep the single battery and pair it with solar, which would increase the average SOC of the battery twice a day to well above 50%.
The comparison below shows an important narrative for how home distributed energy resources and energy efficiency measures work hand-in-hand to faciliate the best outcomes. A customer who replaces an inefficient electric resistance heat pump with a high efficiency pump can see a significant increase in hours available from the battery: in a virtual power plant or grid-sharing retail energy buyback scenario, the customer can increase its grid-sharing contribution and earn a higher credit on energy bills, while also having assurance of a higher number of outage rideout hours.
A virtual power plant program administrator is any entity that helps the home user of a battery energy storage system, whether or not that system is solar-paired, optimize the conditions for daily charging and discharing of the home battery, and support the user’s behavioral response activities, including potential additional investments in energy efficiency. While conventional energy policy discussions and important utility or retail electricity proceedings occur for “DER” and “demand response” in separate proceedings, these are unfortunate silos that a competent program administrator can break to help customers achieve the highest value proposition for their home energy systems.
If you enjoyed this exercise, proceed to utilizing your own assumptions. Check out this state-by-state map to plot your own unique data sets for home consumption needs, or check out a solar generation calculator offered by installers in your zip code to cost out the amount of backup power you believe every customer should have in your community.
— Arushi Sharma Frank