LiveWithEarth

The section you are referring to (Section IV) is a thought experiment to describe the importance of the correlation between power supply and power demand. You are absolutely right. I do need to take time-varying leakage into account, which I didn't because I haven't done the research to figure out how to modify the algorithm. However, after I do take this into consideration, it's just going to give me different results. I'm confident the inverse relationship will still be present because as the PV system size increases the need to store energy for long periods of time decreases.

At the end of the introduction, I state

Future work includes incorporating probability distributions of the power supply and power demand into the algorithm to design off-grid systems that meet statistical requirements (e.g., there is an 80% chance that PV size X and storage capacity Y will reliably supply electric power year-round for this building for this year), incorporating time-varying energy losses, and mixing renewable energy resources and energy storage systems to optimize for the cheapest cost (e.g., PV size X, wind energy size Y, and energy storage Z is the optimal system).

Edit: I created this diagram to show how I believe the graph will change by including time-varying leakage. https://imgur.com/0n2AzIe. Time-varying leakage is practically negligible for the points at the end of the graph because for these configurations the system stores energy during the day for nighttime use, so energy is stored for less than 24 hours.

To continue with your example, my model of a ball bouncing takes into account friction, and if I include air resistance (time-varying leakage), it is going to give me different results.

The power data is on GitHub. It's the file called example_power_data.mat.

I searched online, through academic publications, and the patent database, and I did not find the relationship between solar and energy storage published anywhere.

I created this diagram to show how I believe the graph will change by including time-varying leakage. https://imgur.com/0n2AzIe. Time-varying leakage is practically negligible for the points at the end of the graph because for these configurations the system stores energy during the day for nighttime use, so energy is stored for about 12 hours.

Thanks for the feedback and for sharing what you know about energy storage systems. I will look into time-varying leakage and try to incorporate it into the algorithm to see how the curve actually changes.