This software tries to implement the battery current flow optimization scheme shown in https://ieeexplore.ieee.org/document/6046111/. However the results obtained did not match the results shown in the paper.
The main scripts are:
optim_P3.m: for optimizing the problem P3 as given in the paper.optim_P3_small.m: small version of aforementioned script where all functions are packed in one file.optim_P3_adj.m: an alternative math implementation for solving the problem by me loosly based on the paper.
The math was checked 2 times with symbolic math toolboxes in python (file: math_check_paper_2.ipnb) and MATLAB (files: SymCheck.m and the outputs symbolic_math_check_output.txt as well as html/SymCheck.html) and it was found that the math implemented in this software matches the equations given in the paper.
Whether the problem lies within a misinterpretation of the informaton given in the paper by me, or due to different initial conditions and parameters can not be said at this point. I am making this repository open source in the hope, that it will help people in future.
A report of my findings when analyzing the paper is given in paper_report.md I do not guarantee for correctness though.
When checking the math in the paper before I got a suspicion about a slight error in the math. It is regarding the Appendix where they generate the constraint equation. There they replaced the abs( I_out - I_in ) function with ( I_out + I_in ). At this point they already limited I_out >= 0 and I_in >= 0. However I have the suspicion that this step is not valid. But I doubt that this is the reason for the discrepancy in the results given.
Another thing I noticed is:
vk0 (voltage now) is set as a free variable for the optimization to make the math work. This however is not possible since one can not influence the voltage now anymore.