Derivation of powerflow equations with ideal transformer

Hi, I am looking for a citable source (book or article) deriving the power flow equations used in PowerModels.jl - including an ideal transformer as such:


Mathematical Model · PowerModels (

I would appreciate, if you could point me to some literature.

Sorry for probably choosing a wrong domain of this forum, but Energy does not exist and I have looked where people asked related questions - which was Optimization.

Good question and this is a reasonable place to inquire about it.

It is pretty common use the Matpower manual or the related paper as the primary source for this formulation. If you really want a book, I can recommend Power System Analysis by John J. Grainger and William D Stevenson, which I found quite good for presenting derivations from first principles.

The specific notations used here were first proposed in the paper, “The QC Relaxation: Theoretical and Computational Results on Optimal Power Flow,” as far as I know.