# Derivation of powerflow equations with ideal transformer

**URL:** <https://discourse.julialang.org/t/derivation-of-powerflow-equations-with-ideal-transformer/101926>\
**Category:** Optimization (Mathematical)\
**Created:** [July 22, 2023, 2:27pm UTC](https://discourse.julialang.org/t/derivation-of-powerflow-equations-with-ideal-transformer/101926 "2023-07-22T14:27:51Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![Anton\_Hinneck](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/anton_hinneck/32/22716_2.png) [@Anton\_Hinneck](https://discourse.julialang.org/u/Anton_Hinneck)\
**Post date:** [July 22, 2023, 2:27pm UTC](https://discourse.julialang.org/t/derivation-of-powerflow-equations-with-ideal-transformer/101926/1 "2023-07-22T14:27:51Z")

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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:

![image](https://global.discourse-cdn.com/julialang/original/3X/9/3/939a5d8d9354cb5cf5fa3ca92b12229cdf9f6c17.png)

[Mathematical Model · PowerModels (lanl-ansi.github.io)](https://lanl-ansi.github.io/PowerModels.jl/stable/math-model/)

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

P.S.  
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.

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<div class="post-metadata">

**Author:** ![ccoffrin](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ccoffrin/32/400_2.png) [@ccoffrin](https://discourse.julialang.org/u/ccoffrin)\
**Post date:** [July 22, 2023, 3:04pm UTC](https://discourse.julialang.org/t/derivation-of-powerflow-equations-with-ideal-transformer/101926/2 "2023-07-22T15:04:47Z")

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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.