This short paper presents a Wirtinger's-Calculus based load-flow methodology for power distribution grids. This approach allows to obtain an algorithm which works directly on the complex domain maintaining some useful symmetries and a compact representation. The paper aims to introduce Wirtinger's Calculus as a suitable tool for power systems analysis and simulations; therefore, it is presented as a tutorial, playing especial attention on the implementation in modern scrip languages such as Matlab/Octave, which allow easy representation of complex-arrays with fast calculations. A Newton's-based method is proposed in which the Jacobian is replaced by Wirtinger's derivatives obtaining a compact representation. Simulation results complement the analysis. Despite being a mature theory, Wirtinger's-Calculus has not been applied before in this type of problems.
@article{arxiv.1901.00430,
title = {Wirtinger's Calculus for the Load Flow in Power Distribution Grids},
author = {Alejandro Garces},
journal= {arXiv preprint arXiv:1901.00430},
year = {2019}
}