# Wirtinger's Calculus for the Load Flow in Power Distribution Grids

## TL;DR

This paper introduces a novel load-flow method for power distribution grids using Wirtinger's Calculus, enabling efficient complex domain computations and providing a tutorial for implementation in modern scripting languages.

## Contribution

It applies Wirtinger's Calculus to power system load-flow analysis, offering a new, compact, and efficient computational approach not previously utilized in this context.

## Key findings

- Effective load-flow algorithm using Wirtinger's derivatives
- Implementation guidance for Matlab/Octave
- Simulation results demonstrating method viability

## Abstract

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.