  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.
