Variations of the Gauss Seidel and the gauss implicit z-bus load flow methods for primary-secondary integrated distribution grids

The primary and secondary distribution grids are typically designed separately and operated with a radial configuration; therefore, specialized load flow methods only applicable to radial or weakly meshed networks are normally used. However, projections indicate that the distribution grids will be more interconnected in the future, mainly because of the inclusion of distributed generation, voltage and reliability optimization, as well as an efficiency improvement when the primary and secondary networks are considered in an integrated way. For this new meshed grids scenario, the efficient and precise typically used load flow methods for distribution networks are no longer applicable and it becomes necessary using load flow algorithms that are also applicable for meshed configurations, such as the ones classically used for transmission networks like the Newton-Raphson, Gauss-Seidel and Gauss Implicit Z-bus methods, while also procuring to avoid potential singularity problems which may arise when dealing with long radial grids. In this work, variations of the Gauss-Seidel and Gauss Implicit Z-bus methods are presented, that are adequate for low and medium voltage grids regardless of the network configuration. Additionally, a linear, direct, and non-iterative load flow variation is presented as well as a comparison between different possible convergence criteria for the classical methods.