Signal processing on graphs for estimating load current variability in feeders with high integration of distributed generation

Abstract

The emergence of new elements as distributed generators in power networks is a challenge for supplying energy with quality, reliability and continuity. The impacts of distributed power generation (DG) in these systems vary according to the number of generators, power and topological position of DG and feeder topology. Due to this, power systems simulations are essential to analyze the feeder behavior in this new scenario ensuring a good compliance with electricity quality levels. This paper utilizes a graph-theory based model and proposes a novel method that associates concepts of power flow and graph signals to identify the load current variation in a bus of a distribution feeder with DG, for a steady-state analysis. Graph Theory is used to model the feeders, where the nodes represent the feeder buses. The graphs were performed with Signal Processing on Graphs approach and the graph signal is defined by each bus weight, determined by the power flow assigned to that bus, calculated by algebraic power flow. To fit and validate the methodology, the results obtained are related with the current variation values obtained by solving a power flow problem, using Simulink data. Results were presented for 13 and 34 bus electrical grid systems. The Spearman’s and Pearson’s rank-order correlation showed a good agreement between the results of the graph analysis and the Simulink data. The method proposes an alternative way to identify the topological position of the generator in a feeder that most impact in the current variation, reducing the need of an electrical software and allowing an analysis with large amounts of DG connected to the feeder, which is uncommon in the literature, due to complexity in simulation and computational cost. The methodology can be applied in power utilities studies to analyze the feeders with the DG in the power grid.