Interval current injection method for harmonic analysis in distribution systems: An approach using the Krawczyk operator

Abstract

This paper presents a novel deterministic method for an interval analysis of a harmonic load flow algorithm. In the proposed approach, the current injection method is used for determining harmonic voltages in a distribution network by the iterative Newton-Raphson method. Based on the deterministic Jacobian matrix, the Krawczyk operator is applied in order to calculate interval results, being possible to obtain upper and lower limits of harmonic voltage magnitudes and total harmonic distortion at each system bus of the network. The 33-bus test system is used for the computational simulations to prove the viability and efficiency of the proposed method assuming the introduction of non linear loads into the power grid. Results are compared with Monte Carlo simulations to validate the use of the proposed methodology. The main contribution of the article is the development of a new technique for determining interval harmonic voltages and currents in power systems based on the concept of interval arithmetic in an advantageous computational time.