Tensor-based Probabilistic Harmonic Three-Phase Current Injection Method for Harmonic Analysis in Power Systems

Abstract Probabilistic harmonic analysis has become increasingly important in modern distribution systems due to the growing presence of nonlinear devices and uncertain operating conditions. This paper proposes a novel tensor-based probabilistic harmonic analysis framework derived from the Harmonic Three-Phase Current Injection Method (HTPCIM). The first contribution of the paper consists of reformulating the harmonic admittance matrices and injected current vectors into multidimensional tensor structures, enabling the simultaneous evaluation of multiple stochastic operating scenarios through direct tensor operations. The second contribution is the explicit incorporation of uncertainties associated with loads, distributed generation, and network impedance parameters while preserving three-phase coupling effects. The third contribution is the development of a computationally efficient probabilistic framework capable of substantially reducing processing time when compared with conventional Monte Carlo simulations. The proposed methodology is validated using IEEE 14-bus, 33-bus, and 123-bus distribution systems considering multiple harmonic orders and stochastic operating conditions. The obtained results demonstrate strong agreement with Monte Carlo simulations regarding harmonic voltage distributions and THD (Total Harmonic Distortion) values, with accommodation indices higher than 70% and statistical consistency verified through Kolmogorov–Smirnov hypothesis testing. Furthermore, the proposed tensor-based approach achieves computational speed-up factors of up to 186 times in large-scale benchmark systems. These results demonstrate that the proposed method provides an accurate, scalable, and computationally efficient alternative for probabilistic harmonic assessment in power distribution grids.