Vine-Copula-Based Stochastic Modeling of Iron Losses in Electrical Steels

The uncertainty in the iron loss properties of electrical steel makes traditional deterministic analysis methods insufficient for optimal design and reliability assurance of transformers. In this paper, a stochastic modeling approach for transformer iron loss based on vine copula theory is proposed. A total of 175 electrical steel samples from the same production chain have been investigated. First, the parameters of the deterministic iron loss model are identified and validated using the least squares method. Next, the marginal probability distributions of these parameters are determined and combined with the optimal copula function to model their variability and correlations. A joint probability density distribution has been established using vine copula theory, accurately capturing parameter correlations. The results show that the proposed stochastic model can accurately characterize the probabilistic characteristics of electrical steel losses. Furthermore, the vine copula structure constrains parameter combinations, avoiding the generation of unrealistic magnetization curves. Finally, the stochastic material model is applied to analyze core power losses in a power transformer.