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In this paper, a novel approach for using a function space Markov chain-like to model a nonlinear, highly time-varying load such as an electric arc furnace (EAF) is proposed. After identifying the state space, this approach generalizes the original state case (where state is an element being analyzed) to a function case (in which one analyzes the cycle-vector as an element) and uses the same fundamental idea of Markov-like modeling, thus making it more convenient and powerful for EAF current/voltage prediction in a distribution system. Several approximations for the cycle-vector are investigated to reduce the complexity of the formulation and the burden on computation. The predictions derived from fast Fourier transform (FFT) frequency decomposition method appear to give better results than other proposed approximations based on both accuracy and efficiency indexes. Such an approach is further extended for harmonic compensation with an active harmonic filter (AHF) in a distributed system.