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In this paper we present the global optimization algorithm based on grid search to estimate DC offset time constants from a current recorded during short circuit on transmission line. The grid on which the search for optimum is performed is constructed using the hyperbolic cross points (HCP). We are able to estimate three time-constants of the DC offset in the fault current signal, namely: time constant of the Thevenin's equivalent impedance of the network, current transformer (CT) time constant and auxiliary CT time constant. The global search on the HCP grid is complemented with Levenberg-Marquardt (LM) or Nelder-Mead (NM) local search algorithms, to refine the result. The results presented in the paper show that LM and NM local algorithms find better solution and converge faster if the HCP algorithm is used to determine the starting point. The HCP search, as preprocessing step helps LM and NM algorithms to converge faster to a global minimum.