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The rapid growth of circuit complexity has rendered Model Order Reduction (MOR) a key enabler for the efficient simulation of large circuit models. MOR techniques based on moment-matching are well established due to their simplicity and computational performance in the reduction process. However, moment-matching methods based on the ordinary Krylov subspace are usually inadequate to accurately approximate the original circuit behavior, and at the same time do not produce reduced-order models as compact as needed. In this paper, we present a moment-matching method which utilizes the extended and the asymmetric extended Krylov subspace (EKS and AEKS), while it allows the parallel computation of the transfer function in order to deal with circuits that have many terminals. The proposed method can handle large-scale regular and singular circuits and generate accurate and efficient reduced-order models for circuit simulation. Experimental results on industrial IBM power grids demonstrate that the EKS method can achieve an error reduction up to 85.28% over a standard Krylov subspace method, while the AEKS method greatly reduces the runtime of EKS, introducing a negligible overhead in the reduction error.