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Harmonic resonance mode analysis (RMA) is an effective tool for power system harmonic study. It can determine not only the harmonic resonance potentials, but also the contributions of various network components to a resonance situation. RMA is based on the eigen-decomposition of complex symmetrical nodal matrices, which is known to be difficult and inefficient compared with the decoupling of real symmetrical matrices. The complex eigenvalues also makes the consequent sensitivity analysis complicated. In this paper, an alternative modal formulation utilizing real symmetrical nodal matrices is proposed. The validity of this new formulation is confirmed through theoretical analysis and case studies.