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This paper addresses the state estimation of a power system whose network parameters are known to be within certain tolerance bounds. The power system is assumed to be fully observable by having enough phasor measurement units installed. Using synchronized phasor measurement data and state variables expressed in rectangular forms, the state estimation under the transmission line parameter uncertainties is formulated based on the weight least square criterion as a parametric interval linear system of equations. The solutions are obtained as interval numbers representing the outer bound of state variables. The proposed method is also extended to a power system with mixed phasor and conventional power measurements. A technique based on affine arithmetic for converting state variable into polar form is also presented. The proposed method has been implemented using MATLAB and INTLAB toolbox and applied to some IEEE test systems. The numerical experiment results indicate that, in shorter computation time, the proposed algorithm can find the outer bounds that are close to those computed by performing Monte Carlo simulations or by solving constrained nonlinear optimization problems.