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State estimation (SE) of distribution networks heavily relies on pseudo measurements that introduce significant errors, since real-time measurements are insufficient. Interval SE models are regularly used, where true values of system states are supposed to be within the estimated ranges. However, conventional interval SE algorithms cannot consider the correlations of same interval variables in different terms of constraints, which results in overly conservative estimation results. In this paper, we propose a Linear Programming (LP) Contractor algorithm that uses a relative distance measure (RDM) interval operation to solve this problem. In the proposed model, measurement errors are assumed to be bounded into given sets, thus converting the state variables to RDM variables. In this case, the SE model is a non-convex model, and the solution credibility cannot be guaranteed. Therefore, each nonlinear measurement equation in the model is transformed into dual inequality linear equations using the mean value theorem. The SE model is finally reformulated as a linear programming contractor that iteratively narrows the upper and lower bounds of the system state variables. Numerical tests on IEEE three-phase distribution networks show that the proposed method outperforms the conventional interval-constrained propagation, modified Krawczyk-operator and optimization based interval SE methods.