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This paper presents a load flow solution for radial and weakly meshed distribution system. The problem is formulated as an optimization problem based on minimization of L1 norm of a vector consisting of power mismatch at every node in a distribution system. The optimization problem is solved using interior point (IP) method. The advantage of interior point method is that it converges in polynomial time, and can handle the numerical ill conditioning. A primal-dual interior point (PDIP) method is demonstrated in this paper and performance of the method is evaluated on standard radial and weakly meshed test systems.