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Summary form only given. This paper investigates two weighted least squares (WLS) approaches to the problem of load estimation (LE) in unbalanced power distribution networks: (i) the WLS load parameter method is restated more rigorously and (ii) a constrained distribution state estimation (DSE) based method is introduced to consider operating and loading constraints. Detailed simulation results on 394 bus radial and weakly meshed power distribution systems are evaluated through four error indices. The results of both methods are compared and discussed. Observability issues are also addressed.