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This paper investigates how the efficiency of Weighted Least Squares (WLS) State Estimation changes according to both the uncertainty of network parameters and the uncertainty of measurements. Performance of State Estimator based mainly on the accuracy of its inputs and it is very important for the power system planners to improve the state estimation by determining whether to invest on increasing the measurement preciseness or improve the power network model. For this purpose, an algorithm for simulation of the uncertainty effects on the state estimator is proposed and tested on IEEE 14-Bus power network test case. The implementation of this algorithm enables us to analyze how much the state estimator's output is affected according to the network parameters uncertainty by means of state errors distribution versus the network parameters uncertainty. On the other hand, a serious defect in an estimator is the lack of unbiasedness. Hence a new prominent analysis is performed to find how network parameters uncertainty can affect the state estimator's bias by using distribution of the ratio between the absolute value of state errors mean and the related standard deviations versus the network parameters uncertainty and comparing it with a predefined threshold. Moreover, this analysis is also performed considering correlation in the network parameters, to investigate the effect of parameters correlation on the state estimator.