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The state estimation (SE) has been widely used in power system control centers to optimally estimate the states of the power grid in real time. Using different objective functions, many SE algorithms have been proposed to filter out measurement noise in different ways. In this paper, three widely-used SE algorithms, i.e., the weighted least squares (WLS), least absolute value (LAV), and projection statistics (PS) based algorithms, are compared in their estimation accuracy and computation time. The comparison was made using the simulation data generated from the IEEE 14-bus system and IEEE 118-bus system through the Monte-Carlo method. It is found that when the measurement noise is reasonably small and follows the independent Gaussian distribution, the WLS algorithm has the best accuracy and shortest computation time. When some measurements at leverage points were compromised by outliers, the PS based algorithm is the most robust among the three methods. The study results can be used to assist control centers in choosing the right SE algorithm based on the features of the measurement noise and setup.