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Power system operators use dynamic models of the power grid to determine if the transient responses of transmission devices are within tolerable limits. The focus of this work is on the parameter estimation of a complex load model by using measurements from digital fault recorders or phasor measurement units, and the goal is to create a method which will produce more accurate models. Two methods are presented in this paper: Compare and Resimulate, and Simulate then Calculate. In a validation study, the former achieved a mean accuracy of 0.65% with a 42 minute run time, while the latter had a lower accuracy of 4.13%, but required only 3.2 seconds of computation time. It achieved this by performing the PSS/E simulations beforehand, and then calculating a linear representation of the nonlinear simulation process. However, both algorithms have weaknesses: Compare and Resimulate may be vulnerable to measurement error or noise, and Simulate then Calculate is dependent on the parameter distribution chosen for the simulations.