This paper introduces and analyzes different methods used to solve the problem of state estimation in nonlinear power systems. The classic Newton, Quasi-Newton, Sequential Quadratic Programming (SQP) and Linear Programming (LP) based methods are discussed and implemented to attack the problem. These various techniques have been compared for their computation effort, accuracy and robustness based on the simulation results for a 6-bus power system. Two full sets of erred data with different variances are generated to provide the basis for this comparison. The linear programming method minimizes the norm-1 objective function and has the advantage of rejecting bad measurements or topological errors. The SQP method is an effective method to solve the problem if the estimation is required to satisfy further equality and inequality constraints.