Power system state estimation (PSSE) is an energy management system function responsible for the computation of the most likely values of state variables viz., bus voltage magnitudes and angles. The state estimation is obtained within a network at a given instant by solving a system of mostly non-linear equations whose parameters are the redundant measurements, both static such as transformer/line parameters and dynamic such as, status of circuit breakers/isolators, transformer tap positions, active/reactive power flows, generator active/reactive power outputs etc. PSSE involves solving an over determined set of nonlinear equations by minimizing a weighted norm of the measurement residuals. Typically, the L1 and L2 norms are employed. The use of L2 norm leads to state estimation based on the weighted least squares (WLS) criterion. This method is known to exhibit efficient filtering capability when the errors are Gaussian but fails in the case of presence of bad data. The method of hypothesis testing identification can be incorporated into the WLS estimator to detect and identify bad data. Nevertheless, it is prone to failure when the measurement is a leverage point. On the other hand state estimation based on the weighted least absolute value (WLAV) criterion using L1 norm, has superior bad data suppression capability. But it also fails in rejecting bad data measurements associated with leverage points. Leverage points are highly influential measurements that attract the state estimator solution towards them. Consequently, much research effort has focused recently, on producing a LAV estimator that remains robust in the presence of bad leverage measurements. This problem has been addressed in the thesis work. Two methods, which aims development of robust estimator that are insensitive to bad leverage points, have been proposed viz., (i) The objective function used here is obtained by linearizing L2 norm of the error function. In addition to the constraints corresponding to measurement set, constraints corresponding to bounds of state variables are also involved. Linear programming (LP) optimization is carried out using upper bound optimization technique. (ii) A hybrid optimization algorithm which is combination of”upper bound optimization technique” and ”an improved algorithm for discrete l1 linear approximation”, to restrict the state variables not to leave the basis during optimization process. Linear programming optimization, with bounds of state variables as additional constraints is carried out using the proposed hybrid optimization algorithm. The proposed state estimator algorithms are tested on 24-bus EHV equivalent of southern power network, 36-bus EHV equivalent of western grid, 205-bus interconnected grid system of southern region and IEEE-39 bus New England system. Performances of the proposed two methods are compared with the WLAV estimator in the presence of bad data associated with leverage points. Also, the effect of bad leverage measurements on the interacting bad data, which are non-leverage, has been compared. Results show that proposed state estimator algorithms rejects bad data associated with leverage points efficiently.