A new formulation of power system state estimation problem and a new solution technique is presented. The formulation allows for inequality constraints such as VAr limits on generator and transformer tap ratio limits. The solution technique uses logarithmic barrier function to treat inequality constraints. Non-quadratic criteria for power system state estimation have to facilitate bad data detection and identification. The weighted least absolute value criteria have desired bad data rejection property. This paper shows that logarithmic barrier function can accommodate inequality constraints and then applying Newton method to solve KKT equation leads to problem structure which is identical to that of non-linear least square problem. The number of iterations needed for convergence does not increase linearly with problem size unlike LP algorithm.