Abstract This work presents a method for static contingency analysis. The complex bus voltages after the outage of a transmission line (or a transformer) are estimated from one base case power flow solution and sensitivity relationships. As the steady-state power network equations are expressed in rectangular coordinates, the linearity of the Jacobian and the invariance of the Hessian allow the computation of sensitivity relationships with extra second-order information. This increases considerably the accuracy of the estimates of the power system variables and makes easier to handle the reactive power generation constraints, thus resulting in higher accuracy in the voltage estimation with limited additional computational effort. Numerical results with both test systems of different sizes and a real system illustrate the characteristics of the proposed methodology.