This research aims to achieve the observability of any electrical network by the possibility compensation the lost measurements due to a defect, allowing the possibility of state estimation of the electrical network ,ie, obtaining a single solution for a state estimation. This is done by means of the network observability analysing using the available set of measurements and adding virtual pseudo-measurements if the network is not observable. this is done using a numerical algorithm that ensures obtaining the minimum and optimal number of added critical pseudo-measurements so that the result of state estimation was not adversely affected. The algorithm depends on solving the equation of the linear state estimation and the analysing to the triangular factors of the gain matrix and an easy way to arrange the axis of the jacobian matrix ,ie, the measurements matrix to ensure getting the minimum set of candidate pseudo- measurements to be added to real measurements, the numerical algorithm was acheived by environment in the MATLAB and tested to present the results on the network observabilty analysing and adding the pseudo-measurements algorithm on state estimation .The results of the program were tested on IEEE-14 network, and they showed that if a number of measurements were lost, they would be compensated by critical and pseudo-measurements. The results of state estimation showed small error ratio between estimated values using the real measurements and the estimated values after added the critical pseudo-measurements.