State estimation is nowadays considered the fundamental element of modern electrical power network control centers. In this paper we develop a theoretically robust and computationally efficient state estimator algorithm, to solve the weighted least squares (WLS) problem by using parallel processing. The computational aspects of the parallel processing, was analyzed and tested using the IEEE 14, 57 and 118 bus systems. Computational experiments are compared with standard WLS methods, in the integral and distributed version. An evaluation of the degree of natural decoupling in the state estimation problem is also performed. The results indicate that a distributed processing for state estimation, is the better way to adopt parallel computing in power systems energy.