State estimator for electrical distribution systems based on an optimization model

State estimation (SE) has become an important aspect of real-time management of electrical distribution systems (EDS). However, it is a challenging problem, mainly due to the network model complexity and the lack of a reliable measurement infrastructure capable to cope with a variety of network configurations. This work presents an Extended Optimal Power Flow (E-OPF) for SE in EDS that considers different network configurations. The active and reactive power loads are handled as extended variables in the optimization model that are constrained by upper and lower bounds obtained from historical data. The objective function combines the state estimation error (SEE) from the known Weighted Least Squares (WLS) approach with additional indexes related to the state variables, which improve the SE process. The combination of different indexes and the handling of power loads as optimization variables without needing precise historical data are novelty for SE and consist of the main contributions for an EDS that, in general, has few available data. The computational efficiency when different topologies are considered and in situations where the WLS estimator might fail is also a suitable feature of the proposed approach. The known 16-bus and 33-bus test systems are used to assess the proposed methodology. An illustrative application of the proposed approach in a Phasor Measurement Unit (PMU) allocation problem is also presented.