Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)This study proposes a novel observability analysis approach for power systems state estimation. To support this approach, the study also proposes a constrained linear regularised state estimator in which equality constraints are explicitly represented, thus resulting in a well-conditioned mathematical model where numerical problems are not prone to occur. A proper mode to specify values for the required pseudo-measurements is also proposed. Except for some pathological cases, the coefficient matrix needs to be built and factorised just once. The implementation of the proposed approach is trivial, since the matrix to be factorised is symmetric and positive semi-definite, requiring only classical and well-established methods for sparse storage and factorisation. Additionally, pivoting strategies are not required. Tests based on Small systems are used to present the proposed approach in a didactic way. Additional case studies based on IEEE-14 buses and IEEE-300 buses systems are used to highlight the robustness and usefulness of the proposed approach.101127312738FAPESPCAPESCNPqFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)