The increasing integration of intermittent renewable generation, especially at the distribution level, necessitates advanced planning and optimisation methodologies contingent on the knowledge the topology and line parameters of an electric network, captured in its admittance matrix. However, a reliable estimate of the admittance matrix may either be missing or quickly become obsolete for temporally varying grids. In this work, we present a maximum likelihood identification method utilising voltage and current measurements collected from micro-PMUs. From this method, we build a Bayesian framework accepting prior knowledge to enhance the a-posteriori estimation. In contrast with most existing contributions, our approach not only factors in measurement noise on both voltage and current data, but is also capable of exploiting a wide range of a priori information such as sparsity patterns and known admittances of specific lines. Simulations conducted on benchmark cases demonstrate that, compared to other algorithms, our method can achieve significantly greater accuracy.