The increasing integration of intermittent renewable generation, especially at the distribution level,necessitates advanced planning and optimisation methodologies contingent on the knowledge of thegrid, specifically the admittance matrix capturing the topology and line parameters of an electricnetwork. However, a reliable estimate of the admittance matrix may either be missing or quicklybecome obsolete for temporally varying grids. In this work, we propose a data-driven identificationmethod utilising voltage and current measurements collected from micro-PMUs. More precisely,we first present a maximum likelihood approach and then move towards a Bayesian framework,leveraging the principles of maximum a posteriori estimation. In contrast with most existing con-tributions, our approach not only factors in measurement noise on both voltage and current data,but is also capable of exploiting available a priori information such as sparsity patterns and knownline parameters. Simulations conducted on benchmark cases demonstrate that, compared to otheralgorithms, our method can achieve significantly greater accuracy.

With the advent of renewable energy resources, generation in power networks is drifting from the classical centralized paradigm to an increasingly distributed scenario. While offering many advantages, renewable-based generation can compromise grid reliability, due to its intermittent nature and creation of reverse power flows. In order to guarantee the safe operation of power systems and avoid dangerous phenomena like blackouts, innovative and efficient control algorithms are necessary. Nevertheless, advanced algorithms necessitate grid identification, that is, the knowledge of grid topology and line parameters. Most works on the identification of electric networks focus on topology verification, assuming a known initial topology and aiming at detecting sparse changes, such as line trips or switch activations [1, 2]. More recently, attention has shifted to the estimation of network topology and line parameters without any apriori information. Two main branches of research have appeared. On the one hand, works like [3, 4] propose learning algorithms that exploit the statistical properties of nodal measurements to determine the operational structure and the line impedances. These approaches have the major advantage of accounting for buses with no available measurements (hidden nodes) [4], although restrictive assumptions are required, e.g.

--Solving power flow (PF) equations is the basis of power flow analysis, which is important in determining the best operation of existing systems, performing security analysis, etc. However, PF equations can be out-of-date or even unavailable due to system dynamics and uncertainties, making traditional numerical approaches infeasible. T o address these concerns, researchers have proposed data-driven approaches to solve the PF problem by learning the mapping rules from historical system operation data. Nevertheless, prior data-driven approaches suffer from poor performance and generalizability, due to overly simplified assumptions of the PF problem or ignorance of physical laws governing power systems. In this paper, we propose a physics-guided neural network to solve the PF problem, with an auxiliary task to rebuild the PF model. By encoding different granularity of Kirchhoff's laws and system topology into the rebuilt PF model, our neural-network based PF solver is regularized by the auxiliary task and constrained by the physical laws. The simulation results show that our physics-guided neural network methods achieve better performance and generalizability compared to existing unconstrained data-driven approaches. Furthermore, we demonstrate that the weight matrices of our physics-guided neural networks embody power system physics by showing their similarities with the bus admittance matrices. OWER flow (PF) analysis aims at obtaining complete voltage angle and magnitude information for each bus in a power system, given specified loads, generator real power and voltage conditions [1].