Considering the ubiquitous energy transition and the integration of new technologies, system operators need the best possible insight into the state of the power system. An advanced measurement infrastructure installed in as many network nodes as possible would enable the use of advanced algorithms for system management, such as the methods of machine learning and data science described in this paper. Machine learning methods are first described mathematically and then implemented for the purpose of solving power flow problems on the example of an advanced network for which real data is available. For the observed network, advanced meters collected historical data on voltage and consumption of active and reactive power. Data were first statistically analyzed, and then used as input data in the implementation of the machine learning models. By exploiting the amount of network state information provided by advanced meters, a model based on artificial neural networks can overcome the problem of unknown network topology and calculate voltage opportunities, trends and changes in the network. In addition, on the example of a real network, it was shown that by compressing the data, a model with many times fewer input and output dimensions can be realized with almost intact accuracy. Physically-informed neural networks are also highlighted as models that integrate equations derived from the physical formulation of power flow calculations into the loss function and thus increase the extrapolation ability of the model to more accurately predict values outside the range of data used for training.