This work addresses the monitoring and state estimation of electrical grids, especially at the distribution level. For economic and technical reasons, grid monitoring cannot be implemented with a similarly high measurement density as in transmission grids. Two new monitoring methods, which are designed for low measurement density, are therefore presented for use in real-time grid operation. First, a heuristic monitoring method is presented, which does not require pseudo-measurements and estimates voltage magnitudes and line loadings. Second, a monitoring method based on artificial neural...