In this paper, we present an exact (i.e. nonapproximated) and linear measurement model for hybrid AC/DC micro-grids for recursive state estimation (SE). More specifically, an exact linear model of a voltage source converter (VSC) is proposed. It relies on the complex VSC modulation index to relate the quantities at the converters DC side to the phasors at the AC side. The VSC model is derived from a transformerlike representation and accounts for the VSC conduction and switching losses. In the case of three-phase unbalanced grids, the measurement model is extended using the symmetrical component decomposition where each sequence individually affects the DC quantities. Synchronized measurements are provided by phasor measurement units and DC measurement units in the DC system. To make the SE more resilient to vive step changes in the grid states, an adaptive Kalman Filter that uses an approximation of the prediction-error covariance estimation method is proposed. This approximation reduces the computational speed significantly with only a limited reduction in the SE performance. The hybrid SE is validated in an EMTP-RV time-domain simulation of the CIGRE AC benchmark micro-grid that is connected to a DC grid using 4 VSCs. Bad data detection and identification using the largest normalised residual is assessed with respect to such a system. Furthermore, the proposed method is compared with a non-linear weighted least squares SE in terms of accuracy and computational time.

This paper presents the experimental validation of a linear recursive state estimation (SE) process for hybrid AC/DC microgrids proposed in the authors' previous work. The SE uses a unified and linear measurement model that relies on the use of synchronized AC and DC measurements along with the complex modulation index of voltage source converters (VSCs). The validation is performed on the hybrid AC/DC microgrid available at the EPFL. The hybrid network consists of 18 AC nodes, 8 DC nodes and 4 VSCs interfacing the AC and DC parts of the grid at different nodes. The experimental validation of the measurement model is based on the classical noise model verification via the measurement residuals. It is shown that the measurement residuals of the AC system, DC system and VSC model are zero-biased with a standard deviation well below the three-sigma threshold of the expected noise distribution. An estimation of the prediction error covariance is also implemented and analyzed to automatically adopt the accuracy of the SE during dynamic and steady-state conditions. Furthermore, the time latency of each section in the SE process is analysed to validate its applicability in critical real-time applications.