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Publication# Linear Recursive State Estimation of Hybrid and Unbalanced AC/DC Micro-Grids using Synchronized Measurements

Abstract

In this paper, we present an exact (i.e. non-approximated) 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 transformer-like 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.

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Andrea Ajbl, Maher Kayal, Marc Pastre

This paper presents a fully integrated Hall sensor microsystem with a current-mode output. The system operates in open-loop and includes a Hall sensor with internal biasing, a fully differential front-end, a preamplifier chain and a voltage-to-current converter (V-I). The effects of the V-I block on the sensitivity drift of the system are analyzed and a current biasing of the Hall cells is proposed so that the current output feature adds no drift to the microsystem sensitivity. The whole microsystem is integrated in a 0.35μm CMOS technology. It occupies an area of 11.55mm2. The sensitivity drift of the system is characterized, and shows that the V-I does not degrade the overall sensitivity drift of the system.

2011The current development of generators and power electric drives is characterized by increased power electronic integration. This evolution concerns particularly the variable speed power units allowing both a higher performance and substantial savings on cost but nevertheless, it implies new constraints and difficulties in term of interaction between the various components: generator, converter and network. The design and optimization of such generators is no longer possible with the same approach and same tools as for conventional machines directly connected to a symmetrical three-phase network. This Ph.D. study is related to an industrial project which was developed by ALSTOM in the same time frame in which this thesis work was prepared. Since the project relies on a new high power synchronous generator topology (a multiphase turbo-generator connected to a three phase network via a power electronic converter), not many studies were done especially because of the enormous financial resources required by such studies and limitations in respect of the maximum power that a power electronic device can commute. The goal of this study is the development of an advanced multiphase machine model which can be used in a complex system comprising power electronic elements. The model has to accurately consider the physical phenomena which are taking place in a machine while functioning in such conditions. The selected approach for the development of the machine model is a combined numerical-analytical approach. This solution was preferred since it can take benefit from the precision, a property which is characteristic to the numerical Finite Element Methods (FEM), but also from the fast computation times which is a property of the analytical models. The model presented in this thesis is based on the differential inductance parameter. The differential inductances are calculated analyzing the results of FEM simulations and are used afterwards in analytically expressed circuit equations. The machine circuit equations, having as parameters the differential inductances, are afterwards solved numerically. In order to take advantage of the existing elements necessary for the analysis of the electrical power networks (including power electronic converters), the developed method was integrated into a network simulation software package. This simulation software package was designed for industrial use where a short computation time is desired; the module with the integrated machine model is respecting this principle.

Jean-Yves Le Boudec, Mario Paolone, Styliani Sarri, Lorenzo Zanni

In the operation of power systems, the knowledge of the system state is required by several fundamental functions, such as security assessment, voltage control and stability analysis. By making reference to the static state of the system represented by the voltage phasors at all the network buses, it is possible to infer the system operating conditions. Until the late 1970s, conventional load flow calculations provided the system state by directly using the raw measurements of voltage magnitudes and power injections. The loss of one measurement made the calculation impossible and the presence of measurement errors affected dramatically the computed state.To overcome these limitations, load flowtheory has been combined with statistical estimation constituting the so-called state estimation (SE). The latter consists in the solution of an optimization problem that processes the measurements together with the network model to determine the optimal estimate of the system state. The outputs of load flow and SE are composed of the same quantities, typically the voltage magnitude and phase at all the network buses, but SE uses all the types of measurements (e.g., voltage and current magnitudes, nodal power injections and flows, synchrophasors) and evaluates their consistency using the network model. The measurement redundancy is key to tolerate measurement losses, identify measurement and network parameter errors, and filter out the measurement noise. The foregoing properties of SE allow the system operator to obtain an accurate and reliable estimate of the system state that consequently improves the performance of the functions relying on it. Traditionally, SE has been performed at a relatively low refresh rate of a few minutes, dictated by the time requirements of the related functions together with the low measurement acquisition rate of remote terminal units (RTUs). Nowadays, the emerging availability of phasor measurement units (PMUs) allows to acquire accurate and time-aligned phasors, called synchrophasors, with typical streaming rates in the order of some tens of measurements per second. This technology is experiencing a fast evolution, which is triggered by an increasing number of power system applications that can benefit from the use of synchrophasors. SE processes can exploit the availability of synchrophasor measurements to achieve better accuracy performance and higher refresh rate (sub-second). PMUs already compose the backbone of wide area monitoring systems in the context of transmission networks to which several real-time functionalities are connected, such as inter-area oscillations, relaying, fault location and real-time SE. However, PMUs might represent fundamental monitoring tools even in the context of distribution networks for applications such as: SE [5, 6], loss of main [7], fault event monitoring, synchronous islanded operation [9] and power quality monitoring. The recent literature has discussed the use of PMUs for SE in distribution networks both from the methodological point of view and also via dedicated real-scale experimental setups. Since the pioneering works of Schweppe on power system SE in 1970, most of the research on the subject has investigated static SE methods based on weighted least squares (WLS). Static SE computes the system state performing a “best fit” of the measurements belonging only to the current time-step. Another category of state estimators are the recursive methods, such as the Kalman filter (KF). In addition to the use of the measurements and their statistical properties, they also predict the system state by modelling its time evolution. In general, recursive estimators are characterized by higher complexity and the prediction introduces an additional source of uncertainty that, if not properly quantified, might worsen the accuracy of the estimated state. Besides, their ability to filter out measurement noise could not be exploited due to the low SE refresh rate: even in quasi-steady state conditions, the measurement noise was smaller than the state variations between two consecutive time-steps. However, the effectiveness of power system SE based on KF has been recently reconsidered thanks to the possibility to largely increase the SE refresh rate by using synchrophasor measurements. The chapter starts by providing the measurement and process model of WLS and KF SE algorithms and continues with the analytical formulation of the two families of state estimators, including their linear and non-linear versions as a function of the type of available measurements. Finally, two case studies targeting IEEE transmission and distribution reference networks are given.