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Publication# Advanced Model for Multiphase Generators

Abstract

The 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.

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This thesis focuses on the development and validation of a reduced order technique for cardiovascular simulations. The method is based on the combined use of the Reduced Basis method and a Domain Decomposition approach and can be seen as a particular implementation of the Reduced Basis Element method. Our contributions include the application to the unsteady three-dimensional Navier--Stokes equations, the introduction of a reduced coupling between subdomains, and the reconstruction of arteries with deformed elementary building blocks. The technique is divided into two main stages: the offline and the online phases. In the offline phase, we define a library of reference building blocks (e.g., tubes and bifurcations) and associate with each of these a set of Reduced Basis functions for velocity and pressure. The set of Reduced Basis functions is obtained by Proper Orthogonal Decomposition of a large number of flow solutions called snapshots; this step is expensive in terms of computational time. In the online phase, the artery of interest is geometrically approximated as a composition of subdomains, which are obtained from the parametrized deformation of the aforementioned building blocks. The local solution in each subdomain is then found as a linear combination of the Reduced Basis functions defined in the corresponding building block. The strategy to couple the local solutions is of utmost importance. In this thesis, we devise a nonconforming method for the coupling of Partial Differential Equations that takes advantage of the definition of a small number of Lagrange multiplier basis functions on the interfaces. We show that this strategy allows us to preserve the h-convergence properties of the discretization method of choice for the primal variable even when a small number of Lagrange multiplier basis functions is employed. Moreover, we test the flexibility of the approach in scenarios in which different discretization algorithms are employed in the subdomains, and we also use it in a fluid-structure interaction benchmark. The introduction of the Lagrange multipliers, however, is associated with stability problems deriving from the saddle-point structure of the global system. In our Reduced Order Model, the stability is recovered by means of supremizers enrichment.
In our numerical simulations, we specifically focus on the effects of the Reduced Basis and geometrical approximations on the quality of the results. We show that the Reduced Order Model performs similarly to the corresponding high-fidelity one in terms of accuracy. Compared to other popular models for cardiovascular simulations (namely 1D models), it also allows us to compute a local reconstruction of the Wall-Shear Stress on the vessel wall. The speedup with respect to the Finite Element method is substantial (at least one order of magnitude), although the current implementation presents bottlenecks that are addressed in depth throughout the thesis.

Gyorgy Miklos Dan, Marguerite Marie Nathalie Delcourt, Jean-Yves Le Boudec, Mario Paolone

Phasor measurement units (PMU) rely on an accurate time-synchronization to phase-align the phasors and timestamp the voltage and current phasor measurements. Among the symmetrical components computed from the phasors in three-phase systems, the standard practice only uses the direct-sequence component for state estimation and bad data detection (BDD). Time-synchronization attacks (TSAs) can compromise the measured phasors and can, thus, significantly alter the state estimate in a manner that is undetectable by widely used power-system BDD algorithms. In this paper we investigate the potential of utilizing the three-phase model instead of the direct-sequence model for mitigating the vulnerability of state estimation to undetectable TSAs. We show analytically that if the power system is unbalanced then the use of the three-phase model as input to BDD algorithms enables to detect attacks that would be undetectable if only the direct-sequence model was used. Simulations performed on the IEEE 39-bus benchmark using real load profiles recorded on the grid of the city of Lausanne confirm our analytical results. Our results provide a new argument for the adoption of three-phase models for BDD, as their use is a simple, yet effective measure for reducing the vulnerability of PMU measurements to TSAs.

2021Willem Lambrichts, Mario Paolone

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.

2022