Abstract

The power flow model performs the analysis of electric distribution and transmission systems. With this statement at hand, in this work we present a summary of those solvers for the power flow equations, in both algebraic and parametric version. The application of the Alternating Search Direction method to the power flow problem is also detailed. This results in a family of iterative solvers that combined with Proper Generalized Decomposition technique allows to solve the parametric version of the equations. Once the solution is computed using this strategy, analyzing the network state or solving optimization problems, with inclusion of generation in real-time, becomes a straightforward procedure since the parametric solution is available. Complementing this approach, an error strategy is implemented at each step of the iterative solver. Thus, error indicators are used as an stopping criteria controlling the accuracy of the approximation during the construction process. The application of these methods to the model IEEE 57-bus network is taken as a numerical illustration.

Abstract

The main objective of this work is to describe a general and original approach for computing an off-line solution for a set of parameters describing the geometry of the domain. That is, a solution able to include information for different geometrical parameter values and also allowing to compute readily the sensitivities. Instead of problem dependent approaches, a general framework is presented for standard engineering environments where the geometry is defined by means of NURBS. The parameters controlling the geometry are now the control points characterising the NURBS curves or surfaces. The approach proposed here, valid for 2D and 3D scenarios, allows a seamless integration with CAD preprocessors. The proper generalised decomposition (PGD), which is applied here to compute explicit geometrically parametrised solutions, circumvents the curse of dimensionality. Moreover, optimal convergence rates are shown for PGD approximations of incompressible flows

Abstract

Abstract

Abstract

In aerospace industry, the computations of liquid-propelled launchers vibrations are based on linear elastic tanks coupled with an inviscid, incompressible fluid with free surface. In this specific case, the fluctuation of pressure on the free surface is supposed to be zero (i.e. the sloshing effects are neglected). Those vibrations are usually called hydroelastic vibrations. The discretized finite element dynamic problem is commonly expressed only in terms of displacements considering an added mass matrix, which represents the kinetic energy of the moving liquid expressed in terms of normal displacement interface. Those computations can be performed for various fluid level configurations, but no prestressing from geometrical nonlinearity is usually considered [1]. In the present study, the evaluation of the prestressed state influence on the coupled fluid structure vibrations is estimated numerically. This prestressing is supposed to be due to a gas or liquid pressurization, acting on the internal surface of the tank, inducing relatively large static displacement compared to the tank thickness. In reference [2], we have evaluated efficiently and accurately the nonlinear displacements for various filling rate with the use of an original level-set approach. We present here the hydroelastic vibrations around each known prestressed state corresponding to different level of liquid with the use of the added mass matrix. Using the open-source computing finite element platform FEniCS [3], numerical results are in very good agreements with experimental studies from the literature [4]. Comparisons with and without prestressing illustrates the contribution of the efect. To overcome an expensive added mass matrix computation, an appropriate reduced order model obtained by projection on prestressed dry modes is also proposed and show very encouraging results.

Abstract

Abstract

ne of the major trends in electrical machines for automotive applications is towards higher power-densities and more integrated components. With that, accurate thermal management of the machine and capable cooling systems are of great significance to the safety and reliability of the traction system. Thermal simulations are an integral part in the design process of electrical drives. However, recently thermal models are also more frequently used in the context of machine control. The latter demanding for fast, yet accurate, temperature estimations.