Domenico Lahaye

On the convergence of shifted Laplace preconditioner combined with multilevel deflation

SUMMARY Deflating the shifted Laplacian with geometric multigrid vectors yields speedup. To verify this claim, we investigate a simplified variant of Erlangga and Nabben presented in [Erlangga and Nabben, ETNA, 2008;31:403–424]. We derive expressions for the eigenvalues of the two-level preconditioner for the one-dimensional problem. These expressions show that the algorithm analyzed is not scalable. They also show that the imaginary shift can be increased without delaying the convergence of the outer Krylov acceleration. An increase of the number of grid points per wavelength results in convergence acceleration. This contrasts to the use of the shifted Laplace preconditioner. Our analysis also shows that the use of deflation results in a spectrum more favorable to the convergence of the outer Krylov acceleration. The near-null space components are still insufficiently well resolved, and the number of iterations increases with the wavenumber. In the two-dimensional case, the number of near-zero eigenvalues is larger than in the one-dimensional case. We perform numerical computations with the two-level and multilevel versions of the algorithm on constant and nonconstant wavenumber problems. Our numerical results confirm our spectral analysis. Copyright

Influence of Stator Slotting on the Performance of Permanent-Magnet Machines With Concentrated Windings

The use of slotted stator permanent-magnet machines with concentrated windings is increasing in industry. In this paper, the effect of the slot opening on flux linkage, internal voltage, mean torque, rotor eddy current loss, and stator iron losses is evaluated. This gives new insight into the influence of slotting on the performance of machines with a small slot opening. In addition, the slot opening can be chosen to maximize the internal voltage and the mean torque while minimizing the total iron loss. The limitations of the traditional analytical design model with small slot openings for permanent magnet machines are reported. Carter factor expressions found in literature are evaluated by comparing them with finite-element computations. The finite-element computations in turn are validated using measurements on two machines with semi-open slots and one machine with fully open slots. The measured and simulated values for amplitude and waveform of the flux linkage and internal voltages are in good agreement.

Scalable Newton-Krylov Solver for Very Large Power Flow Problems

The power flow problem is generally solved by the Newton-Raphson method with a sparse direct solver for the linear system of equations in each iteration. In this paper, alternatives based on iterative linear solvers are presented that are faster and scale much better in the problem size, making them ready for the ever-growing power systems of the future. For the largest test problem, with around one million busses, the presented alternative is over 120 times faster than using a direct solver.

Studying rotor eddy current loss of PM machines using nonlinear FEM including rotor motion

This paper studies distribution of eddy currents and eddy current losses in the rotor of concentrated winding exterior rotor permanent magnet machines in flywheels. The two-dimension nonlinear transient finite element method (FEM) model including rotor motion was used. Influence of slot opening on the eddy current loss in magnets and rotor back iron is investigated. Segmented magnets for reducing the eddy current loss are also surveyed. The proposed approach and results can be used to select the slot opening that minimizes rotor eddy current losses while maximizing the internal voltage. The used method allows monitoring of the eddy current losses in rotor as function of time, rotor speed, operating mode and stator slot opening. It therefore constitutes an indispensable tool in the design of PM machines taking the eddy current losses in the rotor into account.

Towards Faster Solution of Large Power Flow Problems

Current and future developments in the power system industry demand fast power flow solvers for larger power flow problems. The established methods are no longer viable for such problems, as they are not scalable in the problem size. In this paper, the use of Newton-Krylov power flow methods is proposed, and a multitude of preconditioning techniques for such methods are discussed and compared. It is shown that incomplete factorizations can perform very well as preconditioner, resulting in a solver that scales in the problem size. It is further shown that using a preconditioned inner-outer Krylov method has no significant advantage over applying the preconditioner directly to the outer iterations. Finally, algebraic multigrid is demonstrated as a preconditioner for Newton-Krylov power flow and argued to be the method of choice in some scenarios.

Finite element modeling of brushless doubly-fed induction machine based on magneto-static simulation

The brushless doubly-fed induction machine (BD-FIM) is a potentially attractive choice for a variable-speed wind generator. Using classical analytical models is not so straightforward, because the motion of the magnetic field in BDFIM is not a simple rotation. Finite element (FE) modeling makes it easier to evaluate the machine performance considering the saturation. However, for the purpose of a better convergence and an accurate calculation of the magnetic field equation and the coupled circuit equation, small time steps are utilized in the adaptive time-step solver of the transient FE model. A long computing time makes FE model be difficult to combine with an optimization program. This paper presents one possible alternative method to predict the BDFIM performance by using the magneto-static FE solutions and the space-time transformation. The simulation time then reduces significantly making it possible to search in a large design space for the optimization purpose.

Modeling and Optimization of Brushless Doubly-Fed Induction Machines Using Computationally Efficient Finite-Element Analysis

The air-gap magnetic fields of brushless doubly fed induction machines (DFIMs) are complicated because of the cross-coupling between two stator fields via a special nested-loop rotor. Compared with classical analytical models, transient finite-element (FE) modeling is easier to evaluate the machine performance taking saturation into account. However, it is not efficient to evaluate lots of candidates in a large design space using transient FE models considering the time cost. In the transient simulation, the induced rotor currents are calculated by solving several time differential equations using the backward differentiation formula. This paper presents a computationally efficient FE analysis for brushless DFIMs. The induced rotor currents can be calculated using a single magnetostatic FE simulation. The average torque, losses, and efficiency can also be predicted using one magnetostatic solution. One candidate design can be evaluated within 1 or 2 min on a personal workstation. The efficient analysis is validated by the transient FE results. The presented model is applied to the optimization of a prototype. The influence of two construction variables, namely, pole-pair combinations and the number of loops per nest, is studied. One pole-pair combination is selected for manufacturing a prototype.

Improved model for design of permanent magnet machines with concentrated windings

In literature, many different expressions for Carter factor can be found leading to confusion. This paper evaluates Carter factor expressions by comparing finite element computations in order to find the most suitable one which can be used in the design of permanent magnet machines. This paper shows limitations of conventional literature of slotting effect in the range of small slot opening. Finite element analysis based results show that calculation of magnetic saturation correction factor based on tooth flux density brings up results more accurate than that based on air gap flux density. The analytical model is improved by incorporating static FEM. This leads to hybrid model. Correction factors for slot opening, fringing and magnetic saturation are calculated online by static FEM model. In order to implement this concept, a static FEM program was developed. The program is able to make geometry model and handle boundary conditions automatically. To speed up the refinement of design results, a nonlinear transient finite solver based on scripts was also developed. Our implementation ensures that design parameters can be changed easily. Nonlinear finite element computations and experiments are compared. They are in very good agreement, with an error in the internal voltage of only 1.5%. Comparison of the analytical models, the proposed model and transient FEM model shows that the proposed model is more accurate in predicting permanent magnet machine behavior than conventional analytical model.

Modeling for the design of fractional slot PM machines with concentrated windings protected from demagnetization during three-phase short circuit

This paper presents a guideline for determining the thickness of permanent magnets in fractional slot permanent magnet machines with concentrated windings so that demagnetization can be alleviated or avoided even during three-phase short circuit fault. An analytical model for calculating the magnetic field, inductance, and three-phase short circuit current is investigated. A transient two-dimension FEM model including rotor motion and coupling with a circuit model is developed for checking the partial demagnetization of magnets. Analytical calculation, FEM simulation, and experimental results of synchronous inductance and three-phase short circuit show good agreement.

Counteracting ring formation in rotary kilns

Avoiding the formation of rings in rotary kilns is an issue of primary concern to the cement production industry. We developed a numerical combustion model that revealed that in our case study rings are typically formed in zones of maximal radiative heat transfer. This local overheating causes an overproduction of the liquid phase of the granular material, which tends to stick to the oven’s wall and to form rings. To counteract for this phenomenon, we propose to increase the amount of secondary air injected to cool the oven. Experimental validation at the plant has confirmed that our solution is indeed effective. For the first time in years, the kiln has been operating without unscheduled shut-downs, resulting in hugely important cost savings.