Alin-Iulian Dolan

Optimization of modular toroid coil geometry of a superconducting Magnetic Energy Storage device using design of experiments and FEM

The Superconducting Magnetic Energy Storage (SMES) system is a modern and expensive technique for storage of electricity through the magnetic energy in superconducting short-circuited coil. An optimized configuration must reduce as much as possible the volume of the superconducting material. In this paper is proposed an optimized solution of modular toroid coil geometry of SMES device using design of experiments (DOE) and finite element method (FEM). DOE is a rational realization of a series of real experiments a priori expensive and therefore it fits to the electromagnetic simulations (virtual experiments). Applied to the electrical systems modeled by FEM, it becomes a basic tool for optimization problems. Two geometric parameters characterizing the torus shape were chosen to determine the optimal configuration of the coil geometry of a SMES device for an optimized storage capacity. The ratio of maximum stored magnetic energy and the minimum volume of superconducting material was set as objective function. To solve it, the method of zooms without computation of models was used. The 2-D FEM implementation uses an equivalent rectangular cross section toroid, conserving the inductance of the system. The optimization results are obtained with less than 1% error. Comparison with previous numerical tests was made.

Numerical modeling of DC busbar contacts

The paper presents two electro-thermal numerical models which can be used for the modeling and optimization of high currents busbar contacts for DC. The models are obtained by coupling of the electric model with the thermal field problem. The coupling is carried out by the source term of the differential equation which describes the thermal field. The models allow the calculation of the space distribution of the electric quantities (electric potential, the gradient of potential and the current density) and of the thermal quantities (the temperature, the temperature gradient, the Joule losses and heat flux). A heating larger than that of the busbar appears in the contact zone, caused by the contact resistance. The additional heating, caused by the contact resistance is simulated by an additional source injected on the surface of contact. The 2D model has been solved by the finite volumes method while the 3D model, by the finite elements method. Both models were experimentally validated. Using the models, one can determine the optimal geometry of dismountable contact for an imposed limit value of the temperature.

Exhaustive optimization method based on DOE and FEM applied on a SMES device

In this paper, an exhaustive optimization method based on design of experiments (DOE) and finite element method (FEM) was applied on a Superconducting Magnetic Energy Storage (SMES) device with modular toroid coil in order to optimize its storage capacity. Two geometric parameters defining the torus shape were chosen to maximize the stored magnetic energy related to the volume of the superconducting material: the coil inner diameter ratio and the coil thickness ratio. The optimization algorithm is based on 2-D FEM numerical experiments in order to calculate polynomial models of second order of the objective function using full factorial design with three levels per factor. The result is the global maximum and it is compared with previous solutions.

Thermal modeling and experimental validation of an encapsulated busbars system

In this paper, we propose an approach for the magnetic and thermal modeling of an encapsulated busbars system for high voltage using QuickField software. This paper proposes a numerical model developed by coupling of the magnetic field problem with the stationary and transient heat field problems for the geometry of a single-phase execution busbars system. The coupling of problems is realized by importing specific losses from the magnetic field problem as heat sources for thermal field problem. The magnetic field problem is also coupled to the electrical circuit. The shields are short-circuited at both ends and they are connected to the ground. For this constructive solution, in the shields occur induced currents, approximately equals to those of conductors. Due to the shielding effect, the magnetic field is practically zero outside of shield and therefore the electrodynamic forces do not occur between phases. In the model it was taken into account the variation of electrical conductivity with the temperature. The thermal model has been validated by experiment. The global coefficient of heat transfer by convection and radiation used in thermal model was estimated using the power losses computed by magnetic model. There is a good agreement between numerical and experimental temperature values. The presented model can be used for analysis, design and optimization of three-phase busbars system in single phase execution.

Numerical modeling of three-phase busbar systems: Calculation of the thermal field and electrodynamic forces

The paper presents numerical models obtained in QuickField software for analysis of the three-phase systems of rectangular busbar, of low or medium voltage, in steady-state and in short-circuit regime. Using a magnetic harmonic model coupled with a steady-state thermal model, the distribution of the thermal field for rated current is determined. By coupling the thermal steady-state model for the rated current and the magnetic model for short circuit current with a thermal model in transient regime, can be determined the time evolution of the temperature distribution in the short circuit regime (undeveloped in this paper). For determining the electrodynamic forces, a transient magnetic model is used. Different types of busbar systems are analyzed, with one or more conductors per phase in aligned arrangement.

Optimization of DC electromagnet using design of experiments and FEM

In this paper is proposed an optimized solution of DC electromagnet using design of experiments (DOE) and FEM. Before optimization, the technique of screening was applied to determine the most influent geometrical parameters on the static force characteristic. For this purpose, the response function was chosen to be the root square of the average of squares of the relative force for five values of the air gap, uniformly distributed on the range. From three parameters taken into account, the coil shape ratio and the support thickness ratio were found having the best influence as well as their interaction. The optimization problem is the maximization of static force characteristic maintaining the global dimensions of electromagnet (external radius, height of carcass, height of plunger with support) and the cross-section of the coil. To solve the optimization problem, the method by zooms without computation of models was used. The optimal solution brings a gain of 3.00% in static force for air-gap of 36 mm and an average gain of 1.12% in static force related to the whole range of the air-gap. These values were strongly limited by the equality constraints. The numerical experiments were performed using FEMM software and the magnetic force was computed using the Maxwell Stress Tensor approach.

Crimped connections heat transfer coefficient law determination using experimental and numerical results

In this paper the global heat transfer coefficient law corresponding to two types of superposed crimped connections has been obtained, using experimental and numerical determination. The samples use copper wire crimped by two methods: the first method uses one crimp indents and the second is a proposed method with two crimp indents. The ferrule is a parallel one. For obtaining the experimental results the samples are heated in A.C. current at different current values until steady state heating regime. Then, the 2D model of crimped connections has been created to obtain the numerical results. Using experimental and numerical results, a law for global heat transfer coefficient corresponding to the two types of crimped connections was proposed. The temperature dependence of global heat transfer coefficient has been taking into account.

FEM-based optimization of the airgap of smoothing inductors

In the paper, the 2-D finite element method implemented with FLUX software was employed to finding the optimal airgap of smoothing inductors with resistive load. The optimal design of nonlinear saturable inductors depends on the power converter characteristics and on the load. The optimal airgap is usually a standard value according to catalog data. The working conditions of the smoothing inductor may require an optimal airgap slightly different of the standard value. It can be determined through an optimization method around the standard value, to obtain the best performances. Similar previous researches were achieved with an optimization tool based on time domain numerical simulation using a model implemented with the powerful circuit simulator SPICE. The best smoothing effect of the inductor is equivalent to the minimum value of the ripple load current corresponding to the optimal airgap. The 2-D finite element method was used to determine the ripple load current depending on the airgap which was set as objective function of the optimization problem. The numerical simulation was performed in transient magnetic regime coupled with electric circuit, taking into account the nonlinearity of ferromagnetic core. To solve the optimization problem, the region elimination method was chosen that best fits to the unconstrained optimization problems with unimodal one-dimensional objective functions. The interval halving procedure has been employed to accelerate the optimization process and acceptable results were obtained.

Static force characteristic of e-type single phase AC electromagnets

In this paper, we propose an approach for the determination of static force characteristic of E-type single phase AC electromagnet using 2D numerical models developed in QuickField and FEMM software. The magnetic attraction force is estimated using Maxwell stress tensor method. The results obtained with numerical models were validated by an analytical method combined with experimental data. The numerical model is an AC magnetics problem coupled with the coil electric circuit. Necessary experimental data are electromagnet coil current values at different air gaps for a known voltage. Also, the ohmic resistance of the coil, the number of turns and wire diameter are known. The numerical results for attraction force obtained in QuickField agree well with those obtained by analytical method combined with experimental data. The correspondent numerical values obtained in FEMM do not match with them, although the air gap magnetic flux density values are practically identical to those obtained in QuickField. More specifically, the numerical values obtained in FEMM for attractive force are half of QuickField values. Considering the distribution of magnetic flux density on polar surfaces and using Maxwell formula in its integral form for calculating the force, it was proved that the numerical values of force are in very good conformity with those obtained in QuickField. The authors point out that in software FEMM the AC force is wrongly calculated based on Maxwell stress tensor method although in DC this calculation is correct.

Three parameters optimization of acting force of DC electromagnet

The paper proposes an optimized geometry for a DC electromagnet combining the experimental design (DOE) and FEM. The optimization problem takes into account three geometrical parameters (coil shape ratio, support thickness ratio and support height ratio) and consists in maximization of the acting force related to the largest air-gap, preserving the global dimensions of the device (external radius, height of carcass, height of plunger with support) and the cross-section of the coil. The method by zooms without computation of models was applied to increase with 3.17% the acting force related to the airgap of 41 mm. The determination of the electromagnetic force was made by the Maxwell Stress Tensor technique implemented in FEMM software.