Xuezhou Wang

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.

Brushless Doubly Fed Induction Machines: Magnetic Field Analysis

The brushless doubly fed induction machine (DFIM) shows great potential as a generator in large-scale wind turbines. The motion of the magnetic field in this machine is not a simple rotation, which makes it not so straight forward to understand its operating principles. This paper develops an analytical magnetic field model for the brushless DFIM that includes the effects of rotor time harmonics and space harmonics due to the winding distribution and slotting. Using a case study machine, the developed analytical model is then validated by comparison with finite-element (FE) calculations. In addition, a 2-D spectral analysis is applied to the FE derived radial air-gap magnetic field as a function of time. This analysis verifies the space-time relations of the rotating magnetic field components in the airgap of the brushless DFIM. Finally, the developed analytical magnetic field model is used to analyze the brushless DFIM operating principles. The interaction of the stator magnetic field with the rotor nested loops is explained, as well as the development of electromagnetic torque.

Finite element based multi-objective optimization of a brushless Doubly-Fed Induction Machine

Although the brushless Doubly-Fed Induction Machine (DFIM) has great potential as generator system in large-scale wind turbines, its complexity has so far retained a commercial breakthrough. This paper contributes by combining brushless DFIM Finite Element (FE) modelling with multi-objective optimization. A static brushless DFIM FE model is applied with the NSGA-II multi-objective optimization algorithm. The result is an accurate and fast brushless DFIM design optimization tool. This tool is then used to generate a machine design with optimized performance, that fits a fixed volume frame size D180. Optimization results of different brushless DFIM construction variations are compared. The best designs of each construction variation are then analysed in more detail using a time-stepping brushless DFIM FE model. This provides good insight in the effects of different construction variations on torque ripple and induced time-harmonics. The optimized design of the best construction variation will be selected to be manufactured as prototype machine.

Brushless doubly-fed induction machines: Torque ripple

The brushless Doubly-Fed Induction Machine (DFIM) without its brush-gear and slip-rings seems interesting as successor of the normal DFIG in wind turbine drivetrains. However, the brushless DFIM magnetic field has a rich space-harmonic spectrum, which causes additional torque ripple. This paper focuses on torque ripple in the brushless DFIM. The causes and origin of torque ripple are discussed and an analytical model is developed that derives the torque ripple from the air-gap magnetic field distribution. Further, a finite element method for torque ripple calculation is presented. Both methods are used to calculate the torque response of a case study machine. Results are compared and the accuracy of the analytical model is validated with good result. The analytical model is then used to further analyse the torque ripple, resulting in exact torque ripple frequencies and additional insight in the cause of the torque ripple.

Effects of rotor skew on the performance of brushless doubly-fed induction machine

Brushless doubly-fed induction machines (BDFIM) have great potential as variable-speed generators in larger-scale wind turbines. Undesired space harmonics exist because the special rotor needs to couple both two stator windings which with different pole-pair numbers and different frequencies. These rich space harmonics lead to a bigger torque ripple comparing to the normal induction machine. This paper makes use of 2D multi-slice finite element (FE) method to study the effect of the rotor skew on the performance of the BDFIM in the cases without and with saturation. The results show the torque ripple is reduced significantly by skewing the rotor both in those two situations. But the rotor skew has negligible influence on the harmonics due to the saturation effect. Furthermore, the rotor skew has little influence on the total amount of losses. However, based on the simulation results, it redistributes the core losses along the axial direction in the BDFIM.

Evaluating Harmonic Distortions in Brushless Doubly Fed Induction Machines

The brushless doubly fed induction machine (DFIM) is a special machine type that is of interest as a generator in wind turbine drive trains. The brushless DFIM has a significant space-harmonic content compared with conventional machine types, due to its construction. This results in additional harmonic distortions, such as torque-ripple and time harmonics. This paper studies the causes and origins of harmonic distortions in the brushless DFIM. Using time- and space-harmonic analysis, an analytical evaluation method is derived to predict the torque ripple frequencies and time-harmonic frequencies in stator and rotor voltages and currents. The evaluation method is applied to a prototype brushless DFIM to demonstrate the severity of harmonic related distortions that can be present in the brushless DFIMs. The evaluation is validated by additional finite-element analysis and measurements. Furthermore, measures are proposed to reduce harmonic distortions. The insight into harmonic distortions in the brushless DFIM and the ability to predict and prevent them must lead to the improved brushless DFIM designs in the future.

Evaluating the cost of energy of a 10 MW direct-drive wind turbine with superconducting generators

Superconducting generators are being proposed and investigated for large offshore wind turbines because of their compactness and light weight. Cost of energy is the key performance indicator to evaluate the feasibility of commercially applying superconducting generators to wind energy. This paper models, estimates and evaluates the cost of energy of a 10 MW direct-drive wind turbine for three superconducting generator designs with MgB2 field windings. These superconducting generator designs are compared regarding the cost of energy as well as other important performance indicators. The results show the fully iron-cored design has the lowest cost of energy and superior overall performance.

A finite element post-processing for skew effects in brushless doubly-fed induction machines

Brushless doubly-fed induction machines have great potential as variable-speed generators in wind turbines. Undesired space harmonics exist because the special rotor needs to couple both stator windings which with different pole-pair numbers and different frequencies. These undesired space harmonics lead to a bigger torque ripple compared with conventional induction machines. Previously, a 2D multi-slice finite element (FE) method was applied to study the effects of rotor skew on torque responses in brushless DFIMs. It results in a significant computing time because several 2D FE slices are coupled and calculated simultaneously in one model. It is not efficient to use such a model to predict how much average torques and torque ripples would be reduced by applying skewed slots at the beginning of design. This paper makes use of normal 2D FEM results and applies skew factors in post-processing to investigate the influence of rotor skew on the torque responses. The proposed method can give an approximate prediction of skew effects on torque responses with limited computing time.

FE based multi-objective optimization of a 3.2MW brushless doubly-fed induction machine

The brushless doubly-fed induction machine (DFIM) has great potential for wind turbine applications. However, it has not yet been commercialized due to its complicated operating principle. Previously, a computationally efficient FE model has been developed. Some design guidelines for the stator pole-pair combinations and the nested-loop rotors have been gained from the previous work. This paper brings the model and design guidelines together to optimize the design of a 3.2MW brushless DFIM. Both the active material cost and the efficiency are optimized. The results show that the magnetic loading of the brushless DFIM is increased for a better design by using the FE based optimization tool. The optimized designs increase the efficiency and the shear stress while reducing the torque ripple and the THD level of the stator voltages. However, the optimized designs result in a high electric loading which would be a challenge for cooling.