Modelling Approaches for Triple Three-Phase Permanent Magnet Machines

Standard modelling approaches for a triple three-phase (i.e. nine-phase) machine include vector space decomposition (VSD) and triple d-q modelling procedure. Each is characterised with certain benefits and shortcomings. This paper introduces a novel transformation, applicable to multiple three-phase winding machines in general, especially aimed at facilitating the power (current) sharing between the three-phase systems. The easiness of the current sharing with the novel transformation, introduced here, is demonstrated via simulations in MATLAB

A Novel Synthetic Loading Method for Multiple Three-phase Winding Electric Machines

The paper develops a version of the synthetic loading method, suitable for testing of multiphase machines with multiple three-phase distributed windings. The method is at first discussed in general terms for a structure with k three-phase stator windings (i.e. total number of phases is n = 3k). Subsequent detailed development is described for a dual three-phase (six-phase) stator winding configuration. With a control architecture that allows the use of half of the three-phase windings as a motor and the other half as a generator, the machine (and/or the converter) can be tested under full rated power without the need for any mechanical load. Moreover, the power consumed from the grid is in essence equal only to the total losses of the system. Modelling, based on the double d-q approach, and the control layout that includes full cross-coupling decoupling are described for a permanent magnet (PM) synchronous machine. An experimental test rig with a double three-phase PM machine of 150 kW rating is detailed and the samples of experimental results are provided to verity the theoretical considerations

Modelling Approaches for an Asymmetrical Six-Phase Machine

With currently available power electronic devices, the power range of a single three-phase power converter is limited well below the power ratings foreseen for remote offshore wind turbines. A solution is to use multiphase systems. By connecting each of the converters to one three-phase winding in the stator of the machine, a multiphase conversion system is obtained allowing to exploit its fault tolerance. In multiphase machines, the basic idea of the model transformations is the same as in the three-phase case, but, due to the increase in the dimension of the system, it introduces additional degrees of freedom. This work at first compares the two widely used modelling approaches regarding physical interpretation of the subspaces, harmonic mapping and representation of asymmetries applied to an asymmetrical six-phase machine. It further introduces an alternative transformation that is aimed at situations where power sharing between three-phase windings is desired and characterises its behaviour using the same figures of merit as for the existing transformations

Modelling Approaches for Triple Three-Phase Permanent Magnet Machines

Standard modelling approaches for a triple three-phase (i.e. nine-phase) machine include vector space decomposition (VSD) and triple d-q modelling procedure. Each is characterised with certain benefits and shortcomings. This paper introduces a novel transformation, applicable to multiple three-phase winding machines in general, especially aimed at facilitating the power (current) sharing between the three-phase systems. The easiness of the current sharing with the novel transformation, introduced here, is demonstrated via simulations in MATLAB

PERMANENT MAGNET MULTIPHASE MACHINE MODELING AND CONTROL FOR MV WIND ENERGY APPLICATIONS

Due to the rapid development of the power electronics in the second half of the twentieth century, a significant research effort has been put into the modelling of electrical machines to provide mathematical models for control purposes. As the power electronics isolate the machine from the grid, the number of phases on both sides no longer needs to be the same, thus allowing for use of multiphase machines. Several studies have shown that multiphase machines can yield lower torque ripple, provide higher torque per phase current, and that they can continue to operate with one or more faulty phases, thus increasing the robustness of the power stage. This, amongst other benefits, has led to increased interest in multiphase machine employment for critical applications, such as more-electric aircraft, electrical propulsion systems for ships and offshore wind, etc. Amongst the different multiphase machine constructions, the multiple three-phase winding structure with isolated neutral points is of special interest. It can be operated using multiple three-phase converters, so that almost no modification of hardware is needed. Furthermore, with high power machines (above the 5 MW class), several converters in parallel should be used when increased availability is desired. This is where multiple three-phase winding machines show an additional benefit, galvanic isolation between the windings. By connecting one three-phase converter to each of the three-phase windings of the machine, the increased availability of paralleling converters is obtained while the problem of the circulating current between paralleled converters is practically eliminated thanks to said galvanic isolation. The control schemes of three-phase machines should not be directly applied to multiple three-phase winding machines, since these show internal cross couplings between the different three-phase windings that may affect dynamic performance. To examine the behaviour and design control schemes for multiple three-phase winding machines, modelling approaches based on vector space decomposition, multiple dq modelling approach and a novel approach, specifically developed in this thesis for the independent power flow control in individual three-phase windings, are studied. It is demonstrated that, by including appropriate decoupling terms in the traditional three-phase control structure, a completely decoupled operation can be obtained in all the three-phase windings in the machine when control scheme is based on the multiple dq modelling approach. With this control approach, the control of these machines is accomplished using control structures and model transformations familiar to those skilled in the art of the three-phase machines. For six-phase machines the existing transformations are sufficient for all control purposes, while the novel transformation becomes a useful tool when there are three or more three-phase windings. The influence of a low switching to fundamental frequency ratio on behaviour of the controlled object is also covered in this work. This has a great impact on the modelling of current control loops, especially when using the synchronously rotating reference frame in variable fundamental frequency applications, such as motor drives. The precise modelling of the actual control loops is of vital importance since it allows development of faithful control tuning techniques. With these, the regulator parameters, which ensure certain specified dynamic performance of the loops, are obtained and their behaviour can be precisely described and predicted by simulations. The machine’s parameter identification has also been approached in this work; accurate parameter knowledge is of essential importance to ensure the correct match between experimental and simulation results. All the experimental work has been done using a 150 kW permanent magnet synchronous generator in six-phase configuration with two three-phase winding placed spatially in phase. Unequal power sharing between different three-phase windings is studied further, including the simultaneous operation of one winding in motoring and the other in generation for a six-phase machine. This particular mode of operation has been found as very useful in development of a novel testing method for the machines with multiple three-phase windings, of synthetic loading type, which is fully verified by experimentation. A corresponding theoretical/simulation work has been performed for a nine-phase (triple three-phase) machine

Modelling of a Stilling Basins with Sloping Apron in IBER to Improve Efficiency in High-slope Rivers

This research shows the influence of stilling basin slopes on energy loss in rivers with a high gradient. This study takes as a case San Pedro water intake (Ayacucho, Peru). The main objective is to improve efficiency of stilling basins in rivers with high slope. Five dissipation pools of different slopes were modelled: 0%, 1.52%, 3.04%, 4.56% and 6.08% to propose the optimum pool among these, for the San Pedro intake. Results were validated by means of a Sensitivity Analysis, trough comparison with the results of previous investigation and results of modelling San Pedro river with HEC-RAS and IBER. It was obtained that the steeper the slope of the stilling basin, the higher the specific energy loss, the higher the output rate, the longer the stilling basin. It can be concluded that the 3.04% slope stilling basin is the most appropriate for the 6.08% slope river since the slope variation is not abrupt as in the case of the horizontal one, that is, 30% more energy loss with respect to the horizontal pool and velocity and Froude results similar to the modelling of the San Pedro river

LCL Grid Filter Design of a Multimegawatt Medium-Voltage Converter for Offshore Wind Turbine Using SHEPWM Modulation

The switching frequency of medium-voltage highpower converters is limited to about 1 kHz due to semiconductor junction temperature constraint. The frequency band between the fundamental and carrier frequency is limited to a little more than one decade and the LCL filter design is usually a challenge to meet grid codes for grid-connected applications. Traditional designs focus on the optimization of the filter parameters and different damping circuits. However, this design is very influenced by the modulation technique and produced low-order harmonics. Widely used pulse width modulations (PWM), such as phase disposition PWM (PDPWM), produce low-order harmonics that constraint the design of the filter. Selective harmonic elimination PWM (SHEPWM) can eliminate theses low-order harmonics, enabling a more efficient design of the LCL filter. In this paper, the LCL grid filter of a multimegawatt medium-voltage neutral-point-clamped converter for a wind turbine is redesigned using the SHEPWM modulation. Experimental results demonstrate that the efficiency of the converter, filter, and overall efficiency are increased compared to that obtained with PDPWM

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