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The large size of models and long computing time prevent the creation of full‐scale, three‐dimensional models of end region of turbogenerators. Only exact three‐dimensional model can illustrate complex phenomena of end region losses. Also some methods of decreasing such losses cannot be simulated in two‐dimensional models. The purpose of this paper is to focus on a method of creating three‐dimensional models of turbogenerators' end regions for calculations of eddy current losses.

Time‐stepping is the most expensive part of computation. A harmonic model would be free from that disadvantage and it can provide a tool to make an accurate, fully three‐dimensional model of a steady state for different loads and provide results in a reasonable time.

The research focuses on the method of creating three‐dimensional models of turbogenerators end region for calculations of eddy current losses. By using two‐dimensional, time‐stepping models and empirical loss functions for a main flux and three‐dimensional models for eddy current losses from a perpendicular flux of an end connections, it is found that fast analysis of that complex part of a machine can be achieved.

The approach proposed in the paper is a universal and novel method of calculation losses of turbogenerators' end regions. Combining two‐dimensional and three‐dimensional models provides advantages of both known methods: fast computation time from simplified models and good representation of complex geometry of a machine.

The axial magnetic field occurs in the end-region of large turbo-generators is known to induce hot points or voltages between laminations, that may cause insulation breakdown and thus stator faults.

It is important to dispose of simple methods for estimating the axial flux rapidly with regard to the operating point of the machine.

The authors provide a practical model of the axial magnetic field based on a simplified vector diagram. The parameters required to build the vector composition of the flux densities are assessed with a limited number of finite element method simulations of the whole end-region of the machine. These simulations were validated by an experimental test on a real turbo-generator. Then the axial flux density was simply estimated for various operating points.

The originality of the paper concerns the practical model of the axial magnetic field based on a simplified vector diagram.

Calculating the stator end-winding leakage inductance, taking into account the rotor, is difficult due to the irregular shape of the end-winding. The end-winding leakage may distribute at the end of the active part and the fringing flux of the air gap. The fringing flux belongs to the main flux but goes into the end-winding region. Then, not all the magnetic flux occurring in the end region is the end-winding leakage flux. The purpose of this paper was to find a method to accurately separate the leakage from the total flux, taking into account the rotor.

In this paper, two methods based on energy calculation are presented. Both methods require the assumption that the machine is symmetrical. The first method depends on the total leakage inductance and the machine’s active region length. The second method is based on the energy stored in the end region of the machine. In this case, removing the energy produced by the fringing flux of the air gap is necessary. The model should have a volume-closing fringing flux to remove the part of energy belonging to the end of the air gap.

The method presented in the paper does not require rotor removal. The values of the end-winding leakage inductance computed based on the proposed method were compared with values computed using the method with the removed rotor. The computations show that the proposed method is closest to the results from the method presented in the literature. Results obtained in the first method present that rotor influence on the value of end-winding leakage inductance exists. The model of the stator end-winding described in the paper is general. Therefore, the proposed methods are suitable for calculating the end-winding leakage inductance of other electric machines.

The method presented in the paper considers the rotor in end-winding leakage inductance calculation. It is not necessary to remove the rotor as in the similar method presented in the literature. The authors elaborated a parametric model with a volume-closing fringing flux to remove the part of energy belonging to the end of the air gap. The authors also elaborated their 3D model of the machine winding for calculations in Opera 3D.

A spherical motor is a novel electromechanical device that has obtained worldwide attention for its attractive advantages. A general analysis of electromagnetic torque in double excited spherical motor has been completed on the calculation of its 3D electromagnetic field distributions. The analysis accounts for the effect of open‐end region in the stator. Double scalar magnetic potentials method has been used in the FEM numerical analysis. On the computation results, the other electromagnetic parameters can be calculated, which will be very significant in the design and performance prediction of the spherical motor. The calculation results indicate that the device is capable of continuous speed control and efficient torque production.

An accurate calculation of eddy current losses in the stator clamping parts of large hydro generators is a matter of particular interest with the initial design and the design optimization because they can reach high values and produce local thermal hot‐spots due to the non‐linear magnetic behaviour of the clamping plate.

With a fully 3D approach of the generator pole pitch, both time‐harmonic and non‐linear transient finite element analyses are carried out for the eddy currents using a magnetic vector potential formulation.

With the introduction of a novel modelling strategy for the non‐linear clamping plate, the total eddy current losses evaluated from both analysis methods show a good agreement. Nevertheless, the time‐harmonic solution in comparison with the non‐linear transient solution yields different local eddy current distributions in particular with the clamping plate.

The presented analyses use only the fundamental harmonic in the end region field. Further research will need to be carried out for the influence of the higher harmonics in the end region field and again the comparison of both analysis methods.

With the intention of including the numerical analyses with design review and design optimization of the generators, the results obtained from both analysis methods are compared regarding the total eddy current losses as well as their local distributions.

With a fully 3D approach of the generator pole pitch, second order pentahedral and hexahedral edge elements are introduced with both time‐harmonic and non‐linear transient eddy current finite element analyses.

The thermal management of electrical insulations poses a challenge in electrical devices as electrical insulators are also thermal insulators. Diamond is the best solid electrical insulator and thermal conductor. This can lead to a paradigm change for electrical machine winding and lamination insulation design and thermal management. The paper introduces these techniques and discusses its effect for the design of electrical machines and its potential consequences for electromagnetic analysis, for example, in multi-physics modelling. The diamond winding insulation is patent-pending, but the diamond enriched lamination insulation is published for the benefit of the scientific community.

The windings of electrical machines are insulated to avoid contact between the coil and other conductive components, for example, the stator core. The principle of using mica tape and resin impregnation has not changed for a century and is well established to produce main insulation on a complex conductor shape and size. These insulations have poor heat-conducting properties. Similarly, the insulation of laminated steel sheets comprising the stator and rotor restrict heat flow. Diamond-based insulation provides a new path. Increased thermal conductivity means reduced temperature rise and the reduced thermal time constants in multi-physics simulations and system analysis.

The largest benefit of a diamond-based core insulation is in electrical machines in which the losses are conducted axially to the coolant. These are machines with radial ducts and effective cooling in the end regions. The main benefit will be in reducing the number of radial ducts that positively affect the size, production costs and the copper losses of the machine. The increased thermal conductivity of the diamond insulation system will reduce the thermal constants noticeably. These will affect system behavior and the corresponding simulation methods.

Diamond insulation can lead to a paradigm change for electrical machine winding and lamination insulation design and thermal management. It might also lead to new modeling requirements in system analysis.

In the paper the boundary‐integral model of the stationary magnetic field in a 3‐D linear region is presented. The region is bounded from inside or from outside by metallic materials of different permeability. Current sources of the field are represented by the filaments coinciding with axes of the conductors, and the magnetic field is described in terms of a scalar magnetic potential. Surface densities of the magnetic charge in monopole and dipole form are used as the variables in the boundary‐integral equations. The calculation of magnetic field distribution in the end region of an electrical machine may be effectively performed with the use of the proposed approach. Some results of computation of boundary quantities are presented.

The paper aims to illustrate a numerical technique to calculate fields and inductances of rotating electrical machines.

The technique is based on an integral formulation of the nonlinear magnetostatic model in terms of the unknown magnetization. The solution is obtained by means of a Picard-Banach iteration whose convergence can be theoretically proved.

The proposed method has been used to build a model of a large turbine generator. In particular, the influence of end effects on flux linkages has been computed. It has been demonstrated that the 2D solution underestimates the flux linkages as well as the no load voltage of 2 per cent, while the leakage fluxes are computed by the 2D solution with errors as high as 20 per cent.

The method is advantageous in comparison to standard methods.

The purpose of this paper is to investigate and compare the influence of end-effect on the torque-speed characteristics of three conventional switched flux permanent magnet (SFPM) machines having different stator/rotor pole combinations, i.e. 12/10, 12/13 and 12/14 as well as three novel topologies with less permanent magnets (PMs), i.e. multi-tooth, E-core and C-core.

SFPM machines combine the advantages of simple and robust rotor and easy management of the temperature due to the location of the PMs and armature windings on the stator. However, due to spoke location of the PMs a large flux leakage in the end region, i.e. end-effect, can be observed which could result in a large reduction in the electromagnetic performance. Therefore, the influence of end-effect on the torque-speed characteristics is investigated. 3D-finite element analyses (FEA) results are compared with their 2D-FEA counterparts in order to account for the end-effect influence.

It has been concluded that due to end flux leakage, lower torque capability in the constant torque region is observed in the six machines. However, improved flux-weakening capability in the conventional machines can be exhibited at high current levels, whereas due to the large inductance lower power capability in the multi-tooth, E-core and C-core machines is obtained.

The influence of temperature rise on the performance is not included.

This paper has analysed the influence of end-effect on the torque-speed characteristics of several SFPM machines.

The end‐turn leakage inductances of the armature winding of the permanent magnet motor have been calculated. In order to describe the magnetic field distribution the edge element method using vector magnetic potential has been applied. First, the formulae that describe the total self‐inductance and total mutual conductance for phase windings are presented. Three‐dimensional and two‐dimensional formulations are considered. The end‐turn leakage inductances have been obtained by comparing the results of these formulations. The symmetrical components transformation has been applied, and the self inductances and mutual inductances have been transformed into the zero‐sequence and positive‐sequence inductances. The calculations have been performed for different dimensions of the coil‐end region. The influence of the position of the boundary surfaces on the results has been investigated.