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Accurate prediction of power loss distribution within an electrical device is highly desirable as it allows thermal behavior to be evaluated at the early design stage. Three-dimensional (3-D) and two-dimensional (2-D) finite element analysis (FEA) is applied to calculate dc and ac copper losses in the armature winding at high-frequency sinusoidal c...
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... this experiment, several winding arrangements are investigated and one of them was built and tested. The prototype is based on armature core, that was constructed using the ferrite core of material M470 50 A with a 13 mm air-gap slot opening. The cross section of the coil version I, and stator core is shown in Figure 1. Standard con- ductors were constructed of 7 turns wound on one stator tooth in series and consisted of six- strand parallel conductors. This particular example of winding version I (only one coil con- sidered) is producing a copper loss of 26 W (10 Hz) to 46 W (800 Hz) at 80 Arms, and at winding temperature assumed to 25°C. To evaluate the ac copper loss in the analysed machine a simplified approach is adopted utilizing the stator cores ( Fig. 2a-b). Several stator cores were connected together (Fig. 2c) to increase active-length of strands wound onto the tooth, and demonstrate high impact of pro- ximity and skin effects on copper loss. To simplify the winding of turns onto the tooth, the stator core was cut in half as shown in Figure 2c. To understand the behaviour of circulating eddy-currents in the solid conductors along the active-length and in the end-winding regions, the mutual coupling between phases which affect the proximity loss is not taken into account. Also, the influence of the rotor was assumed to be negligible. Figure 3a presents the investigated coil (winding version IV, see Fig. 5) wound onto the tooth. The analysed version of coil is representative of mush winding comprising of 6 parallel conductor strands with 7 turns in series, where the location of the conductors are precisely defined by banding them in a defined position in the slot. The distribution of the conductors is accurately represented due to the provided method for winding of the conductors 'hand in hand' with a string to keep the strands together (Fig. 3b). This allows the arrangements of con- ductors in the slots for tested winding to be accurately reproduced in the FE model. Figure 3c presents the one-tooth segment test rig including an ac and/or dc power supply, oscilloscope, measurement equipment, thermocouples, power analyzer, and the tooth as- sembly. A thermal insulation chamber emulating adiabatic boundary condition is not taken into account. The environmental temperature of the test rig is ...
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... discretisation mesh within the cross-section is the same for both 2-D and 3-D models and, for both used methods, calculations were assuming a constant winding reference tempe- rature, set arbitrarily to 25°C. Due to symmetry, the study domain of FE stator models can be limited to half (symmetry in XY plane). The ferrite core size determines the large opening slot hence the copper losses in strands placed near the slot opening region are suspected to produce huge amount of eddy-current due to flux leakage [4,10]. Winding losses can be reduced by properly arranged conductors and designed shape of teeth including the size of slot opening. Additionally, copper losses are dependent on electrical parameters such as operating fre- quency and drive wave-shape. The initial baseline arrangement of conductor in slot is listed as version I (see also Figs. 1 and 4). Outline of the cross-section stator core with different winding versions is shown in Figure 5 and numbered sequentially version II through VII. Each winding version presents a coil, which includes 7 turns and is wounded using round wire with 6 strands in a bundle (∅1.6 mm). Distance between conductors for all winding arrangement cases is fixed (0.25 mm). Winding versions II, III, IV, and V were moved to the back of slot. The other winding versions were moved forward to the tooth-tip (version VI and VII). Six parallel conductor strands of winding versions I, II and III were formed in a rectangular profile as can be seen in Figure 5. The winding versions IV-VII consist of some strands randomly formed in the slot window. Many references have reported the investigation of methods for copper loss reduction with round strands. Less attention has been paid to alternating loss reduction in winding with rectangular shape of conductors [14][15][16]. The value of the filling factor k c in the analysed stator segment with the round conductors as in Figure 5 is 40%. Since the k c depends on the winding wire and the slot geometry, it is difficult to state general values of the filling factor. Wound coil with round conductors (loose bundle) leads to lower filling factors than performed coils with rectangular shape. The filling factor k c is an important design criterion regarding the motor efficiency. Higher k c requires lesser current density for the same magnetomotive force and the smaller the dc copper losses are. Rectangular conductors are predominantly wound with their higher facing the stator pole. Moreover, rectangular conductors have a tendency to decrease ac loss [16]. To demonstrate the phenomena of loss reduction, two different arran- gements of winding are investigated in respect to the ac resistance and copper losses at high frequency operation. Figure 6 shows an outline of the winding configurations with rectangular conductors 1.5 mm×4 mm, where coil includes 7 turns and is wound with 2 parallel strands in a ...
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... discretisation mesh within the cross-section is the same for both 2-D and 3-D models and, for both used methods, calculations were assuming a constant winding reference tempe- rature, set arbitrarily to 25°C. Due to symmetry, the study domain of FE stator models can be limited to half (symmetry in XY plane). The ferrite core size determines the large opening slot hence the copper losses in strands placed near the slot opening region are suspected to produce huge amount of eddy-current due to flux leakage [4,10]. Winding losses can be reduced by properly arranged conductors and designed shape of teeth including the size of slot opening. Additionally, copper losses are dependent on electrical parameters such as operating fre- quency and drive wave-shape. The initial baseline arrangement of conductor in slot is listed as version I (see also Figs. 1 and 4). Outline of the cross-section stator core with different winding versions is shown in Figure 5 and numbered sequentially version II through VII. Each winding version presents a coil, which includes 7 turns and is wounded using round wire with 6 strands in a bundle (∅1.6 mm). Distance between conductors for all winding arrangement cases is fixed (0.25 mm). Winding versions II, III, IV, and V were moved to the back of slot. The other winding versions were moved forward to the tooth-tip (version VI and VII). Six parallel conductor strands of winding versions I, II and III were formed in a rectangular profile as can be seen in Figure 5. The winding versions IV-VII consist of some strands randomly formed in the slot window. Many references have reported the investigation of methods for copper loss reduction with round strands. Less attention has been paid to alternating loss reduction in winding with rectangular shape of conductors [14][15][16]. The value of the filling factor k c in the analysed stator segment with the round conductors as in Figure 5 is 40%. Since the k c depends on the winding wire and the slot geometry, it is difficult to state general values of the filling factor. Wound coil with round conductors (loose bundle) leads to lower filling factors than performed coils with rectangular shape. The filling factor k c is an important design criterion regarding the motor efficiency. Higher k c requires lesser current density for the same magnetomotive force and the smaller the dc copper losses are. Rectangular conductors are predominantly wound with their higher facing the stator pole. Moreover, rectangular conductors have a tendency to decrease ac loss [16]. To demonstrate the phenomena of loss reduction, two different arran- gements of winding are investigated in respect to the ac resistance and copper losses at high frequency operation. Figure 6 shows an outline of the winding configurations with rectangular conductors 1.5 mm×4 mm, where coil includes 7 turns and is wound with 2 parallel strands in a ...
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... discretisation mesh within the cross-section is the same for both 2-D and 3-D models and, for both used methods, calculations were assuming a constant winding reference tempe- rature, set arbitrarily to 25°C. Due to symmetry, the study domain of FE stator models can be limited to half (symmetry in XY plane). The ferrite core size determines the large opening slot hence the copper losses in strands placed near the slot opening region are suspected to produce huge amount of eddy-current due to flux leakage [4,10]. Winding losses can be reduced by properly arranged conductors and designed shape of teeth including the size of slot opening. Additionally, copper losses are dependent on electrical parameters such as operating fre- quency and drive wave-shape. The initial baseline arrangement of conductor in slot is listed as version I (see also Figs. 1 and 4). Outline of the cross-section stator core with different winding versions is shown in Figure 5 and numbered sequentially version II through VII. Each winding version presents a coil, which includes 7 turns and is wounded using round wire with 6 strands in a bundle (∅1.6 mm). Distance between conductors for all winding arrangement cases is fixed (0.25 mm). Winding versions II, III, IV, and V were moved to the back of slot. The other winding versions were moved forward to the tooth-tip (version VI and VII). Six parallel conductor strands of winding versions I, II and III were formed in a rectangular profile as can be seen in Figure 5. The winding versions IV-VII consist of some strands randomly formed in the slot window. Many references have reported the investigation of methods for copper loss reduction with round strands. Less attention has been paid to alternating loss reduction in winding with rectangular shape of conductors [14][15][16]. The value of the filling factor k c in the analysed stator segment with the round conductors as in Figure 5 is 40%. Since the k c depends on the winding wire and the slot geometry, it is difficult to state general values of the filling factor. Wound coil with round conductors (loose bundle) leads to lower filling factors than performed coils with rectangular shape. The filling factor k c is an important design criterion regarding the motor efficiency. Higher k c requires lesser current density for the same magnetomotive force and the smaller the dc copper losses are. Rectangular conductors are predominantly wound with their higher facing the stator pole. Moreover, rectangular conductors have a tendency to decrease ac loss [16]. To demonstrate the phenomena of loss reduction, two different arran- gements of winding are investigated in respect to the ac resistance and copper losses at high frequency operation. Figure 6 shows an outline of the winding configurations with rectangular conductors 1.5 mm×4 mm, where coil includes 7 turns and is wound with 2 parallel strands in a ...
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Citations
... systems [4], [5], [6]. Skin effect is an alternating current that tends to flow through the surface of transmission lines conductors that leads to ac losses [7], [8], and a phenomenon known as the proximity effect occurs when conductors carrying alternating current are close to one another. A circulating current will begin to flow in the conductor as a result of this alternating flux, leading to a non-uniform distribution of current along the transmission line, which raises the conductor's apparent resistance and results in a voltage drop and power loss [9], [10]. ...
Electric power transmission networks should be operated in efficient, safe, and reliable conditions. To improve the stability and transfer capability of power transmission, it is necessary to mitigate the Ferranti effect. This paper investigates the impact of increasing the length of the transmission line on its receiving end voltage under no-load conditions. A variable shunt reactor compensation for transmission lines is used to control the voltage level at different lengths of the transmission line. The proposed method demonstrates that the value of the shunt reactor required to maintain the receiving end voltage can be estimated. Moreover, the system is modeled using the PowerWorld simulator, and the effectiveness of the proposed model has been verified by experimental results. The experimental results demonstrate the efficiency of the proposed methodology and match the simulation results, which are then validated by simulating the WSCC 9-bus and IEEE 30-bus test systems.
... For the calculation of the copper stator loss, we should consider not only the losses caused by strange harmonic currents, but also the losses caused by circulating currents in stator windings [19]. And the difficulty in calculating the copper loss of the rotor is due to the influence of the skin effect of the AC current on the copper loss [20]. For the calculation of iron loss, the detailed geometric structure, distribution model of winding connection and nonlinear factors of electric steel can be well considered by field calculation method. ...
Compared with the fundamental loss, the harmonic losses become very complicated because of the coupling between the power supply harmonics and the motor harmonics. For dispose of this problem, a multi-slice 2-D finite element model considering the interbar currents and a fast rotor harmonics identification method is employed to identify the harmonics of the rotor current density and flux density of the inverter-fed induction motor (IM). Considering the complex coupling phenomenon of time-space harmonics, a two-term iron model with piecewise-defined variable coefficients (PVCIL model) and a finite element analysis (FEA)-based copper loss method are then used to calculate the iron and copper loss components of the inverter-fed IM. Finally, based the introduced methods, both the electromagnetic field and different losses terms of the same 5.5 kW IM inverter-fed under different load and supply conditions are calculated and analyzed. The experimental validation of those two losses calculation methods is performed on a 5.5 kW IM with different operating conditions. The results obtained in this paper can provide theoretical basis for targeted harmonic elimination and loss reduction in the design phase of the inverter-fed IM.
... In the following, the influence of various parameters on the AC losses is analyzed. Additional effects, such as PWM voltage applied by an inverter [26] or the distinct temperature dependent behavior of DC and AC losses [8], [14], [19], [25], [28] are neglected hereby. ...
Analysis of AC effects, such as skin and proximity effect as well as the circulating currents and corresponding losses are usually done by finite element analysis (FEA), while mostly only a single slot is considered, neglecting the influence of neighboring phases on the flux density of the stator iron and thus the resulting slot leakage flux. As the simulation of single stranded FE models is computationally very demanding and time consuming, this work compares different levels of detail of 2D FE models and investi-gates the impact of the modelling depth on the resulting copper loss to find a computation time optimized modeling setup. Moreover, the potential increase of AC-losses is assessed for two machines that are identical except for the stator winding, so that one and the same machine is investigated at two different voltage levels, namely 400 V and 800 V. The reference machine is a 160 kW nominal power and 9000 rpm maximum speed perma-nent magnet synchronous machine. Since the magnetic circuit has to remain constant, both designs share the same overall winding scheme and total number of strands within a slot but differ in the number of parallel and serial connected strands.
... Strictly speaking, the change of the stator resistance associated with both a skin effect and the proximity effect in the activelength and end-winding regions of the stator conductors. In addition, losses generated by eddy currents in the stator pack [2] also influence on the value r1. However, the induction motor models used in control systems usually associate iron losses with the magnetizing current, and often do not consider it, in view of their smallness. ...
... However, with any change of power frequency the resistance r1 value changes owing to the current displacement in the stator slots similar to the current displacement in the rotor slots [1], [3], which well-studied and accounted in designing [4], modeling [5] and control [6], [7] of an induction motors. This phenomenon is noticeable not only for high frequencies of power supply [2], but also for frequencies around 50 Hz also. The study of this phenomenon in stator windings is of considerable practical interest, but significant difficulties associated with higher harmonics, produced by a pulsed power supply, eliminates the possibility of accurate quantification. ...
... We can see that stator deep slot effect manifested quite clearly and causes an approximately twofold change of the r1 when sinusoidal supply voltage is applied. Behavior and value range of the F. Emde curve is in good agreement with the data obtained in [2] for a similar frequency change ratio when threedimensional finite element analysis was applied to copper losses in the stator. ...
... The end-winding region is exposed to the flux patterns that are different from those within the winding active length. Most of the research has been focused on the proximity effects on the conductors placed into the slots [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Less attention has been paid to an influence of end-winding dimensions and size on the phenomena that contribute to the total eddy-current losses. ...
... The DC winding power loss component and its thermal dependence is well understood and commonly used when estimating the machine performance. The AC winding power loss caused by magnetic fields generated by nearby conductors is more troublesome due to the complexity of the problem with various effects to be accounted for [1][2][3]. Those AC power loss components are present in any PM machine and their severity strongly depends on a particular machine design. ...
... In the FE models the same value of copper resistivity at the maximum measured winding temperature was used in the whole coil including the end-winding, whereas the temperature is quite different for both sides of the copper active-length and the end-winding (see Fig. 4), and this also affects the accurate copper loss prediction. According to winding versions I and II, it is clear that defining positions of each conductor in FEM has a significant impact on the AC winding power loss predictions when considering multi-stranded winding design, in particular when a low number of turns per slot is considered [2,16,17]. Here, it is noticed that the multi-strand mush wound winding construction might not be possible to be evaluated in an accurate manner when using the FEA due to a random position of the strands and undefined shape of the bundles. It was observed that randomly placed conductors generate less loss than the model with well known positions of conductors, caused by the temperature and winding fill factor difference which leads to change the heat transfer. ...
This paper presents a finite element investigation into the proximity losses in a high-speed permanent magnet (PM) machine for traction applications. A three-dimensional (3D) finite element analysis (FEA) is employed to evaluate and identify the endwinding contribution into the overall winding power loss generated. The study is focused on the end-winding effects that have not been widely reported in the literature. The calculated results confirm that the end-winding copper loss can significantly affect the eddycurrent loss within copper and it should be taken into account to provide reasonable prediction of total losses. Several structures of the end-winding are analyzed and compared in respect to the loss and AC resistance. The results clearly demonstrate that the size of the end-winding has a significant impact on the power loss. The calculated results are validated experimentally on the high-speed permanent magnet synchronous machine (PMSM) prototype for selected various winding arrangements.
... This is a real problem for high-frequency applications like HF transformers for SMPS (Fig. 4). The problem occurs also in small electronic transformers [5], medium-frequency transformers [6], rotating machines [7], as well as three-phase busbars whose thickness is usually limited to 10 mm for this reason [3]. ...
Skin depth and proximity effects in transformer windings are important phenomena influencing the design even at power frequencies (50-60 Hz). However, they become critically important at elevated frequencies, especially for high-frequency transformers, operating in switched-mode power supplies for example, at any power level. This article presents a numerical study of optimum winding configurations which can drastically reduce the proximity effects. It is possible to make transformers operating even at 1 MHz without the use of very expensive Litz wire.
... In contrast, the ac winding power loss component is more troublesome due to complexity of the problem with various effects to be accounted for. Two different phenomena lead to additional ac losses: skin and proximity effects [1][2][3]. ...
... The end-winding region is exposed to the flux patterns that are different from those within the winding active length. The numbers of authors have investigated the causes of the ac copper loss widely [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. And most of the research is focused on the proximity effects on the conductors placed into the slots. ...
... where kh, keddy, and kexcess are the coefficients of losses by hysteresis, of classical eddy current losses, and of losses in excess, respectively. And the material coefficients used for the iron loss predictions in the presented stator segments are listed in the author's earlier paper [2]. ...
This paper deals with AC winding loss including proximity loss investigation in a high-speed permanent magnet (PM) machine for traction applications. The research is focused on the end-winding effects that have not been widely reported in the literature. The calculated results confirm that the end-winding copper loss can significantly affect the eddy-current loss within copper and it must be taken into account to provide reasonable prediction of total losses. A three-dimensional (3D) finite element analysis (FEA) is employed to evaluate and identify the end-winding contribution into the overall winding power loss generated. To explain how much the power loss may change due to dimensions and size of end-winding, the parameterized 3D FE models are investigated. In this study, the results clearly demonstrate that the size of end-winding has influence on the winding resistance and, consequently, the power loss in the AC operation. The theoretical prediction of the losses within the armature of the high-speed permanent magnet synchronous machine (PMSM) is validated experimentally on a segmented stator.
Vehicle electrification places significant pressures on electric machine design due to the need for increased power densities and mass production. These two requirements couple when designing multistrand stator windings, which exhibit significant AC loss variability as a result of the random nature of the conductor lay within the stator slot caused by automated insert winding. This paper presents two prediction methods for AC loss variability to be deployed at the winding design stage. The first consists of an analytical approach, whilst the second constructs a 2D finite element analysis geometry that captures conductor lay characteristics. Comparison of predictions from both approaches to experimental AC loss measurements established that the proposed models capture the experimentally observed AC loss variability characteristics and that the analytical method is suitable for early design stages whilst the finite element approach should be adopted once the winding configuration is finalised.
