https://doi.org/10.6113/JPE.2018.18.5.1577
ISSN(Print): 1598-2092 / ISSN(Online): 2093-4718
Influence Analysis of Power Grid Harmonics on Synchronous Hydro Generators
Hongbo Qiu*, Xiaobin Fan†, Jianqin Feng*, and Cunxiang Yang*
†,*College of Electric and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou, China
Abstract
The content of harmonic current increases with an increase in the number of power electronic devices in power grid. When a generator is directly connected to the power grid through a step-up transformer, the influence of the harmonic currents on the generator is inevitable. To study the influences of harmonics on generators, a 24-MW bulb tubular turbine generator is taken as an example in this paper. A 2-D transient electromagnetic field model is established. Through a comparative analysis of the data of experiments and simulations, the correctness of the model is verified. The values of the air gap magnetic density, torque and losses of the generator under various conditions are calculated using the finite element method. Taking the rated condition as a reference, the influence of the harmonic currents on the magnetic flux density is analyzed. It is confirmed that the time harmonic is a key factor affecting the generator performance. At the same time, the effects of harmonic currents on the torque ripple, average torque and eddy current loss of the generator are studied, and the mechanism of the variation of the eddy current loss is also discussed.
Key words: Average torque, Bulb tubular turbine generator, Eddy current loss, Harmonic current, Time harmonic, Torque ripple
Manuscript received Jul. 11, 2017; accepted Mar. 20, 2018
Recommended for publication by Associate Editor Seon-Hwan Hwang.
†Corresponding Author: fanxiaobin66@163.com Tel: +86-187-0360-7684, Zhengzhou University of Light Industry *College of Electr. & Inform. Eng., Zhengzhou Univ. of Light Ind., China
Ⅰ. INTRODUCTION
In recent years, with the establishment of high voltage direct current transmission systems, wind power plants and distributed photovoltaic power plants, the number of nonlinear devices in power grids has increased dramatically [1]-[4]. Meanwhile, the content of the harmonic currents in power grids is also increasing. The harmonic currents cause serious damage to the electrical devices.
Due to the increasingly serious environment problems arising in recent years, people have begun to focus on the exploitation and utilization of reproducible energy sources. Among the recyclable and environment resources, water has been widely developed all over the world. Bulb tubular turbine generators have the characteristics of a low applicable head, high flow, high efficiency and low operating cost. These characteristics have helped it become the main type of generator in developing low head water resources [5]. However, there are a number of problems occurring during the operation of bulb tubular turbine generators. The prominent problems in bulb generators are their torque ripple and losses, which directly affect the efficiency and lifespan of a generator. In [6], the unbalanced magnetic pull in a large hydro generator was studied by using the Maxwell stress method. An improved incomplete transposition structure was proposed to reduce the circulating current loss in stator strands [7]. These parameters are affected by the harmonic magnetic fields. Therefore, it is significance to study the influence of harmonic currents on generators.
Many experts and researchers have made some related studies on the influence of harmonics on generators. In [8], a stator current harmonic suppression method was proposed to eliminate harmonic currents in doubly fed induction generators. The influences of the slot harmonics on the magnetic forces and vibration are studied using the finite element method in a low-speed permanent-magnetic machine [9]. However, there are not many studies of the harmonic currents on the air-gap flux density, torque ripple, average torque and losses of hydro generators. Torque ripple causes noise, mechanical wear and damage to the generator parts. The phenomenon of variation has appeared on the generator of the Chai J.X. hydropower station. The faults caused by severe vibrations in the generator are shown in Fig. 1.
Fig. 1. Faults caused by vibrations.
However, the existence of harmonic currents lead to the generation of an unbalanced magnetic pull in the generator. This exerts an influence on the torque ripple, and eventually lead to generator vibrations. In addition, the losses and magnetic flux density of the generator are also affected by harmonic magnetic fields. Therefore, it is necessary to analyze the influences of harmonic current on generators. In this paper, a 24-MW bulb tubular turbine generator is taken as an example. A two-dimensional (2-D) model has been established in accordance with the actual size of the generator. The magnetic flux density, torque ripple, average torque and losses of the generator under different working conditions have been calculated using the numerical method. The influence of the harmonic currents on the eddy current loss of the generator has been studied through the distribution of the eddy current density on the damper bars. Through the above studies, some useful conclusions have been obtained.
Ⅱ. ESTABLISHMENT AND VALIDATION OF THE MODEL
A. Establishment of the Model
The Chai J.X. hydropower station is located on the Yellow River in western China. There are four sets of bulb tubular turbine generators, and the unit capacity of the generators is 24-MW.
A 24-MW bulb tubular turbine generator is considered in this study, and the type of the generator is a SFWG24- 88/7820. Its stator connection type is YY. The stator iron core material is 5mm of silicon steel sheet. The pole iron core material is 3mm of magnetic steel. Some of the parameters of the SFWG24-88/7820 are shown in Table I.
| Parameters |
value |
Parameters |
value |
| Rated power /MW |
24 |
Stator inner diameter /mm |
7370 |
| Rated voltage /kV |
10.5 |
Length of stator core /mm |
1350 |
| Rated current /A |
1389 |
Number of stator slots |
462 |
| Rated speed (r/min) |
68.18 |
Conductors per slot |
2 |
| Number of poles |
88 |
Stator outer diameter /mm |
7820 |
According to the analysis, it is known that the generator is composed of 22 unit motors. The characteristics for each of the unit motors are exactly equal. Therefore, a unit motor was built in this paper to study the characteristics of the generator. The model is shown in Fig. 2.
Fig. 2. Physical model of the generator.
Considering the complexity of the electromagnetic field inside the generator, for the sake of convenience, the following assumptions are given to calculate the 2D transient electromagnetic field of the generator.
1) The influence of the end leakage magnetic field on the magnetic field of the generator straight line segment is ignored.
2) The displacement current is ignored.
3) The leakage field of the stator core is ignored.
The boundaries of the 2D time varying electromagnetic field should meet the following conditions [10], [11].
Where 
is the material reluctivity, 
is the 
axis component of the current density, 
is the 
axis component of the magnetic vector potential
, and 
is the eddy current density.
B. Validation of the Model
A series simulation data of the generator were obtained using finite element software under different working conditions. According to the simulation data, the curves of the no-load characteristic curves, rated characteristic curves and short circuit curves were drawn, as shown in Fig. 3. In this figure, the horizontal coordinate represents the value of the excitation current, the longitudinal on the left side coordinate represents the induced voltage in the armature winding, and the longitudinal on the right side coordinate represents the current in the armature windings.
Fig. 3. Operation characteristic curves.
Through comparison and analysis, it has been concluded that the errors between the simulation result and the experimental data are within 7%, which meets the requirements of engineering research. The correctness of the model is verified through the above analysis.
Ⅲ. ANALYSIS OF HARMONIC CURRENTS
The harmonic currents in power grids are mainly caused by electrical power equipment, rectifiers, converters and other nonlinear loads. In recent years, the constructions of distributed generation systems and electric vehicle charging stations have resulted in a large number of nonlinear devices [12]-[15]. These nonlinear devices lead to an increase of the harmonic contents in power grids. Harmonic currents bring more losses to transmission lines [16], [17]. In addition, with the increase of harmonic current frequency, the skin effect becomes more obvious.
Considering the influence of the proximity effect and skin effect on the generator windings, the existence of harmonic currents leads to a large number of losses in a generator. The harmonic magnetic fields make the magnetic pull unbalanced, which affects the stable operation of the generator. Through the above analysis, it can be known that research on the influence of harmonic currents on generators is significant.
The research object in this paper is a bulb tubular turbine generator. The way of the armature winding connection is the star type in this generator. Therefore, the 3n (n=1,2,3 ...) th harmonic currents cannot form a loop in the armature windings. The even harmonic currents do not exist. Therefore, the generator is mainly impacted by harmonic currents that have more content in the power grid, such as the 5th, 7th and 11th harmonic currents. Like the normal current, three-phase harmonic currents are also symmetrical. The only difference between the currents is the time 
(
is the power frequency). The general expression of the N th harmonic current is:
Where, 
are the three-phase current amplitudes, 
s the harmonic current, 
is the harmonic order, 
is the initial phase, and 
is the power frequency.
Ⅳ. THE INFLUENCE OF HARMONIC CURRENTS ON MAGNETIC FLUX DENSITY
Air gap flux density is an important parameter of synchronous generators. Recently, many experts have made relevant studies on flux density. In [18], an improved analytical method was provided to calculate the air gap flux characteristics of switched reluctance machines. The rotational flux density distribution in a hydro generator is studied by plotting the aspect ratio [19]. The magnetic flux density impacts the generator power density, and directly determines the generator output. There are many factors that affect the magnetic flux density. These factors include the choice of the air gap length [20], rotor material, magnetic steel plate and so on. In this paper, the influence of harmonic currents on the magnetic flux density was discussed.
A series of distribution curves of the magnetic flux density under different conditions was obtained by simulations, as shown in Fig. 4. Here, the harmonic current amplitude is 5% of the fundamental current amplitude. In Fig. 4, curve 1 represents the magnetic flux density distribution curve when the generator is operated at its rated condition. Curve 2 represents the magnetic flux density distribution when the 5th harmonic current was mixed into the fundamental current. Curves 3 and 4 represent distribution curves of the magnetic flux density when the fundamental current and the 5th harmonic current were injected into the armature windings.
|
(a) |
|
(b) |
A comparison of curve 1 and curve 2 shows that the influence of the harmonic current on the magnetic flux density is not obvious at a certain time. In other words, the magnetic flux density of the generator does not change a lot when the fundamental current is mixed with a small amount of harmonic currents. The main reason for this phenomenon is the impact of the main magnetic field and the cogging effect. Although the variation of the magnetic flux density is not obvious, this does not mean that the harmonic current has no effect on the generator.
The air gap magnetic field is constituted by the main magnetic field and the armature magnetic field. Actually, the main magnetic field has no effect on the generator eddy current loss. However, to eliminate the influence of the main magnetic field, this paper makes a comparative analysis of the air gap magnetic fields. Here, the fundamental current and harmonic current are injected into the armature windings. At this time, the curves of the magnetic fields of curve 3 and curve 4 can be obtained, as shown in Fig. 4(a). A comparison of curve 1 and curve 3 shows that the armature magnetic field lags behind the resultant magnetic field.
The air gap magnetic field is still not completely sinusoidal even when the waveform of the output current of the generator is sinusoidal. The torque ripple is affected by the non-sinusoidal magnetic field. In other words, there is still a torque ripple when the generator is injected with the fundamental current. From curve 4, it can be seen that the intensity of the harmonic magnetic field is very weak when only harmonic current is injected into the armature windings.
From Fig. 4(b), it can be seen that the air gap flux density in the generator is various when the harmonic currents are injected into the armature winding. When 2% of the 5th and 11th harmonic currents are injected, the fundamental amplitudes of the air gap flux density are slightly decreased. When 2% of the 7th harmonic current exists in the winding, the fundamental amplitude of the air gap flux density is increased by 0.0034T when compared with the normal condition.
Decomposition of the resultant magnetic field was done, as shown in Fig. 5(a). The corresponding curves of the magnetic fields were also studied, as shown in Fig. 5(b).
|
(a) |
|
(b) |
From Fig. 5(a), it can be seen that only the harmonic magnetic field is asynchronously rotating with the generator rotor. The stator slots cause the generation of space harmonics. However, taking its content and rotation speed into account, the influence of the space harmonics on the generator can be ignored. Therefore, the main factor that affects the performance of the generator is the time harmonics. Although the intensity of the generator magnetic flux density is small when only harmonic current is injected into the armature windings, its high speed has a huge impact on the generator.
The decomposition magnetic fields are marked by serial numbers in Fig. 5(a). In Fig. 5(b), the corresponding curves of the magnetic flux density distribution about the magnetic fields are given. These curves are shown in Fig. 4.
Ⅴ. THE INFLUENCE OF HARMONIC CURRENTS ON TORQUE
The average torque and torque ripple are two important indicators to measure generator performance. The load capacity of a generator is directly decided by the average torque, and the torque ripple is related to the generator stability operation [21].
Among the factors that affect the torque ripple of generators, the prominent factor is higher order harmonic currents [22]. The fundamental current and harmonic current form their own rotating magnetic field in the air gap of a generator. The electromagnetic torque produced by each of the magnetic fields is relatively stable. However, considering the interaction between any two of the magnetic fields, the resultant electromagnetic torque becomes unstable. At this time, torque ripple is generated in the generator.
The formula for the electromagnetic torque of a synchronous generator can be obtained by the virtual displacement method:
Where 
and 
are the magnetic co-energies before and after virtual displacement, respectively; and 
and 
are the positions of the generator part before and after virtual displacement, respectively.
According to formula (3), the generator torque can be calculated in real time. Taking the 5th harmonic current as an example, and the harmonic current amplitude takes a value of 2% of the fundamental current amplitude. The curve of the torque in real time can be drawn only when the fundamental current is injected into the armature windings. The torque curves are shown in Fig. 6. In this figure, H1, H2, H3 and H4 represent the values of the torque ripple under these two conditions.
Fig. 6. Torque curves in real time.
From Fig. 6, it can be seen that the torque ripple of the generator is small when the fundamental current is injected into the armature windings. Meanwhile, once the harmonic currents were mixed into the fundamental current, the fluctuations of the generator torque ripple are obvious increased.
Through the above analysis, it can be seen that the existence of harmonic currents have a serious impact on the torque ripple of the generator. Therefore, the effects of harmonic currents on the generator torque are analyzed in detail in the following section.
A. Influence of the Harmonic Current Amplitude on the Torque Style of the Manuscript for Publication
1) Influence of the Harmonic Currents on the Torque Ripple: Data on the torque ripple of a generator under various conditions can be gained by simulations. According to this data, the growth chart of the torque ripple was drawn, as shown in Fig. 7. In this figure, ‘I’ represents the magnitude of the fundamental current.
Fig. 7. Growth trends of the torque ripple.
Fig. 7 shows the torque ripple, which increase linearly with an increase of the harmonic current amplitude. When the amplitudes of the 5th, 7th and 11th harmonic currents increase from 0% to 5%, the torque ripples of the generator increase by 359.8 kNm, 340.6 kNm and 371 kNm, respectively. In other words, when compared with the rated condition, the torque ripples increase by one to two times under the three conditions mentioned above. Therefore, the influence of harmonic currents on the generator torque ripple cannot be ignored.
2) Influence of the Harmonic Currents on the Average Torque: The influence of harmonic currents on the average torque of the generator was analyzed. Data on average torque are shown in Table II.
| Percentage of the fundamental current amplitude |
Average torque （kNm） |
||
| 5th |
7th |
11th |
|
| 0% |
3546.8 |
3546.8 |
3546.8 |
| 1% |
3546.7 |
3546.9 |
3546.6 |
| 2% |
3546.7 |
3581.3 |
3546.4 |
| 3% |
3546.7 |
3581.8 |
3546.2 |
| 4% |
3546.5 |
3582.1 |
3546.0 |
| 5% |
3546.5 |
3582.4 |
3545.8 |
Through data analysis and considering the errors of the finite element tool, it can be concluded that changes of the harmonic current contents do not significantly affect the average torque of the generator.
B. Influence of Harmonic Current Phase on Torque Ripple
In other cases, the phase angle of the harmonic current can also impact the generator torque. The torque ripples of the generator were analyzed in the presence of harmonic currents with different phases. The harmonic current amplitude takes a value of 2% of the fundamental current amplitude. The variation curves of the torque ripples of the generator have been drawn, as shown in Fig. 8.
Fig. 8. Trend graph of torque ripples.
Fig. 8 shows that with an increase of the harmonic current phases, the torque ripples of the generator have been changed to a certain degree. Through a comparison, it can be seen that the change of the 5th harmonic current phases has the greatest influence on the torque ripple of the generator, and the fluctuation value is 67.6 kNm. The effects of the 7th and 11th harmonic current phases on the generator torque ripple are smaller than that of the 5th harmonic current, and the fluctuation are 47.2 kNm and 48.1 kNm, respectively. When the fundamental current is mixed with the 5th and 7th harmonic currents, the waves of the torque ripples are similar to a sine curve.
Ⅵ. THE INFLUENCE OF HARMONIC CURRENTS ON GENERATOR LOSSES
Efficiency is an important performance index of a hydro generator [23]. This depends on the value of the losses in the generator. The higher the loss is, the lower the efficiency becomes. To reduce the losses, a lower electromagnetic load and current density should be selected.
The fundamental magnetic potential of the stator is synchronously rotating with the rotor in the synchronous generator. In this situation, the eddy current loss of the rotor is usually neglected. However, the existence of stator slots makes the generator generate some space harmonic currents, which leads to the generation of eddy current loss in the damper windings. Since the rotor core and pole core are superposed by magnetic steel plates, the part in the generator that can generate eddy current loss is the damping winding. Eddy current loss can increase the temperature of the generator rotor, result in generator performance degradation, and cause damage to the generator parts. Therefore, it is very important to analyze the influence of harmonic currents on the eddy current loss in a generator.
When the fundamental current is mixed with different harmonic currents, the eddy current losses of the generator can be gained by simulations. Relation curves of the harmonic currents amplitude and eddy current loss are plotted, as shown in Fig. 9. In the figure, curves 1, 2 and 3 represent the relationship between the eddy current loss and the harmonic current amplitude when the 5th, 7th and 11th harmonic current were injected into the armature winding. The ‘I’ represents the magnitude of the fundamental current.
Fig. 9. Change of the eddy current loss.
Fig. 9 shows that with an increase of the harmonic current amplitude, the eddy current loss of the generator is obviously increasing. The increase rate of eddy current loss is also increasing with the increase of the harmonic current amplitude. Research indicates that the harmonic currents have a certain extent effect on generator eddy current losses. When harmonic currents with the same amplitude are compared with the 5th and 7th harmonic currents, the 11th harmonic current has an obvious effect on the eddy current loss.
In order to reveal the mechanism of the eddy current loss of the damping windings, the distribution of the eddy current on the damper windings has been analyzed, as shown in Fig. 10.
Fig. 10. Eddy current distribution and analysis.
The diameter of the damping bars adopted in the generator is 16 mm. Fig. 10 shows that the eddy current is mainly distributed on the surface of damper bars and that it is close to the slots. The maximum value of the eddy current appears on the far right damper bar. Further analysis show that the phenomena of the maximum value of eddy current on the far right damper bar is caused by the armature reaction. The armature reaction makes the magnetic field offset to the right side of the pole. When the 11th harmonic current is mixed into the fundamental current, the distribution acreage of the eddy current on the damper bars increases to some extent. The eddy current virtual values of the three damper winding are increased by 9.3%, 7.4% and 14.3%, respectively, when the 11th harmonic current is added into the armature winding. The increase of the eddy current ultimately makes the eddy current loss on the damping winding increase. The result shows that the eddy current is coincide with the variation of the eddy current loss in the damper windings. In other words, the increase of the eddy current makes the eddy current loss increase. The change mechanism of the eddy current loss in the damping winding is revealed.
Ⅶ. CONCLUSIONS
With the increase of nonlinear devices in the power grid, the content of harmonic currents has greatly increased. The harmonic current is a great threat to the stable operation of generators. In this paper, a 24-MW bulb tubular turbine generator is taken as an example. Changes of the magnetic flux density distribution, torque and losses of the generator were analyzed when harmonic currents were considered. Through analysis, the following conclusions have been made.
1) The existence of harmonic currents has a serious impact on the torque ripple of a generator. The torque ripple of the generator linearly increases with an increase of the harmonic current amplitude. When the amplitudes of the 5th, 7th and 11th harmonic currents increases to 5% of the fundamental current amplitude, the values of the torque ripple of the generator increase by 1~2 times.
2) The eddy current loss in damper bars is obviously affected by harmonic currents. In this generator, the eddy current loss gradually increases with an increase of the harmonic current amplitude. The harmonic current increases the distribution areas of the eddy currents on damping bars to some extent.
3) Considering the space harmonic magnetic field in the armature windings, with the characteristics of low content and speed, the main factor that impacts the generator performance is the time harmonic magnetic field. A small amount of harmonic current has little effect on the average torque of the generator.
4) The phases of the harmonic currents have certain effects on the generator torque. Under the same circumstances, the influence of the 5th harmonic current phases on the generator torque is the most obvious. When the 5th and 7th harmonic currents are mixed into the fundamental current, the changes of the torque ripples are similar to the sinusoidal law, and the variation ranges of the torque are 67.6 kNm and 47.2 kNm, respectively.
REFERENCES
[1] J. Han, C. S. Choi, W. K. Park, L. Lee, and S. H. Kim, “PLC-based photovoltaic system management for smart home energy management system,” IEEE Trans. Consum. Electron., Vol. 60, No. 2, pp. 184-189, May 2014.
[2] S. Md. Munir and Y.-W. Li, “Residential distribution system harmonic compensation using PV interfacing inverter,” IEEE Trans. Smart Grid, Vol. 4, No. 2, pp. 816-827, Jun. 2013.
[3] S. Lauria, M. Schembari, F. Palone, and M. Maccioni, “Very long distance connection of gigawattsize offshore wind farms: Extra high-voltage AC versus high-voltage DC cost comparison,” IET Renew. Power Gener., Vol. 10, No. 5 pp. 713-720, May 2016.
[4] X.-D. Zheng, N.-L. Tai, J.-S. Thorp, and G.-L. Yang, “A transient harmonic current protection scheme for HVDC transmission line,” IEEE Trans. Power Del., Vol. 27, No. 4, pp. 2278-2285, Oct. 2012.
[5] F. J. Garcia, M. K. I. Uemori, J. J. Rocha Echeverria, and E. D. Costa Bortoni, “Design requirements of generators applied to low-head hydro power plants,” IEEE Trans. Energy Convers., Vol. 30, No. 4, pp. 1630-1638, Dec. 2015.
[6] L. Wang, R. W. Cheung, Z. Ma, J. Ruan, and Y. Peng, “Finite-element analysis of unbalanced magnetic pull in a large hydro-generator under practical operations,” IEEE Trans. Magn., Vol. 44, No. 6 pp. 1558-1561, Jun. 2008.
[7] Y.-P. Liang and Y.-Q. Chen, “Circulating current losses analysis and improved incomplete transposition for stator bars in large hydro-generators,” IET Electr. Power Appl., Vol. 10, No. 2, pp. 125-132, Feb. 2016.
[8] C.-J. Liu, F. Blaabjerg, W.-J. Chen, and D.-H. Xu, “Stator current harmonic control with resonant controller for doubly fed induction generator,” IEEE Trans. Power Electron., Vol. 27, No. ,pp. 3207-3220, Jul. 2012.
[9] M. Valavi, A. Nysveen, R. Nilssen, and T. Rolvag, “Slot harmonic effect on magnetic forces and vibration in low-speed permanent-magnet machine with concentrated windings,” IEEE Trans. Ind. Appl., Vol. 50, No. 5, pp. 3304-3313, Sep. 2014.
[10] L.-K. Wang, W.-L. Li, F.-Y. Huo, S.-K. Zhang, and C.-W. Guan, “Influence of underexcitation operation on electromagnetic loss in the end metal parts and stator step packets of a turbogenerator,” IEEE Trans. Energy Convers., Vol. 29, No. 3, pp. 748-757, Sep. 2014.
[11] L.-K. Wang, F.-Y. Huo, W.-L. Li, Y.-H. Zhang, Q. Li, Y. Li, and C.-W. Guan, “Influence of metal screen materials on 3-D electromagnetic field and Eddy current loss in the end region of turbogenerator,” IEEE Trans. Magn., Vol. 49, No. 2, pp. 939-945, Feb. 2013.
[12] A. Dubey, S. Santoso, and M. P. Cloud, “Average-value model of electric vehicle chargers,” IEEE Trans. Smart Grid, Vol. 4, No. 3, pp. 1549-1557, Sep. 2013.
[13] L. Sainz and J. Balcells, “Harmonic interaction influence due to current source shunt filters in networks supplying nonlinear loads,” IEEE Trans. Power Del., Vol. 27, No. 3, pp. 1385-1393, Jul. 2012.
[14] Q. N. Trinh and H. H. Lee, “An enhanced grid current compensator for grid-connected distributed generation under nonlinear loads and grid voltage distortions,” IEEE Trans. Ind. Electron., Vol. 61, No. 12, pp. 6528-6537, Dec. 2014.
[15] J. Mazumdar and R. G. Harley, “Recurrent neural networks trained with back propagation through time algorithm to estimate nonlinear load harmonic currents,” IEEE Trans. Ind. Electron., Vol. 55, No. 9, pp. 3484-3491, Sep. 2008.
[16] A. Kuperman, U. Levy, J. Goren, A. Zafransky, and A. Savernin, “Battery charger for electric vehicle traction battery switch station,” IEEE Trans. Ind. Electron., Vol. 60, No. 12 , pp. 5391-5399, Dec. 2013.
[17] N.-C. Zhou, J.-J. Wang, Q.-G. Wang, and N.-Q. Wei, “Measurement-based harmonic modeling of an electric vehicle charging station using a three-phase uncontrolled rectifier,” IEEE Trans. Smart Grid, Vol. 6, No. 3, pp. 1332-1340, May 2015.
[18] Q. Yu, X.-S. Wang, and Y.-H. Cheng, “Determination of air-gap flux density characteristics of switched reluctance machines with conductor layout and slotting effect,” IEEE Trans. Magn., Vol. 52, No. 8, Aug. 2016.
[19] J. C. Akiror, A. Merkhouf, C. Hudon, and P. Pillay, “Consideration of design and operation on rotational flux density distributions in hydrogenerator stators,” IEEE Trans. Energy Convers., Vol. 30, No. 4, pp. 1585-1594, Dec. 2015.
[20] A. B. M. Aguiar, A. Merkhouf, and K. Al-Haddad, “Influence of the air gap length on the magnetic core loss in large hydro generator,” in Proc. the International Conference on Electrical Machines, pp. 2-5, 2012.
[21] J.-S. Chen and W. Zhang, “Harmonics in brushless doubly fed induction generator for torque ripple analysis and modeling,” IEEE Trans. Magn., Vol. 50, No. 11, Nov. 2014.
[22] N. T. Yogesh and V. A. Mohan, “Torque ripple and harmonic current reduction in a three-level inverter-fed direct-torque-controlled five-phase induction motor,” IEEE Trans. Ind. Electron., Vol. 64, No. 7, pp. 5265-5275, Jul. 2017.
[23] R. J. Dias, C. R. Silva, B. R. Dos Santos, C. Dos Santos Costa, A. F. V. Da Silveira, and D. A. De Andrade, “Innovations on Design of 6x4 and 6x6 Switched Reluctance Generators for Increasing the Efficiency,” IEEE Latin America Trans., Vol. 15, No. 4, pp. 646-655, Apr. 2017.
Hongbo Qiu received his M.S. and Ph.D. degrees from the Harbin University of Science and Technology, Harbin, China. He has been with the College of Electrical and Electronic Engineering, Zhengzhou University of Light Industry, Zhengzhou, China, since 2014. His current research interests include electromagnetic and thermal analysis of electrical machines, particularly permanent-magnet machines.
Xiaobin Fan is presently working towards his M.S. degree at the Zhengzhou University of Light Industry, Zhengzhou, China. His current research interests include the electromagnetic analysis of bulb tubular turbine generators.
Jianqin Feng received his M.S. degree from Northwestern Polytechnical University, Xi'an, China. He is presently working as a Professor in the College of Electrical and Electronic Engineering, Zhengzhou University of Light Industry, Zhengzhou, China. His current research interests include the relay protection of power systems and electric power automation equipment.
Cunxiang Yang received his M.S. degree from Southeast University, Nanjing, China, in 1996. He is presently working as a Professor in the College of Electrical and Electronic Engineering, Zhengzhou University of Light Industry, Zhengzhou, China. His current research interests include the diagnosis of electric motors and the control of intelligent electrical apparatus.