Influence of Extension Length of Rotor End Windings on the Three-Dimensional Electromagnetic Field and Temperature Rise in the Large Turbine Generator End Zone With Magnetic Screen

Leakage magnetic field from the rotor end windings affects obviously the electromagnetic losses and temperature of end components in the turbine generator end zone with magnetic screen. As the capacity of turbine generator increases, this effect of rotor end windings has become more prominent. To investigate influence of the extension length of rotor end windings on the electromagnetic and thermal fields in the turbine generator end zone with magnetic screen, three-dimensional transient electromagnetic field model of 1250 MW turbine generator end zone is given. Leakage magnetic field and losses of end components are compared and studied in the end zone under the different extension lengths of rotor end windings. Based on the calculation results of electromagnetic losses (heat sources) and flow network (boundary conditions), three-dimensional fluid-thermal coupling field is calculated in the turbine generator end zone with magnetic screen. Distribution of complex fluid velocity in the end zone is obtained. Influence of the different extension lengths of rotor end windings on the stator-end copper coil, screen plate, finger plate, press plate, magnetic screen, and stator end core is researched in the turbine generator end zone. The accuracy of calculation results is validated by experimental values.


I. INTRODUCTION
Size of the end windings has a great effect on the electromagnetic losses and temperature rise of end components in the turbine generator end zone with magnetic screen. The current in the stator and rotor end windings of large turbine generator is large, which leads to a high leakage magnetic field and losses of the end components in the turbine generator end The associate editor coordinating the review of this manuscript and approving it for publication was Yi Ren. zone with magnetic screen. If the structure design of the turbine generator end zone with magnetic screen is inappropriate, the leakage magnetic field, losses, and temperature of the end components become higher. It will affect seriously the safety and stability of turbine generator. Accurate calculation of the leakage magnetic field, losses, and temperature of the end components in the large turbine generator end zone with magnetic screen has an important engineering significance.
The total leakage flux in the end zone of the turbine generator is formed by the interaction of the leakage flux VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ from the stator end windings and the leakage flux from the rotor end windings. The extension length of rotor end windings affects the distribution and strength of the total leakage flux in the turbine generator end zone with magnetic screen. Furthermore, the losses and temperature distribution of the end components are changed with the extension length of rotor end windings. Reasonable design of the extension length of rotor end windings could reduce effectively the losses and temperatures of the end metal components, which improves obviously the heat resistance of the large turbine generator. Therefore, it is of great importance for large turbine generator to study influence of the different extension lengths of rotor end windings on the electromagnetic field, losses, and temperature distribution of the end components in the complex turbine generator end zone with magnetic screen. The analysis of the electromagnetic field, fluid flow, and temperature distribution is necessary to the design of the turbine generator. Extensive studies are performed on the multi-physics field in the turbine generator. Albanese et al. focused on the coupled numerical calculations of the forces and stresses on the end winding of turbine generator [1]. Fujita et al. performed the eddy current analysis in the stator end structures of large capacity turbine generators [2]. Xu et al. studied the influence of rotor damping structure on speed fluctuation and asynchronous operating ability of the turbine generators with loss of excitation [3]. Fratila et al. performed the iron loss calculation in a turbine generator using finite element method [4]. Šašić et al. focused on the finite element analysis of turbine generator rotor winding shorted turns [5]. Sufei et al. studied the implementation of surface impedance boundary conditions, impact of press plate structure on the flux and loss distributions, efficient calculation of the strand eddy current loss distributions, parametric study for the design, and fast calculation of the magnetic field and loss distributions in the end region of large synchronous generators [6]- [10]. Some other experts also studied the multi-physics field of turbine generator [11]- [14], but very few focused on the influence of the extension length of rotor end windings on the electromagnetic losses, fluid flow, and thermal field in the large turbine generator end zone with magnetic screen.
In this paper, three-dimensional transient electromagnetic field model of 1250 MW turbine generator end zone with magnetic screen is established. The electromagnetic field and losses of end components are obtained in the turbine generator end zone under the different extension lengths of rotor end windings. Three-dimensional fluid-thermal coupling model of the large turbine generator end zone with magnetic screen is given. Loss values of the end components from three-dimensional transient electromagnetic field are applied to end zone as heat source under the different extension lengths of rotor end windings. Fan outlet pressure and inlet velocity from flow network are applied to end zone as boundary conditions. The fluid field and thermal field in the turbine generator end zone with magnetic screen are calculated by the finite volume method. The distribution of fluid velocity around the finger plate is determined. Influence of the different extension lengths of rotor end windings on the electromagnetic losses and temperature distribution of the end components is studied in the large turbine generator end zone with magnetic screen, which could provide the important reference for the optimization design of the turbine generator end zone.

II. ANALYSIS OF ELECTROMAGNETIC FIELD IN THE END ZONE OF TURBINE GENERATOR
In this paper, the mathematical model of three-dimensional transient electromagnetic field of 1250 MW turbine generator end zone with magnetic screen are established [15], [16]. Fig. 1 shows the solving model of the three-dimensional transient electromagnetic field in the turbine generator end zone with magnetic screen. Fig. 1(a) gives the end components of the turbine generator. Fig. 1(b) gives the electromagnetic solution zone. The electromagnetic solution zone is divided into the eddy current zone and the non eddy current zone.  Eddy current zone: Non eddy current zone: where µ is the permeability (in H/m), T the electric vector potential, J s is the source current density in the winding (in A/m 2 ), ρ is the resistivity (in · m), t is the time (in s), and ψ is the scalar magnetic potential. For the convenience of study, the rotor end windings are marked as A, B, C and D along the axial direction. The distance between the rotor end windings keeps constant. The distance between the rotor end winding (A) and the rotor core is denoted as H. The distance between the rotor end winding (A) and the rotor core means the extension length of rotor end windings in this paper. Fig. 2 shows the location of rotor core and rotor end windings. The complex three-dimensional electromagnetic field, fluid field, and temperature field in the end zone of turbine generator are studied in detail when the extension length of rotor end windings is adjusted to H=45 mm, H=85 mm, H=125 mm, H=165 mm, and H=205 mm, respectively. Fig. 3 gives the distribution of the leakage magnetic field in the end zone of the turbine generator when the extension length of rotor end windings is H=205 mm.
The simulation time of the 3-D transient electromagnetic field model is about 31 hours. Fig. 3 gives the magnetic flux vector within the magnetic screen when the extension length of rotor end windings is H=205 mm. The magnetic flux vector within magnetic screen presents a trend of two-in and two-out. The reason for this is that the pole number of this turbine generator is four.
The eddy current losses of end components can be determined as follows: where T t is the period of time (in s), σ r is the conductivity (in S/m), e is the element volume (in m 3 ), k is the total number of elements in the different end components, J e is the eddy current density (in A/m 2 ), and P e is the eddy current loss (in W). Fig. 4 shows the flux density on the inner surface of the magnetic screen at position F, position G, position K, position I, and position J under the different extension lengths of rotor end windings. In Fig. 4, the numbers 1, 2, 3, 4, and 5 represent 1 st magnetic screen, 2 nd magnetic screen, 3 rd magnetic screen, 4 th magnetic screen, and 5 th magnetic screen.
The overall trend of the flux density on the inner surface of the magnetic screen increases gradually from position F to position J along the axial direction. At position F, the flux density on the inner surface of the magnetic screen is the lowest. When the extension length of rotor end windings is H=45 mm, H=85 mm, H=125 mm, H=165 mm, and H=205 mm, the flux densities of the magnetic screen at position F are 0.84T, 0.81T, 0.76T, 0.72T and 0.68T, respectively, 0.13T, 0.13T, 0.17T, 0.21T, and 0.22T lower than these VOLUME 8, 2020 of the magnetic screen at position J. When the extension length of rotor end windings is H=205 mm, the flux density difference between position F and position J on the inner surface of the magnetic screen is the largest. As the extension length of rotor end windings increases, the flux density on the inner surface of the magnetic screen decreases gradually at the same position. When the extension length of rotor end windings increases from H=45 mm to H=205 mm, the change of flux density at position F is large and it is 0.16T. However, this change of flux density at position J is small and it is 0.07T. When the extension length of rotor end windings is H=45 mm, H=85 mm, H=125 mm, H=165 mm, and H=205 mm, the flux densities are 0.91T, 0.88T, 0.84T, 0.83T, and 0.8T at position K, respectively.
The flux densities of the end components that are generated from an armature reaction and field excitation are B S and B F , respectively. The resultant of these two flux densities is denoted as B a . The subscripts 1 and 2 represent the normal structure and the increased extension of the rotor end windings, respectively. For the end region that is near the rotor, OB 1 represents the resultant flux density for the normal structure. OB 2 represents the resultant flux density with the increased extension of the rotor end windings. The resultant flux density is denoted as OB for the illustrations in Fig. 5(a). For the end region that is far away from the rotor, OD 1 is the resultant flux density for the normal structure. OD 2 is the resultant flux density with the increased extension of the rotor end windings. The resultant flux density is denoted as OD for the illustrations in Figs. 5(b).
As the finger plate is close to the rotor, the loss of the finger plate is mainly affected by the rotor. Therefore, the increased extension of the rotor end windings could cause an increase in the loss of the finger plate. However, as the other end components are far away from the rotor, their losses are mainly affected by the stator. Therefore, the increased extension of the rotor end windings could reduce the losses of the other end components. The losses of the screen plate, magnetic screen, and press plate decrease with the increased extension of the rotor end windings.  As the extension length of rotor end windings increases, the loss values of press plate, screen plate, and magnetic screen decrease gradually. However, the loss value of finger plate increases gradually. When the extension length of rotor end windings is 45 mm, the loss values of the finger plate, screen plate, magnetic screen, and press plate are 19941W, 26278.4W, 3880.5W, and 654.7W, respectively. When the extension length of rotor end windings is 205 mm, the loss values of the finger plate, screen plate, magnetic screen, and press plate are 21064.9W, 20232.8W, 2799.6W, and 428.7W, respectively. The change of the loss value of the screen plate is obvious under the different extension lengths of rotor end windings in the turbine generator end zone with magnetic screen. The loss value of the screen plate when the extension length of rotor end windings is 45 mm is 1263W, 2360W, 4444.2W, and 6045.6W higher than that of the screen plate when the extension length of rotor end windings is 85 mm, 125 mm, 165 mm, and H=205 mm, respectively. Loss value of the screen plate when the extension length of rotor end windings is H=45 mm, H=85 mm, H=125 mm, H=165 mm, and H=205 mm is 25623.7W, 24398.1W, 23313.8W, 21359.5W, and 19804.1W higher than that of the press plate when the extension length of rotor end windings is H=45 mm, H=85 mm, H=125 mm, H=165 mm, and H=205 mm, respectively. Fig. 7 shows the total loss of the end components under the different extension lengths of rotor end windings.
As the extension length of rotor end windings increases, the total loss of the end components decreases gradually. It indicates that the increase of the extension length of rotor end windings could reduce effectively the total loss of the end components. When the extension length of rotor end windings increases from H=45 mm to H=205 mm, the screen plate loss ratio decreases from 51.8% to 45.4%. However, the finger plate loss ratio increases from 39.3% to 47.3%. The magnetic screen loss ratio is about 6%-8%. The press plate loss ratio is lower than the other end components. The press plate loss ratio is almost constant, which is about 1%.

III. FLUID-THERMAL COUPLING MODEL IN THE LARGE TURBINE GENERATOR END ZONE WITH MAGNETIC SCREEN
To study the change of the complex fluid flow and the temperature of the end components in the turbine generator end zone with magnetic screen under the different extension lengths of rotor end windings, 3-D fluid-thermal coupling model of the 1250 MW turbine generator end zone with magnetic screen is established. Fig. 8 shows 3-D fluid-thermal coupling model of end zone. Fig. 8(a) gives the end components, water-pipe inlets, and fan outlet of the coupling model. Fig. 8(b) shows the other inlets and outlets of the coupling model. Fig. 9 gives the prototype of this turbine generator.

IV. INFLUENCE OF THE EXTENSION LENGTH OF ROTOR END WINDINGS ON THERMAL FIELD IN THE TURBINE GENERATOR END ZONE WITH MAGNETIC SCREEN
In the 3-D fluid-thermal coupling model of the turbine generator end zone with magnetic screen, these values of fan outlet pressure and inlet velocity from flow network are used

A. ANALYSIS OF FLUID VELOCITY AROUND THE FINGER PLATE IN THE TURBINE GENERATOR END ZONE WITH MAGNETIC SCREEN
Finger plate could fix the stator end core in the end zone of the turbine generator. Due to the influence of the complex electromagnetic field in the end zone, the loss value of the finger plate is high. The heat of the finger plate could be taken effectively away by the cooling fluid in the axial ventilation holes. Fig. 11 shows the fluid velocity distribution around the finger plate. In Fig. 11, the highest fluid velocity around the finger plate is 41.7 m/s, which appears in the axial ventilation holes of the finger-plate yoke. The high fluid velocity in the axial ventilation holes of the finger-plate yoke could take effectively away the heat of the finger-plate yoke. It results in a low temperature of the finger-plate yoke. The fluid velocity around the top of the finger-plate tooth is also high, which is about 21 m/s. It could decrease obviously the temperature of the finger-plate tooth. The fluid velocity around the top of the finger-plate tooth is higher than that around the bottom of the finger-plate tooth.

B. INFLUENCE OF THE EXTENSION LENGTH OF ROTOR END WINDINGS ON THERMAL FIELD IN THE LARGE TURBINE GENERAOTR END ZONE WITH MAGNETIC SCREEN
This paper focuses on the temperature distribution of the end components when the extension length of rotor end windings is 205 mm. The temperature change of the end components is compared and studied under the different extension lengths of  rotor end windings. Fig. 12 gives the temperature distribution of the stator-end copper coil when the extension length of rotor end windings is 205 mm.
The highest temperature of the stator-end copper coil is 60.3 • C when the extension length of rotor end windings is 205 mm, which appears in the nose of the stator-end copper coil. The cooling water inside the stator-end copper coil could take effectively away the heat of the stator-end upper copper coil in the end zone of the turbine generator. The temperature of the stator-end upper copper coil is lower than that of the stator-end lower copper coil. A high temperature appears in the junction of the stator-end copper coil and stator end core, and it is about 59.1 • C.  The highest temperature of the screen plate is 73.3 • C when the extension length of rotor end windings is 205 mm, which appears around the outer diameter of the screen plate. The highest temperature of the screen plate when the extension length of rotor end windings is 205 mm is 5.7 • C, 4.5 • C, 3.5 • C, and 1.5 • C lower than that of the screen plate when the extension length of rotor end windings is 45 mm, 85 mm, 125 mm, and 165 mm, respectively. There are the axial ventilation holes in the inner diameter of the screen plate. The temperature in the inner diameter of the screen plate is relatively low and it is about 60.5 • C when the extension length of rotor end windings is 205 mm. The average temperature of screen plate when the extension length of rotor end windings is 205 mm is 4 • C, 3.2 • C, 2.4 • C, and 1.1 • C lower than that of the screen plate when the extension length of rotor end windings is 45 mm, 85 mm, 125 mm, and 165 mm, respectively. As the extension length of rotor end windings increases, the temperature drop of the screen plate is obvious. The highest temperature in the turbine generator end zone with magnetic screen always appears around the outer diameter of the screen plate under the different extension lengths of rotor end windings. Fig. 14 shows the temperature distribution of the finger plate when the extension length of rotor end windings is 205 mm.
The highest temperature of the finger plate is 64 • C when the extension length of rotor end windings is 205 mm, which appears in the finger-plate yoke. Due to the cooling effect of the fluid from the axial ventilation holes of the stator core, the temperature of the finger-plate tooth is low. When the extension length of rotor end windings is 205 mm, the temperature of the finger-plate tooth is about 56.8 • C. The highest  temperature of the finger plate when the extension length of rotor end windings is 205 mm is 0.35 • C, 0.12 • C, 0.1 • C, and 0.06 • C higher than that of the finger plate when the extension length of rotor end windings is 45 mm, 85 mm, 125 mm, and 165 mm, respectively. The average temperature of finger plate is 61.2 • C when the extension length of rotor end windings is 205 mm. The velocity of the cooling fluid in the axial ventilation holes of the finger-plate yoke is relatively high. It results in a lower temperature around the ventilation holes of the finger-plate yoke.
To study deeply the temperature distribution within the press plate, the press plate is divided evenly into five equal segments from the inner surface to the outer surface along the radial direction. Circumferential sample lines of radii R1=1.358 m, R2=1.455 m, R3=1.552 m, R4=1.649 m, R5=1.746 m, and R6=1.843 m are selected within the press plate along the radial direction. Fig. 15 shows the location of these circumferential sample lines within the press plate. VOLUME 8, 2020 FIGURE 16. Temperature distribution of these sample lines within the press plate along the circumferential direction when the extension length of rotor end windings is 205 mm. Fig. 16 shows the temperature distribution of these sample lines within the press plate along the circumferential direction when the extension length of rotor end windings is 205 mm.
When the extension length of rotor end windings is 205 mm, the temperature is basically the same in the radii R2, R3, and R4 within the press plate along the circumferential direction. The temperatures in the radii R2, R3, and R4 within the press plate are about 60.4 • C, 60 • C, and 60.2 • C, respectively. Due to the high fluid velocity around the outer diameter of the press plate, the lowest temperature appears in the radius R6=1.843 m and it is about 56.5 • C. Since the convective heat transfer occurs on the inner surface of the press plate, the temperature is relatively low in the radius R1=1.358 m within the press plate and it is about 58.7 • C. The temperature is about 58.3 • C in the radius R5=1.746 m within the press plate. The temperature difference is 3.9 • C between the radius R2=1.455 m and the radius R6=1.843 m within the press plate. Fig. 17 shows the temperature distribution of the magnetic screen when the extension length of rotor end windings is 205 mm. In Fig. 17, the highest temperature of the magnetic screen appears around the inner diameter and it is 60.1 • C when the extension length of rotor end windings is 205 mm. The highest temperatures of 1 st magnetic screen, 2 nd magnetic screen, 3 rd magnetic screen, 4 th magnetic screen, and 5 th magnetic screen are 60.1 • C, 55.9 • C, 55.8 • C, 55.9 • C, and 56.5 • C when the extension length of rotor end windings is 205 mm, respectively, 0.01 • C, 0.4 • C, 0.4 • C, 0.5 • C, and 0.6 • C lower than these of 1 st magnetic screen, 2 nd magnetic screen, 3 rd magnetic screen, 4 th magnetic screen, and 5 th magnetic screen when the extension length of rotor end windings is 45 mm. The extension length of rotor end windings has little effect on the temperature of the magnetic screen. The average temperatures of 1 st magnetic screen, 2 nd magnetic screen,  3 rd magnetic screen, 4 th magnetic screen, and 5 th magnetic screen are 57.9 • C, 55.6 • C, 55.4 • C, 55.5 • C, and 56.1 • C when the extension length of rotor end windings is 205 mm. Fig. 18 gives the temperature distribution of the 1 st stator inner end core when the extension length of rotor end windings is 205 mm.
It can be seen from Fig. 18 that the highest temperature of the 1 st stator inner end core is 61.4 • C when the extension length of rotor end windings is 205 mm. The cooling fluid in the axial ventilation holes could take effectively away the heat of the 1 st stator inner end core tooth. The temperature of the 1 st stator inner end core tooth is relatively low and it is about 56 • C. Due to the influence of the temperature of the end components, the temperature of the 1 st stator inner end core yoke is higher than that of the 1 st stator inner end core tooth. The temperature is about 58 • C in the outer diameter of the 1 st stator inner end core. The difference between the highest temperature and the lowest temperature of the 1 st stator inner end core is 7 • C.

C. CALCULATED RESULTS AND MEASURED VALUES
To verify the accuracy of the calculated results, three temperature sensors are embedded at 120 • angles along the circumference in the 1 st magnetic screen and 5 th magnetic screen, respectively. Fig. 19 shows the positions of three temperature sensors in the 1 st magnetic screen and 5 th magnetic screen. Table 1 gives the measured values and calculated results in the 1 st magnetic screen and 5 th magnetic screen under the no-load operation when the extension length of rotor end windings is 125 mm. The measured values are close to calculated results. It proves that the calculation method and calculated results are reliable and accurate.

V. CONCLUSION
In this paper, influence of the extension length of rotor end windings on the electromagnetic and thermal fields in the large turbine generator end zone with magnetic screen is investigated. The main conclusions are as follows.
1) As the extension length of rotor end windings increases, the loss value of finger plate increases gradually. However, the loss values of press plate, screen plate, and magnetic screen decrease gradually. The total loss of the end components also decreases gradually. When the extension length of rotor end windings increases from H=45 mm to H=205 mm, the screen plate loss ratio decreases from 51.8% to 45.4%.
However, the finger plate loss ratio increases from 39.3% to 47.3%. The magnetic screen loss ratio and the press plate loss ratio change a little.
2) The highest fluid velocity around the finger plate is 41.7 m/s, which appears in the axial ventilation holes of the finger-plate yoke. The fluid velocity around the top of the finger-plate tooth is also high, which is about 21 m/s. The fluid velocity around the top of the finger-plate tooth is higher than that around the bottom of the finger-plate tooth. Fluid velocity distribution around each finger-plate tooth is basically the same along the circumferential direction.
3) The highest temperature in the turbine generator end zone with magnetic screen always appears around the outer diameter of the screen plate under the different extension lengths of rotor end windings. As the extension length of rotor end windings increases, the temperature drop of the screen plate is obvious. However, the temperature changes of the finger plate, press plate, and magnetic screen are small. The highest temperature of the screen plate when the extension length of rotor end windings is 205 mm is 5.7 • C lower than that of the screen plate when the extension length of rotor end windings is 45 mm.