technologies for high efficiency large capacity turbine...

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Abstract — For large capacity turbine generators of thermal power plants, water-cooling system has widely been applied to stator windings. TOSHIBA has developed generators using hydrogen indirectly cooled windings, which are more suitable for high efficiency and easy to maintain, with capacity of 670MVA and efficiency of 99.1%. As the bars of stator windings are cooled with hydrogen gas through the insulation surrounding the bars, it is important to suppress the temperature rise. In this paper, some technologies to realize high efficiency turbine generators, such as multiple parallel circuit winding to reduce current per single bar and ventilation system optimization are described. I. INTRODUCTION The environmental problem has become more and more important these days and as for turbine generators, higher efficiency is required though their efficiency is already around 99%. For large capacity turbine generators such as 600MVA or more, the water-cooled type of stator winding has been widely used. However, the water-cooled system requires complicated system, including the water purification system, pipe arrangement and the special connection between the water circulating system and the hollow strands of the winding, which also require elaborate maintenance. Furthermore, the hydrogen indirectly cooled generators, whose stator windings are composed of the solid strands only, are known by their higher efficiency than the water directly cooled machines whose stator windings comprise hollow strands in which cooling liquid flows. Therefore, TOSHIBA has endeavored to expand the capacity range of indirectly cooled system with hydrogen gas and up to 50Hz-600MVA and 60Hz-500MVA of generators are already in lineup [1]. Then, a new 670MVA generator exceeding previous class has been developed, manufactured and shipped in Feb. 2009, which recorded 99.1% of efficiency at the shop test. Moreover, another 4-pole 370MVA generator, which configures a cross compound power plant with above mentioned 670MVA machine, has made a record of 99.12% in efficiency. In this paper, some of major technologies, which are applied to the high efficiency large capacity turbine generators, are described. First, a multiple parallel winding system, which enables increase of the current and reduction of copper loss in the armature winding, are introduced. On this subject, the circulating currents due to the unbalanced voltage between the parallel circuits and their numerical simulation are also stated. Second, as an example of reducing the ventilation loss, an optimization of the coolant path of the hydrogen gas, which circulates inside the machine, is described. In addition, the circulating current loss, which is caused by the nonuniform core duct pitch, and its reduction are described. Third, a rotor structure, improved in order to reduce the copper loss in the field windings, which accounts for a substantial percentage of the total loss in large capacity machines, is described. Fourth, as another example of reducing the ventilation loss, the rotor cooling system is presented. Then, finally, an environmental compatibility of the high thermal conductivity (HTC) insulation system, which enables the enlargement of the capacity of the high efficiency hydrogen indirectly cooled turbine generators, is described. II. MULTIPLE PARALLEL CIRCUIT WINDING The capacity of the generator is determined as a product of the load current and the terminal voltage. However, it is difficult to enhance the terminal voltage for the indirectly cooling system, because increasing the voltage leads to the increase of the insulation thickness of stator windings. On the other hand, increase of the coil current leads to the increase of the electromagnetic force and temperature rise. Considering these, multiple parallel circuit winding systems have been developed in order to reduce the current per single winding bar [2]. Fig.1 shows a diagram of three-parallel circuit system, as an example of the multiple parallel circuit system [3]. As described above, introduction of the multiple parallel circuit system allows to suppress the terminal voltage and also to let the insulation layer thinner. As the configuration shown in Fig.2, when the insulation thickness can be reduced, the cross section of the stator winding can be increased, that enable to reduce the copper losses. In the meantime, in the winding system with more than three parallel circuits for the 2 pole machines, circulating current is generated in the closed loop configured by the parallel circuits because of the unbalanced voltage induced. Then this additional current leads to the additional loss in the winding bars. In order to predict the winding temperature and the efficiency precisely, a circulating current analysis scheme was developed and unbalanced voltage and circulating current loss was evaluated. Fig.3 depicts the circulating current analysis model in which the FEM region and the external circuits are combined. To evaluate the reactance of the end windings, another FEM is Technologies for High Efficiency Large Capacity Turbine Generator Yoshihiro Taniyama, Takashi Ueda, Masafumi Fujita, Tetsushi Okamoto, Masanori Arata, Hitoshi Katayama, Ken Nagakura and Toru Otaka TOSHIBA Corporation, Japan

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Page 1: Technologies for high efficiency large capacity turbine ...download.xuebalib.com/1o0hp6xXq8mk.pdf · Abstract — For large capacity turbine generators of thermal power plants, water-cooling

Abstract — For large capacity turbine generators of thermal power plants, water-cooling system has widely been applied to stator windings. TOSHIBA has developed generators using hydrogen indirectly cooled windings, which are more suitable for high efficiency and easy to maintain, with capacity of 670MVA and efficiency of 99.1%. As the bars of stator windings are cooled with hydrogen gas through the insulation surrounding the bars, it is important to suppress the temperature rise. In this paper, some technologies to realize high efficiency turbine generators, such as multiple parallel circuit winding to reduce current per single bar and ventilation system optimization are described.

I. INTRODUCTION

The environmental problem has become more and more important these days and as for turbine generators, higher efficiency is required though their efficiency is already around 99%.

For large capacity turbine generators such as 600MVA or more, the water-cooled type of stator winding has been widely used. However, the water-cooled system requires complicated system, including the water purification system, pipe arrangement and the special connection between the water circulating system and the hollow strands of the winding, which also require elaborate maintenance.

Furthermore, the hydrogen indirectly cooled generators, whose stator windings are composed of the solid strands only, are known by their higher efficiency than the water directly cooled machines whose stator windings comprise hollow strands in which cooling liquid flows.

Therefore, TOSHIBA has endeavored to expand the capacity range of indirectly cooled system with hydrogen gas and up to 50Hz-600MVA and 60Hz-500MVA of generators are already in lineup [1]. Then, a new 670MVA generator exceeding previous class has been developed, manufactured and shipped in Feb. 2009, which recorded 99.1% of efficiency at the shop test. Moreover, another 4-pole 370MVA generator, which configures a cross compound power plant with above mentioned 670MVA machine, has made a record of 99.12% in efficiency.

In this paper, some of major technologies, which are applied to the high efficiency large capacity turbine generators, are described.

First, a multiple parallel winding system, which enables increase of the current and reduction of copper loss in the armature winding, are introduced. On this subject, the circulating currents due to the unbalanced voltage between the parallel circuits and their numerical simulation are also stated.

Second, as an example of reducing the ventilation loss, an

optimization of the coolant path of the hydrogen gas, which circulates inside the machine, is described. In addition, the circulating current loss, which is caused by the nonuniform core duct pitch, and its reduction are described.

Third, a rotor structure, improved in order to reduce the copper loss in the field windings, which accounts for a substantial percentage of the total loss in large capacity machines, is described.

Fourth, as another example of reducing the ventilation loss, the rotor cooling system is presented.

Then, finally, an environmental compatibility of the high thermal conductivity (HTC) insulation system, which enables the enlargement of the capacity of the high efficiency hydrogen indirectly cooled turbine generators, is described.

II. MULTIPLE PARALLEL CIRCUIT WINDING

The capacity of the generator is determined as a product of the load current and the terminal voltage. However, it is difficult to enhance the terminal voltage for the indirectly cooling system, because increasing the voltage leads to the increase of the insulation thickness of stator windings. On the other hand, increase of the coil current leads to the increase of the electromagnetic force and temperature rise. Considering these, multiple parallel circuit winding systems have been developed in order to reduce the current per single winding bar [2]. Fig.1 shows a diagram of three-parallel circuit system, as an example of the multiple parallel circuit system [3].

As described above, introduction of the multiple parallel circuit system allows to suppress the terminal voltage and also to let the insulation layer thinner. As the configuration shown in Fig.2, when the insulation thickness can be reduced, the cross section of the stator winding can be increased, that enable to reduce the copper losses.

In the meantime, in the winding system with more than three parallel circuits for the 2 pole machines, circulating current is generated in the closed loop configured by the parallel circuits because of the unbalanced voltage induced. Then this additional current leads to the additional loss in the winding bars. In order to predict the winding temperature and the efficiency precisely, a circulating current analysis scheme was developed and unbalanced voltage and circulating current loss was evaluated.

Fig.3 depicts the circulating current analysis model in which the FEM region and the external circuits are combined. To evaluate the reactance of the end windings, another FEM is

Technologies for High Efficiency Large Capacity Turbine Generator

Yoshihiro Taniyama, Takashi Ueda, Masafumi Fujita, Tetsushi Okamoto, Masanori Arata, Hitoshi Katayama, Ken Nagakura and Toru Otaka

TOSHIBA Corporation, Japan

Page 2: Technologies for high efficiency large capacity turbine ...download.xuebalib.com/1o0hp6xXq8mk.pdf · Abstract — For large capacity turbine generators of thermal power plants, water-cooling

insulation

insulationthickness

strand

performed simulating the leakage flux in the end region [4]. Fig.4 shows the results of the circulating current analyses

for the three parallel and the four parallel windings. The vertical axis presents the unbalanced voltage, which is the difference from the average circuit voltage, and the copper loss increase due to the circulating current. As shown in the figure, both unbalanced voltage and circulating current loss of the four parallel winding are much smaller than those of the three parallel winding which has been already verified. Furthermore, in Fig.4, it is shown that the dependency of the unbalanced voltage and the circulating loss increase demonstrate different tendency especially for the three parallel winding. This implies that the evaluation of the circuit currents not only the unbalanced voltage is required to evaluate the soundness of the multiple parallel winding system.

Fig.1. Multiple parallel circuits in the stator winding

(a) thick insulation (b) thin insulation

Fig.2. Stator coil cross section. (a) CC analysis model (b) External circuit (c) End region model

Fig.3. Analysis model

0

0.2

0.4

0.6

0.8

1

1.2

n-1 n n+1 n-1 n n+1

coil pitch

volta

ge/lo

ss d

evia

tion

(PU

) Loss increase

Unbalanced voltage

Yx3 Yx4

Fig.4 Comparison of circuit voltage deviation and copper loss

increase due to the circulating current between three and four parallel circuit winding

III. MULTIPLE PITCHED VENTILATION DUCTS

Fig.5 shows a diagram of ventilation path of a typical machine. The stator core of a turbine generator, composed of laminated magnetic plates, is subdivided into individual core blocks separated by inside space blocks to form ventilation ducts with a certain pitch in the axial direction. These ventilation ducts are grouped into several sections. At the inlet section, cooled gas which comes out of the cooler flows toward the gas gap and at the outlet section, relatively hot gas flows toward the outer diameter. In the figure, the stator has seven sections, of which both end parts are outlet section and the center part is inlet.

In order to cool the stator windigs efficiently, it is favorable to equalize the conductor temperature by supplying more gas to hotter spot and less gas to cooler portion. One of the schemes to adjust the gas amount is the multiple pitched ventilation duct system in which the ventilation ducts are arranged in different pitches in the axial direction.

Since the cooling gas is supplied from a fan mounted on the rotor shaft, gas temperature at the end portion of stator core is low as compared with other parts. Therefore, the duct pitch is enlarged at the end portion, as shown in Fig.6, so that whole temperature distribution is equalized.

As the duct pitch at the end portion is enlarged, the conductor temperature is heightened around the end portion but the peak value inside the core is lowered comparing to the uniform ducts, which means the winding temperature is equalized.

In the ventilation design, the number of the ducts in each section and the pitch of the ducts can be optimized with DOE to reduce the ventilation loss.

On the other hand, when the ventilation ducts are arranged in different pitches, the magnetic flux in the core becomes nonuniform and the circulating currents are induced in the strands. In the large capacity generators, the strands are normally transposed in 540o whose circulating current loss is less than that of 360o transposition [5][6]. But even the 540o transposition coil, the circulating current loss is induced as

Core

End winding

End winding

Sw1 Sw2

Coi

l C

oil

Coi

l

Coi

l C

oil

Coi

l

Coi

l C

oil

Coi

l

End flange

End winding

Stator core end

Rotor core end

Rotor coil

Page 3: Technologies for high efficiency large capacity turbine ...download.xuebalib.com/1o0hp6xXq8mk.pdf · Abstract — For large capacity turbine generators of thermal power plants, water-cooling

shown in the thin curve of Fig.7. The horizontal axis is the radial strand position, left-hand side is the inner diameter side and right-hand side is the outer diameter side. The vertical axis shows the ratio of loss increase to the dc resistance loss of strands. The results in Fig.7 correspond to F=0.28, where "F" is the ratio of the axial length of the short-pitched duct region indicated in Fig.8.

To reduce the above-mentioned loss, the transposition pitch was optimized and α, the ratio of the axial length of the short-pitched transposition area shown in Fig.8, is searched by a numerical analysis so as to reduce the circulating current loss. The result is also shown in Fig.7 though the distribution is not visible because the loss increase is almost zero. In this way, by optimizing the transposition pitch, the increase of the circulating current loss can be reduced almost perfectly [7].

Fig.5 Ventilation system of indirect cooling turbine generator

Fig.6 Example of multiple-pitched ventilation duct of stator core

-1

-0.5

0

0.5

1

St rand P osit ion

Stra

nd L

oss I

ncre

ase(

PU)

inner <== ==> outer

Top(col.1)

Top(col.2)

Bottom(col.1)

Bottom(col.2)

Fig.7 Strand loss increases distribution with multiple-pitched ventilation ducts and 540 degree transposition.

Fig.8 Multiple-pitched ventilation ducts and 540--degree transposition

IV. REDUCTION OF FIELD WINDING LOSS

In the large capacity generators, the resistance loss in the field windings attains large proportions of the total loss and its ratio often becomes 30%. Therefore, reducing the field winding loss plays an important role in raising the efficiency. As the field winding loss is calculated by the product of the second power of the field current and the resistance of the rotor coils, reduction of the field winding loss includes suppression of field current with optimization of the magnetic circuit and also increasing the copper cross section with optimization of the rotor structure.

Fig.9 presents a schematic diagram of the developed rotor. In this configuration, the magnetic pole width Wp1 and Wp2, which are configured by the slot bottoms of the first and the second slot respectively, are almost the same whereas Wp1 determines the pole width in the conventional cylindrical rotors. Furthermore, the inter-slot angle between the #1 and the #2 slots is smaller than the other inter-slot angles as the first slot depth is much smaller than other slots and the centrifugal force is smaller. Though the pole surface angle becomes smaller in the developed rotor in Fig.9, the influence to the voltage wave shape is much small for this sort of machines with large gas gap length.

In this way, it is possible to reduce 3 to 5% of the field winding copper loss by increasing the area of the coil while keeping the effective pole width.

flux

Wp1

Pole WedgeRotor coil

#1 slot

#2 slot

#3 slotWp2

flux

Wp1

Pole

Rotor coil

#1 slot

#2 slot

#3 slot

#1 slot of conventional rotor

Wp2

(a) conventional rotor (b) developed rotor

Fig.9 Schematic view of high efficiency rotor

V. IMPROVEMENT OF THE COOLING ABILITY FOR ROTOR

In addition to the loss decrease of the rotor coil, it is important to improve the cooling capability of the rotor coil in raising the efficiency, too. The rotor coil is cooled by "the radial flow system" which uses the centrifugal force of the rotor rotating. This ventilation path is shown in the rotor section of Fig.5 and its schematic view is shown in Fig.10. As

Stator end winding Ventilation duct

Core block

strand i

B B strand j

(1-F)Ls

αLs αLs

A

developed (for all strands)

Page 4: Technologies for high efficiency large capacity turbine ...download.xuebalib.com/1o0hp6xXq8mk.pdf · Abstract — For large capacity turbine generators of thermal power plants, water-cooling

shown in these figures, the cooling gas flows into the subslot from the rotor core end, and then it diverges in the radial duct which bored in the radial direction of the rotor coil from the subslot. The rotor coil is cooled mainly by cooling gas in the radial duct which diverged from the subslot. The cooling gas is exhausted in the gas gap after having cooled the rotor coil.

Fig.10 Schematic view of rotor radial flow In the large capacity generator, because the rotor core

length is long, so the length of the subslot is long and the number of the radial duct increases, too. Therefore the placement pitch and the shape of the radial duct may affect cooling performance greatly, its optimization is one of the important point of the cooling design. Then we evaluated these effects by the experiment and analysis.

Fig.11 shows the experimental equipment that evaluate the cooling capability of the radial flow method. This equipment simulates three radial ducts, rotor wedge, rotor coil, subslot and so on. And it can change the duct shape, the duct pitch and the subslot shape as shown in Fig.12.

The experiment simulates heat loss of the rotor coil with heater and measures the steady-state temperature and evaluates the heat transfer coefficient in the radial duct.

Fig.11 Experimental Equipment

One example of the experimental result is shown in Fig.13. The vertical axis of the figure is the heat transfer coefficient,

and the horizontal axis is the Reynolds' number, then each curve in this figure shows the parameter experimental result that changed the duct shape and the subslot shape.

As a result, it was shown that the heat transfer coefficient in the radial duct varied with each shape, and we confirmed that about 1.4 times cooling performance in the radial duct could improve by this experiment.

In addition, we perform three-dimensional CFD analysis to validate these experimental results.Fig.14 shows the analysis model that simulated the experimental equipment, and Fig.15 shows an example of the temperature analysis result.

By this analysis inspection, we could reproduce the experiment results and confirmed the following phenomena.

・ At inlet of the radial duct, the distribution of the cooling gas is partial greatly.

・ During the radial duct, the uneven flow of the cooling gas does not break and does not become the uniform stream.

・ In the radial duct, the upstream flow of the subslot is in stagnated condition, this part does not contribute to cooling of the rotor coil.

These are regarded as the cause why the heat transfer coefficients were different (Fig.13) with the same Reynolds' number, then we considered the analysis knowledge and experiment results in optimizing the design of the radial flow method system.

0.8

1.0

1.2

1.4

1.6

0 5000 10000 15000Reynolds Number [-]

Hea

t Tra

nsfe

r Coe

ffici

ent [

p.u

basecase1case2case3

Fig.13 Experimental result

Fig.12 Radial duct in rotor coil

Outlet Rotor Wedge

Creepage BlockField ConductorTurn InsulationSlot Insulation

Radial Duct

Gas Gap

Gas Flow Sub Slot

Duct Pitch

Length Width Rotor Coil

Radial Duct

Page 5: Technologies for high efficiency large capacity turbine ...download.xuebalib.com/1o0hp6xXq8mk.pdf · Abstract — For large capacity turbine generators of thermal power plants, water-cooling

Fig.14 Analysis Model of rotor radial duct

Fig.15 Analysis Result of Temperature

VI. HIGH THERMAL CONDUCTIVE INSULATING SYSTEM High thermal conductive insulating system is an important

key component realizing the world largest capacity indirectly cooled turbine generators [8]. The larger capacity generators lead to the higher current density of stator winding, resulting in increasing the temperature of the conductor. In case of an indirectly cooled turbine generator, the heat of conductor flows through the ground wall insulation to the iron core. The high thermal conductive insulating systems extremely improve the cooling capacity of stator winding.

The grand wall insulation is formed with a mica tape. Fig.16 shows the insulating process of stator bars used for rotating machine [9]. In general, there are two types of process (Vacuum pressure impregnated insulating system and resin rich insulating system). The vacuum pressure impregnating process was adapted to the first generation of HTC insulating system. A large amount of impregnating vanish was used in this process, and the varnish put away in the constant term. Furthermore, a large amount of solvent is used in the process because of cleaning up the impregnating tank. In the recent

years, the environmental issues have become important in the world. The reduction of the environmentally hazardous substance in the manufacturing process should have paid attention for. Resin rich system has a large advantage in these environmental aspects. The solvent substitution and vanish can be decreased when the resin rich insulating system is adopted.

There are two different types of resin rich insulating system. One is so called press-molding method (PM-RR) and the other is liquid pressurizing method. Toshiba used the vacuum pressured resin rich process (VLP-RR). In this process, after winding prepreg mica tape to the conductor, a set of bars undergoes vacuum treatment in the tank. And the liquid medium is transferred to the tank and pressurized and heated to fully cure the epoxy resin in the mica tape. As using vacuum treatment, the insulation has a good insulating properties as same as the insulation of vacuum pressure impregnating systems. Asphalt has been used as a conventional medium for pressurizing and curing the mica tape. However, there is much room for improvement in the environmental view. Quite a lot of asphalt stuck to the surface of the bars is disposed of as the waste. And the asphalt has a short lifetime because the epoxy resin in mica tape diffuses and solidified the asphalt medium. Working surroundings are adversely by fine particles of solid asphalt in the air. The new medium has been developed and used for the vacuum pressured resin rich system in Toshiba. The waste through the process was reduced 40 percents in weight [10].

Fig.16 Insulating process of stator bars used for rotating machine

Table 1 shows the thermal conductivity of several types of

insulation. The thermal conductivity of HTC insulating system made by VLP-RR process is twice of conventional VLP-RR system and same as that of HTC insulating system made by VRI process. Fig.17 shows dielectric breakdown strength of several types of insulation. As mentioned above, Toshiba’s VLP-RR process includes the vacuum treatment leading to excellent dielectric properties. The dielectric breakdown strength of VLP-RR is same as that of VPI systems. Fig.18 shows the result in voltage endurance test for the several types of insulation. VLP-RR HTC system has good voltage

Rotor Coil

Sub Slot

Radial Duct

Rotor Coil

Sub Slot

Radial Duct

Cooling Gas

Page 6: Technologies for high efficiency large capacity turbine ...download.xuebalib.com/1o0hp6xXq8mk.pdf · Abstract — For large capacity turbine generators of thermal power plants, water-cooling

endurance characteristics. Thus, VLP-RR HTC insulation has both of a good thermal conductive characteristic and excellent electric property. VLP-RR HTC insulation realizes the large capacity and high reliable indirectly cooled turbine generator.

TABLE.1 THERMAL CONDUCTIVITY OF SEVERAL TYPES OF INSULATION

VLP-RR VLP-RR HTC VPI HTC Relative thermal conductivity (arb. unit)

1.0

2.0

2.0

Dielectric bre

akdown strength

(arb. unit)

V PI H TCVLP-RR H TCVLP-RR

1.00

0.75

0.50

0.25

0.00

Fig.17 Dielectric breakdown strength for several types of insulation

0.1

1

10

10 100 1000 10000 100000

Life (hrs)

Dielectric strength (arb.

V LP -RR

VLP-RR HTC

VPI HTC

Fig.18 Result in voltage endurance test of several types of insulation

VII. CONCLUSION

Some technologies, including multiple parallel circuit windings, rotor configuration, ventilation system optimization, and high thermal conductivity insulation system, have been developed to realize high efficiency large capacity turbine generator. By these technologies, TOSHIBA has developed high efficiency turbine generator and completed a 2-pole 670MVA generator with efficiency of 99.1% and a 4-pole 370MVA generator with 99.12%.

REFERENCES [1] S. Nagano, T. Kitajima, K. Yoshida, Y. Kazao, Y. Kabata, et al.

“Development of World’s Largest Hydrogen-Cooled Turbine Generator”, Power Engineering Society Summer Meeting 2002.

[2] Takashi Ueda, Masafumi Fujita, Tadashi Tokumasu, Ken Nagakura, Daisuke Hiramatsu, Toru Ootaka: “Circulation Current Analysis in Parallel Circuit of Stator Winding of Large Turbine Generators”, IEEJ RM-07-129 (2007)

[3] H.D. Taylor: U.S. Patent, 2778962, 1957 [4] T. Tokumasu, H. Matsumoto, K. Ito, and S. Oshima: “ Magnetic Field

Analysis of Quick Response Type Superconducting Generator” , IEEE Trans. Magn., Vol.30, No.5 pp.3713-3716 (1994)

[5] W.L.Ringland, L.T.Rosenberg: “A New Stator Coil Transposition for Large Machines”, Trans. AIEE Vol.78, 99.743-747 (1959)

[6] H.Sequentz, Herstellung der Wicklungen electrisher Maschinen , Springer-Verlag, 1973, pp.70-76

[7] M.Fujita, T.Tokumasu, Y.Kabata, M.Kakiuchi, H.Nakamura, S.Nagano, “Circulating Current Analysis of Large Turbine Generator Stator Coil considering Ventilation Ducts”, in Proc IEMDC, pp.910-917

[8] M. Tari, K. Yoshida, S. Sekito, J. Allison, R. Brütsch and A. Lutz, “A High Voltage Insulating System with Increased Thermal Conductivity for Turbo Generators”, Coil Winding 2001A, Berlin (Germany).

[9] H. Hatano, M. Kawahara, T. Otaka, Proc. of 20th annual Conference of the Industry Applications society of the Institute of Electrical Engineers of Japan, Nagoya (Japan), Aug. 2006.

[10] H. Hatano, N. Iwata, F. Sawa, K. Mukai and T. Aso, “The Technology of Reducing Environmental Load on Stator Coil Insulation for Hydro-Generator,” Proc of 1st International Conference on Hydropower Technology & Key Equipment 2006, Beijing (China), 2006.

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