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Hydromechanics Analysis for Water Cooling Stator Temperature Field of Generator


2008 International Conference on Condition Monitoring and Diagnosis, Beijing, China, April 21-24, 2008

Hydromechanics Analysis for Water Cooling Stator Temperature Field of Generator
Wang Lihui1.2, Li Junqing1, Zhang Xiaorong2
1

Key Laboratory of Power System Protection and Dynamic Security Monitoring and Control under Ministry of Education, North China Electric Power University, Baoding071003, China 2 Communication Training Base of the General Staff, Xuanhua075100, China

line monitor.
Abstract--In order to study fluid state influence on stator temperature of generator, this paper applies heat transfer theory and hydromechanics to analyze water cooling system. The water velocity was studied when the water cooling winding was blocked in turbo-generators and the stator 3D temperature field was calculated by the thermal network method. The result showed different water velocity could be lead to different temperature. The authors put forward block coefficient and analyze it to be feasible in the stator temperature calculation basing on cooling winding blocked in different degree. The research provided the theories basis for the design and on-line monitor in large generator stator cooling system. Index Terms--cooling, hydrodynamics, temperature

II.

THE THERMAL NETWORK MODEL OF STATOR

I. INTRODUCTION

T

he reliability of large generator is importance to maintain the integrity of power supply plant. One of the most common failure mechanisms of turbo-generator stator winding is probably the long term operation of the insulation at relatively high operating temperature. The high temperature mostly comes from deterioration of the cooling system (from blockage of the cooling ducts or fouling of the heat exchangers) which normally just requires cleaning to reverse. The methods of early detection of stator winding overheating due to hollow strand blockages in the winding bars were developed and implemented. Most methods of early blockage and leakage detection in a water cooled stator winding require special measuring devices [1]. The bars are measured with standard thermal resistors (RTD) applied to the insulation mainly under the slot wedges .In some very large generators (1000-1200MW) RTDs in the bottom bars are applied to the side face [2]. Less paper study the waterway blocked from theories and then it is applied to generator design and operation. This paper applied the thermal network method to solve the stator temperature field of generator when the water cooling bar was blocked in different degree. And analyzed the different blockage would lead different temperature in the generator stator. For accurate calculations, we put forward the concept of the block coefficient for the water cooling stator and discussed the effect of connection in the block coefficient and the temperature rise applied heat transfer theory and hydromechanics and electromagnetism. This research provided the theories basis for large generator design and on-

The thermal network method is very useful to analyze the model like Turbo-generators [3]. The temperature of each node can be calculated from the relation of mass rate of coolant flow and power flow when the hollow bar was blocked in the stator. Heat does not flow simply from the higher-temperature to lower-temperature nodes because the cooling air moves with heat from a node to next node(s). Therefore the thermal network which contains the nodes represent the temperature of the stator under the function of moving air and cooling water and the control volume of the solid part of the generator which thermal structure is very complex. The temperature criterion value is based on the theory calculation results when the generators normally operate [4]. In this paper the non-symmetry 3D temperature field of stator water cooling bars blocks and the solved region contains three of a stator teeth distance along tangent direction, part from inner to outer circle of stator iron along radial direction, and the whole stator iron .because of the non-symmetry of cooling water temperature of stator bar along axial direction. The solved region is shown as in Fig.1 to calculation. In accordance with above physical mode and the heat transferring theory, the 3D temperature field model is deduced as following:

1, 2—central plane of stator tooth 4--inner circle surface of stator iron

3—outer circle surface of stator iron 5-- stator bar

Fig.1 The solved region of stator 3D temperature field of Turbo-generators
w wT w wT w wT ? (Ox )  (Oy )  (Oz )  q 0 ° wx wx wy wy wz wz ° wT ° On s2 0 ? wn ° wT ° On s3 Df (T Tf ) ° wn ?

(1)

This work was supported by fund of North China Electric Power University for scientific research of teacher with doctor degree.

978-1-4244-1622-6/08/$25.00 ?2007 IEEE
Authorized licensed use limited to: Harbin Institute of Technology. Downloaded on December 1, 2009 at 21:57 from IEEE Xplore. Restrictions apply.

Where

O x , O y and O z are respectively heat conductivity

In (4), (5) and (6), dT f is temperature difference of cooling fluid along

along x, y and z coordinate directions, T is solid temperature, q is heat source density inside solid, O n is heat conductivity along outer normal direction of adiabatic boundary surface S1, D f is coefficient of heat transfer of convective heat transfer boundary surface S2, T f is temperature of cooling fluid around convective heat transfer boundary surface S2, n is outer normal direction of boundary surface. In accordance with the heat equilibrium law, (1) is dispersed into (2). AT=Q (2)

dl , S f and l f are respectively the

section area and perimeter of fluid flowing, C f ,

Jf

and U f

are respectively specific heat volume, density and velocity of fluid. Solving the differential equation (6), (7) is obtained.
 k ? dl

T f (l )

e

?
0

l

(T f 0  ? kT e 0
0

l

? k ?dl

l

dl )

(7)

In which, A is coefficient matrix, T is temperature column vector and Q is right column vector. The elements of matrix A and Q are as in (3). n ? A ? G G G ii ij wi Hi ° ° j 1 ° (3) G A (i z j ) ? ij ij ° Q p G T G T ° i i wi wi Hi Hi ° ? In (3), GHi is heat conduction between solid and hydrogen,
GWi is heat conduction between solid and water, Gij is mutual

Supposing that length dl is enough small and neglecting variation of solid temperature T in length dl , (7) is simplified as following. (8) T f (l ) T  (T  T f 0 )e  kl For any a cooling channel, if serial number from entrance to outlet of cooling fluid is 1, 2, ……, i-1 , i, ……, m-1, m, and corresponding length of cooling channel is l1 , l 2 ,……,

li ,……, lm , the node temperature of cooling-water in stator
? ° ...... ° °  k .li (9) T fi Ti  (Ti  T f ,i 1 )e ? ° ...... ° T fm Tm  (Tm  T f , m 1 )e  klm ° ? Simultaneously solving (2) and (9), stator temperature field can be obtained.

bar is shown as in (9). T f 1 T1  (T1  T f 0 )e  k .l1

heat conduction between node i and node j, p i is loss of node i , Twi is water temperature of node i , T Hi is hydrogen temperature of node i . Stator bar is in-cooled by water, so heat transfer between stator bar and cooled water is convective that satisfy the third boundary condition. If obtaining solution of (1), the temperature T f of cooling fluid in the third boundary condition must be firstly known. In accordance with [5], the water temperature inside stator bars satisfies (4). wT wT (4) D f l f ? (T  T f )  C f J f ? U f ? S f f C f J f ? S f f wl wW Boundary condition of fluid temperature in entrance is as in (5). (5) T f ( 0) T f 0 When generator operates on steady state, so (4) and (5) are simplified as in (6). dT f ? k (T  T f ) ° dl ? ° T f (0) T f 0 ? D f lf In which, k C f J f ?U f ? S f
wT f wW 0 in (4),

III. THE WATER DYNAMIC ANALYSIS The paper takes the QFSN-220-2 water-hydrogenhydrogen-cooled turbo-generator for the calculation examples, the stator temperature field is studied when turbo-generators operating on steady state the stator cooling waterway is blocking. The water is a liquid cooling for stator winding of turbo-generator. The dynamic character of water will be changed when the hollow-section strand blocks. According to the knowledge of hydrodynamics, in parallel pipeline the mainly two axioms as following: 1) Parallel branch of the pipeline in the same energy loss, that is: hw1 hw 2 hw3 ...... hwn (10) Where hwi is the energy loss of the ith branch pipeline. All of the energy loss is calculated in a simple click pipe or series of pipeline, (10) is dispersed into (11). § · v2 § l1 · v2 § · v2 l l (11)  ? ] ? 1 ¨ D 2  ? ] ? 2 ...... ¨ D n  ? ] ? n ¨D Where Di is the fluid drag coefficient along the ith branch, ] i is the fluid local resistance coefficient along the ith branch, li is the length of the ith branch pipe, di is the diameter of the
?
1

(6)

d1

1

? 2g

?

2

d2

2

? 2g

?

n

dn

n

? 2g

Authorized licensed use limited to: Harbin Institute of Technology. Downloaded on December 1, 2009 at 21:57 from IEEE Xplore. Restrictions apply.

ith branch pipe, vi is the velocity of the fluid in the ith branch pipe, g is the gravitational acceleration. 2) The total flux of each branch is equivalent to parallel pipeline’s flux, that is: Vw Vw1  Vw 2  ......  Vwn (12) Where Vw is the total flux, Vwi is the ith branch’s flux. Or vS v1 S1  v2 S2  .......vn Sn (13) Where Si is the section of the ith branch pipe According to above axioms of hydromechanics the water flowing in waterway of the stator is researched on water-hydrogen-hydrogen-cooled turbo-generator. When hollow-section strand is blocking in part, speaking of stator winding's entire cooling aqueous system, is still the parallel pipeline. Regarding there is the part jamming in the hollowsection strand, its jamming part with not stopped up the part is the series connected pipeline. To simplify the analysis, assuming that only one strand is blocked in some hollow strands. Because of the other hollow-section strands have the same approximate size and the cooling water remains the same character. Therefore it can be simplified two parallel pipelines for water-cooled stator winding of the turbine generator. One is normal, the other one is a plug for the pipeline. The partial loss may be ignored in normal hollow strand, where fluid's energy loss only includes the fluid drag loss. So (11) is simplified to (14). (12) is simplified to (15). 2 v2 L v12 L v2 D1 D2  ] 2 2x (14) d1 2 g d2 2g 2g Where D1 is the fluid drag coefficient along normal hollowsection strand, d1 is the diameter of normal hollow-section strand, d 2 is the diameter of fault hollow-section strand, D2 is the fluid drag coefficient along fault hollow-section strand, ] 2 is the fluid local resistance coefficient along fault hollowsection strand, L is the length of the hollow-section strands. Vw nw  1 Vw1  Vw 2 (15) Where Vw1 is the flux in normal hollow-section strand,
nw is total hollow-section strand’s number, Vw 2 is the flux

Vw ? °Vw 2 2 § S · ° D2 L  ] 2 d ¨ ? ° ° ? S2 x ? (17) 1  nw  1 ? D1 L ° ° Vw  Vw 2 °Vw1 nw  1 ° ? According to Chinese factories’ practical experience [6], water-cooled stator hollow-section strands of generator D follows below formula. ? ? ? ? 1.12 ? D ? (18) ? 7.16  In § Re · ? ¨ 4 ?? ? ? 10 ? ? ? The blockage site follows the principles of pore plate what helps us to identify ] 2 in the blocked hollow-section
2

strand. The stator temperature rise analysis was taken into account the water cooling winding block degree. The authors define the blockage coefficient kd to describe the water dynamic character change according above analysis. The relationship between ] 2 and kd likes TABLE 1.
T ABLE 1

] 2 and kd
0.55 50.4

relationship

kd

0.7 309

0.6 87

0.4 11.3

0.3 4.37

0.2 1.55

]2

IV. THE CALCULATING RESULT AND ANALYSIS Take the QFSN-220-2 water-hydrogen-hydrogencooled turbo-generator for the calculation examples, the stator temperature field is studied when turbo-generators operating on steady state the stator cooling waterway is normal or block. The authors calculated the stator 3D temperature field using the blockage coefficient when the stator water cooling system was blocked in different degree. The solved region is shown as in Fig.1 and dispersed into 295524 nodes. The authors computed all the temperature of the bars in the solved region. In theory the stator temperature field distribution of steady-state generators is compared and analyzed when the cooling waterway is in normal or in different degree blockage. Calculation results are shown as in Fig.2-Fig.6. For contrast the different temperature of upper and lower bars of stator the upper and lower bars’ temperature is extended in axial direction length in Fig.2-Fig.6. Fig.7 gives the temperature of the blocking bar in different kd along axial direction.

in blocking hollow-section strand. In the jamming pipeline, along the pipeline direction, cooling fluid's current flux is unchanged, (16) is obtained. Vw 2 v2 S 2 v2 x S 2 x (16) Where v2 is the velocity of blocking hollow-section strand,
S 2 is the section of blocking hollow-section strand, v2 x is

the velocity of blocking post, S 2 x the section of blocking post. Simultaneously solving (14) and (15) and (16), Vw1 and
Vw 2 can be obtained.

Authorized licensed use limited to: Harbin Institute of Technology. Downloaded on December 1, 2009 at 21:57 from IEEE Xplore. Restrictions apply.

Fig.2

kd =0, Stator 3D temperature field of all stator strands

Fig.6

kd =0.7, Stator 3D temperature field of all stator strands.

Fig.3

kd =0.2, Stator 3D temperature field of all stator strands

Fig.7 the blocking hollow-section strand’s temperature in different k d

V.

CONCLUSION

Fig.4

kd =0.4, Stator 3D temperature field of all stator strands

According to hydromechanics’ knowledge, the blockage spot is regarded as the pore plate principle to determine the speed and the flux of each hollow-section strand after the stator waterway plug. The view point has been applied in the temperature field computation, and then the reasonable result has been obtained. By contrast theoretically stator temperature when hollowsection strand blocking in different degrees, the heat transfer way in the stator is studied and the corresponding laws of the stator temperature field with hollow-section strand in different blockage coefficient is summed up. The results show the applied method is correct and effective in this paper. VI. REFERENCES
[1] V. Poljakov, "Complex diagnostic test of large turbine generators," Eberktricheskie Stantsii [Electric Power Plants], No 3., 1994.[in Russian] V. Poljakov, and V. Tsvetkov, "Methods of stator winding on-line diagnostics for large turbo generator preventive maintenance, " IEEE Trans. On Energy Conversion, Dec. 1999,vol. 14, pp. 1646-1650. C. B. Lu and L. J. Miao, Method of Analyzing the Temperature Field in Water-cooled Stator of Hydro generator" (in Chinese), Large Electric AMachine and Hydraulic Turbine, Nov., 2000, no.6, pp.1-4 Li Heming and Li Junqing, “Analysis and Calculation of Turbogenerators Stator Temperature Field on Cooling Circuit Blocked,” (in Chinese), Proceedings of the CSEE, 2005, vol.25, no.21, pp.163-168 Li Junqing and Li Heming, “A Thermo Hydraulic Model for the Watercooled Stator Bars of Large Turbo-generators on Varying Load” (in Chinese), Proceedings of the CSEE, 2007, vol.27, no.9, pp.87-91

[2]

[3]

[4] Fig.5

kd =0.55, Stator 3D temperature field of all stator strands
[5]

The calculating stator 3D temperature field distributing is reasonable which shows the proposed model and the block coefficient to be feasible

Authorized licensed use limited to: Harbin Institute of Technology. Downloaded on December 1, 2009 at 21:57 from IEEE Xplore. Restrictions apply.


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