3_dimensional Calculation of the Magnetic Field in the End Hydrdogenerators

8/12/2019 3_dimensional Calculation of the Magnetic Field in the End Hydrdogenerators

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3-Dimensional Calculation of the Magnetic

Field in the End Region of Hydrogenerators

at Various Steady-State Operation

Conditions

By: G. Traxler-Samek, A. Schwery, D. Taghezout

Power

Hydro Turbines


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3-Dimensional Calculation of the Magnetic Field in the

End Region of Hydrogenerators at Various Steady-State

Operation Conditions

Georg Traxler-Samek, Alexander Schwery1 and Daho Taghezout2

1 ALSTOM (Switzerland) Ltd., CH5242 Birr, Switzerland, [email protected]

2 applied magnetics, CH1110 Morges, Switzerland, [email protected]

Abstract Synchronous machines in hydro powerplants are able to consume or deliver reactive power.When changing from normal operation to an extremreactive operation (both over- and underexcited), themagnetic field in the end region of the machine changessignificantly. Consequently the design engineer mustbe able to check the magnetic field distribution on theclamping plates and the end laminations of the stator

core. An evaluation of these fields helps to avoid highlocal power losses and thus high local temperature rises(hot spots).

This paper presents a comparision of the mag-netic field distribution at different operation condi-tions computed by different calculation methods: 2DBoundary-Element method, 3D Biot-Savart and 3D-Finite-Element method. The purpose of the study isto validate the self developped calculation methods andto discuss their usability for decision making and inte-gration in design tools.

Keywords End Region, Magnetic Field, SynchronousMachine

I. Introduction

Generally hydro power plants are equipped withsalient pole synchronous machines (figure 1). Suchmachines are able to both consume or deliver reactivepower. At over-excited operation the machine deliversreactive power. Seen from the grid, the machine canbe seen as a capacitor. Whereas at under-excited op-eration reactive power is consumed, from the electrical

Fig. 1. Stator of a 778 MVA, 80-pole hydrogenerator

grid the machine is regarded as an inductor.

The full operation range of such a machine can beshown in the so-called power chart (Fig. 2). The powerchart is derived from the vector diagram of the salientpole synchronous machine and based on the powerequation

p= uus

xd sin +

u2

2

1

xd

1

xq

sin2 . (1)

p (pu) is the active power output, u (pu) the statorwinding voltage, us (pu) the synchronous voltage, xdand xq are the synchronous reactances in the d- andq-axes of the machine and is the rotor displacementangle.

The power diagram shows, that the active and re-active power of the machine are delimited due to thefollowing restrictions:

1. The maximum rotor excitation current and

2. The maximum stator winding current in order toavoid inadmissible overtemperatures.3. The safety distance to the stability limit (maximumrotor displacement angle max).4. The saftety distance to the reluctance circle.

All these conditions are usually kept by the control andregulation system of the power plant in order to avoidconsecutive faults due to overtemperatures or instabil-ity.

The superposition of the stator and rotor fieldsaccording to the vector diagram of the machine is

strongly influenced by the phase angle and the ro-tor displacement angle . When changing from ratedoperation to an extrem reactive operation, over- or un-derexcited, the vector diagram of the machine changessignificantly (Fig. 2). Consequently also the magneticfield distribution in the end region of the machinechanges.

When designing a machine for such an extreme rangeof operation, the design engineer must be able to checkthe magnetic field distribution in the stator windingoverhang [1], [8], [10] and especially on the clampingplates (figure 3) in order to avoid high local power

losses and therefore high local temperature rises (hotspots) [5].


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Fig. 8. 3-Dimensional Finite Element model of a 800 MVAhydrogenerator

and rotor by introducing an auxiliary air-gap conduc-

tor [3]. The pole winding ends are modelled with asurrogate pole winding conductor [11].

IV. 3D - Finite-Element Method

Nowadays the Finite-Element method is a state ofthe art method for electromagnetic field computations.It allows for a detailled modelling of all geometric ele-ments [7], [6] (see fig. 8). The disadvantage of a Finite-Element study is the big time consumtion of such acomputation.

All Finite-Elemente computations presented in this

paper are done with the help of a commercial Finite-Elemente software [4]. This software provides the pos-sibility for modelling the stator winding bars witha Biot-Savart formulation included into the three-dimensional solid Finte-Element model.

For the comparison of the magnetic field distributionat various operation conditions a magnetostatic Finite-Element computation is sufficient.

V. No-load Magnetic Field Calculation

The no-load magnetic field calculation was per-

formed at the rated stator winding voltage applyingthe no-load excitation current on the rotor winding.

The axial componente of the magnetic flux densityBz(r, 0) which is the componente perpendicular tothe clamping plate surface is computed on a radialline from the radial inner ri to the radial outer edgera of the clamping plate (fig. 9). The anglular position0, which is the tangential position on the circumfer-ence of the machine, is choosen in order to obtain themaximum values.

Figure 10 shows a comparison of the Boundary Ele-

ment, theBiot-Savart

and the Finite Element com-putations.

VI. Load magnetic field calculation

The 3D-Biot-Savart method and the Finite-Element method are used to calculate the magneticfield distribution on the stator clamping plates atserveral full load operation conditions (see power chart

in figure 2):

A. Over-excited operation with cos = 0.00B. Over-excited operation with cos = 0.75C. Operation with cos = 1.00D. Under-excited operation with cos = 0.75E. Under-excited operation with cos = 0.00

All examples are calculated with the rated apparentoutput 778 MVA i.e. rated stator current. The exci-tation currents in the rotor winding are obtained fromthe electrical calculation of the machine (performedfor each of the operation points) and correspond tothe given power factors. The rotor is set into the rightposition relative to the stator winding axis accordingto the vector diagram.

For all given operation points, the axial componentof the magnetic flux density Bz on the clamping platesurface is computed (fig. 9). The results are shown infigures 1115.

VII. Disussion of Results

The comparison between the Finite-Element and theBiot-Savart computations at no-load and full load

for different power factors (operation points AE) leadto the following conclusions:

1. The noload simulation shows a good accordancebetween the 3D Finite-Element and the 2D Boundary-Element method. In contrast to this theBiot-Savartmethod is too pessimistic due to the fact that the influ-ence of the rotor excitation on the resulting magneticfield is overestimated in the Biot-Savart model.

2. The distribution of the magnetic flux density calcu-

Fig. 9. Calculation of the radial distribution of the axial com-ponent of the magnetic flux density on the clamping plates


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Fig. 10. Magnetic field distribution on the stator clampingplates at no-load conditions, calculated with three different com-putation methods

Fig. 11. Magnetic field distribution on the stator clampingplates at rated power load, cos = 0.00 over-excited, calculatedwith two computation methods

Fig. 12. Magnetic field distribution on the stator clampingplates at rated power load, cos = 0.75 over-excited, calculatedwith two computation methods

Fig. 13. Magnetic field distribution on the stator clampingplates at rated power load, cos = 1.00, calculated with twocomputation methods

Fig. 14. Magnetic field distribution on the stator clampingplates at rated power load, cos = 0.75 under-excited, calcu-lated with two computation methods

Fig. 15. Magnetic field distribution on the stator clampingplates at rated power load, cos = 0.00 under-excited, calcu-lated with two computation methods


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lated from the Biot-Savartmethod results in a rela-tively flat curve. Contrarily the distribution computedwith Finite-Elements shows a concentration at the in-ner clamping plate edge. This can be explained withthe physical effect, that magnetic field lines are alwaysconcentrating close to edges. Unfortunately the Biot-

Savart calculation cannot consider the exact geome-try including the clamping plate edges.

3. For under-excited operation, the Biot-Savartcomputation calculates too low magnetic flux densi-ties, the influence of the stator winding armature re-action on the resulting magnetic field is always under-estimated.

VIII. Conclusion

The Finite-Element and the much simpler Boundary-Element computation at no-load condition show a goodaccordance.

A comparison of the Finite-Element and the Biot-Savartcomputations shows the following: The Biot-Savartmethod overestimates the influence of the ex-citation current on the resulting magnetic field andunderestimates the influence of the stator winding ar-mature reaction. Therefore the magnetic flux densitycomputed with the Biot-Savart method at under-excited operation conditions is too low.

Especially when it comes to loss calculation theBiot-Savartmethod can not deliver reliable results.

Nevertheless, knowing these limitations, this methodcan be used to decide in a particular case whetherit is necessary to make resource intensive 3D Finite-Element computations.

References

[1] Althammer, P.: Berechnung des magnetischen Feldes inden Wickelkopfen von Turbogeneratoren, Brown BoveriMitteilungen Mai 1964, p. 281292.

[2] Brebbia, C., A.; Dominguez, J.: Boundary Elements -An Introductory Course. WITPress, Southampton (UK),1992.

[3] Carpenter, C.J.: The application of the method of im-ages to machine end-winding fields. Proc. IEE, Vol. 107

A, 1960, p. 487500.[4] Cedrat, Finite-Element Software Flux3D, www.cedrat.com.[5] Choi, S., S.; Jia, X. M.: Under Excitation Limiter and Its

Role in Preventing Excessive Synchronous Generator StatorEnd-Core Heating. IEEE Transactions on Power Systems,Vol. 15, No. 1, February 2000.

[6] Fujita, M.; Tokumasu, T.; Yoda, H.; Tsuda, H.; Ito, K.;Nagano, S.: Magnetic Field Analysis of Stator Core EndRegion of Large Turbogenerators. IEEE Transactions onMagnetics, Vol. 36, No. 4, July 2000.

[7] Holmberg, M.T.: Three-dimensional Finite Element Com-putation of Eddy Currents in Synchronous Machines.Technical Report No. 350, Department of Electric PowerEngineering, Chalmers University of Technology, Goteborg,Sweden, 1998.

[8] Kant, M.: Etude du champ magnetique de la par-

tie frontale dun turbo-alternateur, Revue Generale delElectricite, Juillet-aout 1966, p. 913922.

[9] Krajewski, W.: Computation of the turbogenerator end-region field using the BEM. Archiv fur Elektrotechnik, Vol.75 (1992), p. 173178.

[10] Sikora, R.; Gawrylczyk, K.M.; Gramz, M.; Gratkowski, S.;Ziolkowski, M.: Magnetic field computation in the end-region of electric machines using various boundary condi-tions on iron surfaces, IEEE Transactions on Magnetics,Vol. 22, No. 3, May 1986, p. 204207.

[11] Traxler-Samek, G.: Zusatzverluste im Stirnraum vonHydrogeneratoren mit Roebelstabwicklung. Dissertation,TU-Wien, 2003.

[12] Traxler-Samek, G.; Schmidt, E.: Analytic Determinationof Eddy Current Losses in the Stator Clamping Platesof Salient Pole Synchronous Generators. Proceedings ofthe 15th International Conference on Electrical Machines,ICEM, Bruges (Belgium), 2002.

[13] Traxler-Samek, G.; Schwery, A.: Optimised Calculationof Losses in Large Hydrogenerators using Statistical Meth-ods. Proceedings of the 16th International Conference onElectrical Machines, ICEM, Krakow (Poland), 2004.


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ALSTOM Power Hydro Generator Technology Centre CH-5242 Birr - Switzerland

Phone: +41 56 466 66 11 Fax: +41 56 466 69 83 www.alstom.com

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3_dimensional Calculation of the Magnetic Field in the End Hydrdogenerators

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