3_dimensional Calculation of the Magnetic Field in the End Hydrdogenerators

3D calculation of de magnetic Field
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  3-Dimensional Calculationofthe MagneticField intheEndRegionofHydrogenerators at Various Steady-StateOperation Conditions By: G.Traxler-Samek, A.Schwery, D.Taghezout Power Hydro Turbines  3-Dimensional Calculation of the Magnetic Field in theEnd Region of Hydrogenerators at Various Steady-StateOperation Conditions Georg Traxler-Samek, Alexander Schwery 1 and Daho Taghezout 21 ALSTOM (Switzerland) Ltd., CH–5242 Birr, Switzerland, 2 applied magnetics, CH–1110 Morges, Switzerland, 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 statorcore. 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  =  uu s x d · sin ϑ  +  u 2 2  ·   1 x d −  1 x q  · sin2 ϑ .  (1)  p  (pu) is the active power output,  u  (pu) the statorwinding voltage,  u s  (pu) the synchronous voltage,  x d and  x q  are the synchronous reactances in the  d - and q  -axes of the machine and  ϑ  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 and2. The maximum stator winding current in order toavoid inadmissible overtemperatures.3. The safety distance to the stability limit (maximumrotor displacement angle  ϑ 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 isstrongly influenced by the phase angle  ϕ  and the ro-tor displacement angle  ϑ . 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 powerlosses and therefore high local temperature rises (hotspots) [5].
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