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Novel approach to calculate electrical currents in stator-, field- and damper-windings at three-phase sudden short-circuit for large synchronous generators

Neuartiger Ansatz zur Berechnung der elektrischen Ströme in der Ständer-, Erreger- und Dämpferwicklung beim dreiphasigen Stoßkurzschlusstest für große Turbogeneratoren

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Abstract

In this manuscript the novel methodology of quick and accurate calculation of the rotor and stator currents during a three-phase sudden short-circuit is presented. The proposed approach consists of two parts. First, the detailed finite element model is developed. It accounts for stator core and winding, rotor yoke and winding, damper winding and conductive rotor surface. Second, the revised analytical formulation of the existing approaches to evaluate transient field current behavior during a three-phase sudden short-circuit is presented. Four phenomenological coefficients are introduced for proper representation of the field winding current. The developed methodology is feasible for solid and laminated rotors, with and without damper bars. It is demonstrated that there is good agreement between the results of our theoretical approach and the factory tests.

Zusammenfassung

Dieser Beitrag stellt eine mögliche Methodik vor, welche die Läufer- und Ständerströme im dreiphasigen Stoßkurzschluss von Turbogeneratoren großer Leistung bestimmt. Als erstes wird ein Finite-Elemente-Modell präsentiert, welches das Ständerblechpaket, die Ständerwicklung, das Rotorjoch, die Rotorwicklung und den Dämpferkreis abbildet. Im nächsten Schritt wird eine analytische Gleichung vorgestellt, die den Rotorstromverlauf mittels vier Koeffizienten beschreibt. Die analytische Gleichung kann die zeitveränderlichen Ströme im dreiphasigen Stoßkurzschluss für massive und geblechte Rotoren sowie mit und ohne Dämpferkreis beschreiben. Die analytische Gleichung wurde von den Ergebnissen des Finite-Elemente-Modells abgeleitet. Das Finite-Elemente-Modell und die analytische Beschreibung zeigen gute Übereinstimmung mit den im Prüffeldprobelauf gemessenen Strömen.

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Abbreviations

3P-SSC:

Three-phase sudden short-circuit

\(f\) :

Frequency

FEA:

Finite element analysis

\(i_{f}\) :

Field current

\(i_{s}\) :

Stator current

\(K_{0}, K_{1}, K_{2}, K_{3}\) :

Coefficients for analytical description of rotor currents

\(l_{S}\) :

Length of stator end winding

\(L_{m}\) :

Mutual damper wedge and self-inductance

\(L_{S}\), \(X_{S}\) :

Stator winding leakage inductance/reactance

\(R_{1}, R_{2}, \ldots\) :

Wedge to retaining ring contact resistors

\(R_{a}, R_{b}, \ldots\) :

Axial wedge resistance

\(R_{K}\) :

Damper winding contact resistance

\(R_{A}\) :

Armature resistance

\(R_{f}\) :

Field winding resistance

\(T_{a}\) :

Armature time constant

\(T_{\mathit{dO}}\) :

Transient time constant when rotor surface is conductive

\(T_{d}^{''}\) :

Sub-transient time constant

\(T_{d} '\) :

Transient time constant

\(u_{\mathit{fd}}\) :

Field winding voltage

\(U_{L ( a )}\) :

RMS stator voltage in phase (a)

\(X_{d}\) :

Synchronous reactance

\(X_{d} '\) :

Transient reactance in d-axis

\(X_{d}^{''}\) :

Sub-transient in d-axis direction

\(X_{q}^{''}\) :

Sub-transient reactance in q-axis direction

\(X_{H}\) :

2D Finite element straight part main reactance (excluding end zone leakage, but include stator slot leakage)

\(X_{f}\) :

2D Finite element rotor reactance (excluding end zone leakage)

\(\lambda_{S}\) :

Permeance factor for end winding leakage reactance

\(\vartheta_{0}\) :

Phase angle (0°, \(+120\)°, −120°)

\(w\) :

Number of stator winding turns in series for voltage induction

\(\omega =2\pi f\) :

Angular frequency

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Acknowledgement

The author would like to thank ANSYS-Germany for sponsoring ANSYS EM Licenses for the work presented in this document. Also, the advice of Prof. Dr. Ponick of the Institute for Drive Systems and Power Electronics (IAL) Hanover has been influential in guiding this work.

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Authors and Affiliations

  1. Power and Gas Division, Large Gas Turbines, Generators, Siemens AG, Werner v. Siemens Straße 1, 99085, Erfurt, Deutschland

    Michael Hackbart

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  1. Michael Hackbart
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Correspondence to Michael Hackbart.

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Hackbart, M. Novel approach to calculate electrical currents in stator-, field- and damper-windings at three-phase sudden short-circuit for large synchronous generators. Elektrotech. Inftech. 133, 112–120 (2016). https://doi.org/10.1007/s00502-016-0389-7

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