ELEKTRYKA 2009 Zeszyt 2 (210) Rok LV Sebastian BERHAUSEN, Andrzej BOBOŃ, Stefan PASZEK Instytut Elektrotechniki i Informatyki, Politechnika Śląska w Gliwicach SYNCHRONOUS GENERATOR FIELD-CIRCUIT MODEL AND ITS VERIFICATION BY MEASUREMENTS Summary. A two-dimensional field-circuit model of a large power synchronous generator is presented in the paper. It allows determining electromagnetic waveforms in steady and transient states. Calculations were carried out using the measured waveforms of a TWW-200-2 type generator installed in the power plant Połaniec when subjected to a disturbance in the voltage regulator. The measured waveform of the field voltage under no load and at constant rotor speed was assumed to be the generator computational model input signal. The circuit model was verified on the basis of comparison of the measured and calculated stator voltage waveforms. The calculations were carried out by means of the finite element method using the program Maxwell 2D by Ansoft Corporation. Keywords: large power synchronous generator, two-dimensional field-circuit model, finie element metod, measurement WERYFIKACJA POLOWO-OBWODOWEGO MODELU GENERATORA SYNCHRONICZNEGO NA PODSTAWIE ZMIERZONYCH PRZEBIEGÓW NIEUSTALONYCH Streszczenie. W pracy przedstawiono dwuwymiarowy, polowo-obwodowy model generatora synchronicznego dużej mocy, umożliwiający wyznaczanie przebiegów wielkości elektromagnetycznych w stanach ustalonych i nieustalonych. Obliczenia przeprowadzono na podstawie zmierzonych przebiegów po zakłóceniu w układzie regulacji napięcia generatora typu TWW-200-2 pracującego w Elektrowni Połaniec. Weryfikację modelu przeprowadzono opierając się na porównaniu zmierzonego i obliczonego napięcia stojana. Obliczenia wykonano metodą elementów skończonych przy użyciu programu Maxwell firmy Ansoft. Słowa kluczowe: generator synchroniczny dużej mocy, dwuwymiarowy polowo-obwodowy model, metoda element ow skończonych, pomiar 1. INTRODUCTION It is thought nowadays that the field-circuit modelling of synchronous generators is one of the most accurate computation methods since it allows taking into account essential
24 S. Berhausen, A. Boboń, S. Paszek electromagnetic and electromechanical phenomena as well as factors determining machine properties [1], such as: nonlinearity of magnetic core magnetizing characteristics, action of eddy currents in conducting elements of the rotor, the rotor motion. The main factor limiting the application of field-circuit models to power system simulation is long computation time and necessity of using high-power computers. However, these models are used more and more often for determining the parameters of synchronous machine circuit models. Fieldcircuit computations can be carried out at the stage of machine design. They can also imitate measuring tests sometimes very difficult to realise under generator operating conditions. The aim of this paper is to verify the field-circuit computation basing on measurements of the waveforms in transient states taken in Power Plant Połaniec. 2. SYNCHRONOUS GENERATOR COMPUTIONAL MODEL IN MAXWELL PROGRAM Field-circuit computations were carried out in Transient solver of Maxwell-2D program for a synchronous, cylindrical, high-power generator of the rating: SN = 235,5 MVA, PN = 200 MW, UN = 15,75 kv, IN = 8625 A, Ifn = 2680 A, cosφn = 0,85. The following assumptions were taken when creating the computational model [2],[3]: two-dimensional distribution of the electromagnetic field in the generator cross-section, nonlinear magnetizing characteristics of the stator and rotor cores, constant rotor speed, skin effect in the stator and rotor windings was neglected, eddy currents in the rotor iron were neglected, eddy currents induced in the solid block and slot wedges of the rotor were taken into account. Due to the repeatability of the magnetic field distribution under each pole, there was assumed the machine cross-section containing one pole pitch for computations [4]. The generator computational model cross-section under consideration was discretized triangular finite elements of the second order. The zero Dirichlet boundary condition for the magnetic vector potential was assumed on the stator outer surface. On two other edges Г2 and Г3 being distant by one pole pitch there were assumed the conditions of negative potential periodicity [4]: 2 3 into A A. (1) The excitation circuit winding impedance was increased by the leakage inductance of the end windings which was not included in the two-dimensional model. Its value was determined basing on the design formula [6]: Lσcf =0,034 p.u. In order to take into account the rotor motion, there was created the slip line separating the stationary areas from the movable machine elements.
Synchronous generator field 25 In computations of the transient state there was assumed the constant step of integrating the equations in the time domain Δt =0,0002 s. Fig. 1 shows the computational model and finite element mesh consisting of 40684 triangular elements. Г1 Г2 Fig. 1. Finite element mesh of the computational model Rys. 1. Siatka elementów skończonych modelu obliczeniowego Г3 3. METHODOLOGY OF MEASUREMENTS AND COMPUTATION RESULTS The investigated TWW-200-2 generator, installed in Power Plant Połaniec, is equipped with a static excitation system whose thyristor rectifier is fed from an excitation transformer. The no-load test was performed at the constant rotor speed n = 3000 rot/min. The disturbance in the form of a step change in the signal given in a voltage regulator started the transient state during which the excitation and generator stator voltage waveforms were recorded. They are shown in Fig. 3. The given voltage step applied to the voltage regulator was equal to 10 %. Since the waveforms contained the noise, the generator excitation voltage waveform was filtered. In order to eliminate delays caused by use of the filter, the filtration with a zero phase was applied [5]. The signal after filtration was used as an input signal in the field-circuit computational model. Fig. 3 presents the comparison of the computed and measured waveform of the generator stator voltage. a) b) u f [s] 350 300 250 200 150 100 50 0 0 2 4 6 8 10 12 U [V] 1.6 x 104 1.55 1.5 1.45 1.4 1.35 1.3 0 2 4 6 8 10 12 Fig. 2. Measured waveforms of the excitation (a) and generator stator (b) voltage Rys. 2. Zmierzone przebiegi napięcia wzbudzenia (a) stojana generatora (b)
26 S. Berhausen, A. Boboń, S. Paszek 1.6 x 104 1.55 MEASUREMENT 1.5 U [V] 1.45 FEM 1.4 1.35 1.3 2 4 6 8 10 12 Fig. 3. Comparison of the computed and measured TWW-200-2 generator stator voltage waveform Rys. 3. Porównanie obliczonego i zmierzonego przebiegu napięcia stojana generatora TWW-200-2 4. CONCLUDING REMARKS The phenomena in the machine in no-load and transient state are represented in the TWW-200-2 synchronous generator circuit-field model with a sufficient accuracy. Some differences (maximum percentage deviation is less than 2%) between the computation results and measured waveforms of the stator voltage (particularly evident in dynamic states) can result from different values of the electrical conductivities of the rotor solid block and slot wedges of the real machine and the computational model. These conductivities can change during long exploitation of the machine. Also the forging temperature can influence the presented factors since material parameters and measurement errors depend on it. The latter ones can reach several percent. ACKNOWLEDGMENTS The authors wish to express their gratitude to Ansoft Corp. for possibility of free using the program Maxwell for investigations. This work was partly financed by the Polish Ministry of Science and Higher Education from means of budget on science in years 2009-2012 as research project N N511 352137.
Synchronous generator field 27 BIBLIOGRAPHY 1. Arjona M.A.L.: Parameter calculation of a turbogenerator during an open-circuit transient excitation. IEEE Transaction on Energy Conversion, Vol.19, No.1, March 2004, p. 46-52. 2. Boboń A., Berhausen S.: Determination of synchronous machine parameters from FE simulations of sudden short-circuit transients. International Conference on Low Voltage Electrical Machines, Brno-Slapanice, 3-4 Nov. 2008. 3. Boboń A., Berhausen S.: Estimation of synchronous machine parameters using shortcircuit currents calculated by the finite element method. XVI International Symposium on Electric Machinery in Prague, ISEM'2008, 10-11 Sep. 2008, Prague, p.105-112. 4. Boboń A., Kudła J., Żywiec A.: Electromagnetic parameters of a synchronous machine, application of the finite element (in Polish). Proceedings of the Silesian Technical University ELEKTRYKA, Gliwice, Poland 1998. 5. Majka Ł., Paszek S.: Measurement-based model parameter estimation for electrical part of Rybnik Power Plant generating unit. Elektryka 2008, z. 2 2008, p. 67-78. 6. Turowski J. Electromagnetic calculations of machine engines and electrical apparatuses (in Polish), WNT, Warszawa 1982. Wpłynęło do Redakcji dnia 25 czerwca 2009 r. Recenzent: Prof. dr hab. inż. Ryszard Zajczyk Omówienie W pracy przedstawiono dwuwymiarowy, polowo-obwodowy model generatora synchronicznego dużej mocy, umożliwiający wyznaczanie przebiegów wielkości elektromagnetycznych w stanach ustalonych i nieustalonych. Przy tworzeniu modelu obliczeniowego przyjęto nieliniowe charakterystyki magnesowania rdzeni stojana i wirnika (rys. 1), stałą prędkość wirowania wirnika, uwzględniono prądy wirowe indukowane w litym bloku i klinach żłobkowych. Do obliczeń polowo-obwodowych przyjęto przekrój poprzeczny obejmujący jedną podziałkę biegunową, którego obszar przekroju poprzecznego i siatkę elementów skończonych przedstawiono na rys. 2. Obliczenia przeprowadzono na podstawie zmierzonych przebiegów (rys. 3) po zakłóceniu w układzie regulacji napięcia generatora typu TWW-200-2 pracującego w Elektrowni Połaniec. Weryfikację modelu obliczeniowego dokonano na podstawie porównania obliczonego i zmierzonego przebiegu napięcia stojana generatora (rys. 4)