Synchronous machines parameters determination using finite elements method C. Ramirez, M. Tu Xuan, J.-J. Simond
D. Schafer, Dr C.-E. Stephan
Swiss Federal Institute of Technology Electromechanics and Electrical Machines Laboratory (LEME) CH-1015 Lausanne, Switzerland Tel: +41 21 693 46 90 Fax: +41 21 693 26 87 E-mail:
[email protected]
Alstom Power Generation Ltd R&D / Technology Director CH-5242 Birr, Switzerland Tel: +41 56 466 50 46 Fax: +41 56 466 60 95 E-mail:
[email protected]
ABSTRACT The paper deals with the determination of synchronous machine parameters using a 2D Finite Element Method – FEM (Flux2DCedrat). Simulations of no-load sudden three phase shortcircuits are performed in rotation, the saturation effects and the eddy currents in the rotor solid iron parts are also taken into account. Comparisons between calculations and measurements for two large existing units (turbogenerator & hydrogenerator) are presented. Keywords: Synchronous elements, short-circuit. 1.
machines,
parameters,
finite
INTRODUCTION
The analysis of large power synchronous machines behaviour in steady state or transient conditions requires an accurate knowledge of the equivalent circuit diagram parameters and/or of the characteristic quantities of the machine. These characteristic quantities can be determined through the analysis of the results obtained by different tests, i.e. the no-load sudden three phase short-circuit [1,2]. These tests, however, require an important and expensive equipment. They are not devoid of any risk and cannot be performed up to the material limits. The basic idea of this study is to replace different tests performed by the manufacturer, either on a test platform or on site, through digital simulations using the finite elements method. In other words, a digital test platform replaces the conventional test platform. This paper focuses on the no-load sudden three phase short-circuit test. The standstill tests as well as other special tests will be described in later issues. Figure 1 shows the general approach of this digital test platform in order to determine the equivalent circuits and the characteristic quantities by 2D FEM field calculations. This approach cannot only be used for the verification of the contractual values of the important characteristic quantities of an existing machine, but also for the design optimisation of a new machine [3]. 2.
partial automatic mesh generation, sliding air gap band for calculations in rotation, or external coupled circuits. Due to the fact that a 2D FEM calculation is used, it is necessary to take into account the end-winding leakages through an adequate definition of the external coupled circuits, as defined in Figure 5. The mesh generation in Figure 4 is also a cardinal point of the whole procedure; it has to be carefully performed, especially for machines with solid iron rotor. The post-processing stage contains the analysis of the FEM calculations results; it leads to the characteristic quantities and to the equivalent circuits of the machine. Finally, it is possible to check the results precision with a reverse digital simulation of the same test using the above equivalent circuits. Figure 10 shows the good concordance between the initial 2D FEM calculations results and those coming from the reverse-check digital simulation.
Preprocessing
2D FEM calculation
Fig. 1: Digital test platform simplified structure. Physical properties B
H
Geometry
Command files
Coupled circuit
DIGITAL TEST PLATFORM STRUCTURE
The pre-processing stage consists in preparing data for the FEM calculations. Based on the detailed knowledge of the geometry and physical properties of the machine’s electrical and magnetic circuits, command files are generated as shown in Figure 2. This first stage is done automatically in order to offer an efficient and user-friendly simulation tool. In a second stage, 2D FEM field calculations are performed using Flux 2D. This program is suitable for this kind of applications. It offers a lot of useful features like especially
Post processing
Fig. 2: Pre-processing steps.
Calculation
Parameters identification
Results file
Calculation ia
log
t
t
Equivalent diagram id
ud
Comparison
rs
xσs
xσDf2
xσDf1
x σf
xσD2
x σD1
rD2
rD
rf
if
uf
xda 1
Simsen calculation ia t
Fig. 5: Coupled circuits (hydrogenerator). Fig. 3: Post-processing steps. 3.
APPLICATIONS EXAMPLES
In the following, the results concerning two large existing synchronous machines are presented. The rated values of these machines are summarized in Table 1. Table 1: Machines characteristics. Values Rated power Sn (MVA) Rated voltage Un (kV) Power factor cos φ Pole number Rated frequency f n (Hz)
hydro 32.6 10.5 0.92 76 50
turbo 187.5 13.2 0.80 2 50
According to the previous section, the three stages of the whole procedure have to be performed. Figure 4 illustrates the mesh generation in the case of the hydrogenerator and Figure 5 represents the external coupled circuits. In Figure 6, the field distribution some ms after the no-load sudden three phase short-circuit of the turbogenerator are shown.
Fig. 6: Field distribution (turbogenerator).
4.
RESULTS
Figures 7 and 8 give, for the hydrogenerator, the simulated stator and rotor short-circuit currents during a no-load sudden three phase short-circuit at nominal voltage.
Fig. 4: FEM calculations mesh (hydrogenerator).
Fig. 7: Calculated short-circuit stator currents.
Simulated: u (pu) xd (pu)
0.3 1
1 0.905
x'd (pu)
0.4009
0.3595
0.2777
0.2403
1.2914
1.1002
0.03359
0.02988
'' d
x (pu) ' d
T (s) '' d
T (s)
Fig.8: Calculated short-circuit field current. The analysis of these short-circuit currents based on [1] is represented in Figure 9; it leads to the characteristic quantities given in Tables 2, which can be compared with the corresponding values measured during a real test factory. The concordance is excellent for the reactances. The differences between calculated and measured values of time constants are not alarming. They are due to the temperature effect on the winding resistances. For the simulation, these resistances were calculated at 75oC. The windings test temperatures are not precisely known. In Tables 2, the results analysis is shown and confirms that the saturation effects are properly taken into account.
With respect to the rotor construction of a turbogenerator, a physically correct model must have three rotor circuits in the direct axis [2] representing the field circuit, the damper winding and the solid iron and not only two as for a hydrogenerator with a laminated rotor. Nevertheless, the parameters identification has been performed in two cases, for two and for three rotor circuits using, once again, the FEM simulation results and the measurement results of the manufacturer. Tables 3 shows all the results for the identifications with two or three rotor circuits. Concerning the reactances, the concordance is once again excellent. The slight increase of the xd’ values with the test voltage is physically impossible even if it stays within an acceptable tolerance range. The differences between the calculated and measured time constants are probably due to the mesh dimension at the rotor surface in comparison with the depth of penetration into the solid iron. This important point still needs to be improved in order to define the optimal mesh dimension, without spending too much computer time. This investigation is in progress at the Swiss Federal Institute of Technology. Tables 3 : Results for the turbogenerator a) identification with two rotor circuits: Measured: u (pu) xd (pu)
0.20 2.15
0.35 2.15
0.50 2.15
0.70 2.085
x'd (pu)
0.260
0.254
0.250
0.257
'' d
0.215
0.196
0.187
0.179
' d
1.415
1.327
1.298
1.299
'' d
0.160
0.094
0.090
0.151
u (pu) xd (pu)
0.25 2.15
1 2.09
x'd (pu)
x (pu) T (s)
Fig. 9: Automatic parameters identification for shortcircuit currents. Tables 2: Results for the hydrogenerator Measured: u (pu) xd (pu)
0.15 1
0.3 1
0.5 1
x'd (pu)
0.4056
0.4051
0.3777
x'd' (pu)
0.2738
0.2722
0.2550
Td' (s)
1.6504
1.5838
1.3897
0.03397
0.03172
0.02724
'' d
T (s)
T (s) Simulated:
0.232
0.246
'' d
0.190
0.154
' d
1.519
1.606
'' d
0.109
0.191
x (pu) T (s) T (s)
b) identification with three rotor circuits.
consequently to suppress important costs and different risks. This method is evidently also a supplementary tool useful for the design optimization of new machines.
Measured: u (pu) xd (pu)
0.20 2.15
0.35 2.15
0.50 2.15
0.70 2.085
x'd (pu)
0.260
0.254
0.250
0.257
x'd' (pu)
0.228
0.222
0.219
0.200
x
'' ' d
0.180
0.170
0.162
0.141
' d
(pu)
1.415
1.327
1.298
1.299
'' d
0.224
0.185
0.209
0.214
' '' d
0.0224
0.0234
0.0258
0.0240
u (pu) xd (pu)
0.25 2.15
1 2.084
x'd (pu)
T (s) T (s) T (s) Simulated:
0.232
0.246
'' d
0.220
0.178
'' ' d
0.186
0.145
' d
1.519
1.606
'' d
T (s)
0.296
0.258
Td' '' (s)
0.0725
0.0764
x (pu) x (pu) T (s)
Finally, Figure 10 shows the results of the reverse-check digital simulation compared to those of the initial 2D FEM calculation in the case of the hydrogenerator.
Fig. 10: Reverse-check digital simulation (phase current ia (A)) 4.
CONCLUSIONS
A method based on a FEM calculation for the determination of large synchronous machines characteristic quantities has been proposed and tested. The simulations performed for some noload sudden three phase short-circuits at different voltage levels lead to results which show an excellent concordance with the measurements in the case of a large hydrogenerator with a laminated rotor. In the case of a turbogenerator, the obtained precision for the time constants is not yet satisfactory. These differences are probably due to the not optimal dimension of the mesh at the solid rotor surface. The improvement of this aspect is in progress. The proposed method should allow to replace a part of the tests performed by manufacturers on a test-platform and
REFERENCES [1]
“Methods for determining synchronous machine quantities from tests”, IEC Standard 34-4 Rotating Electrical Machines. Part 4. 1985
[2]
I.M. CANAY: “Modelling of Alternating-Current Machines Having Multiple Rotor Circuits”. IEEE Transactions on Energy Conversion, Vol. 8, No2, June 1993.
[3]
M. TU XUAN, C. RAMIREZ, B. KAWKABANI and J.-J. SIMOND: “Automatic determination of laminated salient-pole synchronous machines parameters based on the finite element method”. Proceedings of the 6th international conference electrimacs 99, Lisboa, Portugal, September 14-16 1999, pp. 105-109.
