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Abstract-- This paper deals with the determination of large synchronous machine characteristic quantities using an extended 2D - finite element method and based on the knowledge of the geometry and of the physical properties of the electrical and magnetic circuits of the machine.
In this respect sudden no-load three phase short-circuits and short-circuits in the quadrature axis under load conditions at cosϕ = 0 are simulated in rotation using a numerical, virtual test platform. The saturation effect, the eddy currents in the damper circuit and in the rotor solid iron parts are taken into account. The results of these two tests lead to all characteristic quantities in both axis of the machine.
Other tests can be performed on this numerical test platform (standstill frequency response, DC decay, low speed, symmetrical and asymmetrical load tests), which can also be used as a design optimization tool.
Comparisons between calculations and measurements for three large existing units (turbo-generators & hydro-generators) are presented.
Index Terms--Large synchronous machines, test, modeling,
simulation, characteristic quantities
I. INTRODUCTION
Today’s market conditions push the large electrical machines manufacturers to optimize very carefully their designs in order to limit the production costs without reducing neither the performances nor the reliability. It is therefore no more possible to remain competitive using the classical analytical design methods which cannot take into account the non-linearities (saturation, eddy currents) accurately enough. Better design tools as well as more efficient test procedures have become absolutely necessary.
------------------------------------------------------------------------ This paper results from a research collaboration project between EPFL (Swiss Federal Institute of Technology, Lausanne) and Alstom Switzerland Ltd in the scope of the Ph.D study of C. Ramirez at the Laboratory for Electrical Machines of the EPFL. This project has been funded by Alstom Switzerland Ltd and the Swiss Innovation Promotion Agency. Jean-Jacques Simond is full professor and head of the Laboratory for Electrical Machines of the EPFL, CH – 1015 Ecublens. [email protected] Carlos Ramirez is working for Alstom Power (Switzerland) as R&D engineer within the Hydrogenerators Technology Center in CH – 5242 Birr. [email protected] Mai Tu Xuan is senior researcher and lecturer at the Laboratory for Electrical Machines of the EPFL, Ch -1015 Ecublens. [email protected] Carl-Ernst Stephan is working for Alstom Power (Switzerland) , he is head of the Insulation Competence Center in CH – 5242 Birr. [email protected]
The most convincing example is given by the subtransient reactances which determine the maximum transient current and torque values during a strong fault (short-circuits, out-of-phase synchronization). A precise knowledge of these saturation depending reactances is not only indispensable for an optimum design of the shaft and of the stator end-windings, it has also a strong influence on the manufacturing costs.
Different tests can be performed on the manufacturers test shop or on site in order to check the characteristic quantities of a large synchronous machine (transient, sub-transient reactances and time constants). These tests have a lot of drawbacks: they are very expensive, not devoid of any risk and they cannot be performed up to the material limits.
The basic idea of this study is to replace different tests performed by the manufacturer (sudden no-load short-circuit -, standstill frequency response -, DC decay -, low speed -, slip test), either on a test platform or on site, with numerical simulations using an extended 2D - finite element method. The proposed numerical test platform [1] requires only the knowledge of the geometry and of the physical properties of the electrical and magnetic circuits of the machine. It can be used either for testing an existing machine without any limitations and risks or for the design optimization of a new machine.
This paper focuses on the sudden no-load three phase short-circuit test and on the short-circuit test in the quadrature axis under load conditions at cos φ = 0. The results of these two tests lead to all characteristic quantities in both axis of the machine.
The characteristic quantities obtained on the numerical test platform can be introduced afterwards into a simulation program, e.g. [2], for the prediction of the dynamic behaviour under transient conditions (short-circuit under load operation, out-of-phase synchronization, fault clearing, stability analysis). One has to guarantee that the saturation levels of the leakage paths remain the same during the preliminary tests and the subsequent simulations in order to have the correct values for the leakage reactances of the different electrical circuits of the machine and therefore the correct values for the sub-transient reactances.
II. NUMERICAL TEST PLATFORM STRUCTURE
The structure of the numerical test platform is shown in
A Numerical Test Platform for Large Synchronous Machines also useful as a Design
Optimization Tool
J.-J. Simond Member IEEE; C. Ramirez; M. Tu Xuan; C.-E. Stephan
1-4244-0493-2/06/$20.00 ©2006 IEEE.
Fig. 1, it is divided into three stages.
Fig. 1: Digital test platform simplified 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 machines electrical and magnetic circuits, command files are generated as shown in Fig. 2. This first stage is done automatically in order to offer an efficient and user-friendly simulation tool.
Fig. 2: Pre-processing steps
In a second stage, 2D FEM field calculations are
performed using Flux 2D [3]. This program is suitable for this kind of applications. It offers a lot of useful features like partial automatic mesh generation, sliding air gap band for calculations in rotation and external coupled circuits; saturation effects and eddy currents are taken into account. This second stage is detailed in the next section. The post-processing stage (Fig. 3) contains the analysis of the FEM calculations results; it leads to the characteristic quantities and to the equivalent circuits of the machine. This analysis is performed according to [4], it is based on the decreasing versus time of the magnitude of the stator vector current after extracting the DC-components. The analysis of the field current is also necessary in order to get all the elements of the equivalent circuit in the d-axis [5]. Depending on the rotor construction, one determines the characteristic quantities and the equivalent circuits based on a model with one, two or three time constants in each rotor axis [6]. In the case of a salient pole machine with laminated rotor, two time constants and reactances (Td’; Td’’; xd’; xd’’) in the d-axis are sufficient. For a turbo-generator with a solid iron rotor and a damper winding three time constants and reactances (Td’; Td’’; Td’’’; xd’; xd’’; xd’’’) at least are necessary in order to guarantee precise values for xd’’’ and xd’, which are essential in the case of strong perturbations or stability analysis. It is also possible
to define a model with more than three time constants according to the following equation:
'
1 '
1 1 1 1 1.....nd d
n n
t tT T
stator no loaddd d d d
i u e ex x x x x−
− −
−
⎡ ⎤⎛ ⎞ ⎛ ⎞⎢ ⎥= − + + − +⎜ ⎟ ⎜ ⎟⎢ ⎥⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎢ ⎥⎣ ⎦
A model with more than 3 time constants leads of course to
a better approximation of the decreasing versus time of the stator vector current after a no-load short-circuit test. However for a machine with a solid iron rotor for which a model with 3 time constants is defined, it is important to reach with priority the best possible precision for xd’’’ and xd’ rather than for xd’’. The reason for that is the fact that xd’’’ and xd’ are playing the major role during the subsequent numerical simulations like 2 or 3-phase faults, out-of-phase synchronization or stability analysis. This post-processing stage is performed automatically using a dedicated tool allowing the above mentioned flexibility with respect to the number of desired time constants.
Fig. 3: Post-processing steps
A similar equation can be written for the short-circuit test
in the quadrature axis under load conditions at cos φ = 0. Finally, it is possible to check the results precision with a
reverse numerical simulation of the same test using the obtained characteristic quantities as input data. Fig. 4 shows the good agreement of the initial 2D FEM calculation results with those coming from the reverse-check numerical simulation [2].
M s1 .v is + iabc30%.v is5 / 24/ 00
Ia [A ] ia [A ]
Time [sec ] 2 1 .5 1 0.5 0
5 000
4 000
3 000
2 000
1 000
0
-1 000
Ms1.v is + iabc 30%.v is5/ 24/ 00
If [A ] if [A ]
Time [sec] 2 1 .5 1 0.5 0
550
500
450
400
350
300
250
200
150
100
50
0
Fig.4: Reverse check of the field and armature current
III. FEM CALCULATIONS
The morphology of the synchronous machine formally requires 3D FEM field calculations. Also if 3D FEM field calculations are possible today, the necessary CPU time remains prohibitive for repetitive industrial applications. This reason justifies the choice of the Flux 2D magneto-evolutive field calculation program [3], where the end winding leakages are taken into account through associated external circuits as shown later on.
The use of a tool like Flux 2D requires special attention regarding the mesh generation and the calculation of the end winding leakages. A too fine mesh leads to a high calculation time; a too large one inhibits to take into account the skin effect. Fig. 5 illustrates two optimized grids.
View of conductors, iron and sliding band mesh
Fig. 5: Mesh generation
Fig. 6a shows how the leakage fluxes of the excitation end winding of a turbo-generator can be obtained through a series of 2D field calculations in axial (Fig. 6b), respectively (Fig. 6c) in perpendicular plans. Fig. 6d illustrates the case of a hydro-generator. The same investigation must be performed for the stator end-winding and for the damper ring of a salient pole machine.
Fig. 6a: End-winding leakage reactance calculation
Fig. 6b: End-winding leakage in the axial plan
Fig. 6c: End-winding leakage in the perpendicular plan
The radial ventilation ducts of an air- or H2-cooled unit are
considered through the definition of an equivalent B-H characteristic of a machine with the same active length and no ventilation ducts. Fig. 7 illustrates the combination of the 2D FEM field calculation with the external coupled circuits in the case of a hydro-generator.
Fig. 6d: End-winding leakage, hydro-generator
Fig. 7: FEM domains and external coupled circuits
This approach could be labelled ”2,5D”, it leads to an
acceptable calculation time and guarantees a precision as good as a classical test on the conventional test platform of the manufacturer.
IV. EXAMPLES OF APPLICATIONS
In the following, the results concerning three large existing synchronous machines, which have been tested by the manufacturer and on the numerical test platform are presented. The rated values of these machines are given in Table1. The 37 MVA turbo-generator is an old machine (commissioning year 1985), nevertheless, it remains very interesting because it has been tested by the manufacturer through a no-load short-circuit test at rated voltage.
TABLE1: MACHINES RATED VALUES
Values Hydro Turbo 1 Turbo 2
Rated power (MVA) 83 37 187.5 Rated voltage (kV) 17.5 11.5 13.2 Power factor cos φ 0.9 0.8 0.8 Pole number 10 2 2 Rated freq. (Hz) 50 50 50
A. Example no 1: Hydro-generator
The no-load short-circuit tests for this hydro-generator have been performed on the HV-side of the transformer. The short-circuit reactance of the transformer is 0.123 p.u. in the reference system (83 MVA; 17.5 kV). Fig. 8 shows the stator currents after a sudden no-load short-circuit test on the HV-side of the transformer at u = 0.8 p.u. obtained using the numerical test platform. Fig. 9 and 10 show the stator and field currents after a short-circuit under load operation at cosφ = 0, also simulated on the numerical test platform.
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-5
-4
-3
-2
-1
0
1
2
3
4
5
t [s]
i [pu]
Fig.8: Stator currents after a sudden no-load short-circuit
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-5
-4
-3
-2
-1
0
1
2
3
4
5
t [s]
i [pu]
Fig.9: stator currents after a short-circuit under load conditions
at cos ϕ = 0
0 0.5 1 1.5 2 2.5 3-1000
-800
-600
-400
-200
0
200
400
600
800
1000
t [s]
if [A]
Fig.10: Field current after a short-circuit under load conditions
at cos ϕ = 0
Table 2 compares the characteristic quantities obtained
from different no-load short-circuit tests mentioned before and from the numerical test platform. The values with index e in Table 2 concern the block connection machine and transformer. The line showing the xd’’ values concerns the machine only (xd’’ = xde’’ – xtransformer).
Coupled electrical circuits for no load short-circuit application
Armature circuit
Damper circuit
Field circuit Additional leackage
inductance (frontal part) The coupled electrical circuits
add external elements to the 2D FEM domain
TABLE 2: HYDRO-GENERATOR, COMPARISON MEASUREMENTS / SIMULATION
RESULTS
uso [p.u.] 0,2 0,4 0,5 0,6 0,8 1,0
measurement / simulation
xde’ [p.u.] 0,430 0,441 0,429 0,426 0,405 / 0,388
0,371
xde’’[p.u.] 0,327 0,315 0,321 0,309 0,307 / 0,307
0,303
Tde’ [s] 2,93 2,84 2,78 2,54 2,26 / 2,33
2,18
Tde’’[s] 0,071 0,059 0,064 0,05 0,05 / 0,063
0,064
xd’’[p.u.] 0,205 0,193 0,199 0,187 0,185 / 0,185
0,181
A good agreement can be observed of measurements and
simulation results, especially for the subtransient reactance xde’’ versus initial test voltage uso as shown in Fig. 11.
0.25
0.27
0.29
0.31
0.33
0.35
0 0.2 0.4 0.6 0.8 1 1.2
uso [ p .u. ]
Simulation
M easurement
Fig.11: Reactance xde
’’ versus test voltage
This result demonstrates that the numerical test platform is
able to take precisely into account the saturation effects in the leakage paths influencing xd’’. Therefore a prediction of the maximum current and torque values appearing after a strong perturbation like a sudden short-circuit under load operation or an out-of-phase synchronization becomes possible. Such strong perturbations can be simulated with a numerical software package like [2] using the characteristic quantities coming from the numerical test platform and corresponding to the same saturation level of the leakage paths. A sudden no-load short-circuit at the machine terminals under rated voltage leads to xd’’ = 0,159 p.u. The short-circuit test in the quadrature axis under load conditions at cosφ = 0 leads to xq’’ = 0,176 p.u. and Tq’’ = 0,062 ms. In this case, the stator currents are decreasing much more quickly because only the damper winding is present on the rotor q-axis. This short-circuit test under load conditions requires the network, it is therefore practically impossible to perform it, except on a virtual test platform!
B. Example no 2: Turbo-generator 1
Sudden no-load short-circuit tests have been performed on the test shop of the manufacturer and on the numerical test platform with the following armature voltage values: 0,14; 0,3; 0,5; 0,7 and 1 p.u. Fig. 12 illustrates the field distribution
some ms after a no-load short-circuit, Fig. 13 and 14 show the stator and rotor currents given by the numerical test platform.
Fig.12: Field distribution 6 ms after a sudden no-load short-circuit
0.2 0.4 0.6 0.8 1 1.2 1.4
0
2
4
6
8
10
12
14
16
i[pu]
t[s]
Fig 13: No load short circuit stator current at rated voltage
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
2
4
6
8
10
12
14
t[s]
if[pu]
Fig 14: No load short circuit field current at rated voltage
Table 3 makes a comparison of the characteristic quantities obtained from measurements and simulations. Due to the fact that this machine has a solid iron rotor and a damper winding, it is necessary to use a model with three time constants in the d-axis. When the machine was measured in 1985, it was usual to extract manually only two time constants from the short-circuit oscillograms. The two reactances corresponding to these two time constants can be compared in Table 3 to the xd’ and xd’’’ values obtained from the numerical test platform.
The analysis of Table 3 shows that, for a test voltage lower than 0,5 p.u., only two and not three time constants or transient reactances are obtained from the numerical test platform.
TABLE 3: TURBO 1, COMPARISON MEASUREMENTS / SIMULATION RESULTS
Uso [p.u.] 0,1391 0,2983 0,4984 0,6959 0,9934
Measurement / simulation xd’ [p.u.] 0,169 /
0,162 0,171/ 0,167
0,179 / 0,168
0,177 / 0,169
0,164 / 0,181
xd’’[p.u.] - / - - / - - / - - / 0,153 - / 0,142 xd’’’[p.u.] 0,134 /
0,136 0,130 / 0,136
0,121 / 0,129
0,111 / 0,119
0,103 / 0,108
Td’ [s] 0,462 / 0,419
0,427 / 0,423
0,420 / 0,42
0,393 / 0,406
0,377 / 0,426
Td’’ [s] - / - - / - - / - - / 0,073 - / 0,117 Td’’’ [s] 0,0207/
0,0183 0,0219 / 0,02
0,0241 / 0,024
0,028 / 0,023
0.0267 / 0,023
The reason for that is the fact, that this old machine has a low rated linear current density. Therefore the rotor solid iron remains unsaturated during a sudden short-circuit test as long as the test voltage does not reach 0,5 p.u. No saturation means a very high relative permeability and a very small depth of penetration leading to a high solid iron impedance. In other words, the rotor solid iron remains inactive as long as the test voltage does not reach at least 0,5 p.u. This situation does not appear in the case of a modern turbo-generator with a higher linear current density.
C. Example no 3: Turbo-generator 2 TABLE 4: TURBO 2, COMPARISON MEASUREMENTS / SIMULATION RESULTS
Uso [p.u.] 0,2 0,5 0,72 1,0
Measurements / simulation xd’ [p.u.] 0.2216 0,227 0,242/0,229 0,228 xd’’[p.u.] 0,1863 0,166 0,179/0,155 0,133 xd’’’[p.u.] 0,1785 0,156 0,142/0,136 0.126 Td’ [s] 1,41 1,41 1,21 / 1,39 1,34 Td’’ [s] 0,162 0,151 0,155/0,163 0,164 Td’’’ [s] 0,0194 0,0203 0,0241/0,021 0,019
This modern air-cooled turbo-generator has also been tested on the platform of the manufacturer and on the numerical test platform. Table 4 summarizes the comparison of measurements and simulation results. A good agreement can be observed again. Due to a much higher rated linear current density than with the previous example, three time constants, and not only two, already appear for a low test voltage.
An other comparison simulation – measurement concerning a 20 MW LCI-12 fed synchronous turbo-motor is described in [7].
V. CONCLUSIONS A numerical test platform for large synchronous machines
has been described and applied on three existing large units. Based on the knowledge of the geometry and of the physical properties of the electrical and magnetic circuits of the machine, this numerical test platform can be used for a series of tests: sudden no-load short circuit, symmetrical or asymmetrical short-circuits under load conditions, standstill
frequency response, DC decay, load tests). These tests can be performed in rotation by taking into account all the non-linearities of the machine (saturation and eddy currents).
This paper focuses on the sudden no-load short-circuit test and on the short-circuit test in the quadrature axis under load conditions at cos φ = 0 leading together to the complete set of characteristic quantities in both axis. The comparison of the results obtained from this numerical test platform and from the classical one is convincing, especially concerning the influence of the saturation of the leakage paths on the sub- and subsubtransient reactances. A precision better than 5% can be guaranteed.
In a practical point of view, the proposed numerical test platform brings a lot of advantages: rapidity of exploitation, no expensive equipment, no risks, no limitation for testing the machine at the material limits. This numerical test platform is also useful as a tool for design optimization.
VI. REFERENCES [1] C. Ramirez: Plate-forme numérique d’essais pour machines électriques
de puissance, Ph.D thesis EPFL no 2821 (2003). [2] SIMSEN : http://simsen.epfl.ch [3] FLUX2D, CEDRAT, Grenoble, 1998. [4] “Methods for determining synchronous machine quantities from tests”,
IEC Standard 34-4 Rotating Electrical Machines, Part. 4. 1985. [5] I.M. Canay: Determination of model parameters of synchronous
machines, IEE Proc. Vol. 130, Pt. B, No2, 1983 [6] I. M. Canay: Modeling of Alternating-Current Machines Having
Multiple Rotor Circuits. IEEE Transactions on Energy Conversion, Vol. 8, No 2, June 1993.
[7] J.-J. Simond, A. Sapin, M. Tu Xuan, R. Wetter, P. Burmeister : 12-Pulse LCI Synchronous Drive for a 20 MW Compressor, Modelling, Simulation and Measurements; paper 64p6, IEEE IAS meeting 2005, Hong-Kong.
VI. BIOGRAPHIES
Jean-Jacques Simond received his master degree in 1967 and his Ph.D. degree in 1976 from the Swiss Federal Institute of Technology in Lausanne. Till 1990 he has been working for BBC / ABB in the field of large electrical machines, first as R&D engineer and later as head of the technical department for hydro- and Diesel-generators. Since 1990 he is full professor at the Federal Institute of technology and director of the laboratory for electrical machines. He is also consultant for different international electrical machines manufacturers and
utilities. Carlos Ramirez received his master degree in
1998 and his Ph.D. degree in 2003 from the Swiss Federal Institute of Technology in Lausanne. Since 2004 he is working for Alstom Power (Switzerland) as R&D engineer within the Hydrogenerators Technology Center in Birr. His main fields of activities concern machine modeling, design optimization and field calculations.
Mai Tu Xuan received his master degree in 1970 and his Ph.D. degree in 1977 from the Swiss Federal Institute of Technology in Lausanne. Since many years he is senior researcher and lecturer at the Laboratory for Electrical Machines of EPFL. His main fields of activities concern machine modeling, optimization and testing, parameters identification, measurement techniques and field calculations.
Carl-Ernst Stephan was born in Germany in
1960. He received the Dipl.Ing. degree in electrical power engineering in 1983 and the Dr.-Ing.Degree in 1991 from the University of Kaiserlautern. He is in his current position head of the Insulation Competence Center in the turbogenerator business unit of ALSTOM, Switzerland, dealing with development of insulation system, diagnosis and monitoring systems for rotating electric machines. He started his professional career in 1990 in the development of
turbogenerators. In particular he was responsible for the electromagnetic design and cooling of air-cooled turbogenerators with highest unit ratings.