Prace Naukowe Instytutu Maszyn, Napędów i Pomiarów Elektrycznych
Nr 63
Politechniki Wrocławskiej
Nr 63
Studia i Materiały
Nr 29
2009
synchronous machines, turbogenerators,
field-circuit modeling, short circuit,
work with power system, dynamic states
Piotr KISIELEWSKI*, Ludwik ANTAL*
TRANSIENT CURRENTS IN TURBOGENERATOR
FOR THE SUDDEN SHORT CIRCUIT
This paper presents two-dimensional field-circuit model of 500 MVA turbogenerator. Model is
designed to calculate static and dynamic characteristics of machine. The model was applied to calculate stator, rotor and damper winding currents for the sudden short circuit. Using the model of turbogenerator it is possible to calculate flux and current densities, field distributions and other physical
quantity for every time step of the simulation.
1. INTRODUCTION
Field-circuit modeling is an useful tool to analyze physical phenomenon occurring
in electrical machines. In every step time, coupled electromagnetic, circuit and motion
equation are solved. Two parts represent electrical machine: field model and circuit
model. In field part electromagnetic field equations are solved. During solving field
equations real physical characteristics of materials, configuration of windings, damper
circuit and motion elements in electromagnetic field are taken into account. In circuit
part there is an electrical scheme. The electrical elements correspond with winding in
the field model. Parameters of frontal connections are included. In circuit part flux –
voltage equations are solved. It is possible to simulate different state of work with
filed-circuit models. The goal of this article is to compute transient currents, torque
and currents distribution in closed circuits of the turbogenerator: damper winding and
solid steel of rotor. In transient states currents and voltages were calculated. Knowledge of currents values give a possibility of calculates forces, torques and increases of
temperatures.
_________
* Wroclaw University of Technology, Poland, Department of Electrical Engineering, Institute of Electrical
Machines, Drives and Measurements, piotr.kisielewski@pwr.wroc.pl, ludwik.antal@pwr.wroc.pl
31
2. FIELD-CIRCUIT MODEL
In this work turbogenerator 500 MVA, 21 kV was simulated. Cross - section of the
turbogenerator model is showed on Figure 1. Two-dimensional model of turbogenerator was prepared by the use of Flux 9.2.2 [2]. Discretisation mesh is made from
41 544 second order face elements and contains 83 197 nodes. The mesh is shown on
Figure 2. Field model takes into account nonlinear magnetic characteristics of steel
and eddy currents in slot wedge. In circuit model there are elements, which represent
windings and solid conductor of field model. Sources, constants resistances and reactances of front connections are included. Parameters of front connections were calculated by the use of equations that are used in synchronous machines design. Circuit
part, which contains stator winding, excitation winding, and damper cage is shown on
Figure 3.
Fig. 1. Cross-section of the turbogenerator model
32
Fig. 2. Part of mesh
Fig. 3. Circuit of the machine
33
3. RESULTS OF SIMULATIONS
In the selected moment three-phase short circuit was simulated. The effect of
simulation transient currents in stator and rotor windings, current distributions in damper cage and solid steel of rotor were calculated. Transients of stator and rotor windings currents are showed on Figures 4–9.
150
I [kA]
100
50
0
-50
-100
t [s]
-150
0
2
4
6
8
10
12
Fig. 4. Phase currents for the sudden short circuit
60
Iw [kA]
50
40
30
20
10
0
t [s]
-10
0
2
4
6
8
10
12
Fig. 5. Transient of rotor current for the sudden short circuit
On Figure 6 transient currents in selected damper bars after sudden short circuit are
shown (according to numeration on Figure 1).
34
100000
I [A]
50000
0
1
2
3
4
5
6
7
-50000
-100000
-150000
0
2
4
6
8
10
14 t [s] 16
12
Fig. 6. Damper winding currents in active parts for the sudden short circuit
To illustrate the shape of currents in damper cage, first time of short circuit is
shown on the Figure 7.
80000
I [A]
40000
0
-40000
1
2
3
4
5
6
7
-80000
-120000
-160000
0
0,02
0,04
0,06
0,08
t [s] 0,1
Fig. 7. Damper winding currents in active parts for the sudden short circuit
Transient currents in the front part of damper cage are shown on the Figure 8 and
Figure 9.
35
200000
I [A]
7654321-
150000
100000
50000
8
7
6
5
4
3
2
0
-50000
-100000
-150000
0
2
4
6
8
10
14 t [s] 16
12
Fig. 8. Damper winding currents in front parts for the sudden short circuit
280000
7
6
5
4
3
2
1
I [A]
200000
120000
-
8
7
6
5
4
3
2
40000
-40000
-120000
-200000
0
0,02
0,04
0,06
0,08
t [s] 0,1
Fig. 9. Damper winding currents in front parts for the sudden short circuit
Current distribution in solid steel of rotor was calculated too. Transient of electromagnetic torque for the sudden short circuit is showed on Figure 10.
36
20
T [MNm ]
15
10
5
0
-5
-10
-15
-20
-25
0
2
4
6
8
10
12
14
t [s] 16
Fig. 10. Transient of electromagnetic torque for the sudden short circuit
Field distributions for selected times during sudden short circuit are shown on Figures 11–16.
Fig. 11. Field distribution in short-circuit state, t = 0,000 s
37
Fig. 12. Field distribution in short-circuit state, t = 0,004 s
Fig. 13. Field distribution in short-circuit state, t = 0,008 s
38
Fig. 14. Demagnetizable effect of armature, t = 0,002 s
Fig. 15. Demagnetizable effect of armature, t = 4,002 s
39
Fig. 16. Demagnetizable effect of armature, t = 15,002 s
Current density distribution in rotor for sudden short circuit is shown on Figure 17.
Fig. 17. Rotor current density distribution
40
4. CONCLUSIONS
Physical phenomenon in the machine in steady and dynamics states is well represented by field-circuit model of turbogenerator. A calculated field distributions, transient currents and torque show mechanism of creating short circuit currents. In excitation winding voltage is induced with the same frequency as currents in damper
winding. This voltage is added to voltage of exciter and in excitation current there is
a periodicity component.
The calculated current distribution in damper cage and steel of rotor shows that solid steel of rotor has a fundamental influence on parameters of machine and values of
currents and torque in first time of sudden short circuit.
Work financed by Polish Ministry of Science and Higher Education under Grant No. N511 021 32/4169
in 2007–2009.
REFERENCES
[1] KISIELEWSKI P., ANTAL L., Identification of the turbogenerator parameters by the field-circuit
simulations, XLII International Symposium on Electrical Machines, Poland, Cracow 2006,
(in Polish).
[2] CEDRAT, FLUX® 9.20 User’s guide, November 2005.
[3] KISIELEWSKI P., ANTAL L., Field-circuit model of the turbogenerator, P. N. IMNiPE PWr. nr 60,
SiM nr 27, 2006, 53–60, (in Polish).
[4] RAMIREZ C., TU XUAN M., SIMOND J., SCHAFER D., STEPHAN C.:,Synchronous machines
parameters determination using finite element method, International Conference on Electrical Machines. ICEM 2000, 28-30 August 2000, Espoo, Finland, ref. 1130.
[5] WAMKEUE R., ELKADRI N.E.E., KAMWA I., CHACHA M., Unbalanced transient-based finiteelement modeling of large generators, Electric Power Systems Research 56 (2000) 205–210.