Prace Naukowe Instytutu Maszyn, Napędów i Pomiarów Elektrycznych Nr 63 Politechniki Wrocławskiej Nr 63 Studia i Materiały Nr 29 29 Piotr KISIELEWSKI*, Ludwik ANTAL* synchronous machines, turbogenerators, field-circuit modeling, short circuit, work with power system, dynamic states TRANSIENT CURRENTS IN TURBOGENERATOR FOR THE SUDDEN SHORT CIRCUIT This paper presents two-dimensional field-circuit model of 5 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 5 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. 15 I [ka] 1 5-5 -1 t [s] -15 2 4 6 8 1 12 Fig. 4. Phase currents for the sudden short circuit 6 Iw [ka] 5 4 3 2 1-1 2 4 6 8 1 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). t [s]
34 1 I [A] 5-5 -1 1 2 3 4 5 6 7-15 2 4 6 8 1 12 14 t [s] 16 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. 8 I [A] 4-4 -8-12 -16,2,4,6,8 t [s],1 1 2 3 4 5 6 7 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 2 I [A] 15 1 5 7-8 6-7 5-6 4-5 3-4 2-3 1-2 -5-1 -15 2 4 6 8 1 12 14 t [s] 16 Fig. 8. Damper winding currents in front parts for the sudden short circuit 28 I [A] 2 12 7-8 6-7 5-6 4-5 3-4 2-3 1-2 4-4 -12-2,2,4,6,8 t [s],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 1.
36 2 15 T [MNm] 1 5-5 -1-15 -2-25 2 4 6 8 1 12 14 t [s] 16 Fig. 1. 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 =, s
37 Fig. 12. Field distribution in short-circuit state, t =,4 s Fig. 13. Field distribution in short-circuit state, t =,8 s
38 Fig. 14. Demagnetizable effect of armature, t =,2 s Fig. 15. Demagnetizable effect of armature, t = 4,2 s
39 Fig. 16. Demagnetizable effect of armature, t = 15,2 s Current density distribution in rotor for sudden short circuit is shown on Figure 17. Fig. 17. Rotor current density distribution
4 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 21 32/4169 in 27 29. REFERENCES [1] KISIELEWSKI P., ANTAL L., Identification of the turbogenerator parameters by the field-circuit simulations, XLII International Symposium on Electrical Machines, Poland, Cracow 26, (in Polish). [2] CEDRAT, FLUX 9.2 User s guide, November 25. [3] KISIELEWSKI P., ANTAL L., Field-circuit model of the turbogenerator, P. N. IMNiPE PWr. nr 6, SiM nr 27, 26, 53 6, (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 2, 28-3 August 2, Espoo, Finland, ref. 113. [5] WAMKEUE R., ELKADRI N.E.E., KAMWA I., CHACHA M., Unbalanced transient-based finiteelement modeling of large generators, Electric Power Systems Research 56 (2) 25 21.