IEEE TRANSACTIONS ON MAGNETICS, VOL. 45, NO. 10, OCTOBER 2009 4605
An Interpolative Finite-Element Modeling and the Starting ProcessSimulation of a Large Solid Pole Synchronous Machine
Y. B. Li�, S. L. Ho�, W. N. Fu�, and W. Y Liu�
Johnson Electric, Inc., New Territories, Hong KongDepartment of Electrical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong
Direct simulation of the starting process of an electric machine using a 3-D transient finite-element analysis (FEA) is very time con-suming. To overcome this difficulty, an interpolative finite-element modeling of a large solid pole synchronous motor (SPSM) is presentedand its starting process is simulated in this paper. In order to take into account the effects of cooling ducts and end turns, three differentsimplified 3-D finite-element models (FEMs) are proposed to reduce the computing time and save memory storage. With the proposedalgorithm, an appropriate postprocess is exploited to deduce an effective core length and an end-turn leakage inductance. Then, a 2-Dtransient FEM with the modified parameters from 3-D FEA is used to simulate the starting process. The proposed method is validatedby the test results of a 15 000-hp, 13.2-kV, 4-pole SPSM.
L ARGE solid pole synchronous motor (SPSM), which isfabricated using solid pieces of forged, welded, or dove-
tailed steel as the rotor pole body, is used commonly to drivelarge compressors, pumps, and blowers in power stations, steelplants, etc. The merits of the SPSM are its self-starting perfor-mance, reliable operation, and high thermal capacity [1], [2].
Similar to the study of traditional salient-pole synchronousmotors, two-axis equivalent circuit method is usually employedin steady-state performance study of SPSM [3]–[5]. For tran-sient performance, such as the starting process behaviors, theresults from traditional methods are not as accurate as ex-pected, due to skin effects on the solid pole surface and seriousmagnetic nonlinearities [6], [7]. With the advent of powerfulcomputing workstations, 2-D and 3-D finite-element analyses(FEAs) have now become feasible in practical applications,not only for steady-state field analysis, but also for transientperformance analysis of electric motors [8], [9]. But for largeSPSMs, due to the existence of axial cooling ducts and alsobecause its performance is sensitive to skin effects and end-turnparameters, 3-D FEA is needed for its starting process simu-lation. Hitherto, transient 3-D FEA study to include the rotormotion is computationally expensive and very often infeasiblefor industrial applications due to its complex 3-D meshingprocess and excessively long solution time required.
An interpolative FEA modeling method for a large SPSMsimulation is introduced in this paper. With the proposed novel3-D models and due consideration to their operational physics,an effective core length is proposed and the end-turn parametersare reevaluated and incorporated into a 2-D FEA model. Thestarting performance of the motor is then obtained using a 2-Dtransient FEA simulation. It is shown that with this approach,
Manuscript received March 06, 2009. Current version published September18, 2009. Corresponding author: W. N. Fu (e-mail: [email protected]).
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TMAG.2009.2022408
Fig. 1. The full geometry model of the motor.
the simulation time is substantially reduced and yet the high ac-curacy of the starting performance is retained.
II. FEA MODELS AND ITS COMPARISON
The full geometry model of the motor is shown in Fig. 1. Itis a 15 000-hp, 13.2-kV, 4-pole, 3-phase solid pole synchronousmachine with direct current (dc) winding in the rotor and axialcooling-duct structures in the stator.
By virtue of its 4-pole geometrical symmetry, only a quarterof the model is needed in the solution domain. Moreover, be-cause of symmetry along the -axis, the length along the -axisdirection can also be cut in half, thus only one eighth of themotor structure is enough for the modeling, as shown in Fig. 2.Consequently, the boundary conditions across the cross sectionin parallel with the plane at the middle of the motor alongthe –axis are shown as
(1)
where - formulation is used [10]; is the electric vectorpotential; is the magnetic scalar potential; and is normal tothe cross section.
Although the one-eighth model in Fig. 2 is much simpler thanthe full model, it still needs very long computing time and a lot
4606 IEEE TRANSACTIONS ON MAGNETICS, VOL. 45, NO. 10, OCTOBER 2009
Fig. 2. The one-eighth model of SPSM.
of memory for the 3-D FEA calculation, because of the com-plicated shapes of the end-turn windings, large number of coils,and axial ducts. For instance, 23.5 h is needed for the surfacemesh generation and almost one month of computing time isneeded to simulate the starting process of around 10 s (indeedthe simulation had to be stopped due to out of memory error inthe end) of the motor with Maxwell V12.0 on a 64-bit, dual coreworkstation computer. Obviously, such analysis is not feasiblefor practical application, especially for transient behavior sim-ulation.
In this paper, three different simplified 3-D models are pre-sented, as shown in Fig. 3. Fig. 3(a) shows Model-I together withits 3-D mesh and this model carries just a one-turn measure coil.In order to separate the effects of cooling ducts and end-turnleakage inductance from the main inductances, two other moresimplified models, i.e., one having just the cooling ducts, butwithout the end turns, referred to as Model-II [Fig. 3(b)], andthe other without both the cooling ducts and end turns, referredto as Model-III [Fig. 3(c)], are proposed.
Obviously, the computing time of the 3-D magnetostatic so-lution is reduced greatly with these simplified models. Table Ishows the solution time for an open circuit voltage simulation ofthe three models. The end-turn leakage inductance calculationwill be discussed as follows.
III. END-TURN LEAKAGE INDUCTANCE
Leakage inductance plays a vital part in establishing the per-formance parameters of a synchronous motor, and this influenceis particularly important upon the starting current and powerfactor during starting. As for the leakage inductances, the end-turn leakage inductance plays an important role, and tradition-ally in 2-D FEA simulation, the end-turn leakage inductance canbe roughly estimated by analytical expressions. A precise esti-mation requires 3-D FEA, but the calculation is the most compli-cated procedure because its contribution is from the 3-D leakagefield in the end regions which have complicated shapes and largewinding number.
To save simulation time, two simplified 3-D FEA models areemployed, i.e., Model-I in Fig. 3(a) and Model-II in Fig. 3(b)which have no end turns. Both models have just one measure
winding. The flux linkages in the measure coil with differentarmature winding currents are shown in Table II.
From these data, one can find that the flux linkages in the mea-suring coil of Model-I are slightly larger than those in Model-II,
LI et al.: AN INTERPOLATIVE FINITE-ELEMENT MODELING AND THE STARTING PROCESS SIMULATION 4607
TABLE IIICOMPARISON OF FLUX LINKAGES
and its difference is the end-turn leakage flux. Hence, the end-turn inductance for this measured coil can be deduced with fol-lowing incremental inductance method:
(2)
Then, the total inductance in the phase winding can be ob-tained by
(3)
where is the slot number per pole per phase; is the turnnumber per coil; and is the winding factor.
Also, one can obtain the field winding leakage inductanceusing the same method in which field dc is fed to the fieldwinding.
IV. COOLING DUCTS AND EFFECTIVE 2-D CORE LENGTH
Effective core length is another issue to be considered forlarge motor with axial cooling ducts. Typically, the net corelength is used as the model depth in a 2-D model, and the netcore length is defined as
(4)
where is the nominal stack length; is the width of eachair-duct; and is the number of cooling ducts.
In order to address the concentrated fringing flux effect ofthe cooling ducts and the material’s nonlinear characteristic, theeffective length is a function of field current. The elliptical circlein Fig. 4 shows the fringing flux distribution along the axialdirection in Model-II. Table II shows the flux linkages in themeasure coil with different field dc in Model-II and Model-III,and in Model-III, the stack length is the net core length from (4).From Table II, one can find that the flux linkages of Model-II areslightly bigger than those in Model-III.
Therefore, the use of net core length cannot give sufficientlyhigh accuracy in 2-D FEA simulation. However, these differ-ences can be compensated with a modified effective core length,i.e., the core length in the 2-D model should be interpolatedbased on the 3-D flux value. This method, which is named asan interpolated method, is illustrated in Fig. 5.
Fig. 6 shows the comparison of the open circuit voltage. In the2-D model, the model depth has been adjusted with a modifiedvalue according to the interpolated method. It is clearly seen that
Fig. 4. Flux distribution along the axial direction.
Fig. 5. Interpolated method flowchart.
Fig. 6. Open-circuit voltage comparison among tested, 2-D and 3D FEA.
these results agree well which means the effect of the coolingducts can be incorporated into the 2-D transient FEA.
V. STARTING PROCESS SIMULATION USING 2-D FEA
Starting process simulation is one of the most important pro-cedures in SPSM design and it should be solved using 3-D tran-sient electromagnetic field computation. For the transient anal-ysis, the time step needs to be sufficiently fine, such as 0.1 msin this study, so as to simulate the eddy current penetration cor-rectly. Based on the observations, it is estimated that it takesmore than five months in order to obtain the complete startingprocess solution with 3-D FEA. Such a long computation periodis impractical for engineering applications.
In this study, a 2-D transient FEA model with the above mod-ified parameters is proposed [11]. The procedures for the com-putation of the starting process are: 1) compute the end-turn
4608 IEEE TRANSACTIONS ON MAGNETICS, VOL. 45, NO. 10, OCTOBER 2009
Fig. 7. The magnetic flux distribution at slip � ����.
Fig. 8. Comparison of the starting time of the SPSM motor between experi-mental and interpolated FEA model.
Fig. 9. Accelerating torque simulation result by interpolated FEA model.
leakage inductance using 3-D Model-I and Model-II; 2) com-pute the effective core length according to the method describedin Section IV; and 3) compute the starting current and torqueusing time-stepping 2-D FEA using the deduced effective corelength. The end-turn winding is included by coupling the elec-tric circuit of end-turn winding with the end-turn leakage in-ductance computed by the proposed 3-D FEM. Fig. 7 shows asnapshot of the field flux and eddy current density distributionduring starting process at which the rotor slip is 0.44. It can beseen that the flux and eddy current are concentrated on the sur-face of the solid pole, illustrating clearly the presence of skineffect during acceleration.
Fig. 8 shows the measured and calculated acceleration curvesof the motor. The accelerating torque waveform is shown inFig. 9. It can be seen that the acceleration time is in good correla-tion with the test results. These waveforms clearly demonstratethe improved accuracy of the 2-D FEA transient model usingthe interpolated parameters.
VI. CONCLUSION
This paper presents the FEA modeling of a large SPSM andits starting process simulation. The conclusions are as follows.
1) The 3-D analysis is essential to obtain accurate predic-tions of transient performance, particularly in the study ofstarting process of large synchronous generators. However,the prohibitively long CPU time needed to perform suchsimulation with traditional methods precludes the applica-tion of 3-D transient FEA with rotor motion.
2) The 3-D models with just one measure coil are created andcompared. These models can save considerably CPU time.The effective core length and end-turn leakage inductanceused in the 2-D transient model can be deduced from suchmodels.
3) Interpolated with the 3-D field analysis, the use of 2-D FEAmodel can give relatively accurate results in large motorperformance simulations with a much shorter time thanusing full 3-D model, therefore the proposed algorithm ismuch more feasible for practical engineering applications.
All these conclusions are validated by the test results on a15 000-hp, 13.2-kV, 4-pole SPSM.
ACKNOWLEDGMENT
The authors would like to thank Prof. C. Mi from the Univer-sity of Michigan for his financial and academic supports of thisresearch. This work was supported in part by the Hong KongPolytechnic University under Grants U489 and 87RX.
REFERENCES
[1] S. M. Silva, B. J. Cardoso Filho, M. Murta, G. Cardoso, and M. RochaBraga, “Blower drive system based on synchronous motor with solidsalient-pole rotor: Performance under starting and voltage sag condi-tions,” IEEE Trans. Ind. Appl., vol. 39, no. 5, pp. 1429–1435, Sep.–Oct.2003.
[2] C. Concordia and H. Poritsky, “Synchronous machine with solid cylin-drical rotor,” AIEE Trans., vol. 56, pp. 49–58, 1937.
[3] A. J. Wood, “An analysis of solid rotor machines, part I, operational im-pedances and equivalent circuits,” AIEE Trans., vol. 78, pp. 1657–1665,1959.
[4] A. J. Wood and C. Concordia, “An analysis of solid rotor ma-chines—Part IV,” AIEE Trans, vol. 79, pt. III, pp. 26–31, 1960.
[5] M. D. Cundev, L. B. Petkovska, and M. Popnikolova-Radevska, “Solidsalient pole synchronous motor analysis,” in Proc. MELECON, May18–20, 1998, vol. 2, pp. 1140–1144.
[6] G. F. T. Widger and B. Adkins, “Starting performance of synchronousmotors with solid salient poles,” Proc. Inst. Electr. Eng., vol. 115, p.1471, 1968.
[7] H. Karmaker and C. Mi, “Improving the starting performance of largesalient-pole synchronous machines,” IEEE Trans. Magn., vol. 40, no.4, pt. 1, pp. 1920–1928, Jul. 2004.
[8] T. W. Preston, M. A. Timothy, and A. M. Sitzia, “3-dimensional evalu-ation of the end parameters of large solid salient pole synchronous ma-chines,” in Proc. 9th Int. Conf. Electr. Mach. Drives, Sep. 1–3, 1999,pp. 100–104.
[9] J. P. Sturgess and T. W. Preston, “An economic solution for 3-D cou-pled electromagnetic and thermal eddy current problems,” IEEE Trans.Magn., vol. 28, no. 2, pp. 1267–1270, Mar. 1992.
[10] P. Zhou, W. N. Fu, D. Lin, S. Stanton, and Z. J. Cendes, “Numericalmodeling of magnetic devices,” IEEE Trans. Magn., vol. 40, no. 4, pp.1803–1809, Jul. 2004.
[11] S. L. Ho, W. N. Fu, and H. C. Wong, “Direct modeling of the startingprocess of skewed rotor induction motors using a multi-slice tech-nique,” IEEE Trans. Energy Conv., vol. 14, no. 4, pp. 1253–1258, Dec.1999.
