同步发电机电磁性能分析计算
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摘要
三相同步发电机是电力系统中最常见的发电设备,具有供电品质好、带负载能力强、既能发出有功又能发出无功等优点。本文为同步发电机多种电磁设计方案的比较分析与优化设计提供理论基础,采用有限元法对电机的部分参数和性能指标进行了分析计算,取得了较为理想的结果。相对于传统的解析计算公式或磁路法,有限元法基于电机的几何结构和材料特性,能较为准确地考虑定、转子铁心饱和与齿槽效应的影响,计算结果更加准确。
在静态场下,依据气隙磁密与感应电势之间的物理关系,利用迭代算法求取了同步发电机不同运行方式下励磁电流。给转子绕组加载试探电流,求出感应电势并与理论值对比,不断修正励磁电流直到满足误差要求即可求得实际工况下的励磁电流大小。通过边界条件的加载区分开主磁场和漏磁场,利用磁场能量法计算了定子、转子槽漏抗并给出了三相绕组漏磁场能量与一相漏感之间的数学关系。
在暂态场下,利用场路耦合-时步有限元法分析了三相突然短路电流的大小与变化趋势。在短路的瞬间,通过与外电路耦合,在励磁绕组中串入恒定电压源来实现绕组电流的突变。为考虑定、转子间相对运动引起的齿谐波磁导变化,即电机铁心开槽对转子损耗的影响,采用暂态场计算转子铁心涡流损耗。通过气隙节点的耦合模拟转子转动,改变时间步长控制电机转速,每进行一步暂态运算都计算一次损耗,最后绘出转子损耗随时间变化的曲线,求取一段时间内的平均损耗即是转子铁心涡流损耗。
本文利用有限元法对同步电机槽漏抗、直轴交轴电枢反应电抗不饱和值、瞬变电抗、超瞬变电抗等重要参数和不同工况下的励磁电流、三相突然短路电流以及转子附加损耗等性能指标进行详细分析和计算,部分结果还与磁路法进行了对比验证,研究工作为大容量、高性能同步发电机的设计优化、运行分析奠定了理论基础。
Three phase synchronous generator is characterized with good electric supply quality, high capacity for carrying loads and outputting both active power and reactive power, which is the most popular equipment of electric power generation. To provide theoretical foundation for generator optimization design and multiple scheme comparison, the finite element method is carried out to calculate generator parameters and analyze operating performance. Compared with the traditional analytical formula and the magnetic circuit method, finite element method gives more accurate results because it is based on actual model, has less assumption, meshes more flexible and the core nonlinear can be taken into account.
Under static field operation, the iterative algorithm is used to calculate the value of exciting current with generator running in different operation mode, according to the expression about magnetic flux destiny in air gap and the induced electromotive force. The heuristic current is loaded on exciting winding to obtain the electromotive force, which is compared with the theoretical voltage. Keep on correcting the value of exciting current until the voltage error within specified tolerance, actual current is obtained at last. The magnetic energy method is applied to solve the stator and rotor slot leakage inductance, besides that the expression about three-phase leakage magnetic energy and slot leakage inductance is given.
The time stepping finite element method with coupled field-circuit analysis is carried out to calculate the three phase sudden short circuit current under transient field operation. By coupled with the external circuit, the voltage source is series connected in the exciting winding to realize the abrupt change of current at the moment of sudden short circuit. To consider magnetic conductance change of tooth harmonic caused by relative motion between stator and rotor, the transient field operation is applied to obtain the rotor iron loss, aiming to analyze the slotted core effect on rotor iron loss. To simulate rotor rotation, the nodes on air gap are coupled and motor speed is controlled by changing time step length. The rotor iron loss curve with variation of time is given and the average loss in a period of time is obtained.
The motor parameters, exciting current, three phase sudden short circuit current and rotor eddy flow loss calculation are calculated by finite element method, and some results by the finite element method are compared with that by the analytical method, and the validity of the finite element method is checked. Researches in this paper provide theoretical foundation to optimization design for the large capacity and high performance synchronous generator.
在静态场下,依据气隙磁密与感应电势之间的物理关系,利用迭代算法求取了同步发电机不同运行方式下励磁电流。给转子绕组加载试探电流,求出感应电势并与理论值对比,不断修正励磁电流直到满足误差要求即可求得实际工况下的励磁电流大小。通过边界条件的加载区分开主磁场和漏磁场,利用磁场能量法计算了定子、转子槽漏抗并给出了三相绕组漏磁场能量与一相漏感之间的数学关系。
在暂态场下,利用场路耦合-时步有限元法分析了三相突然短路电流的大小与变化趋势。在短路的瞬间,通过与外电路耦合,在励磁绕组中串入恒定电压源来实现绕组电流的突变。为考虑定、转子间相对运动引起的齿谐波磁导变化,即电机铁心开槽对转子损耗的影响,采用暂态场计算转子铁心涡流损耗。通过气隙节点的耦合模拟转子转动,改变时间步长控制电机转速,每进行一步暂态运算都计算一次损耗,最后绘出转子损耗随时间变化的曲线,求取一段时间内的平均损耗即是转子铁心涡流损耗。
本文利用有限元法对同步电机槽漏抗、直轴交轴电枢反应电抗不饱和值、瞬变电抗、超瞬变电抗等重要参数和不同工况下的励磁电流、三相突然短路电流以及转子附加损耗等性能指标进行详细分析和计算,部分结果还与磁路法进行了对比验证,研究工作为大容量、高性能同步发电机的设计优化、运行分析奠定了理论基础。
Three phase synchronous generator is characterized with good electric supply quality, high capacity for carrying loads and outputting both active power and reactive power, which is the most popular equipment of electric power generation. To provide theoretical foundation for generator optimization design and multiple scheme comparison, the finite element method is carried out to calculate generator parameters and analyze operating performance. Compared with the traditional analytical formula and the magnetic circuit method, finite element method gives more accurate results because it is based on actual model, has less assumption, meshes more flexible and the core nonlinear can be taken into account.
Under static field operation, the iterative algorithm is used to calculate the value of exciting current with generator running in different operation mode, according to the expression about magnetic flux destiny in air gap and the induced electromotive force. The heuristic current is loaded on exciting winding to obtain the electromotive force, which is compared with the theoretical voltage. Keep on correcting the value of exciting current until the voltage error within specified tolerance, actual current is obtained at last. The magnetic energy method is applied to solve the stator and rotor slot leakage inductance, besides that the expression about three-phase leakage magnetic energy and slot leakage inductance is given.
The time stepping finite element method with coupled field-circuit analysis is carried out to calculate the three phase sudden short circuit current under transient field operation. By coupled with the external circuit, the voltage source is series connected in the exciting winding to realize the abrupt change of current at the moment of sudden short circuit. To consider magnetic conductance change of tooth harmonic caused by relative motion between stator and rotor, the transient field operation is applied to obtain the rotor iron loss, aiming to analyze the slotted core effect on rotor iron loss. To simulate rotor rotation, the nodes on air gap are coupled and motor speed is controlled by changing time step length. The rotor iron loss curve with variation of time is given and the average loss in a period of time is obtained.
The motor parameters, exciting current, three phase sudden short circuit current and rotor eddy flow loss calculation are calculated by finite element method, and some results by the finite element method are compared with that by the analytical method, and the validity of the finite element method is checked. Researches in this paper provide theoretical foundation to optimization design for the large capacity and high performance synchronous generator.
引文
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13王东,吴新振,马伟明等.非正弦供电十五相感应电机定子漏抗计算.中国电机工程学报,2010,30(6)：41-47
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2戴庆忠.当代国外汽轮发电机工业特点及技术发展概况.发电设备,2000,5：39-42
3 Reinhard E.J.. Advance in synchronous machines:a turbogenerator view. IEEE Power engineering review,2002:7-11
4 Gott. B.E.. Advances in turbogenerator technology. IEEE Electrical insulation magazine, 1996,12(4):28-38
5 Boldea I., Nasar S.A.. The induction machine handbook. Florida:CRC Press,2002
6陈世坤.电机设计(第二版).北京：机械工业出版社,2005
7傅丰礼,唐孝镐.异步电动机设计手册.北京：机械工业出版社,2002：46-48
8 Ramirez C., Simond J., Schafer D.. Synchronous machines parameters determination using finite elements method. ICEM Conference Proceeding, Helsinki 2000
9 Kazuo S., Kazumasa I.. Steady state magnetic circuit analysis of salient pole synchronous machines considering cross magnetization. IEEE Transactions on Energy Conversion,2003,18(2):213-218
10 Marco A., Arjona L.. Parameter calculation of a turbogenerator during an open circuit transient excitation. IEEE Transactions on Energy Conversion,2004,19(1):46-52
11刘陵顺,李岩,王朕.双绕组感应发电机定子槽漏感计算研究.微电机,2008：9-11
12 Keller, S., Tuxuan M., Simond, J. J., Computation of the no-load voltage waveform of laminated salient pole synchronous generators. IEEE Transactions on industry applications,2006, 42(3):681-687
13王东,吴新振,马伟明等.非正弦供电十五相感应电机定子漏抗计算.中国电机工程学报,2010,30(6)：41-47
14刘健平.同步电机突然三相短路的短路电流向量图分析法.中小型电机,2002,24(2)：31-33
15 Albanese. R., Rubinacci. G.. Numerical procedures for the solution of nonlinear electromagnetic problems. IEEE Transactions on magnetic,1992,28(2):1228-1231
16 Marrone M. Frasson A. M. Figueroa H.. A novel numerical approach for electromagnetic scattering the cell method. IEEE Antenna and Propagation Society AP-S International Symposium, San. Antonio, Texas,2002,23(6):156-159
17 Bae D., Kim D., Jung H., et al. Determination of induction motor parameters by using neural network based on FEM results. IEEE Transactions on Magnetics,1997,33(2):1924-1927
18 Ashtiani C.N., Lowther D.A.. The use of finite elements in the simulation of the steady state operation of a synchronous generator with a known terminal loading condition. IEEE Transtions on magnetic,1983,19(6):2381-2384
19 Bartosz L., Kevin F. G., Jan K.. Finite element assisted method of estimating equivalent circuit parameters for a superconducting synchronous generator with a coreless rotor, Transactions on magnetics,2009,45(3):1226-1229
20 Silvester P. P., Ferrari R. L.. Finite element for electrical engineers. Cambridge:Cambridge University Press,1983
21 Deng F., Demerdash N. A.. A coupled finite element state-space approach for synchronous generators. IEEE Transactions on aerospace and electronic systems,1996,32(2):775-784
22 Jawad F. A complete lumped equivalent circuit of three-phase squirrel-cage induction motors using two dimensional finite elements technique. IEEE Transactions on Energy Conversion,2002,17 (3): 363-367
23 Escarela P. Campero L. E., Laureano C. A.. Steady state inductance calculation of a turbine generator in the ABC reference frame. The 4th International Conference on Electrical and Electronics Engineering (ICEEE 2007), Mexico,2007
24 Dolinar D., Stumberger G., Grcar B.. Calculation of the linear induction motor model parameters using finite elements. IEEE Transactions on magnetics,1998,34(5):3640-3643
25 Demerdash N. A., Fello T. W.. Electric machinery parameters and torques by current and energy perturbations from field computations-Part Ⅰ:Theory and formulation. IEEE Transactions on energy conversion,1999,14(4):1507-1513
26 Jose C. P., Camilo J. C., Andres E. F.. Probabilistic model for mechanical power fluctuations in asynchronous wind parks. IEEE Transactions on power systems,2003,18(2):761-768
27 Wieseman R.W.. Graphical determination of magnetic fields practical applications to salient pole synchronous machine design. AIEE,1956:1351-1365
28 Toliyat H. A., Nuaim N. A.. Simulation and detection of dynamic air gap eccentricity in salient pole synchronous machines. IEEE Transactions Ind.1999,35(1):86-93
29 Oliver P., Markus C., Thomas W.. New flexible subgridding scheme for the finite integration technique. IEEE Transactions on magnetic,2003,39(3):1662-1665
30 Costa M.C., Nabeta S.I., Cardoso J.R.. Modified nodal analysis applied to electric circuits coupled with FEM in the simulation of a universal motor. IEEE Transactions on magnetics,2000,36(4): 1431-1434
31 Leonard P.J., Lai H. C..Treatment of symmetry in three dimensional finite element models of machines coupled to external circuits. IEEE Transactions on energy conversion,1999,14(4):76-79
32 Williamson S., Volschenk A.F.. Time stepping finite element analysis for a sychronous generator feeding a rectifier load. IEE Proc.-Electr. Power Appl,1995,142(1):50-56
33 Williamson S., Ralph J.W.. Finite element analysis of an induction motor fed from a constant voltage source. IEE Proceedings B,1983,130(1):18-24
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