Nonlinear Electrical FEA Simulation of 1MW High Power Synchronous Generator System Jie Chen Jay G Vaidya Electrodynamics Associates, Inc. 409 Eastbridge Drive, Oviedo, FL 32765 Shaohua Lin Thomas Wu ABSTRACT An innovative nonlinear simulation approach for 1 MW high power density synchronous generator system is developed and implemented. Due to high power density, the generator operates in nonlinear region of the magnetic circuit. Magnetic Finite Element Analysis (FEA) makes nonlinear simulation possible. Neural network technique provides nonlinear functions for system level simulation. Dynamic voltage equation provides excellent mathematical model for system level simulations. Voltage, current and flux linkage quantities are applied in Direct-Quadrature (DQ) rotating frame. The simulated system includes main machine, exciter, Rectifier Bridge, bang-bang control and PI control circuitry, forming a closed loop system. Each part is modeled and then integrated into the system model. PROPOSED APPROACH High power density of generator design requires operation under saturated magnetic circuit conditions. This paper focuses on electrical simulation of the system. Electrical simulation includes Finite Element Analysis (FEA), and system level simulation. FEA has been widely implemented to conduct electromagnetic simulation of individual machines. System level simulation can be done by combining FEA and other software tools. Sadowski combined finite element simulation and current inverters for motor simulation [1]. Fardoun simulated permanent-magnet machine drive system using SPICE [2]. Natarajan simulated motor with Saber package [3]. Some commercially available software tools use the same scheme for motor transient simulations. These tools directly combine machine s FEA model and system circuitry models. Transient simulation can be done in this scheme. The simulation is accurate but time consuming. This work proposes and develops an innovative approach to simulate a six-phase 1MW high power generator system. Instead of directly combining machine s FEA model with its supporting circuitry, this work separates FEA simulation and system level simulation, and links them with neural network training results of FEA simulation. The benefit of this treatment is that FEA is not involved in each step of transient simulation. Therefore, simulation speed is greatly improved with high accuracy. Neural network technique has been used in simulation for different purposes. Pillutla used
neural network observers to estimate un-measurable rotor body currents [4] [5] [6]. Tsai used neural network based saturation model for synchronous generator analysis [7]. FEA simulation collects datasets of field currents and their flux linkages. And neural network builds a function with flux linkages as input and currents as outputs.. (2) System level simulation is based on dynamic voltage equation [11]. Dynamic voltage equation provides excellent mathematical model for machine simulation. Different techniques are combined to provide comprehensive solution for generator system simulation. Other parts of the system include PI control, Rectifier Bridge, and bang-bang control. The proposed model provides flexibility for different system configuration. Transient simulation with varying load, speed and thermal conditions can be accomplished. PRINCIPLES OF GENERATOR MODELING The primary objective of FEA analysis is to get quantitative relationship between different current inputs and its flux linkages. Quantities in natural a- b-c frame are time varying. Quantities in DQ rotating frame are constant under balanced load conditions. It is convenient to refer all the quantities in DQ rotating frame through alternative form of Park s transformation [8] [9] [10] The inversion form of Park s transformation is given as: For synchronous machine with balanced load, zerosequence components are set as zero. Quantities in DQ frame are DC values, which makes the analysis easier. Fig. 1 shows one pole of the main machine s FEA model. The stator is shifted from the rotor for simplicity of modeling. (3) (1) where stands for, or. The Flux linkage equation in matrix form is transformed as: Fig. 1: One pole of main machine Values of current in the stator and the rotor vary from very small to large. Since the power factor is not known, different D-, Q-axis currents are simulated. Together with field current, a current matrix is formed which represents thousands of
setups. FEA simulations are conducted for each set, and the same number of flux linkage sets is extracted. Each set of current inputs corresponds to one particular set of flux linkage. The voltage equation in DQ frame can be written as: Equation (4) is the mathematical model of the simulation. (4) Fig. 3: Individual Simulink model ELECTRICAL SYSTEM MODELING The electrical system includes two machines, the main and the exciter. Circuit models can be extracted for each individual machine. Fig. 2 shows the circuit diagram of an individual machine. In this figure, a constant DC voltage is applied to the field winding, which includes a field winding resistance ( ) and a field winding inductance ( ). The armature circuit consists of six-phase inductance and six-phase winding resistance. The six-phase output is connected to a rectifier bridge, which converts AC voltage to DC output. The load is connected to the DC power. After modeling the individual machine, a closed loop system can be modeled. Fig. 4 shows the block diagram of the system. The main machine provides the output of the system. The exciter provides output power, which is the field input power for main machine. The field input to the exciter is DC. The output voltage of the main machine is connected to PI control block. The output of the PI control block is the field command current, which turns on and off the exciter field power supply. Fig. 4: System diagram NEURAL NETWORK Fig. 2: Circuit diagram of the individual machine The main machine and the exciter share the same model. Fig. 3 shows the block diagram of the simulation model for the individual machine. In this work, the nonlinear relationship between flux linkage and current is expressed by neural network functions. Nonlinear treatment is crucial to the accuracy of saturating machine simulation. The neural network takes the inputs to calculate results based on selected functions and compares them with target values. Error message is used to adjust
weight and bias values. The result of a typical 3- layer neural network can be written as: (1) Fig. 6: Steady state current output with 1 MW load Fig 7 shows field current of the main machine under steady state condition with 1 MW load. It varies around 47.4A with less than 0.5A AC current. RESULTS Fig. 5 shows the steady state voltage output of the closed loop system with 1 MW loads. The voltage varies between 196 to 199 Volts. It is very small ripple for this high voltage output. Fig. 7: Steady state field current of main machine with 1 MW load Fig. 8 shows the field current of the exciter under steady state condition. It varies around 7.8 A with 0.5A AC current. The behavior of the ripple is controlled by bang-bang control design. Fig. 5: Steady state voltage output with 1 MW load Fig.6 shows the steady state current outputs of the closed loop system with 1 MW load. Because of the rectifier bridge, the current output has ripples with a frequency 6 times higher than the system frequency. Fig. 8: Steady state field current of the exciter with 1 MW load CONCLUSION An innovative nonlinear simulation approach is used to analyze a high power density 1MW synchronous generator system under steady-state conditions. Principles of system level simulation are introduced. The Simulink models of synchronous machine and associated control system are
presented. Neural network technique is introduced. Performance results in simulations are shown. ACKNOWLEDGMENTS The funding for this work was provided by Electrodynamics Associates, Inc., Oviedo, FL under Contract from Lockheed Martin Corporation. REFERENCES [1] N. Sadowski, B. Carly, Y. Lefevre, M. Lajoie- Mazenc, and S. Astier, Finite element simulation of electrical motors fed by current inverters, IEEE Trans. Magnetics, Vol. 29, No. 2, pp.1683-1688, March 1993. [2] A.A. Fardoun, E. F. Fuchs, and H. Huang, Modeling and simulation of an electronically commutated permanent-magnet machine drive system using SPICE, IEEE Trans. Industry Applications, Vol. 30, No.4, pp. 1550-1555, July/August 1994. [3] S. P. Natarajan, C. Chellamuthu, B. Karki, and C.A. Kumar, Simulation and performance evaluation of permanent magnet brushless DC motor using Saber package, Computers in Power Electronics 2000. pp. 235 240, July 2000. [4] S. Pillutla, and A. Keyhani, Development and implementation of neural network observers to estimate the state vector of a synchronous generator from on-line operating data, IEEE Trans. Energy Conversion, Vol. 14, No.4, pp. 1081-1087, December 1999. [5] S. Pillutla, and A. Keyhani, Neural network based modeling of round rotor synchronous generator rotor body parameters from operating data, IEEE Trans. Energy Conversion, Vol. 14, No. 3, pp. 321-327, September 1999. [6] S. Pillutla, and A. Keyhani, Neural network based saturation model for round rotor synchronous generator, IEEE Trans. Energy Conversion, Vol. 14, No. 4, pp. 1019-1025, December 1999. [7] H. Tsai, A. Keyhani, J. A. Demcko, and D. A. Selin, Development of a neural network based saturation model for synchronous generator analysis, IEEE Trans. Energy Conversion, Vol. 10, No. 4, pp. 617-624, December 1995. [8] A. E. Fitzgerald, C. Kingsley, Jr., and S. D. Umans, Electric Machinery, 6 th Edition, McGraw- Hill, 2003. [9] R. H. Park, Two-Reaction theory of synchronous machines Generalized methods of analysis Part I, AIEE Trans., vol. 48, pp.716-727, July 1929. [10] R. H. Park, Two-Reaction theory of synchronous machines, Part II, AIEE Trans. Vol. 52, pp. 352-355, June 1933. [11] B. P. Muni, S. K. Pillai, and S. N. Saxena, Digital simulation of internal power factor angle controlled surface mounted permanent magnet synchronous motor, Proc. of the 1996 International Conference on, Vol. 2, pp. 900-906, Jan. 8-11, 1996