Syn. Generator Simulatin

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Nonlinear Electrical Simulation of High-PowerSynchronous Generator SystemJie Chen and Thomas WuUniversity of Cen tral Florida

Jay G VaidyaElectrodynamics Associates, Inc.James Tschantz

Air Force R esearch Laboratory, Wright-Patterson AFB

Copynght 0 00 6 S AE l n t e m a t ~ o r ~ a l

ABSTRACTAn innovative nonlinear simulation approach forhigh power density synchronous generator systemsis developed and implemented. Due to high powerdensity, the generator operates in nonlinear regionof the magnetic circuit. Magnetic Finite ElementAnalysis (FEA) makes nonlinear simulationpossible. Neural network technique providesnonlinear functions for system level simulation.Dynamic voltage equation provides excellentmathematical model for system level simulations.Voltage, current, and flux linkage quantities areapplied in Direct-Quadrature (DQ) rotating frame.The simulated system includes main machine,exciter, rectifier bridge, bang-bang control, and PIcontrol circuitry, forming a closed loop system.Each part is modeled and then integrated into thesystem model.INTRODUCTIONHigh power density of generator design requiresoperation under saturated magnetic circuitconditions. This paper focuses on electricalsimulation o f the system.

Electrical simulation includes Finite ElementAnalysis (F EA ), and system level simulation. FEAhas been widely implemented to conductelectromagnetic simulation of individual machines.System level simulation can be done by combiningFEA and other software tools. Sadowski combinedfinite element simulation and current inverters formotor simulation [I ]. Fardoun simulatedpermanent-magnet machine drive system usingSPlCE [2] . Natarajan simulated motor with Saberpackage [3]. Some commercially available softwaretools use the same scheme for motor transientsimulations. These tools directly combinemachine'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 innovativeapproach to simulate generator systems. Instead ofdirectly combining machine's FEA model with itssupporting circuitry, this work separates FEAsimulation and system level simulation, and linksthem with neural network training results of FEAsimulation. The benefit o f this treatment is that FEAis not involved in each step of transient simulation.Therefore, simulation speed is greatly improvedwith high accuracy.


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Neural network technique has been used insimulation for different purposes. Pillutla usedneural network observers to estimate un-measurablerotor body currents [4] [5] [6]. Tsai used neuralnetwork based saturation model for synchronousgenerator analysis [7]. FEA simulation collectsdatasets of field currents and their flux linkages.Neural network builds a function with flux linkagesas input and currents as outputs.System level simulation is based on dynamicvoltage equation [I I] [12]. Dynamic voltageequation provides excellent mathematical model formachine simulation. Different techniques arecombined to provide comprehensive solution forgenerator system simulation. Other parts of thesystem include PI control, re ctif ier' bridge, an dbang-bang control. The proposed model providesflexibility for different system configuration.Transient simulation with varying load, speed andthermal conditions can be accom plished.

PRINCIPLES OF GENERAT OR MODELING

Flux linkage equation in matrix form can be writtenas [8] :

where Lmn is mutual inductance, L,,,, is the selfinductance, Ir n s the current of m phase, /ln is theflux linkage of m phase, and m , n = a,6, c , .The primary objective of FEA analysis is to getquantitative relationship between different currentinputs and its flux linkages. Quantities in naturalabc frame are time varying. Quantities in DQrotating frame are constant under balanced loadconditions. It is convenient t o refer all the quantitiesin DQ rotating frame through alternative form ofPark's transformation [8] [9] [ 101

( 2 )r cos B cos(H - 120") cos(B + 120") 11s"1

where S stands for L , I or A .(1) is transformed as:

The inversion form of Park's transformation isgiven as:

For synchronous machine with balanced load, zero-sequence components are set as zero. Quantities inDQ frame are dc values, which makes the analysiseasier. Fig. 1 shows two poles of the mainmachine's FEA m odel. The Direct (D-) axis of thestator is aligned with the center line of the rotorpole. The stator is shifted from the rotor for ease ofmodeling.


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Fig. 1 Two poIes of main m achine with alignedstator's D Q frame and rotor'sValues of current in the stator and the rotor varyfrom very small to large. Since the power factor isnot known, different D-, Q-axis currents aresimulated. Together with field current, a currentmatrix is formed which represents thousands ofsetups. FEA simulations are conducted for each set,and the same number of flux linkage sets isextracted. Each set of current inputs corresponds toone particular set of flux linkag e.The modeling of individual machine is based on thevoltage equation [1 1] [12 ]:

where V, is the voltage of rn phase, andm ,n = a ,b , c ,f

VVv c

- -

- v / -

(6 ) is the ma thematical m odel o f the simulation.

ELECTRICAL SYSTEM MODELING

The electrical system includes two machines, themain and the exciter. Circuit models can beextracted for each individual machine. Fig. 2 showsthe circuit diagram of an individual machine. In thisfigure, a constant dc voltage is applied to the fieldwinding, which includes a field winding resistance( R , ) and a field winding inductance ( L , ). The

4.1( 5 )

--

armature circuit consists of three phase inductanceand three phase winding resistance. The three phaseoutput is connected to a rectifier bridge, whichconverts ac voltage to dc output. The load isconnected to the dc output terminals.

-R, O O O I U0 - R , 0 0 1 ,

- 0 R- O O O R , -

1 ' Lf 3 Zload

:- --- -I

Fig. 2. Circuit diagram o f the individual machineThe main machine and the exciter share the samemodel. Fig. 3 shows the block diagram of thesimulation model for individual machine.

The voltage equation in D Q frame can be written as:


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Fig. 3 Individual Sim ulink model

After modeling individual machine, a closed loopsystem can be modeled. Fig. 4 shows the blockdiagram of the system. The main machine providesthe output of the system. The exciter providesoutput power, which is the field input power formain machine. The field input to the exciter is dc.The output voltage of the main machine isconnected to PI control block. The output of the PIcontrol block is the field command current, whichturns on and off the exciter field power supply.

Olitp~lt pzrrelin(w3 * (w 2 * tans ig(wl *Input + bl) + b2) + b3 ) (7 )

R E S U L T SFig. 5 shows the transient response of the closedloop system. During 0 to 0.12s, the load of thesystem is 2.5 M W. Th e load changes to 0.25MW at0.12s, and changes back at 0.4s. This figure showsthe overshoot, undershoot and the transient time.These parameters are all within specifications.

rn;oo nL4E

Fig. 5 Transient response

Fig. 4 System diagram

NEURAL NETWORK

In this work, the nonlinear relationship betweenflux linkage and current is expressed by neuralnetwork functions. Nonlinear treatment is crucial tothe accuracy of saturating machine simulation. Theneural network takes the inputs to calculate resultsbased on selected functions and compares themwith target values. Error message is used to adjustweight and bias values. The result of a typical 3-layer neural network can be written as:

Fig. 6 shows the steady state voltage output of theclosed loop system with 2.5 MW loads. The voltagevaries between 1650 to 167 0 Volts. It is very smallripple for this high voltage output.

Fig. 6 Steady state voltage output with 2.5MW load


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Fig. 7 shows the steady state current outputs of theclosed loop system with 2.5 MW load. Because ofthe rectifier bridge, the current output has rippleswith a frequency 3 times higher than the systemfrequency.

Fig. 7 Steady state current output with 2.5 M W loadFig. 8 shows field current of the main machineunder steady state condition with 2.5 MW load. Itvaries around 55A with less than 3A ac currentripple.

Fig. 8 Steady state field current of main m achinewith 2.5 M W load

Fig. 9 shows the field current of the exciter understeady state condition. It varies around 9.6A with0.6A ac current ripple. The behavior of the ripple iscontrolled by bang-bang control design.

o 1 1 n . i i n s n 1 1 1 0 1115TIrr~(s )Fig. 9 Steady state field current of the exciter with

2 .5 MW load

CONCLUSION

An innovative nonlinear simulation approach isused to analyze a high power density synchronousgenerator system under steady-state and transientload conditions. Principles of system levelsimulation are introduced. The Simulink models ofsynchronous mac hine and associated control systemare presented. Neural network technique isintroduced. Performance results in simulations areshown.ACKNOWLEDGMENTS

The funding for this work was provided byElectrodynamics Associates, Inc., Oviedo, FL underUS Air Force Research Laboratory ContractNumber F33615-02-C-22 16.REFERENCES

[I] N . Sadowsl


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[3 ] S . P. Natarajan, C. Chellamu thu, B. Karki, and [I21 1. Tabatabaei, J. Faiz, H. Lesani, and M. T.C.A. Kumar, "Simulation and performance Nabavi-Razavi, "Modeling and simulation of aevaluation of permanent magn et brushless dc motor salient-pole synchronous generator with dynamicusing Saber package," Computers in Power eccentricity using modified winding functionElectronics 2000. pp. 235 - 240, July 2000. theory," IEEE Trans. Magnetics, Vol. 40, No.3,pp.1550-1555, May 2004.[4] S. Pillutla, and A. K eyhani, "Development andimplementation of neural netwo rk observers toestimate the state vector of a synch ronous generatorfrom on -line operating data," IEE E Trans. EnergyConversion, Vol. 14, No.4, pp. 1081- 1087,December 1999.[5] S. Pillutla, and A. Keyhani, "Neural networkbased modeling of round rotor synchronousgenerator rotor body parameters from operatingdata," IEEE Trans. Energy Conversion, Vol. 14, No.3, pp. 321-327, September 1999.[6] S. Pillutla, and A. Keyhani, "Neural networkbased saturation model for round rotor sync hronou sgenerator," IEEE Trans. Energy C onversion, Vol.14, No. 4, pp. 10 19-102 5, Decem ber 1999.[7] H. Tsai, A. Keyhani, J. A. Demck o, and D. A.Selin, "Development of a neural netw ork basedsaturation model for synchronous generatoranalysis," IEEE Trans. Energy Conversion, Vol. 10,No. 4, pp. 617-624, December 1995.

[8] A. E. Fitzgerald, C. Kin gsley, Jr., and S. D.Umans, Electric Machinery, 6t" Edition, M cGraw-Hill, 2003.[9] R. H. Park, "Two-Reaction theory ofsynchronous machines - Generalized methods ofanalysis - Part I," AIEE Trans.. vol. 48, pp.716-727,July 1929.[I 01 R. H. Park, "Two-R eaction theory ofsynchronous machines, Part 11," AIEE Trans. Vol52, pp. 352-355, June 1933.[ l l ] B. P. Muni, S . K. Pillai, and S. N. Saxe na,"Digital simulation of internal power factor anglecontrolled surface mounted permaent magnetsynchronous motor," Proc. of the l Y Y 6International Conferenc e on, Vol. 2, pp. 900 - 906,Jan. 8 - 11, 1996.

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