Nonlinear Electrical FEA Simulation of 1MW High Power
Synchronous Generator System
Jie Chen
School of Electrical Engineering and Computer Science, University of Central Florida,
Orlando, FL 32816
Jay G Vaidya
Electrodynamics Associates, Inc. 409 Eastbridge Drive, Oviedo, FL 32765
Shaohua Lin
School of Electrical Engineering and Computer Science, University of Central Florida,
Orlando, FL 32816
Thomas Wu
School of Electrical Engineering and Computer Science, University of Central Florida,
Orlando, FL 32816
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.
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 ab-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]
(2)
.
The inversion form of Park’s transformation is
given as:
(3)
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.
(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:
(4)
Equation (4) is the mathematical model of the
simulation.
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.
Fig. 3: Individual Simulink model
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 3layer 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.
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