Prediction of Performance Characteristics of
Salient Pole Synchronous Generators by
Finite Element Method
K. S. Jiji*, Jayadas N. H. ** and C. A. Babu**
* Department of Electrical engineering, Rajiv Gandhi Institute of Technology, Kottayam – 686 501, India
Jiji.sajeev@rit.ac.in
** School of Engineering, Cochin University of Science and Technology, Kochi – 682 022, India
jayadasnh@cusat.ac.in and cababu@cusat.ac.in
Abstract— Performance prediction in electrical machines
is often carried out by traditional methods which combine
analytical and empirical knowledge. These methods lack
accuracy as the calculation of magnetic field pattern and
characteristics yield approximate results due to complicated
machine geometry and nonlinear characteristics of magnetic
materials associated with the machine. Finite element
method is a numerical tool being extensively used as a
design tool for prediction of machine parameters by
electromagnetic field analysis. In this paper an attempt is
made to predict the performance characteristics of salient
pole synchronous generators by finite element method.
Index Terms— Synchronous generators, Total harmonic
distortion, FEM, Armature windings, Maxwell’s equations.
I. INTRODUCTION
Salient pole synchronous generators coupled to IC
engines are being extensively used as standby power
supply units for meeting industrial power demands.
Design of such generators demands for high power to
weight ratio, high efficiency and low cost per KVA
output. Moreover, the performance characteristics of such
machines like voltage regulation, short circuit ratio (SCR)
etc. are critical when these machines are put into parallel
operation and alternators for critical applications like
defence, aerospace etc demand very low harmonic
content in the output voltage. While designing such
alternators, accurate prediction of machine characteristics
is essential to minimize development cost and time.
Performance prediction in synchronous generators is
often carried out using traditional methods which
combine analytical and empirical knowledge. These
methods lack accuracy due to complex geometry and
nonlinear characteristics of magnetic materials associated
with the machine and performance characteristics such as
magnetization characteristics, losses, currents, voltage
etc. are calculated based on averaging assumptions for
the magnetic field in the air gap and the core. Hence, the
results of machine performance characteristics by
analytic methods are enough accurate only at steady state
operation of the machine and the results are unreliable for
transient operation. Hence numerical field computation
methods like Finite Difference Method (FDM), Boundary
Element Method (BEM) and Finite Element Method
(FEM) have been deployed for prediction and analysis of
machine characteristics [1] by electromagnetic field
analysis. However, FEM is increasingly used by
designers due to its ability to handle complex geometry
and presence of nonlinear magnetic materials. Due to
advancements in computational capabilities over recent
years FEM has become an attractive alternative to well
established semi analytical and empirical design methods
as well as to the still popular trial and error approach
[2-3].
This paper presents the FEM based prediction of
performance characteristics of a salient pole brushless
synchronous generator and comparison of output voltage
harmonics of the machine provided with two different
layouts for the armature winding.
II. SYNCHRONOUS MACHINE DESIGN – SIGNIFICANCE OF
ARMATURE WINDING LAYOUT
The synchronous generators used in diesel
generating units are normally designed with different
winding layouts based on the desired machine parameters
like THD, transient characteristics like transient voltage
dip/rise (TVD/TVR), transient time constants etc. The
simplest type of armature winding provided for such
machines is the full pitched winding which has got the
advantages like single layer structure which reduces the
labor put for winding process, maximum voltage induced
in the windings owing to high winding factor which
ultimately leads to lower size of the machine for the same
KVA output and hence reduced cost. But, this type of
winding is having a disadvantage like high harmonic
content in the output voltage across line and neutral
which may have ill effects on the sophisticated single
phase loads connected across these machines. To
circumvent the problem of high total harmonic distortion
(THD) in the output voltage, conventionally, the main
winding is wound for 2/3rd pitch which introduces
complexity in winding due to arrangement of the winding
in two layers leading to increased labor cost and
additional insulation requirements in the slots and in the
winding overhang. This type of winding results in
reduced KVA due to poor winding factor and hence
increase in size by about 13%.
III. FEM BASED DESIGN OF ELECTRICAL MACHINES
by the nonlinear partial differential equation,
FEM is being extensively used as a design tool for
modeling of electrical machines [4-7] and prediction of
machine parameters like open circuit voltage distortion
[8-11], direct axis and quadrature axis synchronous
reactances [12] etc. In this paper, the performance
characteristics of a 45 KVA brushless alternator like open
circuit characteristics (OCC), zero power factor
characteristics (ZPFC) and air gap flux density
distribution at no load and full load conditions are plotted
and harmonic content in the output voltage of the
machine with two different winding layouts are analyzed
by finite element method.
1
A. FEM Formulation
The mathematical modeling of magnetic field
problems in closed and bounded systems is based on
Maxwell’s equations and constitutive relationships as
detailed below.
 H  J 
 E  
D
t
B
t
(1)
(2)
 B  0
(3)
 D  
(4)
where H = Magnetic field strength
J = Current density
D = Electric displacement
E =Electric field intensity
B = Magnetic flux density
 = volume charge density
The constitutive relationships are
where
B  H
(5)
D E
(6)
J E
(7)
 = Magnetic permeability
 = Electric permittivity and
 = Electric conductivity
The field properties of the machine are invariant along
the z – axis and hence 2D FEM formulation is sufficient
for analysis of electrical machines thereby considerably
reducing the computational time. The distribution of
magnetic field in the 2D machine structure is expressed
 2 AZ   J Z
(8)
 2 AZ  2 AZ

  J Z
x 2
y 2
(9)

ie.,
where
 = absolute permeability of magnetic field
AZ = Magnetic vector potential in Z direction and
J Z = Current density vector normal to the section
(in Z direction)
The current density vector J has z-axis component
only and the magnetic vector potential A being parallel to
J has components only in the z-direction.
Solving the nonlinear partial differential equation by
FEM yields the magnetic vector potential A from which
the magnetic flux density B having components only in
the (x,y) plane is computed using the relation
B   A
(10)
From the calculated value of B at each and every point
in the 2D machine structure, all field values and hence
machine parameters can be computed.
B. FEM Modeling and Analysis
The FEM modeling of the synchronous machine is
done using the geometrical data, material properties,
winding data, period of symmetry and the boundary
conditions. The specifications and the main geometrical
data of the machine modeled are given in Table I. The
winding data are prepared separately for full pitched
machine and the 2/3rd pitched machine. The FEM models
of the two machine configurations are analyzed
separately for the harmonic content in the output voltage
to ascertain the effect of the two different winding
layouts on the output voltage harmonics.
TABLE I
SPECIFICATIONS AND GEOMETRICAL DATA OF THE MACHINE
Capacity
Frequency
Output Voltage
Number of poles
Number of phases
Number of stator slots
Air gap
Inner diameter of stator
Outer diameter of stator
Inner diameter of rotor
Outer diameter of rotor
Stack Length
Core material
45 KVA
50 Hz
415 V
4
3
36
0.9 mm
240 mm
356 mm
90 mm
238.2 mm
130 mm
M43C4
IV. RESULTS AND DISCUSSION
The FEM models of the 45 KVA machine with the
two different winding layouts are simulated for 0.8 pf,
full load and the output voltage harmonics are analyzed
in each case. The performance characteristics of the full
pitched machine like OCC, ZPFC and air gap flux density
distributions for no load and full load conditions are
plotted.
The winding layouts of the two configurations are
shown in Figs. 1 and 2.
Fig. 1. Winding layout of the full pitched machine
Fig. 4. FEM model of the 45 KVA 2/3rd pitched generator
First order triangular elements are used to discretize
the field region and the finite element mesh applied to the
machine models are shown in Figs. 5 to 6.
Fig. 5. FEM model of the full pitched generator after meshing
Fig. 6. FEM model of the 2/3rd pitched generator after meshing
Fig. 2. Winding layout of the machine with 2/3rd pitch winding
The FEM models of the synchronous generator with
the two different winding layouts are shown in Figs. 3
to 4.
Flux distribution and the flux density plots of the
generator with two different winding layouts are shown
in Figs. 7 to 10.
Fig. 3. FEM model of 45 KVA full pitched generator
Fig. 7. Flux distribution of 45 KVA full pitched generator
ANSOFT
2.50
Curve Info
Air-Gap Flux Density
(Tesla)
1.25
0.00
-1.25
-2.50
0.00
Fig. 8. Flux density plot of 45 KVA full pitched generator with rotor
rotted through 15o
125.00
250.00
Electric Degree
375.00
Fig. 12. Air gap flux density plot at full load
ANSOFT
Curve Info
1.50
No-Load Voltage
Load Voltage with PF=0
Phase Voltage (per unit)
1.25
1.00
0.75
0.50
0.25
0.00
0.00
100.00
200.00
300.00
Exciting Current (A)
400.00
500.00
600.00
Fig. 13. Open circuit characteristic (OCC) and the zero power factor
characteristics (ZPFC) of the generator
Fig. 9. Flux distribution of 45 KVA full pitched generator
The output voltage waveforms and their harmonic spectra
for the two different cases are shown in Figs. 14 to 17.
XY Plot 1
Maxwell2DDesign4_FP
ANSOFT
Curve Info
InducedVoltage(PhaseA)
Setup1 : Transient
375.00
InducedVoltage(PhaseB)
Setup1 : Transient
250.00
InducedVoltage(PhaseC)
Setup1 : Transient
Y1 [V]
125.00
0.00
-125.00
-250.00
-375.00
100.00
125.00
150.00
175.00
200.00
225.00
250.00
275.00
Time [ms]
Fig. 14. Output voltage waveform of 45 KVA full pitched generator
Fig. 10. Flux density plot of 45 KVA 2/3rd pitched generator with rotor
rotated through 13.5o
FFT XY Plot 2
Maxwell2DDesign4_FP
119.96
FFT InducedVoltage(PhaseC)
The air gap flux density plot of the machine under no
load and full load conditions are shown in Figs. 11 to 12
and the open circuit characteristics (OCC) and the zero
power factor characteristics (ZPFC) are shown in Fig. 13.
ANSOFT
Curve Info
FFT InducedVoltage(PhaseC)
Imported
105.00
85.00
65.00
45.00
25.00
5.00
32.89
250.00
500.00
750.00
Curve Info
Air-Gap Flux Density
1000.00
1206.14
FFT Time
ANSOFT
1.00
Fig. 15. Harmonic spectra of output voltage waveform of 45 KVA full
pitched generator
0.50
XY Plot 1
Maxwell2DDesignICEMS12
(Tesla)
356.80
ANSOFT
Curve Info
InducedVoltage(PhaseA)
Setup1 : Transient
250.00
0.00
InducedVoltage(PhaseB)
Setup1 : Transient
InducedVoltage(PhaseC)
Setup1 : Transient
Y1 [V]
125.00
-0.50
0.00
-125.00
-1.00
0.00
125.00
Electric Degree
250.00
375.00
-250.00
-356.91
Fig. 11. Air gap flux density plot at no load
102.40
125.00
150.00
175.00
200.00
225.00
250.00
268.30
Time [ms]
Fig. 16. Output voltage waveform of 45 KVA 2/3rd pitched generator
FFT XY Plot 2
Maxwell2DDesignICEMS12
ANSOFT
Curve Info
250.00
[2]
FFT InducedVoltage(PhaseC)
Imported
FFT InducedVoltage(PhaseC)
200.00
150.00
[3]
100.00
50.00
[4]
0.00
50.00
100.00
150.00
FFT Time
200.00
250.00
Fig. 17. Harmonic spectra of output voltage waveform of 45 KVA
2/3rd pitched generator
[5]
On analyzing the harmonic spectra of the output
voltage of the generator with full pitched winding it is
observed that there is high harmonic content especially of
orders third and fifth. The simulation results confirm that
by introducing 2/3rd pitch armature winding; the third
harmonic components are completely eliminated from the
output voltage.
[6]
17, No. 3, pp. 306-312, September 2002.
[7]
V. CONCLUSIONS
In this paper, a simple, fast and efficient method
based on 2D FEM for predicting the performance
characteristics of a salient pole brushless synchronous
generator is presented. FEM proves to be an efficient
numerical tool for prediction of performance
characteristics of electrical machines in the design stage
thus saving development time and cost by avoiding
expensive and time consuming prototyping. This method
can also be used for predicting machine parameters like
TVD/TVR, transient time constants, transient reactances
etc. without resorting to sudden short circuit test which is
hazardous to the machine.
[8]
[9]
[10]
[11]
[12]
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