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Content uploaded by Naseer Ahmad
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All content in this area was uploaded by Naseer Ahmad on Jul 18, 2018
Content may be subject to copyright.
Analytical Modeling of Low Cost Single Phase
Wound Field Flux Switching Machine
S. Ishaq1, F. Khan2, N. Ahmad3, K. Ayaz4, W. Ullah5
Department of Electrical Engineering,
COMSATS institute of information and technology Abbottabad, Pakistan
1samraishaq@ciit.net.pk , 2faisalkhan@ciit.net.pk
Abstract—For applications demanding low cost
and high efficiency, Wound Field S witched Flux
(WFSF) machines are good candidate. However,
the complex structure, nonlinear behavior and
magnetic saturation increase the challenge in
adaptation of analytical method to model the
magnetic flux distribution. Finite Element Method
is not feasible for initial des ign level of machine
owing to computational complexity. Fourier
Analysis has less accurate results. To date,
Magnetic Equivalent Circuit (MEC) modeling is
best for initial design level. Magnetic Equivalent
Circuit (MEC) modeling inherits the feature of less
computational complexity and better accuracy.
Therefore, this paper presents the Magnetic
Equivalent Circuit (MEC) modeling of proposed
8slots-6poles Wound Field Switched Flux (WFSF)
machines with trapezoidal slot structure. Magnetic
Equivalent Circuit (MEC) modules of different
parts of WFSF machine are examined. Global
Reluctance Network (GRN) obtained and solved to
get incidence matrix in MATLAB. No-load flux
linkage of GRN methodology is compared with
Finite Element Analysis (FEA) results. The error
computed is les s than ~2% which demonstrate the
GRN methodology validation.
Keywords— Finite element analysis; Magnetic
equivalent circuit; Global reluctance network;
non-overlapped windings; wound field flux
switching machine.
I. INTRODUCTION
The Wound Field Switched Flux (WFSF) machines
deals with distinctive feature of robus t rotor structure,
low material cost, and easy thermal control. WFSF
machine is compatible for extreme environmental
situation and can be used in various applications [1].
Basic structure of WFSF machine is described by
replacing the Permanent Magnet (PM) with DC field
windings on stator, which provide the advantage
robust rotor s tructure s uitable for high speed
applications . WFSF machine is the combination of
inductor alternator and switched reluctance machine.
WFSF machine is inexperienced class of machine
before 1955 [2]. However, in last 2 decades various
topologies of single and three phas es WFSF machines
have been introduced posses sing low cos t structure
and high efficiency. Although W FSF machines have
relatively low torque density as compared to PM
Synchronous Machine (PMSM) [3], [4]. In cos t
sensitive applications the use of PM is avoided due to
high cost of rare-earth magnets .
Advanced analytical methods like Magnetic
Equivalent Circuits (MEC), Finite Element Analysis
(FEA), and Fourier Analysis (FA) are used to predict
performance parameters of electrical machines. Each
analytical method has significant merits and demerits.
Appropriate analytical model should be selected,
depending upon the purpose of designing the electrical
machine. FEA requires large computational time and
substantial computational asserts . While, FA require
small computational time as a results less accuracy
involved in the calculations [5], [6]. Cons equently,
MEC is the fastest numerical method with less
computational complexity and more accuracy.
Reluctance Network Method (RNM) topology is used
to inves tigate MEC modeling. MEC model is mos t
commonly used tool which evaluates the performance
of electrical machine at initial sizing level. MEC
models of PMFSM with 12stator slots and 10 rotor
poles have been examined in [7], investigated PMFSM
had rectangular slots structure.
Novel s tructure of single-phase FSM for
conventional fan application has been presented in [8].
The proposed des ign has 12 stator s lots and 6 rotor
poles topology with trapezoidal s lots structure. Both
FEC and armature coils have non -overlapped
windings. The advantage of proposed topology lies in
low copper los ses, less weight , and high efficiency.
However, design had s ome limitations s uch as
segmental rotor and alternate winding arrangement of
FEC. Thus , machine is not suitable for high speed
applications and has less flux linkage. Two novel
structures of s ingle-phase W FSF machines
areproposed in [9]. Both designs are validated
experimentally in which 8slots -4poles WFSF design
has better performance. However, overlapped
windings arrangement causes high copper losses and
low efficiency. The s tructure of 8slots -4poles design
is presented in Fig. 1. To overcome the limitations of
12slots-6poles and 8slots -4poles WFSF machines
novel design of 8slots -6poles WFSF machine is
proposed depicted in Fig. 2. Proposed design has
salient rotor structure with non-overlapped windings
arrangement with FEC is in forward direction. Non-
overlapped windings arrangement exhibits low copper
consumption, low copper loss es and high efficiency.
Similarly, s alient rotor is robust rotor structure
employed for high s peed applications. Forward
direction of FEC results in better flux linkage and
larger average torque of proposed WFSF machine.
This paper emphas izes on the MEC models of single
phase 8s lots-6poles WFSF machine with trapezoidal
slots structure proposed in Fig. 2. MEC models
inves tigated corresponding to different rotor positions
known as Reluctance Networks. Reluctance Networks
are combined to get Global Reluctance Network
(GRN). Subsequently, GRN are solved employing
incidence matrix approach using MATLAB.
Furthermore, JMAG s oftware is used for no-load
analys is and load analys is to validate WFSF machine
with 2D-FEA .
II. DESIGN STRATEGY
Japan Research Institute released JMAG Design 14.1
version, utilized as 2D- FEA solver. WFSF machine
stator consists of 8 trapezoidal slots structure
containing field and armature windings . 4 stator slots
contained armature windings in alternate winding
arrangement. However, remaining 4 s tator slots
contained DC field winding in forward winding
arrangement producing single phase flux. Geometric
parameters of 8slots -6poles WFSF machine are listed
in Table 1. WFSF machine rotor’s s tructure has
similarity with rotor of SRM. Consequent of this
property an undesired sensitive relation of rotor
pos ition with airgap magnetic flux distribution is
depicted in Fig. 3. Reluctance network required to
update according to the rotor position as at different
rotor pos ition permeance values as well as reluctance
network topology changed. Therefore, electrical
machine having low periodicity requires the manual
effort to implement the RNM. Global Reluctance
Fig. 1: 8slots-4poles WFSF Machine St ructure [9].
Fig.2: 8slots-6p oles WFSF Machine with Non-overlapped
Windings Arrangement.
Fig.3: Finit e Element Analysis results of WFSF Machine at (a)
Segment No. 1 and (b) Segment No. 2
T able 1: Design Parameters
Feature
Dimension
Rated Speed (rpm)
1000
Axial Length (mm)
25
Split Ratio
0.5
Rotor po les number
6
Stator pole number
8
Stator Back-iron th ickness (mm)
5
Rotor po le width (mm)
10.6
Stator slot width ( mm)
8.2
Outer radius of roto r (mm )
45
T otal field slot area (mm2)
1123.009
T otal armat ure slot area
(mm2)
1123.009
T otal number of turns of field windings
180
T otal number of turns of arm ature windings
180
Filling fact or
0.4
Lengt h of air-gap
0.5
Network (GRN) of 8slots-6poles WFSF machine is
obtained from stator MEC modules, rotor MEC
modules and airgap MEC modules res ultant from
different rotor’s positions. Rotor position much
influence on airgap flux distribution as compared to
stator and rotor. Different s egment are taken
corresponding to rotor position. Half portion of the
8slots -6poles WFSF machine is taken for MEC
modeling to reduce the computational time and
complexity. Series of MEC modules are cons ider for
airgap region s ome of which are duplicate, where the
permeances of each airgap MEC module vary as
functions of the rotor position, the phenomena is
known as position state shifting. Due to position state
shifting the GRN may reduce.
III. MEC Modules
MEC modules depends upon the analogy exist
between electric and magnetic circuits [10] as depicted
in equation 1.
(1)
is magnetic flux, F is magneto motive force, R is the
reluctance of magnetic circuit and P is the permeance.
Two types of elements are present in MEC model.
Pass ive elements and active elements, Pas sive
elements includes reluctance of the magnetic circuits
while active elements includes sources. Sources of the
magnetic circuits further categorized into two types:
magnetic flux and mmf source. Mmf is us ed as a
source for current carrying coil. Value of mmf can be
calculated using Amper’s law for current carrying coil
shown in equation 2.
(2)
Where F is mmf, N is no of turns of current carrying
coil and I is the amount of current pass ing through
conductor. MEC module include the calculation of
permeances , however the permeance can be calculated
using flux tubes. 6 types of flux tubes are used for
MEC modeling. Flux tubes having identical flux line
length their reluctance can be calculated using
equation 3. Fig. a and c flux tubes having identical flux
line length.
(3)
µ and A are the material’s permeability and cros s
section of flux tube respectively. µ and A changes
through the length of flux tubes. Flux tube of figure b,
Fig. d-f depicted that length of flux lines are varying.
However, cross section of faces is identical.
(4)
Table 2 shows the formulas for permeances
calculations of different types of flux tubes. Fig. 4a
and 4b employed cylindrical coordinates for
pearmeance calculations while cartas ian coordinate
system is us ed for remaining flux tubes.
A. Stator MEC Modules
Unit s ection of stator is used to model magnetic flux
distribution in stator. Unit s ection is defined the region
between two adjacent stator winding. The unit section
of stator and cross ponding MEC module is depicted
in Fig. 5. Leakage flux path is denoted by Psl. Similarly
flux path in stator tooth and back iron length of s tator
is represents by Pst and Psi respectively. FEA analysis
is used to identify the flux tubes in stator unit area.
Observed flux tube types are mentioned in table 3.
8slots -6poles WFSF machine consist of 8 s lots
similarly whole s tator consists of s imilar MEC
modules. Stator MEC modules assume to be invariant
to rotor position.
B. Rotor MEC Modules
Magnetic flux distribution in unit section of rotor is
defined as rotor MEC module. For MEC module of
rotor, whole rotor is divided into equal parts which are
depending upon the rotor’s tooth number. Unit section
of rotor is shown in Fig. 6. Flux path in rotor tooth and
back iron length of rotor is represents by Prt and Pri
respectively. Permanence of rotor is calculated by
identifying the flux tube in rotor unit section 8slots-
6poles WFSF machine reluctance network consists of
6 identical rotor s ections shown in Fig. 6. MEC
module of rotor is as sume to be constant and will not
change by changing the rotor pos ition.
C. Airgap MEC Modules
Magnetic flux distribution observed in the area around
the rotor tooth in the airgap is defined as airgap MEC
module. A ir gap MEC module is varying
corresponding the rotor position. Consequently, the
different MEC modules are determined in accordance
with rotor position.
To lessen the computational time and complexity,
stator section of 8slots -6poles WFSF machine is
divided into 10 segments. Rotor tooth changing the
pos ition corresponding to stator s egments , different air
gap MEC modules are obs erved. Stator tooth is cons i-
-dered as center axis for 10 segments of s tator MEC
modules. 5 s egments on left of central axis However,
5 segments on right of central axis. Segments on left
of central axis of stator tooth are similar to segments
present on the right. As consequence of similarity the
whole airgap MEC modules required only five air
MEC modules . FEA on 8slots -6poles WFSF machine
is performed to get the air gap MEC modules, when
the rotor’s tooth travel on the stator se gments.
Consider the number of flux tubes are grouped
together which are observed from FEA analys is.
Magnetic flux distribution is examined for each
segment of air gap MEC module. Each s egment with
identification of flux tubes are depicted in Fig. 7a, 8a,
9a, 10a, and 11a.Table 4 identify the type of flux tube
present in each segment of airgap according to the Fig.
4. Permeance of each segment is calculated us ing the
formulas mentioned in table 2. Number of parallel
permeance are combined together for single branch of
permence. Subsequently 5 different topologies are
obtained depicted in Fig. 7c-11c.
D. Solution Methodology
Magnetic flux dis tribution in the air gap highly
sensitive to the rotor position. MEC models are
varying with the change in the rotor position. Shifting
scheme for 8slots -6poles WFSF machine is
determined. Shifting scheme of proposed machine
inves tigates the MEC modules in terms of matrices,
GRN of propos ed machine is obtained by combining
these matrices. To obtain each entry of incident matrix
GRN is solved in MATLAB [7].
Properties of incident matrix are imported to be
consider. A is the incident matrix of circuit, circuit
contains m number of nodes, and n number of
branches. Similarly matrix has:
Following equations are obtained by applying
Kirchhoff Circuit Laws:
(6)
(7)
Where, A is incidence matrix having o rder U
is vector defines the mmf drop across each
branch. V is vector and repres ents the magnetic
potential on each node. is als o a vector and
defines the magnetic flux through each branch of
circuit.
(8)
Similarly, R is the diagonal matrix of order and
defines the reluctance of each branch. repres ents the
permeance of each branch and have diagnol
matrix and define the mmf source in each branch.
(c) (d) (e) (f)
Fig. 4. Cro ss Section s of Flux T ubes
T able 2: Flux Tubes Permeance (P) Calculation Form ulas
Flux
Tubes
Permeance
(P)
Flux Tubes
Permeance (P)
a
d
b
e
c
f
T able 3: T ypes of Flux Tubes o bserved from FEA Simulations in St ator
and Rotor MEC Module
Psl
Pst
Prt
Pri
Psi
e
a
b
a
b
Fig. 5: Stat or MEC module
Fig. 6: Rot or MEC module
(a) (b)
-1, if branch end to node
0, if branch is not connected to node
-1, if branch begins from node
(5)
Magnetic potential (V) in terms of A, and E can be
written as:
(9)
At each node magnetic potential (V) is calculated
using above equation 9. Subs equently, the value of
magnetic potential is used to calculate magnetic flux
() through each flux tube.
IV. Validation with Finite Element Analysis
8slots -6poles WFSF machine nonlinear MEC model is
validated by comparing the no -load flux linkage with
FEA results. Magnetic flux obtained from GRN
methodology and no-load flux obtained from FEA
T able 4 Types of Flux Tubes observed from FEA Simulatio ns in different
Airgap MEC Modules
FLUX
T ube
Number
Segmen
t
1
Segmen
t
2
Segmen
t
3
Segmen
t 4
Segment
5
1
C
C
C
C
C
2
D
C
D
D
D
3
D
D
D
D
C
4
D
D
D
D
D
5
C
D
D
D
D
6
D
D
D
C
D
7
D
C
C
D
D
8
D
D
D
D
C
9
C
D
C
C
D
10
-
B
F
F
D
11
-
D
F
F
D
12
-
D
-
-
-
`
(a)
(b)
Fig. 7: Airgap MEC Module 1; (a) Airgap flux tubes correspo nding to rotor
to oth for Segmen t No . 1, and (b) Airgap MEC topolo gy
(a)
(b)
Fig. 8: Airgap MEC Module 2; (a) Airgap flux tubes co rresponding to rotor
to oth for Segmen t No . 2, and (c) Airgap MEC top ology
(a)
(b)
Fig. 9. Airgap MEC Module 3; (a) Airgap flux tubes corresponding
to rot or tooth for Segment No. 3, and (b) Airgap MEC topology
(a)
(b)
Fig. 10: Airgap MEC Module 4; (a) Airgap flux tubes corresponding
to rot or tooth for Segment No. 4, and (b) Airgap MEC t opolo gy
(a)
(b)
Fig. 11: Airgap MEC Module 5; (a) Airgap flux tubes co rresponding
to rot or tooth for Segment No. 5, and (b) Airgap MEC t opolo gy
results are depicted in Fig. 12. Error between two
numerical methods is also computed and shown in Fig.
13. Error computed is less than ~2% which proves the
validation of GRN methodology.
V. Average Torque Characteristics
Fig. 14 depicted the average torque of 8slots-6poles
WFSF machine. The range of armature current density
is 0 A/mm2 to 12.25A/mm2, and field current density
is 4A. The Torque es tablished in the WFSF machine
is directly proportional to armature current and FEC
current as specified in [11] and is calculated us ing
equation 10:
(10)
Where, ia and if is armature and FEC current
respectively, M is the mutual inductance of FEC and
armature coil. The self-inductances of armature and
FEC are independent of rotor pos ition and hence
constant. Results from analysis shows that the average
torque increas es as the armature or field current
increase. 8slots -6poles WFSF machine has higher
average torque as compared to 8slots-4poles WFSF
machine.
VI. Conclusion
This paper propos ed the methodology to model the no -
load magnetic flux distribution of nonlinear, complex
and saturated machine. MEC models employed for
rotor, s tator, and air gap of 8slots-6poles WFSF
machine having trapezoidal s lots structure. GRN is
formed from the combination of different MEC
models. GRN is solved to get incidence matrix and no-
load flux is calculated using incidence matrix. The
results obtained from GRN methodology compared
with FEA results. Error computed is less than ~2%
which predicts the validation of GRN methodology.
Furthermore, the proposed 8slots -6poles W FSF
machine has achieved high average torque compared
to existing WFSF designs.
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Fig. 12: Comparison of no -load flux lin kage of GRN
met hodology
Fig. 1 3 Err or of n o-load flux link age between GRN
met hodology and FEA
Fig.14: Av erage Torque of 8 slots-6 poles WFSF Machine
0
0.1
0.2
0.3
0.4
0.5
0246810
Average Torque (N-m)
Armature RMS Current (A)
8slots-6poles
