Authors

  • Emmanuel C. Obuah
    Department of Electrical Engineering, Rivers State University, Port Harcourt, Nigeria
  • Uche C. Eze
    Department of Electrical Engineering, Rivers State University, Port Harcourt, Nigeria
  • Benjamine Akinloye
    Department of Electrical Engineering, Federal University of Petroleum, Effurum, Nigeria

DOI:

https://doi.org/10.37547/tajet/Volume07Issue06-11

Keywords:

Concentrated Winding Direct-Phase Variables Inductance Permanent Magnet Winding Function Theory.

Abstract

The dynamic and transient performance analysis of a three-phase interior rotor concentrated winding permanent magnet synchronous generator (CW-IPMSG) with was presented.  In this paper. The study was done in direct-phase variables concentering only the fundamental magneto-motive force (MMF). The machine’s inductance was determined using winding function theory (WFT). The derived inductance was used to determine performance characteristics of the machine’s variables such as phase current, load current and electromagnetic torque. The study was validated in MATLAB/Simulink to observe the performance of the characteristics of the generator. The study was carried out at no-load condition, under load perturb, as well as increase and decrease of capacitor. It was observed that the permanent magnet synchronous generator had slightly better output performance with capacitor assistance.     


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TYPE

Original Research

PAGE NO.

102-114

DOI

10.37547/tajet/Volume07Issue06-11



OPEN ACCESS

SUBMITED

19 April 2025

ACCEPTED

22 May 2025

PUBLISHED

14 June 2025

VOLUME

Vol.07 Issue 06 2025

CITATION

Emmanuel C. Obuah, Uche C. Eze, & Benjamine Akinloye. (2025). Direct-
Phase Variables Performance Analysis of Concentrated Winding
Permanent Magnet Synchronous Generator with Capacitive Assistance.
The American Journal of Engineering and Technology, 7(06), 102

114.

https://doi.org/10.37547/tajet/Volume07Issue06-11

COPYRIGHT

© 2025 Original content from this work may be used under the terms
of the creative commons attributes 4.0 License.

Direct-Phase Variables
Performance Analysis of
Concentrated Winding
Permanent Magnet
Synchronous Generator
with Capacitive Assistance

Emmanuel C. Obuah

Department of Electrical Engineering, Rivers State University, Port
Harcourt, Nigeria

Uche C. Eze

Department of Electrical Engineering, Rivers State University, Port
Harcourt, Nigeria

Benjamine Akinloye

Department of Electrical Engineering, Federal University of Petroleum,
Effurum, Nigeria

Abstract:

The dynamic and transient performance

analysis of a three-phase interior rotor concentrated
winding permanent magnet synchronous generator
(CW-IPMSG) with was presented. In this paper. The
study was done in direct-phase variables concentering
only the fundamental magneto-motive force (MMF).

The machine’s inductance was determined using

winding function theory (WFT). The derived
inductance was used to determine performance

characteristics of the machine’s variables such as

phase current, load current and electromagnetic
torque. The study was validated in MATLAB/Simulink
to observe the performance of the characteristics of
the generator. The study was carried out at no-load
condition, under load perturb, as well as increase and
decrease of capacitor. It was observed that the
permanent magnet synchronous generator had
slightly better output performance with capacitor
assistance.

Keywords:

Concentrated Winding; Direct-Phase

Variables.; Inductance, Permanent Magnet; Winding
Function Theory.

Introduction:

Most electric machines have distributed

winding (DW). Distributed windings were preferred over


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the concentrated winding (CW) because the distributed
winding gives a sinusoidal uniform MMF [1-3].

In recent years electric machines with concentrated
windings have become a competitive alternative to
machines with distributed windings for certain
applications. Machine with concentrated winding is
easier and cheaper to manufacture because of the short
ends winding feature. It has higher power density and
good fault tolerance capabilities especially the
fractional-slot concentrated winding machine. Again,
machine with CW has higher slot fill factor and good
efficiency compared to distributed winding permanent
magnet (PM) machine [4]. A concentrated winding is
preferred for a cost-effective application which requires
higher power density.

The benefits of concentrated windings and dual-
windings together have not been taken advantage of in
the synchronous reluctance motor. Previous researches
carried out on the synchronous reluctance motor
considered the stator of the machine as having only
distributed, or having distributed dual stator winding.

Performance characteristic of permanent magnet
synchronous motor (PMGM) with CW and DW was
carried out. The study compared the performance of the
two arrangements using certain rotor parameters such
as back EMF, resistance, efficiency, output torque etc
with two identical rotor dimensions. Parasitic
characteristics such as cogging torque, torque pulsation,
unbalanced magnetic force, mechanical vibration and

acoustic noise are always of significant concern during
the machine design. The parasitic effects could be

potentially more harmful in CW PMSM since there are
additional space harmonic contents in the stator MMF
distribution of the machine [5].

The synchronous reluctance generator with transversely
limited rotor has been studied. It was reported that the
generator is more robust, and has relatively lower core
loss, and provides spaces for embedding cage, and can
easily be skewed, and gives allowance for inserting
magnet. [6].

Reference [7] carried out comparative analysis of
synchronous reluctance machines (SynRM) with 6, 8 and
12 poles. The effect of different pole numbers on
average torque, loss, torque-ripple, d and q inductances
is investigated. It was shown that the 8-pole machine
has similar performance to the 6-pole machine but the
12-pole machine has worse performance.

Reference [8] developed an analytical model in the d-q
reference frame to recognize the steady-state of the
self-excited reluctance generator, considering no-load
and resistive load conditions. A fast method to estimate

the minimum capacitance requirements was also
proposed, and experiments were carried out to verify
the analytical results. After that, attention was paid on
the capability of self-excitation in reluctance generator
with different residual magnetisms in the rotor.
Different levels of residual rotor magnetism are
achieved by different magnetizing DC currents. An
indicative value of phase current was defined to
determine the self-excitation, and the required
minimum residual rotor magnetism for self-excitation in
the reluctance generator connected with different
capacitances was discussed. At last, the capability of
self-excitation in reluctance generators by connecting
charged capacitors was investigated.

Reference [9] presented a performance comparison of
an interior mounted permanent magnet synchronous
generator (IPMSG) with a synchronous reluctance
generator with the same size for a wind application. It
was found that using the same geometrical dimensions,
a SynRG can convert 74 % of the power that an IPMSG
can convert, while it has 80% of the IPMSG weight.
Moreover, it is found that the efficiency for the IMPSG is
99 % at rated power compared to 98.7 % for the SynRG.

Reference [10] in their work, investigated the capability
of simple salient-pole rotor synchronous reluctance
generators at a 5 MW power level. Different salient pole
rotor profiles are considered in the finite element design
optimization of the generator. It was found that with the
simple salient pole rotor, similar torque density and
efficiency are obtained as in published equivalent
distributed flux barrier rotor reluctance synchronous
generators. Also,

Reference [11] presented a performance comparison of
a 5MW interior permanent magnet synchronous
generator (IPMSG) with a 5 MW PMa-SynRG with the
same stator, to be used for a wind energy application. It
was found that PMa-SynRG has lower rotor weight as
well as 14 % lower magnet weight with the same
maximum torque performance. For wind speeds lower
than 8.5 m/s the PMa-SynRG has less loss. Moreover,
the machine annual energy efficiency for the PMa-
SynRG is higher for average wind speeds between 5-10
m/s.

Reference [12] presented a study of permanent magnet
assisted synchronous generator for autonomous

application using the classical Park’s d

-q model. It was

observed that the generator with permanent magnet
had better output performance than the conventional
generator when compared. Also [13] carried out steady
state performance analysis of permanent magnet
synchronous generator with capacitive assistance using
d-q model, where capacitor was used to improve power
output of the generator and voltage regulation.


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The study of electric machines based on the actual
geometry of the machine is importance because it gives
the actual behaviour of the machine. Widing Function
Theory is used to study machines beheviour considering
the actual placemen of machine windings. Some studies
that adopted the theory of winding function in machine
analysis include the use of WFT on induction machines
[14], synchronous reluctance motors [15], switched
reluctant motors [16] a machine with doubly salient
structure [17], and for model of a synchronous
reluctance motor including all slot and winding
harmonics [18].

Reference [19] derived a symmetrical component for
asymmetrical multiphase windings for a motor, where
an analytical formulation is presented to relate the
harmonic content of winding functions to winding
factors. The harmonic leakage factor is accurately
formulated from the winding function, and the
suggested analysis method was validated with the star
of slots and sinusoidal functions of distribution and pitch
factors

A five-phase synchronous reluctance motor and
permanent magnet synchronous reluctance motor was
modelled and simulated in phase variables and the
results in phase variables tend to agree with that of the
Finite Element Analysis [20-21].

Reference [22] also carried out a performance analysis
of a concentrated dual-winding synchronous reluctance
machine with capacitive assistance. The machine got its
power supply directly on power line. The transient and
dynamic performance analysis of a proposed line-start,
three-phase concentrated dual-winding synchronous
reluctance motor in comparison with the conventional
concentrated winding synchronous reluctance motor
was made. The modelling of the synchronous reluctance
machine was done in direct-phase variables considering
only the fundamental magneto-motive force. The
machine inductances of both machine models were
determined using winding function theory. The derived
inductances were used to determine machine
performance characteristics such as torque, speed,
phase currents etc. The performance characteristics of
both motors were monitored using MATLAB/Simulink,
and the proposed line-start machine with capacitive
assistance was observed to have improved performance

characteristics when compared to the conventional
machine.

Most study on CW machine considered the machine as
motor. There is paucity of literature where the machine
was used as generator. This study shall look at the
analysis of the synchronous reluctance generator with
assistance from permanent magnet for excitation.

To accomplish the goal of the study, the following
objectives were addressed.

i.

To develop the clock diagram of the CW-IPMSG
machine based on the arrangement

ii.

To present mathematical models for the
inductance of the CW-IPMSG in direct-phase
variable using Winding Function Theory

iii.

To use the calculated inductance to obtain the
phase voltage, phase voltage, load current and
electromagnetic torque of the CW-IPMSG at no-
load condition using MATLAB/Simulink

iv.

To study of the performance of the CW-IPMSG
on sudden addition and removal of load using
MATLAB/Simulink

v.

To study of the effect of variable capacitance on
the performance of the CW-IPMSG on using
MATLAB/Simulink.

2. MATERIALS AND METHODS

There are several methods used to model or analysis of
electric machine in literature. In this section, a list of
materials and method adopted is presented.

2.1. Materials

The materials used for the study include typical

machine parameters winding presented in Table 1, and
MATLAB/Simulink.

2.2. Method

Winding Function Theory was used to accomplish the

study's aim. Winding Function involves calculating
machine inductances based on actual geometry or
placement of the machine coil.

2.1.1. Modeling of the CW-IPMSG

In modeling the CW-IPMSG, it is assumed that

i.

the magnetic flux across the air gap is

perpendicular. only radial flux is considered

ii.

the magnets are seen to be placed adjacent to

each other; and the flux density between the adjacent
magnets is assumed to be equal to zero. By this, there is
no flux linkage between the adjacent magnets.

iii.

two coils are series connected and behave like a

single phase.


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With these assumptions, the magnets can be modeled
as coils which are wound in opposite direction with
number of turns. So, because of the way they are
stacked, the maximum turn is 2. The task here is to use
Winding Function Theory to calculate the machine
inductance and used the calculated inductance to

obtained other relevant quantities like power output,
voltage etc. Figure 1 shows the coil clock diagram of the
machine based on the winding pattern. The machine is
a 4 pole 12 slot machine with double-layer winding.
Figure 2 shows an ideal 4 pole machine based on the
assumption made

Figure 1 Clock diagram for the machine with double layer


Figure 2 A basic machine

The winding function method is used for calculation of
the machine inductances along with the actual machine
geometry. Winding function corresponding to the stator
windings are defined as a function of stator angle
according to their winding layouts in [23]. The procedure

used in [24] was adopted to obtain the expression for
turn function in (1).

⦑𝑛⟮𝜑

𝑠

⟯⦒ = ⦋

1

2𝜋

∫ 𝑛(𝜑

𝑠

)

𝜋

0

⦌ =

𝑁

𝑐

4

(1)

The turn function shows the number of turns as a


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function of the stator angle.

According to

[24]

,

the inductances will be calculated for

the case in which the two coils, A and B, are treated as
distinct coils, and ones which are connected in series.
Equation (2) gives the expression for the first series.
While equation (3) gives the expression for the second
series

𝑁

𝐴

(𝜑

𝑠

) =

3𝑁

𝑐

4

(2)

𝑁

𝐵

(𝜑

𝑠

) =

−𝑁

𝑐

4

(3)

The magnetizing-inductance of phase A is calculated by
integrating the turn function with respect to the stator
angular position from the reference period zero degree
as the machine rotates to 360 degrees for complete
revolution. as found in (4)

𝐿

𝐴

=

𝜇

𝑜

𝑟

𝑠

𝑙

𝑠

𝑔

𝑒𝑓𝑓

𝑁

𝐴

2

(𝜑

𝑠

)𝑛

𝐴

2𝜋

0

𝑑𝜑

𝑠

(4)

Solving gives (6)

𝐿

𝐴

=

1
8

𝜋𝑁

2

𝜇

𝑜

𝑟

𝑠

𝑙

𝑠

𝑔

𝑒𝑓𝑓

∗ 𝑔

𝑜

(5)

Similarly, the magnetizing-inductance of B is calculated
as

𝐿

𝐵

=

𝜇

𝑜

𝑟

𝑠

𝑙

𝑠

𝑐

𝑁

𝐵

2

(𝜑

𝑠

)𝑛

𝐵

𝑑𝜑

𝑠

2𝜋

0

(6)

Again, Solving gives (8)

𝐿

𝐵

=

3
8

𝜋𝑁

2

𝜇

𝑜

𝑟

𝑠

𝑙

𝑠

𝑔

𝑒𝑓𝑓

∗ 𝑔

𝑜

(7)

where

0

is the relative permeability of free space

𝑟

𝑠

is the stator radius

𝑙

𝑠

is the stator length

𝑁

𝑐

is the number of turns of coil

𝑔

𝑒𝑓𝑓

is the effective air-gap

𝑔

𝑜

is the amplitude of the first order harmonic

From (5) and (7), the magnetizing-inductance is
proportional to the square of the number of turns per
tooth, stator length and stator radius, and inversely
proportional to the effective air gap length. It is also
clear that total inductance does not depend on the
number of stator slot. Therefore, air-gap inductance
does not depend on the number of slots. Furthermore,
the inductance does not depend on the number of
poles. So, air-gap inductance is not a function of a
combination of number of poles per slot.

To achieve a sinusoidal field, each of the stator windings
of machine is shifted in space relative to the others by

2π/3

. In the stator reference frame, the self-inductances

of the stator for phase B and C describing the electrical
circuit of a three-phase synchronous machine using
conventional notations are given as (8) through (11), if
leakage inductance is accounted for

[25]

.

𝐿

𝑎𝑎

= 𝐿

𝑙𝑠

+ 𝐿

𝐴

− 𝐿

𝐵

𝑐𝑜𝑠 2 𝜃

𝑟

(8)

𝐿

𝑏𝑏

= 𝐿

𝑙𝑠

+

1
2

𝐿

𝐴

− 𝐿

𝐵

𝑐𝑜𝑠 2 (𝜃

𝑟

𝜋

3

)

(9)

𝐿

𝑐𝑐

= 𝐿

𝑙𝑠

+

1
2

𝐿

𝐴

− 𝐿

𝐵

𝑐𝑜𝑠 2 (𝜃

𝑟

+

𝜋

3

)

(11)

The mutual inductances are in (12) through (17)

𝐿

𝑎𝑏

= −

1
2

𝐿

𝐴

− 𝐿

𝐵

𝑐𝑜𝑠 2 (𝜃

𝑟

𝜋

3

)

(12)

𝐿

𝑎𝑐

= 𝐿

𝑙𝑠

+ 𝐿

𝐴

− 𝐿

𝐵

𝑐𝑜𝑠 2 (𝜃

𝑟

2𝜋

3

)

(13)

𝐿

𝑏𝑎

= −

1
2

𝐿

𝐵

− 𝐿

𝐴

𝑐𝑜𝑠 2 (𝜃

𝑟

+

𝜋

3

)

(14)

𝐿

𝑏𝑐

= −

1
2

𝐿

𝐵

− 𝐿

𝐴

𝑐𝑜𝑠 2 (𝜃

𝑟

+

𝜋

3

)

(15)

𝐿

𝑐𝑎

= −

1
2

𝐿

𝐴

− 𝐿

𝐵

𝑐𝑜𝑠 2 (𝜃

𝑟

+ 𝜋)

(16)

𝐿

𝑐𝑏

=

1
2

𝐿

𝐴

− 𝐿

𝐵

𝑐𝑜𝑠 2 (𝜃

𝑟

2𝜋

3

)

(17)

The stator total inductances can be given in matrix form
in equation (18) for phase A, B and C


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=

cc

cb

ca

bc

bb

ba

ac

ab

aa

S

L

L

L

L

L

L

L

L

L

L

(18)

Also, considering stator phase displacement angle, the
phase A, B and C flux linkage is expressed as in equations
(19) (20) (21)

𝜆

𝑎𝑠

= 𝐿

𝑎𝑎

𝑖

𝑎

+ 𝐿

𝑎𝑏

𝑖

𝑏

+ 𝐿

𝑎𝑐

𝑖

𝑐

+ 𝜆

𝑚

(𝑠𝑖𝑛 𝜃

𝑟

)

(19)

𝜆

𝑏𝑠

= 𝐿

𝑏𝑏

𝑖

𝑎

+ 𝐿

𝑏𝑎

𝑖

𝑏

+ 𝐿

𝑏𝑐

𝑖

𝑐

+ 𝜆

𝑚

𝑠𝑖𝑛 (𝜃

𝑟

2
3

𝜋)

(20)

𝜆

𝑐𝑠

= 𝐿

𝑐𝑐

𝑖

𝑎

+ 𝐿

𝑐𝑏

𝑖

𝑏

+ 𝐿

𝑐𝑐

𝑖

𝑐

+ 𝜆

𝑚

𝑠𝑖𝑛 (𝜃

𝑟

+

2
3

𝜋)

(21)

where

m

is the permanent magnet constant flux.

Using Kickoff’s voltage law, the generator voltage

equation is given as (22).

(

)

c

S

S

S

S

V

I

L

dt

d

R

I

E

+

+

=

(22)

Rearranging (23) gives (24)

( )

( )

c

r

S

r

r

S

r

S

S

S

V

L

d

dL

R

I

E

dt

dI





+

=

1

*

*

(23)

where

𝑉

𝑐

is the capacitor voltage

𝐼

𝑆

is the stator three phase current given in matrix form

as:

𝐼

𝑆

= ⦋𝐼

𝑎

𝐼

𝑏

𝐼

𝑐

(24)

𝑅

𝑆

is the stator three-phase resistance, given in matrix

form as (24).

𝑅

𝑆

= 𝑑𝑖𝑎𝑔 [

𝑅

𝑎

0

0

0

𝑅

𝑏

0

0

0

𝑅

𝑐

]

(25)

where

𝑅

𝑎

= 𝑅

𝑏

= 𝑅

𝑐

𝑬 is given as = [𝑬

𝒂

; 𝑬

𝒃

; 𝑬

𝒄

; ]

(26)

where

wt

m

E

a

cos

*

=

(27)

=

3

2

cos

*

wt

m

E

b

(28)

=

3

4

cos

*

wt

m

E

c

(29)

For the sake of making the capacitor voltage as a system
state variable for simulation, the integral equation for
the capacitor voltage is given as (30).

dt

I

C

V

s

ca

=

1

(30)

where

𝐶

is the capacitance of the capacitor.

The load equation is given in as

[26]

as:

1

cos

1

2

=

r

aL

aL

R

L

(31)

where

𝑅

𝑎𝐿

is the per phase resistive load

Consequently, the output power is given as (32).

𝑃

𝑜𝑢𝑡

= 3𝐸𝐼

𝑎

𝑐𝑜𝑠 𝛷

(32)

where

𝛷

is the load power factor.

The electromagnetic torque can be derived in (33) using
co-energy method.

(33)

3. Results and Discussion

The performances of the CW-IPMSG at no-load

condition, load perturbs and capacitance variation are

 

( )

m

r

r

S

S

e

d

L

d

I

T

+

=

2

2

1


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shown in Figures 3 to 13. The results were obtained
using equations (5), (7) through (21), (23) through (25),
(27) through (33) with the relevant parameters shown in
Table 1. Excitation capacitor of 90 µF was used while the
permanent magnet flux used was 0.8 at 0.8 power
factor.

3.1. Dynamic Performance of CW-IPMG at No-Load
Condition

Figure 3 through 7 shows the phase voltage, stator
phase current, capacitor phase current per phase load

current and electromagnetic torque of the CW-IPMSG
at no-load condition. The CW-IPMSG exhibited the
quality of producing voltage of about 230 V. This
closely match the value given in the machine
nameplate. The corresponding phase current is shown
in Figure 4. The phase current for the CW-IPMSG is
about 7 A while the capacitor current is about 7.5 A as
illustrated in Figure 5. In Figure 6, the load current is
about 0.0015 A. The electromagnetic torque is
illustrated in Figure 7. At initial start, the value of the
torque rose to about 5.6 Nm. The generator continues
to run, it started gaining stability. That was from 0.2
seconds through 0.4 seconds when it stopped running.

Figure 3: Per phase voltage of the CW-IPMSG on no-load condition

Figure 4: Per phase current of the CW-IPMSG at no-load condition


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Figure 5: Per phase capacitor current of the CW-IPMSG at no-load condition

Figure 6: Per phase load current of the CW-IPMSG at no-load condition

Figure 7: Electromagnetic torque of the CW-IPMSG at no-load condition

3.2. Performance of the CW-IPMG on Sudden
Addition and Removal of Load

Performance of the of the CW-IPMSG on sudden
addition and removal of load was also studied in Figure
8 through Figure 10. The generator operated with load


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from zero seconds to 0.7 second when load was
suddenly removed and the added again at 2 seconds. As
seen in Figure 8, there was voltage flicker observed as
the load was added. There was also some level of
oscillation on the electromagnetic torque, from 0.5

second to 1 second when the load was added and
removed in Figure 9. Figure 10 shows the same effect for
the load current. The load current was 0.4 A when the
generator operated on load. When load was removed,
the load current is about zero

Figure 8: Phase voltage of the CW-IPMSG on sudden removal and addition of load condition

Figure 9: Electromagnetic torque of the CW-IPMSG on sudden removal and addition of load condition



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Figure 10: Load current of the CW-IPMSG on sudden removal and addition of load condition

3.3. Performance of the CW-IPMG on Varriable
Capacitance

Since the generator is equipped with a balanced three
phase capacitor, which can be varied, the analysis
extended to the effect of change in excitation capacitor.
The capacitance is made to change from 32 µF to 52 µF
and then to 92 µF. The corresponding time of change is
from 0 to 0.5 second and then 1.0 second. The change

in the capacitance and the corresponding voltage build-
up, load current and the electromagnetic torque is
illustrated in Figure 11 through Figure 13. The behavior
of the generator with respect to the performance
parameters indicates that increase in capacitor
capacitance yields more voltage and electromagnetic
torque and this can also be applicable to other
parameters or quantities. The simulation was done at
resistive-

inductive load of 500 Ω-300 mH and permanent magnet flux of 0.8

Figure 11: Voltage of the CW-IPMSG on variable capacitance


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Figure 12: Load current of the CW-IPMSG on variable capacitance

Figure 13: Electromagnetic torque of the CW-IPMSG on variable capacitance

Table 1: Studied Machine Parameters

S/N

Parameters

Value

1

Rated voltage

220 V

2

Rated power

110 kW

3

Rotor speed

2400 rpm

4

Number of turns per coil

115

5

Amplitude of the 1st order

harmonics

5.8

6

Stator Stack length

800 mm

7

Frequency

50Hz

8

Resistance

0.03 Ω

9

Effective airgap

1.2 mm

10

Stator radius

82.4 mm


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CONCLUSION

Dynamic and transient performance analysis of
concentrated winding permanent magnet synchronous
generator with capacitor assistance has been studied.
The coil winding diagram of the studied permanent
magnet synchronous generator with concentrated
winding was developed. The inductance of the
machines was also calculated based on Winding
Function Theory. It was seen that inductance is
proportional to the square of the number of turns per
tooth, stator length and stator radius, and inversely
proportional to the effective air gap length. It is also
clear that total inductance does not depend on the
number of stator slot. The calculated inductance was

used to obtain the voltage, electromagnetic torque etc
of the generator at no-load condition, sudden addition
and removal of load, and capacitor variation using
MATLAB/Simulink tool. At no-load condition, it was
observed that CW-IPMSG maintain the desired
performance where the output voltage is 230 V and
electromagnetic torque is 5 Nm. When load was
suddenly added to the generator, there were
oscillations at the time when the load was added, and
another oscillation was observed when load was
removed. Increase in value of capacitor also increase
the output performance of the generator at particular
load and permanent magnet flux. This study was
performed for a 4 pole 12 slot concentrated winding of
permanent magnet synchronous generator.

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M. (2014). Comparison of a 5MW permanent magnet
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, Berlin, 711-

715, doi: 10.1109/ICELMACH.2014.6960259.

Obuah E. C., O. E. Ojuka, E. I. Wodi, W. Ikonwa. (2022).
Dynamic modelling of a rotor cage permanent magnet
synchronous generator with capacitive assistance,

Global scientific Journals (GSJ),

10(6), pp. 211-266, June,2

022.

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analysis of permanent magnet synchronous generator
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Technology, (NIJOTECH)

, 41(3), pp. 527-534, May, 2022.

Joksimovic G. "AC winding Analysis using winding
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www.researchgate.net

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Accessed on January 2024.


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Toliyat H. A. and Al-Nuaim N. A. "Simulation and
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Proc. IEEE-IAS,

753-760. 1996.

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efficient method for electromagnetic inductance
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harmonics",

Energy

Conversion

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Management,

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in IEEE Transactions on

Magnetics

, 53 (10), 1-9, Art no. 8203809, doi:

10.1109/TMAG.2017.2712570. 2017.

Umoh G.

et al.,

"Direct-Phase Variable Modelling and

Analysis o Five-Phase Synchronous Reluctance Motor for

Direct-On-Line Starting,

Przeglad Elektrotechniczny

,

97(1): 24

29, 2020.

Umoh G.

et al.,

"Modelling and Analysis of Five-Phase

Permanent Magnet Synchronous Motor in Machine
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Przeglad, Elektrotechniczny

, 96(1): 87

92.

2020.

Epemu A. M.

et al

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concentrated dual-winding synchronous reluctance
machine with capacitive assistance", 2021. (on line via

https://www.researchgate.net

), obtained on 13

th

December 2024)

Aliyu N. "Natural variable modeling and performance of
interior permanent magnet motor with concentrated
and distributed windings, a dissertation presented the

Department of Electrical Engineering, Faculty of
Engineering, University of Nigeria, Nsukka,

(2014).

Kraus P. C.., Wasynczuk O. & Sudhoff S. D. "Analysis of
Electric Machinery",

Piscataway: IEEE Press

, 2002.

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self-excited two-phase reluctance generator

", Nigerian

Journal of Technology, (NIJOTECH)

, 30 (2), June 2014.

References

Tola J. et al., "Modeling and analysis of dual stator windings permanent magnet

synchronous motor", IEEE 3rd International Conference on Electro-Technology for National Development, 2017.

Lee et al., "Comparison between concentrated and distributed winding in IPMSM for traction application, 2010. International Conference on Electrical

Machines and Systems, in IEEE Transportation Electrification Conference, 485-490.

Dehghanzadeh A.R. and Behjat V. "Dynamic modeling and experimental validation of a dual-stator PMSG for low-speed applications", Gazi University Journal of Science, 28(2). 275–283. 2015.

Choea Y-Y., Oha S-Y., Hamb S-H., Janga I-S., Choa S-Y., Lee J., Koa K-C. "Comparison of Concentrated and Distributed Winding in an IPMSM for Vehicle Traction", Science direct, Energy Procedia 14 1368 – 1373 [Available online at www.sciencedirect.com]

Wang J., Patel V. I. and Wang W. "Fractional-Slot Permanent Magnet Brushless Machines with Low Space Harmonic Contents, IEEE Transactions on Magnetics, 50 (1), 1-9, 2014. [Available at www.researchgate.net].

Obe E. S. & Anih L. U. "Influence of rotor cage on the Performance of a synchronous reluctance generator, Journal of Electric Power Components and Systems, Taylor & Francis Group, 38, 960-973. 2010.

Roshanfekr P., Lundmark S., Anvari B. and Thiringer T., Investigation of pole number selection in a synchronous reluctance generator for wind applications, 2017 IEEE International Electric Machines and Drives Conference (IEMDC), Miami, FL, USA, 1-6, doi: 10.1109/IEMDC.2017.8002336. 2017.

Wang Y. and Bianchi N. Investigation of self-excitation in reluctance generators, 2017 IEEE International Electric Machines and Drives Conference (IEMDC), Miami, FL, USA, 2017, 1-8, doi: 10.1109/IEMDC.2017.8002303, 2017.

Roshanfekr P. Lundmark S., Thiringer T. and Alatalo MA "Synchronous reluctance generator for a wind application-compared with an interior mounted permanent magnet synchronous generator", 7th IET International Conference on Power Electronics, Machines and Drives (PEMD 2014), Manchester, UK, 1-5, doi: 10.1049/cp.2014.0411. (2014.

Dippenaar J. & Kamper M. J. "Simple Robust Rotor 5 MW Synchronous Reluctance Generator", 2020 IEEE Energy Conversion Congress and Exposition (ECCE), Detroit, MI, USA, 1426-1432, doi: 10.1109/ECCE44975.2020.9235920. 2020.

Roshanfekr P., Lundmark S. T., Thiringer T. and Alatalo M. (2014). Comparison of a 5MW permanent magnet assisted synchronous reluctance generator with an IPMSG for wind application," 2014 International Conference on Electrical Machines (ICEM), Berlin, 711-715, doi: 10.1109/ICELMACH.2014.6960259.

Obuah E. C., O. E. Ojuka, E. I. Wodi, W. Ikonwa. (2022). Dynamic modelling of a rotor cage permanent magnet synchronous generator with capacitive assistance, Global scientific Journals (GSJ),10(6), pp. 211-266, June,2 022.

Obuah, E. C., Epemu A. M and Obe E. S., "Steady state analysis of permanent magnet synchronous generator with capacitive assistance", Nigerian Journal of Technology, (NIJOTECH), 41(3), pp. 527-534, May, 2022.

Joksimovic G. "AC winding Analysis using winding function approach, available at www.researchgate.net, Accessed on January 2024.

Toliyat H. A. and Al-Nuaim N. A. "Simulation and detection of dynamic airgap eccentricity in salient-pole synchronous machines", IEEE Trans. Ind. Appl., 35(1), 86–93, (1999).

Johnson J. P., Rajarathnam A. V., Toliyat H. A., "Gopalakrishnan S. & Fahimi B. Torque optimization for a SRM using winding function theory with a gap-dividing surface", Proc. IEEE-IAS, 753-760. 1996.

Ezzat M. "Winding function analysis technique as an efficient method for electromagnetic inductance calculation", Journal of Electrical Engineering www.jee.ro, 2015. [Accessed on January, 2024].

E. Obe & A. Binder "Direct-phase-variable model of a synchronous reluctance motor including all slot and winding harmonics", Energy Conversion and Management, 2011.

Raziee S. M., Misir O. & Ponick B. "Winding Function Approach for Winding Analysis", in IEEE Transactions on Magnetics, 53 (10), 1-9, Art no. 8203809, doi: 10.1109/TMAG.2017.2712570. 2017.

Umoh G. et al., "Direct-Phase Variable Modelling and Analysis o Five-Phase Synchronous Reluctance Motor for Direct-On-Line Starting, Przeglad Elektrotechniczny, 97(1): 24–29, 2020.

Umoh G. et al., "Modelling and Analysis of Five-Phase Permanent Magnet Synchronous Motor in Machine Variables", Przeglad, Elektrotechniczny, 96(1): 87–92. 2020.

Epemu A. M. et al., "Performance analysis of line-start concentrated dual-winding synchronous reluctance machine with capacitive assistance", 2021. (on line via https://www.researchgate.net), obtained on 13th December 2024)

Aliyu N. "Natural variable modeling and performance of interior permanent magnet motor with concentrated and distributed windings, a dissertation presented the Department of Electrical Engineering, Faculty of Engineering, University of Nigeria, Nsukka, (2014).

Kraus P. C.., Wasynczuk O. & Sudhoff S. D. "Analysis of Electric Machinery", Piscataway: IEEE Press, 2002.

Obe E. S. & Onwuka I. K., "Modeling and performance of self-excited two-phase reluctance generator", Nigerian Journal of Technology, (NIJOTECH), 30 (2), June 2014.