Abstract.

The subject of this paper is the wind powered
Switched Reluctance Generator - SRG and its behavior.
Simulations and experimental results are presented. It was
analyzed the efficiency of SRG under different conditions.
Many operational test were conduced to state clearly the
behavior of a prototype drove by a half-bridge (HB) converter.
Variable excitation voltage and angular speed relationship is
clearly established. It shows that the suitable excitation control
for a wind powered SRG must adjust the operation parameters
to match the desired point on certain surfaces.

Key words

Switched Reluctance Generator, wind power, variable
speed.

1. Introduction

Currently, due the large global consumption of power,
researches
on
renewable
energy
sources,
like
photovoltaic, wind power, biomass and others are being
conducted. Although the uncertainties in the availability
of the renewable energy sources are a fact. And so it is
difficult to operate a power system based only on
renewable sources [1].
Among all the renewable energy sources wind power
presents the higher global growth in the last years. By
having large geographic opening it can generate electrical
energy close to the load centers avoiding the construction
of large transmission lines. Wind power does not
damages the environment. The verticality of the towers
allows the use of the ground below the wind turbines for
agriculture.
This paper proposes the Switched Reluctance
Generator - SRG as an special electrical generator for
wind power. A PWM inverter can be used to adjust the
output as required.
A prototype was built and tested to know the
operational behavior of this kind of machine under
variable excitation and variable speed. The results are
presented here. Through these tests the need of a specific
control of the excitation voltage is proved for the wind
powered SRG systems.

2.
Energy Conversion


In a SRG mechanical power achieved from a prime
mover through a shaft is converted into electrical power.
When a pole of the rotor is aligned with the excited pole
of the stator, there is a state of stable equilibrium. Thus,
in the SRG there is a natural tendency to align the rotor
and the stator active poles in order to maximize de
inductance of that phase. When an external mechanical
agent forces the rotor to leave the stable equilibrium
position, the electromagnetic torque produced results in a
back electromotive force that increases the applied
voltage. In this way the machine generates electrical
power.
The electrical equation for a phase of the SRG is:
e
dt
di
L
Ri
v
+
+
=
(1)

The back electromotive force is given by:
=
L
i
e
(2)
where:
dt
d
=

The stator winding is fed in DC. As and
i
are both
positive, the sign of e is the same as that of
L
. From (2)
it can be seen that when
0
> L
the back electromotive
force is positive. In this case, electric power is converted
to mechanical power and the machine works as a motor.
But when
0
< L
the back electromotive force is
negative and it increases the current converting
mechanical power into electrical power [2].
The dynamic mechanical equation for the SRG is
given by (3). It is to be noted that the electromagnetic
torque
emag
C

comes as a negative quantity, i. e., acting
against the rotor mechanical speed.

0
.
=
+
D
dt
d
J
C
C
emag
m
(3)
The co-energy of a phase of this machine is given by:
=
i
0
co
di
W (4) And the corresponding electromagnetic torque for an n
phase SRG is given by: +
+
=
co
c
co
b
co
a
emag
W
W
W
C

(5)
The mathematical model of a 6 x 4 SRG is shown
below:

+























=












c
b
a
c
c
b
b
a
a
c
b
a
m
c
b
a
i
i
i
D
i
r
i
r
i
r
R
R
R
C
v
v
v
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0






























+ &
&
&
&
&
c
b
a
c
a
c
b
b
b
a
a
a
i
i
i
1
0
0
0
0
0
J
0
0
0
L
i
0
L
0
0
L
i
0
0
L
0
L
i
0
0
0
L
(6)
where: =
co
a
a
W
r
; =
co
b
b
W
r
And =
co
c
c
W
r
(7)

3.
Wind behavior


The wind is an intermittent and variable energy source
both in magnitude and in direction. There are several
components in the wind speed [3], for example:
noise
gust
ramp
base
wind
V
V
V
V
V
+
+
+
=

(8)
The wind turbines has its power as a function of the
wind speed cube as showed below.
3
.
.
.
2
1
wind
p
turbine
V
A
C
P =
(9)
= air specific weight
A = swept area of the blades
p
C
= Power Coefficient
The power coefficient
p
C
is the fraction of the wind
kinetic power that is captured by the wind turbine blades
[4]. It is the efficiency of the rotor. This coefficient
changes from turbine to turbine and its value is given by:

2
1
1
2
0
0










+
=
V
V
V
V
C
p
(10)
where
0
v
is the wind speed after turbine and . This
function is described in Fig. 1.
It can be seem that this coefficient is maximum at
around 0.59, then the maximum transfer of energy takes
place with almost 60% of the initial value. For turbines of
three blades and low speed - the most used -, the
efficiency of the rotor is between 0.2 and 0.4.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Vo/V ratio
R
o
t
o
r

e
f
f
i
c
i
e
n
c
y

Fig. 1 Power coefficient versus speed ratio for a
generic wind turbine
.


It is a consensual appreciation that the wind speed in a
certain site follows the Weibull probability distribution
function like this:


(11)


Where
)
(
i
v
p
is the fraction of time where wind speed
is between
i
v
and
i
i
v
v +
, divided by
i
v ,
c
is a
scale parameter and
k
is a shape parameter. Generally
)
(
i
v
p
is expressed in hours per year per
s
m
/
. On most
places c varies from
5 to
s
/
m
10
and k varies between
5
.
1
and
5
.
2
.

Fig. 1 shows the curves of Weibull
probability distribution for the shape factor
2
k
= where
the scale parameter varies between
s
m
/
5
and
s
m
/
13
.

0
5
10
15
20
25
0
2
4
6
8
10
12
14
16
18
Wind speed in m/s
T
i
m
e

i
n

p
e
r
c
e
n
t
Wind speed according to Weibull probability distribution (k=2)
c = 5 m/s
c = 7 m/s
c = 9 m/s
c = 11 m/s
c = 13 m/s

Fig. 2. Wind speed permanency curves.

Fig. 2 shows that the wind speed is low most of the
time. The rotor speed has the same behavior of the wind
speed. A generation has to follow this profile should start
with low wind speeds and increase the generation with
the increase of wind speed.
In the experimental results is shown that the behavior of
the SRG fits the profiles of wind of the curves of
Weibull.
k
i
c
v
k
i
i
e
c
v
c
k
v
p








=
1
)
(
4.
Simulations


The simulations were done using data from a small
prototype of SRG. Its parameters and dimensions are
given in Table I.

TABLE I. - Characteristics of SRG used

Parameter
Value
Units
Stator Diameter
140
mm
Rotor Diameter
70
mm
Stack Length
107
mm
Air Gap Length
0.4
mm
Stator Teeth Width
19
mm
Rotor Teeth Width
20
mm
Stator Slot
22.5
mm
Rotor Slot
11.7
mm
Stator Yoke
12
mm
Rotor Yoke
12.4
mm
Shaft Diameter
22
mm
Number of turns per
phase
50
turns/phase
Inertia
0.0028
kg.m
2

Coefficient of Friction
0.026
N.m.s
Inductance (Aligned
Position)
36
mH
Inductance (Unaligned
Position)
3
mH

Each phase winding has 50 turns of copper wire AWG
15. The driving strategy states that each phase is fired
during 30 degrees and just one phase is fired at time.
The SRG was simulated under different conditions.
Simulation results at a typical speed of 900 rpm are
presented. Figure 2 shows the DC voltages and currents
at the input (VE, IE) and at the output (VS, IS) of the
converter.

0
0.05
0.1
0.15
0.2
0.25
0.3
-10
0
10
20
30
40
50
60
70
second
v
o
l
t
,

a
m
p
è
r
e
Input and output voltages and currents, and the current for a phase
VS
VE
IE
IS
Iphase
These patterns remain stable
during long time simulations.

Fig. 3 Input and Output voltages and currents and a phase
current

Fig. 3 also shows the phase current. Fig. 4 shows the
simulation results for the winding voltage, the excitation
current, and the current of power transfer to the load are.
These are the voltage and the current for a single winding
during the excitation and the generation periods. It could
be seen there that when the excitation ended, the back
EMF became negative, supplying additional power to the
load.