Studies regarding the modeling of a wind turbine with energy storage
GIRDU CONSTANTIN CRISTINEL
School Inspectorate of County Gorj,
Tg.Jiu, Meteor Street, nr.11
ROMANIA
Abstract: This paper presents the modeling in Matlab-Simulink of a stand-alone wind turbine system with
energy storage dedicated for small power wind turbines of 3kW with a variable speed permanent magnet
synchronous generator (PMSG), diode rectifier bridge, buck-boost converter, bidirectional charge
controller, transformer, inverter, ac loads and energy storage devices. Are presented the general system
configuration, the Simulink block diagram and the main simulated characteristics resulting from the
dynamic performances during the wind speed variation.
Key words: wind energy, Matlab-Simulink modeling, wind turbine, energy storage.
1 Introduction
The renewable resources named also “green
resources” are theoretically inexhaustible and
permit to replace the use of fossil fuels for coming
in order to reduce the greenhouse gases effects.
Furthermore, they are present all over the world,
free to use, and do not cause pollution. The use of
renewable energies will continue to grow, and such
plants will become cheaper and more readily
accepted by the market. Since, they represent a
great alternative to fossil fuels, the European
countries start policies to promote renewable
energy technologies and to supply electricity using
a mix of traditional fossil fuels and “green
resources”.
Among these resources, wind is the cheapest on
a large scale to transform into electrical energy.
That is why much attention is paid nowadays to
wind energy conversion systems.
2 Wind turbine system configuration
The wind turbine studied is a small power one
with a rated power of 3kW and the blade diameter of
4m.
It contains a permanent magnet synchronous
generator (PMSG), buck-boost converter,
transformer, inverter, ac load, and lead acid batteries
(LAB) and supplies single-phase consumers, at
230V and 50Hz, as shown in Fig.1.
wind
PMSG
Buck-Boost
Converter
Dump Load
+
-
AC
Load 230V
50Hz
Regulator
Battery
Storage
Inverter
Transformer
Fig.1 Wind turbine system configuration
This topology is built in order to obtain a
maximum efficiency for the system. The regulator
measures the main system’s parameters – wind
speed, battery voltage and current, PMSG’s rotor
speed – and controls the buck-boost duty-cycle,
commands the dump load and gives the inverter’s
modulation index.
The main advantage of variable speed operation is
that more energy can be generated for a specific
wind speed regime. Although the electrical
efficiency decreases, due to the losses in the power
electronics that are essential for variable speed
operation. There is also a gain in aerodynamic
efficiency due to variable speed operation. The
aerodynamic efficiency gain exceeds the electrical
efficiency loss, overall resulting in a higher energy
yield. There is also less mechanical stress, and noise
problems are reduced as well, because the turbine
runs at low speed when there is little wind.
DESIGN, CONSTRUCTION, MAINTENANCE
DOI: 10.37394/232022.2022.2.11
Girdu Constantin Cristinel
E-ISSN: 2732-9984
69
Volume 2, 2022
Fig. 2 Simulink diagram of the wind system
3 Matlab – Simulink system modeling
The proposed system has been modeled and
simulated using the Matlab - Simulink software and
is depicted in Fig.2. The wind variation for a typical
site is usually described using the so-called Weibull
distribution. The statistical distribution of wind
speeds varies from place to place around the globe,
depending upon local climate conditions, the
landscape, and its surface. The wind speed variation
is best described by the Weibull probability
distribution function [6].
To obtain the Simulink whole wind system
diagram, has been considered the models for the
wind turbine, PMSG, buck-boost converter, diode
bridge rectifier, inverter and the storage LAB
presented in [1,2,3,4,5].
The electrical part of the wind turbine modeled is
composed by a 3kW PMSG, diode bridge rectifier,
converter, transformer, inverter, ac loads and storage
devices. The turbine Simulink model (see Fig. 2) is
based on the Maximum Power Point Tracking
(MPPT) method used in order to maximize the
electric output power extracted from the wind
energy conversion [1]. In this case, the tip speed
ratio λ in pu of λ_nom is obtained by the division of
the rotational speed in pu of the base rotational
speed and the wind speed in pu of the base wind
speed. In this aim we consider the output power of
3kW, the base wind speed of 12 m/s, the maximum
power at base wind speed of 0.9 pu (kp = 0.9) and
the base rotational speed equal 1 pu). The output
is the torque applied to the generator shaft Tm, is
based on the nominal generator power and speed.
The mechanical power Pm as a function of
generator speed, for different wind speeds and for
the blade pitch angle β = 0 degree, is illustrated
in Fig.3.
00.2 0.4 0.6 0.8 11.2 1.4
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1 pu
Max. power at base wind speed (12 m/s) and beta = 0 deg
6 m/s
7.2 m/s
8.4 m/s
9.6 m/s
10.8 m/s
12 m/s
13.2 m/s
Turbine speed [pu]
Turbine output power [pu]
Fig. 3 Wind turbine characteristics at 3 kW
This figure is obtained with the default
parameters (nominal mechanical output power =
3kW, base wind speed = 12 m/s, maximum power at
base wind speed = 0.9 pu (kp = 0.9) and base
rotational speed = 1 pu). The wind turbine power
curve permits a maximum power of 3.5kW [8].
For the system modeling, the main library used
was Sim-PowerSystem.
The PMSG has a sinusoidal flux distribution, 4
pole pairs, per-phase stator resistance R=0.458 Ω,
Ld = Lq = 0.00334 H, flux induced by permanent
magnets in the stator windings Ψ = 0.171 Wb.
The battery bank consists in five 24V batteries
series connected.
DESIGN, CONSTRUCTION, MAINTENANCE
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Volume 2, 2022
A P=1kW and Q=500var ac load is considered
and it’s switched on and off in order to analyze the
system’s dynamic behavior.
4 Dynamic behaviour simulations
Simulations were carried out in the following
situations:
- start-up process;
- variable wind speed behavior;
- variable load behavior.
The start-up process takes place at a wind speed
of 4m/s. The PMSG is considered connected at t
=1s, when the generator operates under steady-state
condition. In the Fig. 4 are shown the rotor speed
and the electromagnetic torque.
0.8 11.2 1.4 1.6 1.8 2
0
0.2
0.4
0.6
0.8
PMSG Speed [p.u.]
0.8 11.2 1.4 1.6 1.8 2
-10
-8
-6
-4
-2
0
Time [s]
PMSG Electromagnetic Torque [Nm]
Fig. 4 PMSG rotor speed and electromagnetic torque
The initial disturbance is amplified by the inertia
moments of the rotating elements.
In the Fig.5 is depicted the electromagnetic
torque variation around its steady-state value.
The electromagnetic torque has an initial sharp
step.
The transitory regime lasts about 0.2s and after
that, another steady-state regime is established.
Fig. 5 PMSG electromagnetic torque variation
The dc rectifier bridge voltage link, is about
85V according to the wind speed and is depicted in
the Fig.6.
0.8 11.2 1.4 1.6 1.8 2
0
10
20
30
40
50
60
70
80
90
100
Time [s]
DC Link Rectifier Bridge Voltage [V]
Fig. 6 The dc link rectifier bridge voltage
During the PMSG non-operating moments, the
loads are fed by the battery bank.
For the variable wind speed behaviour, is
considered a wind speed decrease from 10 m/s to 7
m/s at the moment t = 1s, which affects the system’s
power balance. In the Fig.7, the rotor speed is
shown.
0.8 11.2 1.4 1.6 1.8 22.2 2.4
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Time [s]
PMSG Rotor Speed [p.u]
Fig. 7 The PMSG rotor speed
The system is initially in steady-state. The battery
voltage is about 135V. The PMSG’s operating point
depends on the wind speed and on wind
characteristics.
This change affects the system power balance.
The PMSG’s electromagnetic torque (Fig.8)
decreases to about 60% (negative is generating),
consequently the generated power decreases also.
DESIGN, CONSTRUCTION, MAINTENANCE
DOI: 10.37394/232022.2022.2.11
Girdu Constantin Cristinel
E-ISSN: 2732-9984
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Volume 2, 2022
0.8 11.2 1.4 1.6 1.8 22.2 2.4
-12
-10
-8
-6
-4
-2
0
Time [s]
PMSG Electromagnetic Torque [Nm]
Fig. 8 The PMSG electromagnetic torque
The dc link rectifier bridge voltage, depicted in
the Fig.9, decreases from 205V to about 145V.
0.8 11.2 1.4 1.6 1.8 22.2 2.4
130
140
150
160
170
180
190
200
210
220
Time [s]
Dc Link Rectifier Bridge Voltage [V]
Fig. 9 The dc link rectifier bridge voltage
During this process, the average battery current falls
from 6.5A to about –1.5A, as shown in the Fig.10. In
order to provide a loads permanent supply, the
battery will pass from charging to discharging mode.
0.8 11.2 1.4 1.6 1.8 22.2 2.4
-3
-2
-1
0
1
2
3
4
5
6
7
8
Time [s]
Average Battery Current [A]
Fig.10 The battery average current
At variable load behavior, the wind velocity is
assumed constant at 10 m/s, the initial load has P
=500W and Q=100VAR and the PMSG is operating
in steady state conditions.
At the moment t=2s an initial load is suddenly
connected.
Then, after t=3s, this load is disconnected. In this
case, in Fig.11, the ac voltage’s shape is depicted.
1.5 22.5 33.5
-400
-300
-200
-100
0
100
200
300
400
Time [s]
AC Voltage [V]
Fig. 11 The ac link voltage
During the transitory time, the voltage shape
presents small sags. Because the mechanical power
delivered to the PMSG is constant, the power
balance is maintained by varying the battery’s
charging current, as shown in Fig.12.
DESIGN, CONSTRUCTION, MAINTENANCE
DOI: 10.37394/232022.2022.2.11
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Volume 2, 2022
1.5 22.5 33.5
6
7
8
9
10
11
12
13
Time [s]
Avarage Battery Current [A]
Fig. 12 The average battery current
While an additional load is connected, the
average battery current decreases from 12A to about
8.5A.
5 Conclusion
The proposed wind stand-alone system is dedicated
to a residential location and is able to supply
single-phase consumers of 230V and 50Hz. The
control of a variable speed PMSG for wind
generation system is based on the MPPT method
and has been presented in this paper. The start-up
process begins when the wind velocity exceeds the
threshold value of 4m/s. The turbine-generator
speed is controlled by the buck-boost converter,
which acts as a maximum power point tracker.
The balance between the generated power and the
consumed power is maintained by an electrical
battery or by the dump load. The load variations are
well managed and the dynamic performance is
good.
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variable - speed wind turbine”, Bulletin of
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(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the Creative
Commons Attribution License 4.0
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DESIGN, CONSTRUCTION, MAINTENANCE
DOI: 10.37394/232022.2022.2.11
Girdu Constantin Cristinel
E-ISSN: 2732-9984
73
Volume 2, 2022