Wind energy extraction and conversion: optimization through variable speed
generators and non linear fuzzy control
Paulo Costa
Instituto Politécnico de Viana do Castelo, Avenida do Atlântico,
4900 Viana do Castelo, Portugal, tel : +351258819700, pjc@fe.up.pt
António Martins, Adriano Carvalho
Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias
4200-465 Porto, Portugal, tel +351225081818, ajm@fe.up.pt, asc@fe.up.pt
Summary
The maximization of wind energy extraction can be obtained using variable speed electrical generators in conjunction
with non linear control algorithms.
This paper presents an incremental speed control method which is independent from both wind speed measurement
and specific systems characteristics.
The algorithm is based on the dynamic behaviour of the electrical generator and uses fuzzy logic as a non linear
reasoning tool. The simulation results obtained with this controller applied to a double feed induction generator show
that it is possible to increase the efficiency in the conversion from wind power to variable speed and torque.
Key words : power coefficient, variable speed, , fuzzy control, active power, wind farm
Introduction
Wind energy is an important source of electrical energy in years to come. Its main advantages come from the fact of
being a renewable and environmental-friendly energy. At the beginning it was cheap and very robust but the
generated power quality was poor. Most of wind power installations were limited to a few hundreds kilowatts
connected to distribution grids [1]. Wind turbines and farms grew in size and ratio from the few hundreds kilowatts to
megawatst size. The increased rated power of wind farms to areas with good wind resources leads to a new problem
approach – to which extent the wind power interferes to the power system.
The performance of a wind generation system can be separated into three main conversion stages. The first one is the
transformation of the wind speed kinetic energy in the turbine speed and torque. In the second one, the turbine
mechanical energy is transformed by an electrical generator, which can be an asynchronous or synchronous machine.
The performance of these two power conversions will strongly impose the global performance of the wind power
system. Generally, the grid connection is made by an electronic power converter with high efficiency. So, it is very
important to maximize the performance of the first conversion, what can be done by using variable speed generators.
Many previous researches have focused at the same goal, maximizing wind power extraction, by three different
methods: tip speed ratio control, power signal feedback control and hill-climb searching control [2], [3], [4] and [5].
The paper presents an incremental speed control method which is independent from wind speed measurement as well
as from specific systems characteristics, and it can be applied to all kinds of turbines, with small or high inertia.
The performance of the first energy conversion is measured by the power coefficient parameter; high performance is
obtained working close to maximum value for it.
The presented algorithm is based on a simple but robust approach: if the power on the turbine input shaft is equal to
the generator electrical output the resulting speed slope is zero, i.e. the torque reference is maintained. If the turbine
shaft accelerates, it is possible to increase the generator torque and extract more energy from the mechanical system.
Otherwise, if the shaft decelerates the generator torque should be reduced.
Fuzzy logic is the right tool to use for implementing this control strategy, due to the complexity and non linear system
behaviour. The fuzzy controller has three inputs: speed error, speed slope and last torque change, and one output
variable: the change of the generator torque reference. For achieving good results it is necessary to avoid maximum
relative points, which the method guarantees.
Wind turbines
A wind turbine is characterized by its power-speed characteristics. For a horizontal axis wind turbine, the amount of
power Pt that a turbine is capable of producing is given by
Pt =
1
2
*Cp * ρ * A*v
3
(1)
where ρ is the air density, A is the swept area of the turbine and v is the wind velocity. The Cp parameter is called the
power coefficient and is dependent on the ratio between the linear velocity of the blade tip (R*Wt) and the wind
velocity (v). This ratio, known as the tip-speed ratio, is defined as
w *R
λ= t
(2)
v
where R is the radius of the turbine. This kind of application is designable with constant or variable speed.
Different types of wind turbines are available on the market. The different types of wind turbines have their own
advantages and disadvantages. Fixed-speed wind turbines normally cause a voltage drop during start-up [6]. The
voltage drop is mainly caused by reactive power consumption during magnetization of the generator. Another
problem concerned to wind turbines with fixed speed is the flicker produced during normal operation of the wind
turbine. Once this method the energy extraction is optimized for one point of operating, it means that for only wind
speed is achieved the maximum value of extraction.
The variations in the generated power are mainly caused by the wind turbines and the tower shadow effect. These
variations can lead to flicker emission. Variable-speed wind turbines can reduce these power variations and eliminate
the flicker caused by power pulsation, becoming possible to maximize the energy extraction using an appropriated
control method.
Fuzzy logic
Modern systems include large and complex subsystems and sophisticated technical devices that need to be controlled.
They require the development of mathematical models. However, these models are rather complicated and include
some vagueness. So it is hard classical mathematics that processes these models [7]. The approach of fuzzy logic is
based on a mathematical framework where imprecise conceptual phenomena in modeling and decision making may
be precisely and rigorously studied. It lets mathematical models at describing rather unmodelled situations and it
finds solutions for “not formulated” problems.
Fuzzy logic is applied to wind farm control with the goal of pass-through the complex, non-linearity and uncertainty
of these control systems. In [8] are present some limitations of conventional controllers as: nonlinear models are
computationally intensive and have complex stability problems. A plant does not have accurate models due to
uncertainty and lack of perfect knowledge, uncertainty in measurements and multivariables and multiloops systems
have complex constraints and dependencies.
Control method
The control algorithm has as main objective to keep the tip speed ratio, always inside of a small bandwidth near to the
maximum value, independently of the existence of the pitch controller, because it has a lower time constant. So, the
emphasis of the control is on turbine rotational speed and its time behavior due to the balance between aerodynamic
torque, energy from the wind, and electric torque produced by electrical machine, energy extracted to the turbine
shaft. Figure 1 illustrates the global framing of this controller in the wind system.
Figure 1. Integration of power coefficient controller on the glogal wind control structure.
The control algorithm, figure 2, is based on a global controller that receives all information, it prepares the inputs
variables and it sends them to his nuclear fuzzy controller system. This module processes the behaviour of the inputs
variables and finds the right solution to apply in the wind turbine speed to achieve the main goal - maximize the
operation point by achieving a maximum value to the power coefficient, increasing power extraction. The process
begins with a value for wind speed.
Figure 2: Algorithm structure of the power coefficient optimization
The approach of the authors is based on the development of a fuzzy controller, what implies an appropriate structure
and rules of inference for this controller, at optimizing operation of the wind turbine. The structure used is presented
in figure 3. Linguistic variables are used to translate real values into linguistic values. The possible values of a
linguistic variable are not numbers but so called 'linguistic terms’.
The fuzzy controller has three inputs: speed error (error), speed slope (dv) and last torque change (ldt), and one
output variable (output): the change of the generator torque reference.
Figure 3. Fuzzy logic controller
The rules' 'if' part describes the situation, for which the rules are designed. The 'then' part describes the response of
the fuzzy system in this situation. The degree of support is used to weigh each rule according to its importance. The
wind turbine controller is constituted by the following rules, figure 4:
a)
b)
c)
Figure 4 Fuzzy rules considering: a) speed error negative, b) speed error null and c) speed error positive
With the following significance:
N - Negative
Z – Zero
P – Positive
NP – Negative Small
NM – Negative Médium
NG – Negative Big
PP – Positive Small
PM – Positive Médium
PG – Positive Big
The resulting control surface using the min-max and centroid operators is shown in figures 5, 6 and 7. These figures
show a 3D surface result of the applied rules, with the two input variables on horizontal axes, while the output is
plotted on the vertical axis. In order to have a three dimensional representation, the third input value is considered
constant. In the first figure (figure 5) it is considered that the last torque change has no variation, in figure 6 the speed
slope is constant and the last representation (figure 7) takes speed error as a constant value.
Figure 5 Fuzzy controller surface (last torque change as a constant input)
Figure 6 Fuzzy controller surface (speed slope as a constant input)
Figure 7 Fuzzy controller surface (speed error as a constant input)
System behaviour
Nowadays significant increases in the wind power generation have to make use of new control methods, like fuzzy
logic. The power coefficient measures the efficiency of the first conversation of wind into electricity. This coefficient
depends on the relationships between wind speed and rotational turbine speed.
In this work it is demonstrated that it is possible to increase the energy extraction using the right controller, especially
at low wind speeds. This control method imposes the turbine rotational speed to achieve always the maximum value
of the power coefficient, independent of the wind speed measurement and specific systems characteristics.
The wind speed variation on a wind turbine is very complex and demand sophisticated techniques to optimize the
power extraction. In order to show the algorithm validity two different wind turbines were analyzed.
The first simulation considers the characteristics of a NEG-MICON NM52/900 wind turbine, figure 8. In the second
simulation, figure 9, the Enercon E44/600 wind turbine characteristics are considered.
a)
b)
Figure 8: a) and b) The operation of the controller applied to a wind turbine MM52/900 for optimize the power
coefficient. Traces from top: Cp - Power coefficient, P_ref - Power reference, vento - Wind speed and w_rad/s wind turbine speed.
a)
b)
Figure 9: a) and b) The operation of the controller applied to a wind turbine E44/600 for optimize the power
coefficient. Traces from top: Cp - Power coefficient, P_ref - Power reference, vento - Wind speed and w_rad/s wind turbine speed.
Conclusions
The control algorithm developed in this work has assumed one goal: whole system performance could be maximized
and optimized considering only the control of wind turbine Speed. So, this control method is not based in analytical
or empirical expressions but in real effects allowing having a control method independent from systems
characteristics. The use of fuzzy logic allows at solving the problems of non-linear and high complexity of the power
coefficient behavior. The simulation results obtained with this controller applied to a double feed induction generator
show that it is possible to increase the energetic performance of the first conversion and consequently of the all wind
power generator system. The developed controller presented in this paper shows that it is controllable to keep on a
narrow bandwidth the power coefficient close to its maximum value. Presented results show that, considering present
high power turbines, with 4 or 5 MW, this kind of controller is able of achieving significant increase on generated
power.
References
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Acknowledgments
The first author would like to thank PRODEP (Programa de Desenvolvimento Educativo para Portugal) for the support
of this work.