# Maximum Power Control of  Hybrid Wind-Diesel-Storage System

Authors: Elkhatib Kamal; Magdy Koutb; Abdul Azim Sobaih; Sahar Kaddah
Journal: Advances in Fuzzy Systems
 (2008)

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## Abstract

Extraction of maximum wind power of variable speed wind turbines in hybrid wind-diesel-storage system (HWDSS) is considered due to economical purposes. The proposed control algorithm utilizes extended fuzzy-linear matrix equalities (FLMEs) systems design of stabilizing fuzzy controllers for nonlinear systems described by Takagi-Sugeno (TS) fuzzy models. The algorithm maximizes the power coefficient for a fixed pitch. Moreover, it reduces the voltage ripple and stabilizes the system over a wide range of wind speed variations. The control scheme is tested for different profiles of wind speed pattern and provides satisfactory results.


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## Body

## 1. Introduction

Since ancient times, wind turbine
technology has been used to improve humankind’s quality of life where people
have used wind turbines to pump water and mill grain, along with many other
uses. Today, wind turbines are used for similar purposes (i.e., water or oil
pumping, battery charging, or utility generation) as a cheap, clean source of
electricity, and well suited for isolated places with no connections to the
electric grid [1].In remote
areas such as small islands, diesel generators are the main power supply.
Diesel fuel has several drawbacks: it is quite expensive because transportation
to remote areas adds extracost, and it causes pollution via engine exhaust.
Providing a feasible, economical, and environmental alternative source to
diesel generators is important. A hybrid wind-diesel system with battery
storage of wind power can benefit islands and other isolated communities and
increase fuel savings. However, control of such system is very important as
wind turbine produces excessive fluctuation of power output, which negatively influences the quality of
electricity supplied to the load, particularly frequency and voltage [2].Optimum wind
energy extraction is achieved by running the wind turbine generator (WTG) in variable-speed,
variable-frequency mode. The rotor speed is allowed to vary in sympathy with
the wind speed, by maintaining the tip speed ratio to a value that maximizes
aerodynamic efficiency. In order to achieve this ratio, the permanent magnet
synchronous generator load line should be matched very closely to the maximum
power line of the wind turbine generator [3].The problem
of wind energy conversion system output power control has been considered
extensively [4–7]. Maximization
of the wind energy conversion efficiency based on a brushless doubly fed
reluctance generator is discussed in [4]. Reference [5] maximizes power based
on a standard V/Hz converter and controls the frequency to achieve the desired
power at a given turbine speed. Reference [6] maximizes power based on
controlling the slip power, which is extracted from the rotor circuits and fed
to the grid though a rectifier-inverter branch. The firing angle of the
inverter is used to control the slip power. Reference [7] presents a hill-climb
searching (HCS) control for the maximum wind turbine power at variable wind
speeds.The main
contribution of this research is to maximize the energy from the wind in the
presence of a wide range of wind variations using the proposed FLME controller.
Also, it provides a robust controller that stabilizes the HWDSS and overcomes
the system nonlinearity. In addition, it guarantees good robustness and
performance of the controller. Finally, it reduces the voltage ripple on the
main bus voltage. The proposed FLME controller is based on the Takagi-Sugeno
(TS) fuzzy model and linear matrix inequalities [8–10].This paper is
organized as follows. Section2 provides system analysis. Section 3 presents
the design of the proposed FLME controller. Section 4 shows the stability and
robustness conditions for the proposed algorithm. Section 5 presents simulation
of the wind turbine. Finally, concluding remarks are made in Section 6 followed
by the list of references.


## 2. System Analysis

### 2.1. Wind Turbine Modeling

The kinetic energy of the wind due to its
speed is captured by the turbine and is converted to mechanical energy. Along
with the turbine, there is a generator present at the tower top which is
coupled to the wind turbine by a shaft and often with a gear box. The generator
converts mechanical energy of turbine to electrical energy and it feeds at
demand point. The global scheme of a variable speed is displayed in Figure1. The
expression for aerodynamic power (Pa) captured by the wind turbine is given by the
nonlinear expression [11] (1)Pa=0.5Cp(λ)ρπR2V3, where ρ is the air density (kg⋅m-3), R is the rotor radius (m), V is the wind speed (m⋅s-1), and Cp is the power coefficient defined by the
following relation [12]: (2)Cp=(0.44−0.0167β)sin[π(λ−3)15−0.3β]−0.00184(λ−3)β,  where β is the blade pitch angle of the wind turbine, λ is the tip speed ratio (TSR) and is
given by [11] (3)λ=ωtRV, where ωt is the rotational speed of the blades.Figure 1
Wind turbine system.Referring to (2), optimal TSR λopt can be obtained as follows: (4)λopt=(15−0.3βπ)cos−1[0.00184β(15−0.3β)π(0.44−0.167β)]+3. Thus, the maximum power captured from the wind is given
by (5)Pa(max)=0.5Cp(max)(λopt,β)ρπR2V3.A typicalCp−λ curve is shown in Figure 2. It can be seen
that there is a maximum power coefficient Cp(max).
Normally, a variable speed wind turbine follows the Cp(max) to capture the maximum power up to the
rated speed by varying the rotor speed to keep the system at λopt,
then operates at the rated power with power control during the periods of high
wind by the  active control of the blade pitch angle or the passive regulation
based on aerodynamic stall. A typical power-wind speed curve is shown in Figure
3.Figure 2
Power coefficientCp versus TSR λ.Figure 3
Power-wind speed
characteristics.


### 2.2. System Description

The
underlying hybrid wind-diesel-storage system is illustrated in Figure4. The hybrid generation
system is composed of a wind turbine coupled with a synchronous generator, a
diesel-induction generator, and an energy storage system. In the given system,
the wind turbine drives the synchronous generator that operates in parallel
with the storage battery system. When the wind generator alone provides
sufficient power for the load, the diesel engine is disconnected from the
induction generator. The PEI
connecting the load to the main bus is used to fit the frequency of the power
supplying the load as well as the voltage.Figure 4
Structural diagram of hybrid wind-diesel-storage system.The dynamics of the system can be characterized by the
following equations [2]: (6)x˙=Ax(t)+Bu(t),y=Cx(t), where  (7)x(t)=[Vbωs]T,u(t)=[EfdIref]T,A=[1101][Lfτdo′ωsLmdLfτdo′Lmdωs(Ldisd−(raisq/ωs))Pind−PindJsωsVb−DsJs],B=[1−VcJsωs0−VcJsωs],C=[1001],  where Vc is  the AC side line-to-line voltage, Efd is the
SG field voltage, ωs is the bus frequency (or angular speed of SG), Js  and  Ds are the inertia and frictional damping of SG, isd  and  isq are the direct and quadrature current
components of SG, Ld  and  Lf are the
stator d-axis and rotor
inductance  of  SG, Lmd is the d-axis
field mutual inductance, τdo′ is the transient open circuit  time constant, ra is the
rotor resistance of SG, Pind is the power of the induction generator, Pload is the power of the load, Iref is the direct current set point, and Vb is the bus voltage. Equation (6) indicates
that the model is the linear form for fixed matrices A, B, and C.
However, matrices A and B are not fixed, but change as functions
of state variables, thus making the model nonlinear. Also, this model is only
used as a tool for controller design purposes. The used system parameters are
shown in Table 1 [13–15].Table 1
System  parameters.
Rated power1 [MW]Blade radius37.38 [m]Air density0.55 [kg/m3]Rated wind  speed12.35 [m/s]Cut-in speed4 [m/s]Cut-out speed25 [m/s]Blade pitch angle0°Rated line ac voltage230 [V]AC rated current138 [A]DC rated current239 [A]Rated load power40 [kW]The inertia  of SG1.11 [kg m2]Rated  power of  IG55 [kW]The inertia of the IG1.40 [kg m2]Torsional damping0.557 [Nm/rad]Rotor resistance of SG0.96 [Ω]Statord-axis inductance
of  SG2.03 [mH]Rotor  inductance  of
SG2.07 [mH]d-axis
field mutual inductance1.704 [mH]The transient open circuit time constant2.16 [ms]


## 2.1. Wind Turbine Modeling

The kinetic energy of the wind due to its
speed is captured by the turbine and is converted to mechanical energy. Along
with the turbine, there is a generator present at the tower top which is
coupled to the wind turbine by a shaft and often with a gear box. The generator
converts mechanical energy of turbine to electrical energy and it feeds at
demand point. The global scheme of a variable speed is displayed in Figure1. The
expression for aerodynamic power (Pa) captured by the wind turbine is given by the
nonlinear expression [11] (1)Pa=0.5Cp(λ)ρπR2V3, where ρ is the air density (kg⋅m-3), R is the rotor radius (m), V is the wind speed (m⋅s-1), and Cp is the power coefficient defined by the
following relation [12]: (2)Cp=(0.44−0.0167β)sin[π(λ−3)15−0.3β]−0.00184(λ−3)β,  where β is the blade pitch angle of the wind turbine, λ is the tip speed ratio (TSR) and is
given by [11] (3)λ=ωtRV, where ωt is the rotational speed of the blades.Figure 1
Wind turbine system.Referring to (2), optimal TSR λopt can be obtained as follows: (4)λopt=(15−0.3βπ)cos−1[0.00184β(15−0.3β)π(0.44−0.167β)]+3. Thus, the maximum power captured from the wind is given
by (5)Pa(max)=0.5Cp(max)(λopt,β)ρπR2V3.A typicalCp−λ curve is shown in Figure 2. It can be seen
that there is a maximum power coefficient Cp(max).
Normally, a variable speed wind turbine follows the Cp(max) to capture the maximum power up to the
rated speed by varying the rotor speed to keep the system at λopt,
then operates at the rated power with power control during the periods of high
wind by the  active control of the blade pitch angle or the passive regulation
based on aerodynamic stall. A typical power-wind speed curve is shown in Figure
3.Figure 2
Power coefficientCp versus TSR λ.Figure 3
Power-wind speed
characteristics.


## 2.2. System Description

The
underlying hybrid wind-diesel-storage system is illustrated in Figure4. The hybrid generation
system is composed of a wind turbine coupled with a synchronous generator, a
diesel-induction generator, and an energy storage system. In the given system,
the wind turbine drives the synchronous generator that operates in parallel
with the storage battery system. When the wind generator alone provides
sufficient power for the load, the diesel engine is disconnected from the
induction generator. The PEI
connecting the load to the main bus is used to fit the frequency of the power
supplying the load as well as the voltage.Figure 4
Structural diagram of hybrid wind-diesel-storage system.The dynamics of the system can be characterized by the
following equations [2]: (6)x˙=Ax(t)+Bu(t),y=Cx(t), where  (7)x(t)=[Vbωs]T,u(t)=[EfdIref]T,A=[1101][Lfτdo′ωsLmdLfτdo′Lmdωs(Ldisd−(raisq/ωs))Pind−PindJsωsVb−DsJs],B=[1−VcJsωs0−VcJsωs],C=[1001],  where Vc is  the AC side line-to-line voltage, Efd is the
SG field voltage, ωs is the bus frequency (or angular speed of SG), Js  and  Ds are the inertia and frictional damping of SG, isd  and  isq are the direct and quadrature current
components of SG, Ld  and  Lf are the
stator d-axis and rotor
inductance  of  SG, Lmd is the d-axis
field mutual inductance, τdo′ is the transient open circuit  time constant, ra is the
rotor resistance of SG, Pind is the power of the induction generator, Pload is the power of the load, Iref is the direct current set point, and Vb is the bus voltage. Equation (6) indicates
that the model is the linear form for fixed matrices A, B, and C.
However, matrices A and B are not fixed, but change as functions
of state variables, thus making the model nonlinear. Also, this model is only
used as a tool for controller design purposes. The used system parameters are
shown in Table 1 [13–15].Table 1
System  parameters.
Rated power1 [MW]Blade radius37.38 [m]Air density0.55 [kg/m3]Rated wind  speed12.35 [m/s]Cut-in speed4 [m/s]Cut-out speed25 [m/s]Blade pitch angle0°Rated line ac voltage230 [V]AC rated current138 [A]DC rated current239 [A]Rated load power40 [kW]The inertia  of SG1.11 [kg m2]Rated  power of  IG55 [kW]The inertia of the IG1.40 [kg m2]Torsional damping0.557 [Nm/rad]Rotor resistance of SG0.96 [Ω]Statord-axis inductance
of  SG2.03 [mH]Rotor  inductance  of
SG2.07 [mH]d-axis
field mutual inductance1.704 [mH]The transient open circuit time constant2.16 [ms]


## 3. The Proposed FLME Controller

### 3.1. Takagi-Sugeno's Fuzzy Plant Model

The Takagi-Sugeno fuzzy
model represents a nonlinear system by partitioning the system into subsystems
and then combining them with linguistic rules. In this paper, three linear
subsystems are considered for the nonlinear state-space models (6), The
continuous fuzzy dynamic model, proposed by Takagi-Sugeno, is described by fuzzy
IF-THEN rules, which represent local linear input-output relations of nonlinear
systems [16]. The ith rule of this fuzzy model is given by Plant
Rule(8)IFq1(x(t))isN1iAND⋯ANDqψ(x(t))isNψi.Thenx˙(t)=Aix(t)+Biu(t),y=Cix(t), where NΩi is a fuzzy set, Ω=1,2,…,ψ,  i=1,2,…,p, x(t)∈Rn×1 is the state vector, u(t)∈Rn×1 is the input vector, Ai∈Rn×n and Bi∈Rn×m are  system matrices of appropriate dimensions, p is the number of IF-THEN rules (p=3). q1(x(t)),…,qψ(x(t)) are the premise variables. The plant dynamics
are then described
by (9)x˙(t)=∑i=1phi(x(t))[Aix(t)+Biu(t)], where (10)hi(x(t))=Γi(x(t))∑i=1pΓi(x(t)),Γi(x(t))=∏Ω=1ψNΩi(x(t)),hi>0,∑i=1phi(x(t))=1.


### 3.2. Fuzzy Controller

Three controllers are designed for the three
linear subsystems, and then the total control output is obtained by defuzzification.
A state feedback by linear matrix equalities (LMEs) is used to design a controller
for each subsystem. The control is performed so that the power coefficient is
maximized, thus the maximum power captured from the wind is obtained.Thejth rule of fuzzy controller is given by Plant Rule(11)IFf1(x(t))isM1jAND⋯ANDfψ(x(t))isMψj.Thenu(t)=Gjx(t)+r, where Mϕj is a fuzzy set ϕ=1,2,…,ψ,  j=1,2,…,c, r is the reference input, f1(x(t)),…,fψ(x(t))
are the premise variables, c is the number of IF-THEN rules (c=3), and Gj are local
feedback gains. The inferred output of the fuzzy controller is given by (12)u(t)=∑j=1cmj(x(t))[Gjx(t)+r], where (13)mj(x(t))=ϖj(x(t))∑j=1cϖj(x(t)),ϖj(x(t))=∏ϕψMϕj,mj>0,∑j=1cmj=1.


### 3.3. Parallel Design Approach (PDA)

It
allows the stability criterion to be satisfied more easily. It is used when the
membership functions are known and the same rule antecedents of the TS fuzzy
plant model are used in the fuzzy controller. Referring to (9) and (12), the
fuzzy control system is given by (14)X˙(t)=∑i=1p∑i=1phi(x(t))hi(x(t))[HiiX(t)+Bir], where Hii=Ai+BGi.For each subspace,
different model (i=j=1,2,3), (p=c=1,2,3) is applied. The degree of membership function for states Vbψ and ωs is depicted in Figure 5. Each
membership function also represents model uncertainty for each subsystem.Figure 5
Membership functions of states.


## 3.1. Takagi-Sugeno's Fuzzy Plant Model

The Takagi-Sugeno fuzzy
model represents a nonlinear system by partitioning the system into subsystems
and then combining them with linguistic rules. In this paper, three linear
subsystems are considered for the nonlinear state-space models (6), The
continuous fuzzy dynamic model, proposed by Takagi-Sugeno, is described by fuzzy
IF-THEN rules, which represent local linear input-output relations of nonlinear
systems [16]. The ith rule of this fuzzy model is given by Plant
Rule(8)IFq1(x(t))isN1iAND⋯ANDqψ(x(t))isNψi.Thenx˙(t)=Aix(t)+Biu(t),y=Cix(t), where NΩi is a fuzzy set, Ω=1,2,…,ψ,  i=1,2,…,p, x(t)∈Rn×1 is the state vector, u(t)∈Rn×1 is the input vector, Ai∈Rn×n and Bi∈Rn×m are  system matrices of appropriate dimensions, p is the number of IF-THEN rules (p=3). q1(x(t)),…,qψ(x(t)) are the premise variables. The plant dynamics
are then described
by (9)x˙(t)=∑i=1phi(x(t))[Aix(t)+Biu(t)], where (10)hi(x(t))=Γi(x(t))∑i=1pΓi(x(t)),Γi(x(t))=∏Ω=1ψNΩi(x(t)),hi>0,∑i=1phi(x(t))=1.


## 3.2. Fuzzy Controller

Three controllers are designed for the three
linear subsystems, and then the total control output is obtained by defuzzification.
A state feedback by linear matrix equalities (LMEs) is used to design a controller
for each subsystem. The control is performed so that the power coefficient is
maximized, thus the maximum power captured from the wind is obtained.Thejth rule of fuzzy controller is given by Plant Rule(11)IFf1(x(t))isM1jAND⋯ANDfψ(x(t))isMψj.Thenu(t)=Gjx(t)+r, where Mϕj is a fuzzy set ϕ=1,2,…,ψ,  j=1,2,…,c, r is the reference input, f1(x(t)),…,fψ(x(t))
are the premise variables, c is the number of IF-THEN rules (c=3), and Gj are local
feedback gains. The inferred output of the fuzzy controller is given by (12)u(t)=∑j=1cmj(x(t))[Gjx(t)+r], where (13)mj(x(t))=ϖj(x(t))∑j=1cϖj(x(t)),ϖj(x(t))=∏ϕψMϕj,mj>0,∑j=1cmj=1.


## 3.3. Parallel Design Approach (PDA)

It
allows the stability criterion to be satisfied more easily. It is used when the
membership functions are known and the same rule antecedents of the TS fuzzy
plant model are used in the fuzzy controller. Referring to (9) and (12), the
fuzzy control system is given by (14)X˙(t)=∑i=1p∑i=1phi(x(t))hi(x(t))[HiiX(t)+Bir], where Hii=Ai+BGi.For each subspace,
different model (i=j=1,2,3), (p=c=1,2,3) is applied. The degree of membership function for states Vbψ and ωs is depicted in Figure 5. Each
membership function also represents model uncertainty for each subsystem.Figure 5
Membership functions of states.


## 4. Stability and Robustness for the Proposed Algorithm

A proof of the stability
and robustness conditions for the plant dynamics described by (9) is shown in
the appendix. The main result is summarized in Lemma  1.Lemma 1.
Under
PDA, the fuzzy control system as given by (14) is stable if (15)μ[THiiT−1]≤−ζ, where ζ is nonzero positive constant and T is a
transformation matrix. The analysis given in the appendix indicates that ∥x(t)∥ will go to its steady state faster if we use
larger values of ζ.
Calculation of Gj of the fuzzy controller that satisfies the
stability and robustness conditions is formulated as an LME problem.
IfTT=T,P=TT,(16)Gj=−RBjTP,∀j,P>0,R∈κm×m are symmetric positive definite matrices. The transformation
matrix (T) should be found in such a way that the uncertainty free
system is stable [17]. Using (14), (17)PHii+HiiTP<0,PAi+AiTP−2xPBRBTP=−σIP>0,∀i, where σ is robustness index.


## 5. Simulation Results

The proposed
controller for the HWDSS is tested for many cases of wind speed variations. Four
wind speed signals are tested in this section to prove the effectiveness of the
proposed algorithm.


### 5.1. Random Variation of Wind Speed Signal

In this case, the wind speed signal is
considered as a random wave as shown in Figure6. The rotor speed to capture
the maximum power from the wind turbine is shown in Figure 7 (solid line). It
is clear that the dotted curve in Figure 7 which represents the actual rotor
speed coincides with the solid curve. As the wind speed ranges between the
cut-in and rated speed of the wind turbine, the produced power curve takes
almost the wind speed curve as shown in Figure 8. The power generated at wind
speed of 12 m/s is 0.75 Mw. Comparing this value  with that obtained using PI controller [14]
which is 0.4 Mw, it is clear that a 45% increase is obtained in the maximum
value. Figure 9 shows
that the voltage profile is nearly constant and that the voltage ripple is
reduced to 90% compared with the adaptive fuzzy logic control [15].Figure 6
Wind speed.Figure 7
Rotor speed tracking.Figure 8
Per unit wind turbine
produced power.Figure 9
Bus voltage.


### 5.2. Sinusoidal Variation of Wind Speed Signal

In this case, the wind speed signal is
considered as a sine wave as shown in Figure10. The rotor speed to capture the
maximum power from the wind turbine is shown in Figure 11 (solid line). It is
clear that the dotted curve in Figure 11 which represents the actual rotor
speed coincides with the solid curve. As the wind speed ranges between the
cut-in and rated speed of the wind turbine, the produced power curve takes
almost the wind speed curve as shown in Figure 12. Figure 13 shows that the
voltage profile is nearly constant and the voltage ripple is reduced to 90%
compared with [15].Figure 10
Wind speed.Figure 11
Rotor speed tracking.Figure 12
Per-unit wind turbine produced
power.Figure 13
Bus voltage.


### 5.3. Step Change of Wind Speed

In this case, a big step change of wind speed
is tested as shown in Figure14. Figure 15 shows the rotor speed while the
dotted line in this figure represents the actual rotor speed that the
controller is able to capture. It is clear from this figure that the controller
effectively tracks the rotor speeds. Figure 16 indicates the output power of
the wind turbine as a per-unit value, it is clear that when the wind speed is
below the cut-in speed or over cut-off speed, the power reaches zero. Figure 17
indicates that the bus voltage is nearly constant.Figure 14
Wind speed.Figure 15
Rotor speed
tracking.Figure 16
Per-unit wind turbine produced
power.Figure 17
Bus voltage.


### 5.4. Sinusoidal Variation of Wind Speed Signal

This case
is another sinusoidal wind speed signal but its minimum values is 8 m/s and its
maximum value is 26 m/s which is bigger than the cut-off speed of the turbine
as shown in Figure18. Figure 19 indicates the effectiveness of the algorithm which tracks the
rotor speed for different wind speed, while Figure 20 shows the output power
from the wind turbine, which indicates that when the speed become over the
cut-off speed, the power equals zero. Figure 21 indicates that the bus voltage
is nearly constant and voltage ripple reduced to 90% compared with [15], since
the ripple voltage reduced to 0.045 V with the proposed algorithm, but in [15]
the ripple voltage is 0.4 V.Figure 18
Wind speed.Figure 19
Rotor speed tracking.Figure 20
Per-unit wind turbine produced
power.Figure 21
Bus voltage.Comparing the results of the proposed
algorithm with that given in [14, 15], it could be seen that the proposed
controller has the following advantages.(i)
It can control the plant well over a wide
range of wind speeds.(ii)
The generated
power is increased up to 45% compared with [14].(iii)
The algorithm
is more robust in the presence of high nonlinearity.(iv)
Bus voltage is
nearly constant and voltage ripple is reduced to 90% compared with [15].


## 5.1. Random Variation of Wind Speed Signal

In this case, the wind speed signal is
considered as a random wave as shown in Figure6. The rotor speed to capture
the maximum power from the wind turbine is shown in Figure 7 (solid line). It
is clear that the dotted curve in Figure 7 which represents the actual rotor
speed coincides with the solid curve. As the wind speed ranges between the
cut-in and rated speed of the wind turbine, the produced power curve takes
almost the wind speed curve as shown in Figure 8. The power generated at wind
speed of 12 m/s is 0.75 Mw. Comparing this value  with that obtained using PI controller [14]
which is 0.4 Mw, it is clear that a 45% increase is obtained in the maximum
value. Figure 9 shows
that the voltage profile is nearly constant and that the voltage ripple is
reduced to 90% compared with the adaptive fuzzy logic control [15].Figure 6
Wind speed.Figure 7
Rotor speed tracking.Figure 8
Per unit wind turbine
produced power.Figure 9
Bus voltage.


## 5.2. Sinusoidal Variation of Wind Speed Signal

In this case, the wind speed signal is
considered as a sine wave as shown in Figure10. The rotor speed to capture the
maximum power from the wind turbine is shown in Figure 11 (solid line). It is
clear that the dotted curve in Figure 11 which represents the actual rotor
speed coincides with the solid curve. As the wind speed ranges between the
cut-in and rated speed of the wind turbine, the produced power curve takes
almost the wind speed curve as shown in Figure 12. Figure 13 shows that the
voltage profile is nearly constant and the voltage ripple is reduced to 90%
compared with [15].Figure 10
Wind speed.Figure 11
Rotor speed tracking.Figure 12
Per-unit wind turbine produced
power.Figure 13
Bus voltage.


## 5.3. Step Change of Wind Speed

In this case, a big step change of wind speed
is tested as shown in Figure14. Figure 15 shows the rotor speed while the
dotted line in this figure represents the actual rotor speed that the
controller is able to capture. It is clear from this figure that the controller
effectively tracks the rotor speeds. Figure 16 indicates the output power of
the wind turbine as a per-unit value, it is clear that when the wind speed is
below the cut-in speed or over cut-off speed, the power reaches zero. Figure 17
indicates that the bus voltage is nearly constant.Figure 14
Wind speed.Figure 15
Rotor speed
tracking.Figure 16
Per-unit wind turbine produced
power.Figure 17
Bus voltage.


## 5.4. Sinusoidal Variation of Wind Speed Signal

This case
is another sinusoidal wind speed signal but its minimum values is 8 m/s and its
maximum value is 26 m/s which is bigger than the cut-off speed of the turbine
as shown in Figure18. Figure 19 indicates the effectiveness of the algorithm which tracks the
rotor speed for different wind speed, while Figure 20 shows the output power
from the wind turbine, which indicates that when the speed become over the
cut-off speed, the power equals zero. Figure 21 indicates that the bus voltage
is nearly constant and voltage ripple reduced to 90% compared with [15], since
the ripple voltage reduced to 0.045 V with the proposed algorithm, but in [15]
the ripple voltage is 0.4 V.Figure 18
Wind speed.Figure 19
Rotor speed tracking.Figure 20
Per-unit wind turbine produced
power.Figure 21
Bus voltage.Comparing the results of the proposed
algorithm with that given in [14, 15], it could be seen that the proposed
controller has the following advantages.(i)
It can control the plant well over a wide
range of wind speeds.(ii)
The generated
power is increased up to 45% compared with [14].(iii)
The algorithm
is more robust in the presence of high nonlinearity.(iv)
Bus voltage is
nearly constant and voltage ripple is reduced to 90% compared with [15].


## 6. Conclusion

This paper presents a hybrid power
system consisted of a wind turbine, a diesel generation unit, and energy
storage devices. Both the wind power generator and the SG operate at variable
speeds so as to maximize the wind energy capture as a force source and minimize
the diesel fuel consumption for economic purpose. Both types of generation
units are connected to the ac load system through PEI
to stabilize the system frequency. The
control is performed so that the power coefficient is maximized. The operating
principles have been discussed and the simulation model of the systems has been
developed. The proposed algorithm utilizing FLME is simple and leads to robust
control performance. Simulation results have confirmed that maximum power
conversion efficiency obtained increases to the order of 45% compared with
previous methods and voltage ripple reduced to 90%. Maximum power control of
hybrid wind power generation with storage battery is achieved.



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*Source: 963710-2008-12-11.xml*