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Adaptive Speed Regulation of Gearless Wind
Energy Transfer Systems
Sina Hamzehlouia, and Afshin Izadian, Senior Member, IEEE
Abstract- The energy of wind can be transferred to the
generator either by direct connection through a gearbox or by
employing an intermediate medium such as hydraulic fluid.
Gearless hydraulic wind power transfer systems are considered
noble candidates to transfer wind energy to generators since they
can collect the energy of multiple wind turbines in one generation
unit. However, non-ideal dynamics of hydraulic systems imposed
by pressure drops, leakage coefficient variations, and
motor/generator damping coefficient, degrade the performance
of power generation. This paper introduces a model reference
adaptive controller (MRAC) to maintain and track a reference
speed profile at the generator of a hydraulic wind power transfer.
The mathematical modeling of a gearless hydraulic wind power
transfer is presented and used to generate an accurate model of
the plant. The control performance is verified with simulation
results, which demonstrates a close tracking profile.
I. INTRODUCTION
INTEGRA TED in a nacelle, typical horizontal axis wind
turbines (HA WT) house a drivetrain consisting of a gearbox and an electric generator. The drivetrain
components and the gearbox are expensive, bulky, and require
regular maintenance, which makes the wind energy production
costly. Furthermore, power electronic converters are required
to provide reactive power for the induction generator and to
provide AC power for the grid. Operation of such system is
also costly and requires sophisticated control systems.
Placement of the gearbox and generator at top of the tower
demands frequent maintenance and replacement parts. While
the expected lifetime of a utility wind turbine is 20 years,
gearboxes typically fail within 5-7 years of operation and their
replacement costs approximately 10 percent of the turbine
installation cost [1].
Gearless hydraulic wind energy harvesting systems offer
many advantages over their geared counterparts. The main
advantage is the elimination of a variable speed gearbox and
the coupling of wind turbine with a hydraulic transmission
system. Unlike traditional wind power generation, this system
has lower operating and maintenance costs and allows for
integration of multiple wind turbines to one central generation
unit.
Manuscript received March 15,2012. This work was supported by a grant from IUPUI Solution Center.
S. Hamzelouia, and A. Izadian are with the Purdue School of Engineering and Technology, Indianapolis, TN. 46202. Corresponding author: [email protected]
A Hydraulic Transmission System (HTS) is identified as an
exceptional means of power transmission when variable
output velocity is required in engineering applications such as
manufacturing, automation, and heavy duty vehicles [2]. It
offers fast response times, maintains precise velocity under
varying loads [3], exhibits high durability, and is capable of
producing large forces at high speeds [4]. It also offers
advantage of decoupled dynamics for mUltiple input/multiple
output configurations, not permitted by its geared drivetrain
counterpart. Hydraulic systems have not been widely used in
wind energy transfer because of low energy efficiency,
leakage, and noise [5].
Despite the benefits that a hydraulic wind power transfer
demonstrates, non-idealities imposed by pressure drop along
with the connecting hoses, dependency of leakage coefficients
of hydraulic machinery on pressure variation, and other
unknown system parameters such as motor/generator
coupling, and damping coefficient degrade the performance of
the primary generator and reduce the output velocity
compared to an ideal system. To compensate for system
uncertainties, a model reference adaptive controller is
developed in this paper. The controller is used to regulate the
frequency of AC synchronous wind generators. This paper introduces a detailed mathematical model and
governing equations of a gearless hydraulic drivetrain for
design of a model reference adaptive controller. The controller
is used to overcome the system non-idealities and maintain the
generator speed. In section II of this paper, the hydraulic
energy transfer system is described, and component models
are introduced. Section III represents the overall dynamics and
modeling of the hydraulic energy transmission system.
Sections IV and V discuss the ideal and plant models. In
section VI, a model-reference output synchronizer is
introduced. Final section of the paper verifies the effectiveness
of the controller.
II. HYDRAULIC WIND ENERGY TRANSFER SYSTEM
DESCRIPTION
A Hydraulic Transmission System (HTS) consists of a
displacement pump driven by the prime-mover (Wind) and
one or more either fixed or variable-displacement hydraulic
motors. The hydraulic transmission uses the pump to convert
the input wind mechanical energy into pressurized fluid.
Hydraulic hoses are used to deliver and distribute the potential
978-1-4673-2421-2/12/$31.00 ©2012 IEEE 2162
energy to the energy conswners such as hydraulic motors to convert the potential energy back to mechanical energy [6].
Schematic diagram of the wind energy hydraulic
transmission system is illustrated in Figure 1. As the figure
demonstrates, a fixed displacement pump is mechanically
coupled with the wind turbine and supplies pressurized
hydraulic fluid to two fixed displacement hydraulic motors.
The hydraulic motors are coupled with electric generators to
produce electric power. Since the wind turbine generates a
large amount of torque at a relatively low angular velocity
(15-20 rpm), a high displacement hydraulic pump is required
to flow high-pressure hydraulics to transfer the power to the
generators.
Flexible high-pressure pipes/hoses connect the pump to the
piping toward the central generation unit.
Fig. 1. Schematic of the high pressure hydraulic power transfer system. The hydraulic pump is in a further distance from the central generation unit.[23]
The hydraulic circuit uses check valves to ensure
unidirectional flow of the hydraulic flows. A pressure relief
valve protects the system components from the destructive
impact of localized high-pressure fluids. The hydraulic circuit
contains a specific volume of hydraulic fluid, which is
distributed between hydraulic motors using a proportional
valve. In the next section, the governing equations of the
hydraulic circuit are obtained.
III. MATHEMATICAL MODEL
The dynamic model of the hydraulic system is obtained by
using governing equations of the hydraulic components in an
integrated configuration. The governing equations of hydraulic
motors and pwnps that result in flow and torque values [7-11],
[23] are utilized to express the closed loop hydraulic system.
A. Fixed Displacement Pump Dynamics
Hydraulic pumps deliver a constant flow determined by
Qp=DpOJp-kL,pPp, (1)
where Qp is the pump flow delivery, D p represents pwnp
displacement, kL,p denotes pump leakage coefficient and Pp is the differential pressure across the pump defined as
�=�-� , m
where � and � are gauge pressures at the pump terminals.
The pump leakage coefficient is a nwnerical expression of
the hydraulic component probability to leak, and is expressed
as follows
kL,p = KHP,p/ pv , (3)
where p is the hydraulic fluid density and v is the fluid
kinematic viscosity. KHP,p represents the pump Hagen
Poiseuille coefficient and is defmed as
(4)
where OJnolll,p is the pump's nominal angular velocity, Ynolll
represents the nominal fluid kinematic viscosity, Pnolll,p symbolizes the pump's nominal pressure and 17vo/,p denotes
the pump's volumetric efficiency. Finally, torque at the pump
driving shaft is obtained by
Tp = DpPp/17lllech,p' (5)
where 17mech,p is the pump's mechanical efficiency and is
expressed as
17mech,p = 17IOIOI,P/17vo/,P . (6)
B. Fixed Displacement Motor Dynamics
Similarly the flow and torque equations are derived for the
hydraulic motor. The hydraulic flow supplied to the hydraulic
motor is written as
(7)
where Qm is the motor delivery, Dm denotes the motor
displacement, kL,m is the motor leakage coefficient and Pm represents the differential pressure across the motor
�=�-� , 00 where � and � are gauge pressures at the motor terminals a
and b. The motor leakage coefficient is a numerical
expression of hydraulic component possibility to leak, and is
expressed as follows
kL,m = KHP,m/ pv , (9)
where P is the hydraulic fluid density and v is the fluid
kinematic viscosity. KHp,m indicates the motor Hagen
Poiseuille coefficient and is defmed as
�om,m (10)
where OJnom,m is the motor's nominal angular velocity, Ynom
is the nominal fluid kinematic viscosity, Pnom,m is the motor
nominal pressure and 17vo/,m is the motor's volumetric
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efficiency. The torque at the motor driving shaft is obtained by
T,11 = DmP'l11]mech,m ' (11)
where lJmech.m is the mechanical efficiency of motor and is
expressed as
lJmech,m = lJIOIGI,m/lJvo/,1II . (12)
The total torque produced in the hydraulic motor is
expressed as the sum of the torques from the motor loads and
is given as
T,n = � + TB + TL ' (13)
where T,n is total torque in the motor and �,TB' TL represent
inertial torque, damping friction torque and load torque
respectively. This equation can be rearranged as
T,n -TL = Jill (dOJIII/ dt) + BIIIOJIII, (14)
where Jill is the motor inertia, OJIII denotes the motor angular
velocity and Bill indicates the motor damping coefficient.
C. Hose Dynamics
The fluid compressibility model for a constant fluid bulk
modulus is expressed in [12]. The compressibility equation
represents the dynamics of hydraulic hose and hydraulic fluid
assuming that the pressure drop in the hydraulic hose is
negligible. From the mass conservation principle and the bulk
modulus, the fluid compressibility within the system equation
boundaries yields
Qc = (V/ fJ)(dP/dt), (15)
where V is the fluid volume subject to pressure effect, j3 is
the fixed fluid bulk modulus, P is the system pressure, and
Qc is the flow rate of fluid compressibility expressed by
Qc = Qp -QIII' (16)
Hence, the pressure variation can be expressed by
(dP/dt) =
(Qp -QIII)(fJ/V). (17)
D. Pressure Relief Valve Dynamics
Pressure relief valves are widely used for limiting the
maximum pressure in hydraulic power transmission. A
dynamic model for pressure relief valve (PRV) is presented in
[13]. A simplified model to determine the flow rate passing
through pressure relief valve in opening and closing states [12]
is obtained by
_ {kvC P - PJ, P > P., Qprv -
0 , P � P., , (18)
where kv is slope coefficient of valve static characteristic, P
is system pressure, and P., is valve opening pressure.
E. Check Valve Dynamics
The purpose of the check valve is to permit flow ill one
direction and to prevent back flows. Unsatisfactory
functionality of check valves may result in high system
vibrations and high-pressure peaks [14]. For a check valve
with spring preload, [15] operating models to calculate flow
rate passing through the check valves are obtained by {CI (P -PJAdisc ,P > Pv Q _
b k cv - s o ,P�p"
(19)
where Qcv is flow rate through the check valve, C is the
flow coefficient, Ib is hydraulic perimeter of the valve disc,
P is system pressure, and P., is valve opening pressure,
Adisc is the area which hydraulic liquid acts on the valve disc
and ks is the stiffness of the spring.
F. Directional Valve Dynamics
Directional valves are mainly employed to distribute flow
between rotary hydraulic components. The dynamic model of
a directional valve is categorized into two divisions, namely
the control device and the power stage. The control device
adjusts the position of the valve's moving membrane, while
the power stage controls the hydraulic fluid flow rate.
A directional valve model is represented in [16] by
specifying the valve orifice maximum area and opening. The
hydraulic flow through the orifice Qpv is calculated by
Q" =
CdA�! I PI sgn(P), (20)
where Cd represents the flow discharge coefficient, p is the
hydraulic fluid density, P indicates the differential pressure
across the orifice, and A is the orifice area and is expressed as
A =
Amax h I' (21)
hmax where �nax is the maximum orifice area, hmax is the
maximum orifice opening, and h is the orifice opening and is
obtained from
(22)
where x, is the orifice displacement, hi is the valve opening,
and hi-J is the previous valve position.
IV. MODEL AND UNCERTAIN PARAMETERS OF HYDRAULIC POWER TRANSFER
Figure 2 displays a block diagram of the proposed ideal
model for the hydraulic energy transfer system. MATLAB/
Simulink ® is used to create an ideal model of the system. The
model incorporates the governing mathematical equations of
every individual hydraulic circuit component in block
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diagrams. Figure 3 shows the governing equations of the
hydraulic wind energy harvesting system.
Fig. 2. Ideal Hydraulic wind energy harvesting model schematic diagram.
Fig. 3. Simulink model of hydraulic wind energy harvesting system.
V. HYDRAULIC POWER TRANSFER PLANT
The ideal system model neglects the effect of pressure drop
in the hydraulic system which is mainly due to inner hose friction, hose geometry, temperature variation, fluid viscosity,
couplings and adapters, and flow rate [17]. Moreover, the practical leakage coefficient of the rotary machinery is a
function of operating pressure. The non-ideal model of the
system incorporates these imperfections. ,-------,
QPRV
Fig. 4. Non-ideal Hydraulic wind energy harvesting model schematic diagram.
Fig. 5. Non-ideal Hydraulic wind energy harvesting simulink model.
Figures 4 and 5 illustrate a schematic diagram of a gearless
wind energy transfer system. A prototype of the hydraulic system is used to derive the correlation between pressure values and leakage coefficient. In this model, unlike the ideal model, where the hydraulic motors are supplied with the
differential pressure across their terminals, a proportional
valve distributes the flow between motors. The main purpose of this valve is to maintain the required angular velocity
profile in the main hydraulic motor.
VI. ADAPTIVE CONTROLLER DESIGN
This section introduces a model reference adaptive control
approach to regulate the flow of hydraulic liquid to the main
hydraulic motor. The flow regulation should maintain a specified frequency of generated voltage in standalone, and
control the amount of generated power in grid connected applications. The control law and gain adaptation technique
are represented for hydraulic wind power transfers [18-20].
The control law is expressed as
Iy = krr+ ke(yp - Ym)+kpYp' (23)
where Y p and Ym are the reference model and plant output
signals, r is the reference input and kr' ke ' k p are controller
gains that are adjusted simultaneously according to a gain adaptation law to mitigate the tracking error. Considering the
estimated values of the control gains, the equivalent control
command C is defined as " " " "
C = krr + kee + kpYp' A A A
(24)
where kr' ke ' k p are the estimations of the control gain and
are computed according to the gain adaptation technique as A
kr = -Po sgn(s)r, (25)
kp = -Po sgn(s)yp' (26)
A
ke = -Po sgn(s)e, (27)
where Po is the adaptation gain and S denotes the sliding
surface. The stability proof of this controller is provided in
[21-22]. Figure 6 illustrates the control system configuration
with two hydraulic power transfers comprised of an ideal hydraulic system (model) and an imperfect system with
unknown parameters (plant). The controller synchronizes the angular velocity of the plant with that of the model and
compensates for the non-idealities to reduce the effect of
pressure drop, leakage coefficient variation and unknown load damping coefficient of the plant.
2165
I 1 J Model I Model Output V(,locity Wind Speed 11---.-->1
� :L..:
P I--,.n--,I O-,-u--, IP,-,u,---"--,'c--,IOC.:c.iI:::"Y_->I Controller Plant r
r------ I f"J 1 Rcfc ... nc. S;gn.1
L. ___________________________________________________________________________ .J Fig. 6. Controller configuration, the output motor frequency synchronization.
VII. TRACKING PERFORMANCE AND DISCUSSION
The system non-idealities degrade the open loop
perfonnance of the power generation and deviate from the
specified velocities. Closed loop control of the output velocity,
and therefore the generated voltage frequency, requires
compensation of time varying parameter variations with
adaptive controllers. The control command is a PWM signal
that is generated to open a proportional valve and control the
flow of hydraulic liquid. Table 1 illustrates the simulation
parameter values and their units.
Symbol
Dp
DmA
DmB
ImA 1mB BmA BmB KL.fJ KL,mA
KL.mB
'7lOtal
'71'01
f3 P v
Po
TABLET
SIMULATION PARAMETERS
Quantity Value
Pump Displacement 0.517 Primary Motor 0.097 Displacement Auxiliary Motor 0.097 Displacement
Primary Motor Inertia 0.0014 Auxiliary Motor Inertia 0.0014 Primary Motor Damping 0.0026 Auxiliary motor Damping 0.0022 Pump Leakage Coefficient 0.17 Primary Motor Pump 0.1 Leakage Coefficient Auxiliary Motor Pump 0.001 Leakage Coefficient
Pump/Motor Total 0.90 Efficiency
Pump/Motor Volumetric 0.95 Efficiency Fluid Bulk Modulus 183695
Fluid Density 0.0305
Fluid Viscosity 7.12831
Adaptation Gain 10
Unit
in3/rev in3/rev
kg.m2
kg.m2
N.m1(rad/s) N.m1(rad/s)
psi
Ib/in3
cSt
Figure 7 shows an estimated pump leakage coefficient
variation with changes in pump tenninal pressure. This
leakage coefficient variation pattern is integrated to the plant
model to account for a plant parameter uncertainties. Since
lower or higher relative damping coefficients impose diverge
dynamics on the system response, the damping coefficient
uncertainties in the motor/generator were considered ±1O% of
the damping coefficient of the ideal model for the primary
motor and auxiliary motors respectively.
Figure 8 shows a step in angular velocity of pump, which is
applied to the hydraulic power transmission system. Figure 9
demonstrates mathematical model and plant response due to
unknown parameter values and variations. Clearly, the
uncertainties in the system parameters resulted in a different
behavior than what was expected. Pump Leakage Coemclent VS Pressure 02' .--,.__--.---�'--�=--�-__.--,._-,.----.---_,
.<' 02 � t 019 U • 018 oS � 017
! 016
o l ioo!:f----;'�20,-----;-!c .. 0;;--�' 60;;-----;';:;;BO--,200'*'-�220;;-----,2"'!;;----;260;;;--�2IIl;;-----;300 Pressure [psI]
Fig. 7. Hydraulic pump leakage coefficient variation with pressure change.
'00 '[&Xl � "" f-----'----"'-----1 � 400 :; �300 ." g'2OO
«
'00
°0�--�---7_--�---�--_7.,___-� Fig. 8. Hydraulic pump angular velocity profile.
Primary Motor Angular Velocity ,�,---�---,.--�-��-����--.---, '200
0.5 .. 5 Time(s]
-Model
---Plant at ·10% Damping
- - -Plant at+10% Damping
2 25 3
Fig. 9. Model and plant primary motor angular velocity without controls
(a) Primary Motor Angular Velocity Synchronization
I�M�w��t[::�1it��\�w;�i;t*�i� 93
6.51·"."";-;--;-;"""�5 ---;-.. ",,056o--;,.,o.0555C;;C--;-; .. 056!;;:--;-; .. Il565= ---;-,"".05C;-' ---;'-;;! .05C;;75'--:-;"058!;;;---:-:"0585�---'
Time(s]
(b) Fig. 10. Model and plant primary motor angular velocity with controls. (a) Angular velocity tracking of the plant, (b) A magnified output tracking for a
time increment.
The tracking performance of the adaptive controller is
illustrated in Figure 10. As the Figure demonstrates, the plant
tracks the reference generated from the model with variations
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less than ±1 rpm. A close look at the velocity profile
(Fig.lO.b) determines the accuracy of tracking. The adaptive
controller generates a PWM signal with duty cycle between
%0 and %100 to drive a hydraulic proportional valve and to
compensate for hydraulic system uncertainties.
E Auxiliary Motor Angular Velocity
i ::I�-.�--�-��-'A�---_-�-�.-- .'.� -.� . -� .. ��----.. . �-.��i�� .. . _: . . �: .... =.�:�:�t;��= .. �� . .. : .. ::�:::=� o ,
' . .. � 500 - - - -Plant at .10%Damping � ° O�----�O.5�----�----�1�.5----�����2.�5 ��� t Time[s) � 1500
�----,-
-----,
------�::::::�::�:=::::� ! l00J /���"'+"W''''''!''4'., ... � ��,.'. +���� .... .'�.':�� .. .. . > 500 � � oo� ____ -;;?-____ ---+ ____ ---,�
__ ---,="'�"'=
"'�PI�an�t a� t+�'0�.!'�. D�a�mp� in�g,,! _ 0.5 1.5 2.5 « Time{s]
Fig. II. Plant Auxiliary motor velocity variation to maintain reference tracking in the primary motor
As the flow is controlled to maintain the angular velocity of
the main motor, the excess high-pressure fluid is diverted to an
auxiliary motor to collect the excess energy. As the control
command is applied to track the reference request, the average
of auxiliary motor velocity is illustrated in Figure 11.
Figure 12 illustrates the control effort to maintain the
angular velocity. The control effort is normalized between 0-1
to demonstrate the fully closed and fully open valve conditions
respectively. Controller Effort
� U 0.5 � o
As simulation results demonstrated, adaptive controller
could achieve a high perfonnance in velocity tracking of a
hydraulic wind power system The tracking performance with
deviation of less than 2 rpm delivers a constant frequency
output voltage despite the variations in the system input or
parameter uncertainties.
VIII. CONCLUSION
This paper introduced a model reference adaptive controller
to synchronize the velocity of hydraulically driven wind
generators in a non-ideal energy transfer system. The system
non-idealities degraded the performance of the primary
generator and reduced the output frequency compared to a
model reference. To generate an ideal model, the hydraulic
system was accurately modeled and the governing equations
were derived. The adaptive controller demonstrated an
effective synchronization profile of the plant with the model.
ACKNOWLEDGMENT
This work was supported by a grant from IUPUI solution
Center.
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