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: izadian@ieee.org

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

2166

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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