Adaptive Estimation-Based Leakage Detection Fro a Wind Turbine Hydraulic Pitching System

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Adaptive Estimation-Based Leakage Detection for aWind Turbine Hydraulic Pitching System

Xin Wu, Yaoyu Li, Member, IEEE, Feng Li, Zhongzhou Yang, and Wei Teng

AbstractOperation and maintenance (OM) cost has con-tributed a major share in the cost of energy for wind power gener-ation. Condition monitoring can help reduce the OM cost of windturbine. Among the wind turbine components, the fault diagnosisof the hydraulic pitching system is investigated in this study. Thehydraulic pitching system is critical for energy capture, load re-duction, and aerodynamic braking. The fault detection of internaland external leakages in the hydraulic pitching system is studiedin this paper. Based on the dynamic model of the hydraulic pitch-ing system, an adaptive parameter estimation algorithm has beendeveloped in order to identify the internal and external leakagesunder the time-varying load on the pitch axis. This scheme candetect and isolate individual faults in spite of their strong couplingin the hydraulic model. A scale-down setup has been developed asthe hydraulic pitch emulator, with which the proposed method isverified through experiments. The pitching-axis load input is ob-tained from simulation of a 1.5-MW variable-speed-variable-pitchturbine model under turbulent wind profiles on the FAST (fatigue,aerodynamics, structural, and tower) software developed by theNational Renewable Energy Laboratory. With the experimentaldata, the leakage and leakage coefficients can be predicted via theproposed method with good performance.

Index TermsAdaptive estimation, hydraulic systems, leak de-tection, wind energy.

I. INTRODUCTION

WIND power has become the worlds fastest growing re-

newable energy source. The installed wind power ca-

pacity world wide has exceeded 160 GW. The U.S. targets 20%

wind-based electricity generation, i.e., over 300 GW, by 2030.

As wind power is growing toward a major utility source, reduc-

ing the cost of energy (COE) becomes a critical issue to make

wind power competitive to conventional sources [1].

A major portion of the COE for wind power generation is the

relatively high cost for operation and maintenance (OM). Wind

turbines are hard-to-access structures, and they are often lo-

Manuscript received August 12, 2010; revised February 18, 2011; acceptedApril 2, 2011. Recommended by Technical Editor Y. Li. This work was sup-ported in part by the Fundamental Research Funds for the Central Universitiesof China.

X. Wu and W. Teng are with the School of Energy, Power and MechanicalEngineering, North China Electric Power University, Beijing 102206, China(e-mail: [email protected]; [email protected]).

Y. Li and Z. Yang are with the Department of Mechanical Engineering,University of Wisconsin, Milwaukee, WI 53211 USA (e-mail: [email protected];[email protected]).

F. Li is with the School of Mechanical Engineering, University of Scienceand Technology, Beijing 100083, China (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMECH.2011.2142400

cated in remote areas. These factors alone increase the OM cost

for wind power systems. Also, poor reliability directly reduces

availability of wind power due to the turbine downtime [1]. The

OM cost for an offshore wind turbine is estimated to be 20%

25% of the total income [1], [2]. Condition monitoring and fault

diagnosis of wind turbines has, thus, greater benefit for such sit-

uations. In addition, wind turbine repair and maintenance that

require extensive usage of cranes and lifting equipment create

a highly capital-intensive operation as well as delayed services

due to lack of crane availability and needs for optimal weather

conditions. Also, the trend that hascurrentlyemerged to dampen

prospects is lack of personnelavailable to perform theconsistent

OM required to keep turbines functioning and efficient.

A blade pitch control system is critical for turbine opera-

tion, as pitching is an important actuation for enhancing energy

capture, mitigating operational load, stalling and aerodynamic

braking [3][6]. Under very strong wind, in particular, it is used

as aerodynamic brake to stop the turbine. Avoiding pitching

failure is thus important for system operation and safety. Pitch-

ing motion is typically driven by hydraulic actuators or electric

motors. The hydraulic pitching system is advantageous in large

stiffness, little backlash, and higher reliability. Electric motor

driven pitching systems have larger bandwidth, which is more

desirable for faster actions such as individual pitching, however,suffering from smaller stiffness, quicker wear in transmission,

and larger backlash. For large to extreme aerodynamic load-

ing situations, hydraulic systems are considered more fail-safe.

Hydraulic actuation system failure takes a remarkable portion

among different factors of wind turbine failure. For the opera-

tion under extreme wind, failure of hydraulic pitching may lead

to catastrophic failure of the whole turbine, which must be pre-

vented from. Fault detection of the hydraulic pitching system is

critical for protecting turbine under windy operation as turbine

stalling is a critical measure of protecting wind turbine [1].

Leakage is a critical fault for hydraulic systems, which may

reduce the effective stiffness and efficiency. As consequence,the control performance and stability robustness can be dramat-

ically undermined. There are two kinds of leakages in hydraulic

systems: external leakage in hose and connector, and internal

(cross-port) leakage in piston seal. The external leakage may

cause a sluggish response of the hydraulic system. The internal

leakage happens when the fluid crosses the cylinder piston seal

that closes the gap between the moving piston and the cylin-

der. As the internal leakage increases, the cylinder may lose the

ability to manipulate the load [12].

Fault diagnosis of hydraulic control systems has been studied

for many other industrial applications, with both data-driven and

model-based approaches. For the data-driven fault detection,

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2 IEEE/ASME TRANSACTIONS ON MECHATRONICS

the prior knowledge about the faulty behavior on the hydraulic

systemisneeded. DaleyandWang [7]proposed a simplescheme

based on artificial neural networks (ANN) for detecting and

diagnosing faults in the fluid power systems. The ANN is first

trained on a healthy system to provide a detection signal of

small amplitude when the system operates normally. With the

knowledge of the effects of some known faults on this signal,a diagnostic vector is constructed to determine the location and

size of all similar faults. Watton and Kwon [8] developed an

ANN method for identifying the behavior of fluid power control

systems with frequency-rich input excitation. Seong et al. [9]

developed a back propagation ANN method for detecting and

diagnosing a disk wear failure anda foreign objectfailure among

the various failure and modes of check valves. Crowther et

al. [10] presented a neural network approach for fault diagnosis

of the hydraulic system based on the classification of surfaces

in system output vector space. Chen et al. [11] developed a new

ANNapproach to thefault diagnosisof a waterhydraulic system

based on the wavelet analysis of a vibration signal.

Model-based approach has been investigated, based on thenonlinear dynamic models for hydraulic systems. An and

Sepehri [12] presented theapplication of extended Kalman filter

in order to identify internal- and external-leakage faults, which

are assumed to occur individually, in hydraulic actuators. As a

combination of ANN (data-driven) and model-based methods,

Shi et al. [13] developed a gray-box model, aiming to provide

accurate and robust fault detection for electrohydraulic control

systems. Gayaka and Yao [14] used an adaptive robust approach

for fault detection and accommodation in electrohydraulic sys-

tems. Du [15] proposed a health monitoring method for the

hydraulic system through the adaptive parameter estimation of

effective bulk modulus and leakage coefficient in the system.It is also worthwhile to mention that the adaptive control

methods areapplied on thehydraulicsystem widely. Papadopou-

los et al. [16] focused on the modeling, parameter estimation,

and control for a heavy-duty electrohydraulic manipulator of a

harvester machine. Mohanty and Yao [17] developed an inte-

grated directindirect adaptive robust control algorithm for an

electrohydraulic manipulator with unknown valve dead band to

improve the achievable output-tracking performance. Kaddissi

et al. [18] studied the real-time position control of an electrohy-

draulic system using indirect adaptive backstepping.

The hydraulic pitching systems for the modern utility wind

turbines feature variable rotor speed, pitch angles, and torque

loads on the pitch axis. Also, turbulence nature of wind, wind

shear, and wake lead to strongly time varying and unsteady

loads. Such complexity determines that a good fault diagnosis

solution for the hydraulic pitch system should work well under

transient and unsteady operation and load, in addition to steady-

state operation and load.

This study is focused on the faults of internal and external

leakages for the hydraulic pitching system. Considering the ef-

fect of the time-varying load on the hydraulic system, a model-

based adaptive parameter estimation algorithm has been devel-

oped to identify the internal and external leakages. Comparing

with aforementioned estimation methods, this scheme can, not

only detect, but also isolate individual leakages in spite of their

Fig. 1. Hydraulic actuation system for the wind turbine blade pitching mech-anism [6], [19].

coupled relationship in the hydraulic model, which is advanta-

geous for the maintenance practice. The proposed methods are

verified through the experiments performed on a scale-down

hydraulic pitching emulator. The aerodynamic loading on the

pitching axis is emulated by the disturbance load provided by

an additional hydraulic cylinder. The pitching load is obtained

from the simulation of a 1.5-MW variable-speed variable-pitch

turbine model under turbulent winds on theFAST(fatigue,aero-

dynamics, structural, and tower) software developed by the Na-

tional Renewable Energy Laboratory (NREL).

The remainder of this paper is organized as follows. The

model-based adaptive leakage-detection algorithm is then intro-

duced in Section II. Section III describes the hydraulic pitching

emulator and fault diagnosis oriented test. Section IV presents

the experimental results for the estimation of internal and exter-

nal leakages in thehydrauliccylinderunder differentwind speed

and different levels of coupled internal and external leakages.Section V concludes this paper with discussion.

II. ADAPTIVE PARAMETER ESTIMATION FOR HYDRAULIC

PITCHING SYSTEMS

Theschematicof a typical hydraulicpitching systemis shown

in Fig. 1.

Similar to many other hydraulicactuationsystems, thesystem

consists of a fluid tank, a hydraulic pump, an electrohydraulic

proportional directional valve, a relief valve, a hydraulic cylin-

der. The pitching motion is realized with a slider-crank mech-

anism by attaching the piston of cylinder to the pitching blade

shaft via a rigid bar [6], [19].

The dynamic model of hydraulic pitching cylinder is given

by [20], [21]

QA =AA xp

ePA + AA xp + Cip (PA PB ) + Cep A PA

QB =AB (L xp )

ePBAB xpCip (PAPB )+Cep B PB

(1)

F = PA AA PB AB mxp (2)

where P denotes chamber pressure, subscripts A and B

denote chambers A and B, respectively, Cip denotes the


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WU et al.: ADAPTIVE ESTIMATION-BASED LEAKAGE DETECTION FOR A WIND TURBINE HYDRAULIC PITCHING SYSTEM 3

internal-leakage coefficient in the piston, Cep A denotes the ex-

ternal leakage at chamber A, Cep B denotes the external leakage

at chamber B, e denotes the effective bulk modulus,xp denotes

the piston position, Q denotes the hydraulic fluid flow rate in

the circuit, A denotes the piston area, and m denotes the piston

mass. F denotes the sum of external load and friction, and for

the particular case of hydraulic pitching system as in this study,this is governed by the pitching load.

In thefollowing, an adaptiveestimation algorithmis proposed

for identifyingthe leakage-relatedparametersfor faultdiagnosis

purpose. Thedynamic equations(1) and(2)canbe modified into

QA AA xp =AA xp

e

dPA

dt+ Cip (PA PB ) + Cep A PA

QB +AB xp =AB (Lxp )

e

dPB

dtCip (PAPB )+Cep B PB

PA AA PB AB = mxp + F.(3)

Then, (3) can also be written as [15]

PL =

QA

AA xp+ Q

B

AB (L xp )

e PL

1

AA xp+

1

AB (L xp )

e Cip

PA

AA xpe Cep A

+PB

AB (L xp )e Cep B

1

xp+

1

L xp

e

m

(PA AA PB AB F)dt (4)

where PL = PA PB is the pressure differential across thepiston.

Let

1 = e , 2 = e Cip , 3 = e Cep A ;

4 = e Cep B , 5 =e

m(5)

f1 =QA

AA xp+

QB

AB (L xp )

f2 = PL

1

AA xp+

1

AB (L xp )

f3 = PA

AA xpf4 =

PB

AB (L xp )

f5 =

1

xp+

1

L xp

(PA AA PB AB F)dt (6)

where i (i = 1, . . ., 5) are unknown constants in terms of systemparameters, including the effective bulk modulus, internal- and

external-leakage coefficients, and the inertia mass.Identification

ofi would achieve the purpose of detecting leakage and also

the change of bulk modulus (e.g., due to air contamination).

Equation (3) can, thus, be written as [22]

PL =5

i=1

i fi . (7)

An estimation dynamic rule can be established as

PL = PL PL +

5i= 1

i fi (8)

where is a positive constant and represents parameter and

statevariableestimation. Subtracting (7) from(8), theestimation

error dynamics is

PL = PL +5

i= 1

i fi (9)

where PL = PL PL , i = i i (i = 1, ..., 5).Define a Lyapunov function as

V =1

2P2L +

1

2

5i= 1

2i . (10)

The time derivative of (10) is

V = PL PL +

5i=1

i fi

+

5i=1

i i

(11)

where is a positive constant learning rate.

An adaptive learning rule canbe applied to identify the values

ofi . Let

i = PL fi (12a)

i.e.,

1 = 1 = PL

QA

AA xp+

QB

AB (L xp )

(12b)

2 = 2 = PL PL

1AA xp

+ 1AB (L xp )

(12c)

3 = 3 = PL PA

AA xp(12d)

4 = 4 = PL PB

AB (L xp )(12e)

5 = 5 = PL

1

xp+

1

L xp

(PA AA PB AB F)dt

.

(12f)

Then,

V = P2L 0 (13)

where and are both positive constants.

Notice that f5 is bounded as

f5 =

1

xp+

1

L xp

(PA AA PB AB F)dt

=

1

xp+

1

L xp

(mxp ). (14)

Load F can be obtained through (3) with the least-squares

estimation method [21], [22]. Since fi are all bounded and


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Fig. 2. Schematic of hydraulic pitching emulator.

Fig. 3. Flowchartof thehydraulicpitchingemulatorwith theinput from FAST.

PL (t) 0 as t , thus i 0 as t . When PLand fi are all bounded, the time derivation of V is negative

semidefinite [22]. Thus, the adaptive learning rule of (12) can

achieve unbiased estimation for i when the input signals (i.e.,

chamber pressure, flow rate, and piston position) satisfy the

persistent excitation condition.

This estimation scheme can detect the change of bulk modu-

lus (e.g., due to the presence of air contamination or change of

fluid temperature), internal andexternal leakage on both sides of

hydraulic cylinder piston. Detection of bulk modulus, internal

and external leakage can, thus, be decoupled, which is conve-

nient for maintenance practice. This study is limited to leakage

detection only, but the method can be easily extended to that

including the change of bulk modulus. This detection scheme

relies on the sensor measurements of piston position, and flow

rate and pressure of chambers in the hydraulic cylinder, which

are available on typical products.

III. HYDRAULIC PITCHING EMULATOR AND LEAKAGE TESTS

A scale-down hydraulic pitching emulator has been built to

conduct experiments for validating the proposed fault detection

scheme. The objectives of the hydraulic pitching emulator are

twofold: 1) emulate the motion of hydraulic pitching and the

dynamic load about the pitching axis under realistic winds; and

Fig. 4. Illustration of the pitching mechanism [6], [19].

Fig. 5. Different kinds of wind speed simulated through FAST.

2) emulate the faults of interest in current stage, i.e., the internal

and external leakages for the hydraulic cylinder.

The schematic of hydraulic pitching emulator is shown in

Fig. 2. It mainly consists of two back-to-back hydraulic cylin-

ders: one is used to emulate an actual hydraulic actuator for a

wind turbine blade pitching system (named as pitching cylin-

der), while the other is used to generate the aerodynamic

loading torque as disturbance to the hydraulic pitching system

(named as load cylinder). The piston of the pitching cylinder

is controlled to follow the pitch angle profile obtained from the

simulation under different wind profiles on the FAST software.

The loading cylinder can provide corresponding force output

from the FAST simulation with different cases of wind speed.

The cylinder parameters in the hydraulic emulator are: AA =1.26 103 m2 , AB = 0.94 10

3 m2 , xp [0, 0.2] m, and

L = 0.2 m.Fig. 3 shows the simulation platform for this study and how

the emulated pitching load can be obtained. The NRELs FAST

software models the wind turbine as a combination of rigid and

flexible bodies [23]. TurbSimis used to create full field turbulent

wind files which are input to AeroDyn. AeroDyn is used along-

side FAST to simulate the aerodynamic forces on the turbine

blades and structure. The pitch angles and the pitching load

torque obtained from FAST simulation can be used as reference


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Fig. 6. Reference and output of pitching cylinder position and load.

Fig. 7. Estimation of large internal leakage and small chamber A external leakage and leakage coefficients for different wind input profiles. (a) Estimation of

internal and chamber A external leakage. (b) Estimation of internal and chamber A external leakage coefficients.


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Fig. 8. Estimation of small internal leakage and large chamber A external leakage and leakage coefficients for different wind input profiles. (a) Estimation ofinternal and chamber A external leakage. (b) Estimation of internal and chamber A external leakage coefficients.

for the pitching and load cylinders to follow in the respective

position and force control loops in experimental study.

Thesystemis powered by twomotor-driven hydraulicpumps.The pitching and load cylinders are both single-piston cylinders

and their movements are controlled by the proportional valves,

respectively. The valves are controlled by Advantech 610 in-

dustrial PC with PCI 1713 analog input module and PCI 1721

analog output module. The PID controllers are designed to con-

trol the piston position in the pitching cylinder, and the force

output of the load cylinder [24].

The emulator includes a set of auxiliary circuits to simulate

leakage faults of the pitching cylinder. As shown in Fig. 2,

the internal leakage was intentionally introduced between two

chambers, and the external leakage at chamber A of the pitching

cylinder. The internal leakage is simulated through bypassing

fluid across the piston. This is achieved by connecting the two

chambers and controlling the flow through an adjustable flow

control valve. The flow rate is measured again using a turbineflow meter. The range of flow meter is 20 L/min with the accu-

racy of 1% full scale.

For the simulation of the external leakage on chamber A

of the cylinder, a portion of the fluid flow from the side of

chamber A is bypassed to the reservoir by adjusting the flow

control valve. The output of the external-leakage flow control

valve is measured with the same kind of flow meter as earlier.

The estimation of internal and external leakages Qip and Qep Afollow the definition by Merritt [12], [20]:

Qip = Cip (PA m PB m ) (15a)

Qep A = Cep A PA m (15b)


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where Cip denotes the estimation of internal-leakage coefficient

and Cep A denotes the estimation of chamber A external-leakage

coefficient. PA m and PB m represent the measurements of

pressure of chambers A and B, respectively.

Through sensors measurement, the internal- and external-

leakage coefficients Cip m and Ce p A m follow the definition by

Merritt [20]:

Cip m =Qip m

PA m PB m(16a)

Ce p A m =Qe p A m

PA m(16b)

where Qip m denotes the flow rate measurement of internal

leakage, and Qe p A m denotes the flow rate measurement for

chamber A external leakage.

IV. EXPERIMENTAL RESULTS

In order to illustrate thegeometric relationshipbetween cylin-

der dimension and the pitching angle, the variables or the hy-draulic pitching mechanism is shown in Fig. 4.

For data acquisition, the sampling rate was set as 100 Hz,

and the data collection window was set to be 20 s with the

onboard memory capacity. A second-order Butterworth low-

pass filter with cutoff frequency of 5 Hz is designed to filter

the data measured from linear variable differential transformers

(LVDT), flow rate and pressure sensors on the pitching cylinder

[21], [24].

The piston position of pitching cylinder can be obtained as

xp (p ) = L2

p + r2

p 2 Lp rp cos( + p ) lp (17)

where Lp , lp , rp , and are dimension shown in Fig. 5. p is the

pitch angle and xp is the pitching cylinder position. The pitch

torque can be described as

Tp = Jp + Tw = Fc rp cos(p ) (18)

where J is the moment of inertia of the blade about the pitch

axis and Tw is the wind load torque imposed on the pitch axis.

In this study, we set Lp = 1.1 m, lp = 1.0 m, rp = 0.5 m, and = 63. Considering the capacity of hydraulic cylinders in thetest bed, the reference piston position of pitching cylinder and

load provided by the load cylinder are scaled down by twice and

1000 times, respectively.

The pitching angle and load force profiles for different wind

inputs are obtained from the dynamic simulation of a 1.5-MW

wind turbine model (WindPact) on FAST. For this 1.5-MW

wind turbine, the cutoff wind speed is set to be 27.5 m/s. The

experiments include cases for mean of 5-, 13-, and 21-m/s wind

speed with 20% turbulence. The extreme condition of 30-m/s

wind speed is also considered in the experiments. Four cases of

wind profiles simulated through FAST are shown in Fig. 5.

For four cases of wind input profiles, the reference and output

of piston position and load in the pitching and load cylinder are

calculated by (17) and (18), as shown in Fig. 6. For the piston

position output in pitching cylinder with different wind speed,

the steady-state errors are within 3%. For the load output in load

cylinder with different wind speed, the steady-state errors are

within 21.4%.

The leakage and leakage-coefficient estimation for the two

testing cases is presented as follows. In the experiments, all

input signals satisfy the persistent excitation condition. The

measurement of leakage is also filtered by the second-order

Butterworth low-pass filter with cutoff frequency of 5 Hz de-signed earlier. The leakage estimationis calculatedthrough (15).

The leakage coefficient can be obtained through (16) with the

measurement of leakage and chambers pressure.

Based on the parameter estimation algorithm described in the

previous section, the leakage estimation are derived and shown

with measured leakage (with filter) in Figs. 7 and 8 for different

wind input profiles. The developed algorithm can detect the in-

ternal and chamber A external leakage in the pitching cylinder

within 7.8% mean steady-state error and 11% peak steady-state

error. For the internal and chamber A external leakage coeffi-

cients, the estimation errors are within 7.3% mean steady-state

error and 13.3% peak steady-state error.

Based on Figs. 7 and 8, the convergence time for the leakageestimation is within 12 s for all simulated cases.

Case 1: Large internal andsmall chamber A external leakage.

Case 2: Small internal and large chamber A external leakage.

Based on Figs. 7 and 8, the mean of steady-state leakage

estimation errors are smaller under the wind speed of 5 and

30 m/s than under the wind speed of 13 and 21 m/s for different

levels of internal and chamber A external leakage. Similarly,

the maximum steady-state estimation errors are smaller under

the wind speed of 5 and 30 m/s than under the wind speed of

13 and 21 m/s for different levels of internal and chamber A

external leakage. Variable piston position (pitch angle), which

corresponds to varying reference internal and external leakageand leakage coefficient, seems to have greater impact on the

estimation accuracy.

Based on Figs. 7 and 8, the mean of steady-state leakage-

coefficient estimation errors are also smaller under the wind

speed of 5 and 30 m/s than under the wind speed of 13 and

21 m/s for different levels of internal and chamber A external-

leakage coefficients. The maximum steady-state estimation er-

rors are smaller under the wind speed of 5 and 30 m/s than

under the wind speed of 13 and 21 m/s for different levels of

internal and chamber A external leakage coefficients. The mean

of leakage coefficient steady-state estimation errors are within

0.53% smaller than the mean of leakage steady-state estima-

tion errors. The peak leakage coefficient steady-state estimation

errors are within 2.33% larger than the peak leakage steady-

state estimation errors. The leakage estimation appears to have

better tracking performance under the variable-pitch operation,

while the tracking error for the leakage coefficient seems to be

bearable to certain extent.

Considering the accuracy range of the sensors (1% of

full scale) and the varying reference internal and external

leakages and leakage coefficient in the cases of varying pitch-

ing position, the developed estimation algorithm demonstrates

acceptable performance for fault detection and isolation to quite

an extent. Regarding to the choice diagnostic probe, leakage

coefficients and leakage have respective advantages. Leakage


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coefficient reflects a good normalized quantity, which is easier

to be defined as a single diagnostic probe. For variable-pitch

operation, it is difficult to use the instantaneous leakage as a di-

agnostic probe, rather, the accumulative/average leakage (e.g.,

for several turns of turbine rotor) makes more sense.

V. CONCLUSION

The hydraulic pitching system is critical for securing energy

capture, load reduction, and aerodynamic braking for wind tur-

bine operation. This paper has presented a model-based adap-

tive leakage-detection algorithm. The proposed method con-

siders the realistic wind turbine operation condition, i.e., with

time-varying cylinder position and load. In spite of the coupled

relation for the faults of cylinder internal and external leakages

in the hydraulic system, the method can detect and isolate each

individual fault through the measurement of sensors, i.e., pis-

ton position, and the flow rate, and pressure in chambers at the

pitching cylinder. The proposed scheme is also applicable when

bulk modulus needs to be included.

A scale-down hydraulic pitch emulator has been developed,

with which experimental data have been obtained under dif-

ferent turbulent wind inputs. The piston position in the cylinder

and load referenceprofiles were obtained from the simulation of

a 1.5-MW variable-speed turbine model on the NRELs FAST

software. Two cases of coupled different levels of internal and

chamber A external leakage are simulated in the experiments.

With the sensors measurement of piston position, chambers

pressure, and chambers flow rate, the proposed algorithm can

detect the internal and chamber A external leakage in the pitch-

ing cylinder within 7.8% mean steady-state error and 11% peak

steady-state error. With the same sensors measurement, the de-

veloped algorithm can estimate the internal and chamber A ex-ternal leakage coefficients in the pitching cylinder within 7.3%

mean steady-state error and 13.3% peak steady-state error. With

the consideration of accuracy range of sensors (1% of the full

measurement scale)andthevarying referenceinternal andexter-

nalleakagesand leakage coefficient in thecasesof varyingpitch-

ing position, these results sustain the validity of the proposed

estimation scheme. In the future, more experiments with differ-

ent levels of coupled internal and external leakages, and bulk

modulus may be carried out to verify the developed algorithm.

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