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Adaptive Estimation-Based Leakage Detection for a Wind Turbine Hydraulic Pitching System Xin Wu, Yaoyu Li, Member, IEEE, Feng Li, Zhongzhou Yang, and Wei Teng
Abstract—Operation and maintenance (OM) cost has contributed a major share in the cost of energy for wind power generation. Condition monitoring can help reduce the OM cost of wind turbine. Among the wind turbine components, the fault diagnosis of the hydraulic pitching system is investigated in this study. The hydraulic pitching system is critical for energy capture, load reduction, and aerodynamic braking. The fault detection of internal and external leakages in the hydraulic pitching system is studied in this paper. Based on the dynamic model of the hydraulic pitching system, an adaptive parameter estimation algorithm has been developed in order to identify the internal and external leakages under the time-varying load on the pitch axis. This scheme can detect and isolate individual faults in spite of their strong coupling in the hydraulic model. A scale-down setup has been developed as the hydraulic pitch emulator, with which the proposed method is verified through experiments. The pitching-axis load input is obtained from simulation of a 1.5-MW variable-speed-variable-pitch turbine model under turbulent wind profiles on the FAST (fatigue, aerodynamics, structural, and tower) software developed by the National Renewable Energy Laboratory. With the experimental data, the leakage and leakage coefficients can be predicted via the proposed method with good performance. Index Terms—Adaptive estimation, hydraulic systems, leak detection, wind energy.
I. INTRODUCTION IND power has become the world’s fastest growing renewable energy source. The installed wind power capacity 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, reducing 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-
W
Manuscript received August 12, 2010; revised February 18, 2011; accepted April 2, 2011. Recommended by Technical Editor Y. Li. This work was supported in part by the Fundamental Research Funds for the Central Universities of China. X. Wu and W. Teng are with the School of Energy, Power and Mechanical Engineering, 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 Science and Technology, Beijing 100083, China (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at 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 situations. 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 has currently emerged to dampen prospects is lack of personnel available to perform the consistent OM required to keep turbines functioning and efficient. A blade pitch control system is critical for turbine operation, 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. Pitching 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 loading 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 operation under extreme wind, failure of hydraulic pitching may lead to catastrophic failure of the whole turbine, which must be prevented 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 dramatically 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 cylinder. 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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the prior knowledge about the faulty behavior on the hydraulic system is needed. Daley and Wang [7] proposed a simple scheme 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 and a foreign object failure 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 ANN approach to the fault diagnosis of a water hydraulic system based on the wavelet analysis of a vibration signal. Model-based approach has been investigated, based on the nonlinear dynamic models for hydraulic systems. An and Sepehri [12] presented the application 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 systems. 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 are applied on the hydraulic system widely. Papadopoulos 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 integrated direct–indirect 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 electrohydraulic 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 steadystate operation and load. This study is focused on the faults of internal and external leakages for the hydraulic pitching system. Considering the effect of the time-varying load on the hydraulic system, a modelbased adaptive parameter estimation algorithm has been developed 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
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Fig. 1. Hydraulic actuation system for the wind turbine blade pitching mechanism [6], [19].
coupled relationship in the hydraulic model, which is advantageous 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 the FAST (fatigue, aerodynamics, structural, and tower) software developed by the National Renewable Energy Laboratory (NREL). The remainder of this paper is organized as follows. The model-based adaptive leakage-detection algorithm is then introduced 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 external leakages in the hydraulic cylinder under different wind 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 The schematic of a typical hydraulic pitching system is shown in Fig. 1. Similar to many other hydraulic actuation systems, the system consists of a fluid tank, a hydraulic pump, an electrohydraulic proportional directional valve, a relief valve, a hydraulic cylinder. The pitching motion is realized with a slider-crank mechanism 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] ⎧ AA xp ˙ ⎪ PA + AA x˙ p + Cip (PA − PB ) + CepA PA ⎨QA = βe ⎪ ⎩−QB = AB (L − xp ) P˙B −AB x˙ p −Cip (PA −PB )+CepB PB βe (1) F = PA AA − PB AB − m¨ xp
(2)
where P denotes chamber pressure, subscripts A and B denote chambers A and B, respectively, Cip denotes the
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internal-leakage coefficient in the piston, CepA denotes the external leakage at chamber A, CepB denotes the external leakage at chamber B, β 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 the following, an adaptive estimation algorithm is proposed for identifying the leakage-related parameters for fault diagnosis purpose. The dynamic equations (1) and (2) can be modified into ⎧ AA xp dPA ⎪ + Cip (PA − PB ) + CepA PA QA − AA x˙ p = ⎪ ⎪ ⎨ βe dt AB (L−xp ) dPB −Cip (PA −PB )+CepB PB −QB +AB x˙ p = ⎪ ⎪ ⎪ βe dt ⎩ PA AA − PB AB = m¨ xp + F. (3) Then, (3) can also be written as [15] QA QB P˙L = + βe − PL AA xp AB (L − xp ) 1 1 PA × + βe CepA βe Cip − AA xp AB (L − xp ) AA xp 1 βe PB 1 βe CepB − + + AB (L − xp ) xp L − xp m
(4) × (PA AA − PB AB − F )dt where PL = PA − PB is the pressure differential across the piston. Let γ1 = βe ,
γ2 = βe Cip ,
γ4 = βe CepB ,
γ3 = βe CepA ;
βe γ5 = m
(5)
An estimation dynamic rule can be established as ˙ γˆi ·fi Pˆ L = αPL − αPˆL + 5
QA QB + AA xp AB (L − xp ) 1 1 f2 = −PL + AA xp AB (L − xp )
where α is a positive constant and “ˆ” represents parameter and state variable estimation. Subtracting (7) from (8), the estimation error dynamics is ΔP˙L = −αΔPL +
5
Δγi ·fi
where ΔPL = PˆL − PL , Δγi = γˆi − γi Define a Lyapunov function as
where γ i (i = 1, . . ., 5) are unknown constants in terms of system parameters, including the effective bulk modulus, internal- and external-leakage coefficients, and the inertia mass. Identification of γ i 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]
i=1
γi · fi .
(i = 1, ..., 5).
1 1 λΔPL2 + Δγi2 . 2 2 i=1 5
V =
(10)
The time derivative of (10) is
5 5 V˙ = λΔPL · −αΔPL + Δγi ·fi + Δγi ·Δγ˙ i i=1
i=1
(11) where λ is a positive constant learning rate. An adaptive learning rule can be applied to identify the values of γ i . Let Δγ˙ i = −λΔPL · fi i.e.,
(12a)
QA QB + AA xp AB (L − xp ) 1 1 ˙ + Δγ˙2 = γˆ2 = λΔPL · PL · AA xp AB (L − xp )
Δγ˙1 = γˆ˙1 = −λΔPL ·
Δγ˙3 = γˆ˙3 = λΔPL ·
PA AA xp PB AB (L − xp )
(12b) (12c) (12d) (12e)
Δγ˙5 = γˆ˙5 = λΔPL
1 1 · + (PA AA − PB AB − F )dt . xp L − xp
PA PB f4 = AA xp AB (L − xp )
1 1 f5 = − + (PA AA − PB AB − F )dt (6) xp L − xp
5
(9)
i=1
(12f)
f3 = −
P˙L =
(8)
i=1
Δγ˙ 4 = γˆ˙4 = −λΔPL ·
f1 =
3
(7)
Then, V˙ = −αλΔPL2 ≤ 0
(13)
where α and λ are both positive constants. Notice that f5 is bounded as
1 1 f5 = − + (PA AA − PB AB − F )dt xp L − xp 1 1 + (14) =− (mx˙ p ). xp L − xp 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.
Flowchart of the hydraulic pitching emulator with the input from FAST.
ΔPL (t) → 0 as t → ∞, thus Δγi → 0 as t → ∞. When ΔPL and 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 γ 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 modulus (e.g., due to the presence of air contamination or change of fluid temperature), internal and external leakage on both sides of hydraulic cylinder piston. Detection of bulk modulus, internal and external leakage can, thus, be decoupled, which is convenient 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 cylinders: one is used to emulate an actual hydraulic actuator for a wind turbine blade pitching system (named as “pitching cylinder”), 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 × 10−3 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 NREL’s FAST software models the wind turbine as a combination of rigid and flexible bodies [23]. TurbSim is used to create full field turbulent wind files which are input to AeroDyn. AeroDyn is used alongside 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
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. WU et al.: ADAPTIVE ESTIMATION-BASED LEAKAGE DETECTION FOR A WIND TURBINE HYDRAULIC PITCHING SYSTEM
Fig. 6.
5
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 of internal 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. The system is powered by two motor-driven hydraulic pumps. 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 industrial PC with PCI 1713 analog input module and PCI 1721 analog output module. The PID controllers are designed to control 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 turbine flow meter. The range of flow meter is 20 L/min with the accuracy 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 QepA follow the definition by Merritt [12], [20]: Qip = Cip · (PA QepA = CepA · PA
m m
− PB
m)
(15a) (15b)
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where Cip denotes the estimation of internal-leakage coefficient and CepA 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 externalleakage coefficients Cip m and CepA m follow the definition by Merritt [20]: Cip CepA
m
m
= =
Qip m PA m − PB
(16a) m
QepA m PA m
(16b)
where Qip m denotes the flow rate measurement of internal leakage, and QepA m denotes the flow rate measurement for chamber A external leakage. IV. EXPERIMENTAL RESULTS In order to illustrate the geometric relationship between cylinder dimension and the pitching angle, the variables or the hydraulic 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 lowpass 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 (θp ) = L2p + rp2 − 2 · Lp · rp · cos(α + θp ) − lp (17) where Lp , lp , rp , and α are dimension shown in Fig. 5. θp is the pitch angle and xp is the pitching cylinder position. The pitch torque can be described as Tp = J θ¨p + Tw = Fc · rp · cos(θp )
(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 α = 63◦ . Considering the capacity of hydraulic cylinders in the test 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
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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 designed earlier. The leakage estimation is calculated through (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 internal 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 coefficients, 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 leakage estimation is within 12 s for all simulated cases. Case 1: Large internal and small 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 leakage and leakage coefficient, seems to have greater impact on the estimation accuracy. Based on Figs. 7 and 8, the mean of steady-state leakagecoefficient 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 externalleakage coefficients. 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 coefficients. The mean of leakage coefficient steady-state estimation errors are within 0.53% smaller than the mean of leakage steady-state estimation errors. The peak leakage coefficient steady-state estimation errors are within 2.33% larger than the peak leakage steadystate 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 pitching 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 diagnostic 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 turbine operation. This paper has presented a model-based adaptive leakage-detection algorithm. The proposed method considers 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., piston 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 different turbulent wind inputs. The piston position in the cylinder and load reference profiles were obtained from the simulation of a 1.5-MW variable-speed turbine model on the NREL’s 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 pitching cylinder within 7.8% mean steady-state error and 11% peak steady-state error. With the same sensors measurement, the developed algorithm can estimate the internal and chamber A external 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) and the varying reference internal and external leakages and leakage coefficient in the cases of varying pitching position, these results sustain the validity of the proposed estimation scheme. In the future, more experiments with different levels of coupled internal and external leakages, and bulk modulus may be carried out to verify the developed algorithm. REFERENCES [1] B. Lu, Y. Li, X. Wu, and Z. Yang, “A review of recent advances in wind turbine condition monitoring and fault diagnosis,” in Proc. IEEE Power Electron. Mach. Wind Appl., 2009, pp. 1–7. [2] D. McMillan and G. W. Ault, “Quantification of condition monitoring benefit for offshore wind turbines,” Wind Eng., vol. 31, no. 4, pp. 267– 285, May 2007. [3] R. W. Hyers, J. G. McGowan, K. L. Sullivan, J. F. Manwell, and B. C. Syrett, “Condition monitoring and prognosis of utility scale wind turbines,” Energy Mater., vol. 1, no. 3, pp. 187–203, Sep. 2006.
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