Wind turbine doubly fed induction generator rotor electrical asymmetry detection based on an adaptive least mean squares filtering of wavelet transform

Abstract

A new strategy for the detection of rotor electrical asymmetry in wind turbine doubly fed induction generators is presented. In comparison with the previous work, the major novelty of this article is the addition of an adaptive noise cancelation block in the process of detecting the rotor winding fault. This work demonstrates an improvement in the signal-to-noise ratio using robust least mean squares filtering of the wavelet transform method. In the new strategy, robust least mean squares filtering of wavelet transform is used for the first block of fault detection before the fault estimation block. The proposed strategy is verified with the experimental data measured on doubly fed induction generator test rigs and real wind turbine. A comparative study is carried out based on experimental measurements (stator current and power output) under the steady-state and variable-speed operation representative of real wind turbine operations for both healthy and faulty generator conditions.

Keywords

Noise cancelation adaptive filter least mean squares wavelet transform rotor electrical asymmetry

Introduction

Condition monitoring (CM) and fault diagnostic systems of rotary machines, such as wind turbines, often are based on the vibration signal (Leung and Yang, 2012; Liu et al., 2015; Stetco et al., 2018). A cost-effective CM is very important for a rotary machine (Dameshghi and Refan, 2019). However, because the location of turbine installation is far, a reduction in repair facilities in the cold seasons of the year exacerbates the problem (Tavner et al., 2011). On the contrary, the cost of repair and maintenance of a turbine is approximately 30% of energy cost (Sheng and O’Connor, 2017). The use of electrical signals instead of mechanical signals has reduced the cost of CM. These signals are available in the control system, and there is no need for installing additional sensors or data collection devices. These signals include voltage, current, and power output (Artigao et al., 2018; Merabet et al., 2015). A wind turbine consists of different parts, such as a blade, a gearbox, a control system, and a generator (Abouhnik and Albarbar, 2012; Kusiak et al., 2012). Nowadays, high-power generators are used in wind turbines. These generators are induction generators and transfer power to the grid from both the stator and the rotor winding sides; these are called as doubly fed induction generators (DFIGs; Pannell et al., 2013). The rotor is connected to a back-to-back converter via a slip ring and its power is 30% of the nominal power (Ghoudelbourk et al., 2016; Prajapat et al., 2018). In Figure 1, the structure of a DFIG wind turbine is shown. The DFIG of the wind turbine has different components including stator, rotor, and bearing (Djurovic et al., 2012). Faults in generators are one of the important faults in wind turbines, which are responsible for 30% of the downtime, reduction in power generation, and huge financial losses (Zaggout et al., 2014). In these generators, the percentage of faults related to stator, rotor, and bearing are 30%, 40%, and 12%, respectively (Gong and Qiao, 2012; Zappalá, 2014).

Figure 1.

Structure of the DFIG wind turbine.

In this case study, the fault considered for the study is rotor winding failure at different percentages. A representation of various failures in the wavelet transform (WT) generator rotor winding is a rotor electrical asymmetry (REA) fault. For detecting the rotor fault of a generator operating in a wind turbine, different methods have been used. These methods are mostly signal processing methods in the time, frequency, or time–frequency domains. Each method has advantages, but it is essential that the selected method should have a high sensitivity to incipient faults.

A technique was presented for induction generator electrical asymmetry of the wind turbine in Watson et al. (2010). The utilized signals in this reference were power and stator current and the experiment was performed at constant and varying speeds. A cost-effective method for REA detection was introduced in Yang et al. (2010), which uses the generator output power and rotational speed to derive fault detection (FD). In Yang et al. (2010), the detection algorithm was based on continuous wavelet transform (CWT) and adaptive filter to track energy in the power signal. Machine control loop signals are new signals which can be used to monitor the situation; frequency analyses of control current signals were presented in Zaggout et al. (2014). Gong and Qiao (2012) presented a study to identify the best diagnostic procedure for unbalanced DFIG phase FD. Based on the simulation and experimental evaluations of this reference, the current signature analysis is appropriate.

Based on the literature review, various electrical signals have been used to detect rotor faults. The problem of these signals is their inadequate efficiency in real wind turbine applications. The conventional current signature analysis strategy has the drawbacks of noise overcoming the signal and low power of the signal. In this article, the objective is to use electrical signals such as the stator current and power signal for detecting the generator REA. However, these signals in variable-speed turbines (with unstable dynamics) are very weak and have a low signal-to-noise ratio (SNR). The signal processing algorithm is not robust in dealing with these signals. Conventional algorithms for signal processing do not have the noise cancelation ability. Wind speed and mechanical tensions in the drive train increases the instability of current and power signals. In this article, robust least mean squares filtering of wavelet transform (R-LMS-WT) is developed for signal conditioning of the wind turbine. These techniques of noise cancelation enhance the SNR and make it easier to observe the important components of the signal. The base of the proposed method is to break the input vector into a multi-scale space and reduce the dynamic range of the input spectrum, which increases the stability and convergence speed.

In order to investigate the efficiency of R-LMS-WT, the real data collected from a MAPNA 2.5-MW turbine is used. The stator current and output power data of signals in the control system can be collected without the need for installing additional sensors and hardware. On the contrary, it is not possible to create a real fault (REAs) in the real wind turbine, so fault-based experiments are performed in a 90-kW test rig. This test rig is designed and developed by the authors of this article.

The novelties of the proposed strategy and the continuation of this article are summarized as follows:

A noise cancelation block is added to perform fault diagnosis of the wind turbine. The technique used for this purpose is LMS self-adaptive filtering of WT. Evaluation of R-LMS-WT is based on the real data collected from the real wind turbine and the 90-kW DFIG test rig.

Compression of different signals for the generator REA FD is performed based on measuring the generator total power signal and stator current signal measurements validated by experiments on a 90-kW DFIG test rig with a simple fault setup.

Different indexes for FD were used based on the operation of the test rig. Fault tracking is conducted under fixed- and variable-speed conditions based on fast Fourier transform (FFT) and CWT, respectively.

Kurtosis index is used for the evaluation of the R-LMS-WT noise cancelation method in comparison to the other noise cancelation methods. The method is applied to a laboratory test rig under known fault conditions, first under fixed-speed and then under variable-speed operations.

Section “The proposed strategy” explains the general theory in the proposed system. Analysis tools and implementation are introduced in section “Analysis tools.” Experimental results of the implementation method on the test rig and real wind turbine data are presented in section “Experimental results” and finally section “Conclusion” presents the conclusion.

The proposed strategy

The structure of the proposed REA FD topology is shown in Figure 2. In the first stage, the stator current and power output signals are collected using the data acquisition system. In the second stage, the acquired signals are processed for noise cancelation using R-LMS-WT to suppress the domination of noise components. Afterwards, the noise-canceled signals are processed depending on the operational area of the wind turbine using FFT at a fixed speed and using WT under variable speeds. The kurtosis index of the denoised signal is computed to evaluate R-LMS-WT. Fault tracking (based on Figure 3) and decision making are the fourth and fifth steps, respectively.

Figure 2.

Block diagram of the proposed REA fault detection topology.

Figure 3.

Frequency of REA fault in different signals.

Fault frequency of REA in electrical signals

The sequence of electromagnetic phenomena due to the rotor asymmetry in the stator and the rotor of an induction machine that causes the current components was explained in Gong and Qiao (2012) and Zaggout et al. (2014). Frequency propagation of REA in different signals and control variables is shown in Figure 3.

Fault frequency in rotor current

The rotating magnetic field in a healthy machine is generated at a given frequency f by the stator windings, while the magnetic field due to the rotor windings is generated at sf. An asymmetrical rotor causes an imbalanced current in the rotor. This leads to an inverse magnetic field. This field expresses itself as an alternative current of rotor at –sf.

Fault frequency in stator current

The positive and inverse sequences of rotor current are reflected on the stator side and induce electromotive force (EMF) with frequencies $f and (1 - 2 s) f$ .

Fault frequency in fluxes of the stator

The harmonic component $(1 \pm 2 s) f$ in stator current interacts with the rotor current signal at –sf. Furthermore, this frequency interacts with the fundamental magnetic flux. The fluxes induce two EMFs in the stator windings at the frequency $(1 \pm 2 s) f$ . An important point is that the frequency $(1 - 2 s) f$ causes a component in the stator current that interacts with the frequency –sf. In addition, the frequency component $(1 + 2 s) f$ generates a rotating magnetic field at 3sf.

Fault frequency in power output

Two frequency components of the instantaneous power with a low frequency are selected, namely, $2 sf and 2 sf / P, P : number of poles$ .

Fault frequency in the dq-rotor current error

The rotor current is transferred into Rotor Side Inverter (RSI) control loop signals in the dq form. A proportional–integral (PI) control loop uses error signals. The error signal is extracted by subtracting the dq-rotor current from the dq-rotor reference current. The main component of fault frequency in dq-rotor current error is $\pm 2 sf$ .

Noise cancelation

The purpose of this study is not to provide an in-depth analysis and present a new method of noise cancelation algorithm, rather to illustrate the practical application of a noise cancelation technique that is able to provide more detectability for a non-stationary signal.

Generally, some of the received electrical signals are very weak, and it is very difficult to derive the fault signature from them. In rotary machines, extreme noises mask the fault signature and this is more obvious in electrical signals.

In real CM, it is not always the case that the signal is extracted from the exact faulty part. In addition, the modulation of other signals on the main signal is effective in decreasing the SNR. Considering the application of wind turbines, one of these signals is the rotational speed of the shaft and the blades. This issue is more obvious in the variable dynamics of the wind turbine.

The noise cancelation structure used in this study is based on a multi-WT with a self-adaptive filter. The advantages of the presented structure are as follows: This algorithm (1) reduces the self-correlation of the input signals, (2) maintains the balance between the high convergence rate and steady state of the LMS algorithm, and (3) is highly convergent.

All multi-WT decomposition levels have to be chosen for the corresponding signal with regard to the characteristics of the signal. These characteristics include the components and frequency rate of the signal. In addition, the frequency components belonging to characteristics of the signals are divided into narrow frequency bands. The signal is made based on the multi-scale wavelet decomposition in different frequency bands. These bands include low- and high-frequency signals. By adjusting the parameters of each filter, signal decomposition is performed in an adaptive filter in order to obtain the desired filtering effect, and when the filter is applied to all of the signals in all frequency bands, adaptive filtering is complete (Dong et al., 2019; Qu et al., 2019; Xie and Guo, 2018).

According to the theory of WT of the input signal, $x (n)$ can be given by a time series in equation (1)

x (n) = \sum_{j = 0}^{j - 1} \sum_{k \in z} c_{jk} ψ_{j, k} (n)

(1)

The objective of equation (1) is to divide the signal $x (n)$ into discrete levels. Considering $x_{j}$ as $x_{j} (n) = \sum_{k \in z} c_{j, k} ψ_{j, k} (n) where j = 0, \dots, J - 1$ , according to equation (2), $V_{j} (n)$ is approximated as

V_{j} (n) = \sum_{k \in z} {\hat{C}}_{j, k} {\bar{ψ}}_{j, k} (n)

(2)

where ${\hat{C}}_{j, k}$ is a discrete approximation of the wavelet coefficient given by

{\hat{C}}_{j, k} = \sum_{l} x (l) {\bar{ψ}}_{j, k} (l)

(3)

Now substituting equation (3) into equation (2), we obtain

V_{j} (n) = \sum_{l} x (l) r_{j} (l, n)

(4)

where $r_{j} (l, n) = \sum_{k \in z} {\bar{ψ}}_{j, k} (l) ψ_{j, k} (n)$ . Equation (4) is an approximation of $x_{j} (n)$ , which is a discrete convolution of the input signal $x (n)$ and the filter $r_{j} (l, n)$ . These filters include $ψ (t)$ of the wavelet and the convolution after sampling. These filters are band pass filters having a constant bandwidth-to-center-frequency ratio with which to be able to reconstruct the various levels of the input signal. Supposing that the time is steady, we obtain

\sum_{k \in z} {\bar{ψ}}_{j, k} (l) ψ_{j, k} (n) = \sum_{k \in z} {\bar{ψ}}_{j, k} (l - n) ψ_{j, k} (l - n)

(5)

Therefore, $r_{j} (l, n) = r_{j} (l - n)$ , and as a result the following equation holds

V_{j} (n) = \sum_{l} x (l) r_{j} (l - n)

(6)

Equations (1) to (6) show the discrete WT of the signal x(n) (Dai et al., 2019; Li et al., 2011). Adaptive noise cancelation is a method for reducing noise in the signal and increasing the SNR. This improves the observability of the signal components in the frequency spectrum. The adaptive noise cancelation structure is illustrated in Figure 4. The input x(n) consists of the desired signal S and the noise n₀. The reference input is then filtered adaptively in order to become as close to the value of n₀ as possible to be subtracted from the primary input x(n) = S + n₀, and consequently the line signal is generated as e = S + n_0 –y. This output contains the signal in addition to undesired residual noise. The adaptive filter minimizes indirectly the average power of the residual noise at the system output. The output is fed back to the adaptive filter and the weights of the filter are adjusted in each calculation step. It can be shown that minimizing the output power means minimizing the noise power by maximizing the SNR. However, in FD applications which are performed in real ambient conditions using the data acquisition hardware, identifying the noise source, n₁, is not easily possible. In fact, it is not possible to find a noise source that correlates with the noise n₀ (the same source), while it does not include the error signal. In this article, a self-adaptive filter is used. In this structure, a fixed time delay, Δ, is applied to the input signal for constructing a signal that is uncorrelated to the primary signal with a given phase difference. Initially, the adaptive filter compensates for the phase shift in a way that the sinusoidal components cancel each other at the output. Then, in the second step, the noise is canceled so that the output error is minimized. Consequently, the adaptive filter equations are described as follows (Xie and Guo, 2018)

V (n) = {[v_{0} (n), v_{1} (n), \dots, v_{y - 1} (n)]}^{T}

(7)

X (n) = {[x (n), x (n - 1), \dots, x (n - N + 1)]}^{T}

(8)

{[B]}_{jm} = r_{j} (m), j = 0, 1, \dots, J - 1; m = 0, 1, \dots, N - 1

(9)

W (n) = {[w_{0} (n), w_{1} (n), \dots, w_{J - 1} (n)]}^{T}

(10)

W (n) = BX (n)

(11)

where B is the WT matrix with the dimensions $J \times N$ . $V (n)$ is the input signal after passing the discrete WT filter. According to the structure illustrated in the figure, $W_{j} (n)$ and $r_{j} (n) (j = 0, 1, \dots, J - 1)$ are the coefficients of the delay line. The output signal of the adaptive filter is written as follows (Li et al., 2011)

y (n) = V^{T} (n) W (n) = \sum_{j = 0}^{J - 1} V_{j} (n) W_{j} (n) = \sum_{j = 0}^{J - 1} \sum_{l} x (l) r_{j} (l - n) W_{j} (n) = \sum_{l} α_{l} x (l)

(12)

where $α_{l} = \sum_{j = 0}^{J - 1} r_{j} (l - n) W_{j} (n)$ . The error signal of the adaptive filter is shown as follows (Xie and Guo, 2018)

e (n) = x (n) - y (n) = x (n) - V^{T} (n) W (n)

(13)

Figure 4.

R-LMS-SAF noise cancelation structure.

The equation for updating the weights is as follows

W (n + 1) = W (n) + 2 μ V (n - Δ) e (n)

(14)

The adaptive law (equation (14)) was extracted in a previous study and its stability is provided by the authors of this article based on the Lyapunov theory in Appendix 1.

Fault estimation

Based on the minimization of e(n), the output signal of Robust-Least Mean Squares-Self Adaptive Filtering (R-LMS-SAF) is desired for FD. Therefore, the spectral analysis of an electrical signal after noise cancelation is presented in the following subsection. After evaluating the fault component, fault estimation based on the frequency analysis can be performed in two ways: FFT and CWT.

FFT

The FFT analysis of the rotor winding fault component will give the details of the fault such as frequency response and magnitude response in the fixed-speed operation of the wind turbine. The FFT analysis can be performed using the following expression (Djurovic et al., 2012)

X (ω) = \sum_{n = 0}^{N - 1} x (n) e^{- j (2 π ϑ n / N) n}

(15)

where N is the length of the signal x(n) and $ϑ = 0, 1, \dots, N - 1$ .

Energy tracking based on CWT

The majority of large modern DFIG wind turbines operate under variable speeds. There are different potential tools for the time–frequency domain analysis of the electrical signal. These tools must be able to detect a fault on a generator. WT is a time–frequency fault estimation algorithm which has a high frequency resolution and a high time resolution at low frequencies and at high frequencies, respectively. In this article, an adaptive CWT is used. This method is based on sliding window and it calculates the energy in the specific fault frequency band. Based on these calculations on the whole signal, a curve of energy variation in the fault frequency band is obtained (Zaggout et al., 2014)

CW T_{specific frequency} (b, a) = \frac{1}{\sqrt{| a |}} \int_{- \infty}^{\infty} x (v) ψ^{*} (\frac{t - b}{a}) dt

(16)

The energy of the frequency component is given by

\begin{matrix} A (t_{0} + \frac{T}{2}) = \max (| CW T_{sf} (b, a) |), {\begin{matrix} a \in [a_{\min} a_{\max}] \\ b \in [t_{0} t_{0} + T] \end{matrix} \\ with a_{\min} = \frac{ω_{0}}{ω_{uppper}} and a_{\max} = \frac{ω_{0}}{ω_{lower}} \end{matrix}

(17)

where $ω_{upper} = ω_{c} + ω_{f} / 2$ and $ω_{lower} = ω_{c} - ω_{f} / 2$ with $ω_{c}$ being the mean frequency during the time interval T

ω_{f} = η ω fg

(18)

where $ω fg$ is the rotational speed of the generator and $ω_{f}$ is dependent on the turbulence of the wind.

Evaluation of noise cancelation algorithms

The R-LMS-WT, WT, and LMS denoising methods are implemented for noise cancelation of electrical signals. The kurtosis indicator is selected for the evaluation of these methods; the kurtosis indicator is well suited to the detection of impulses in a temporal electrical signal. The kurtosis is a statistical parameter for analyzing the signal distribution. The kurtosis factor is an indicator sensitive to the shape of the signal (equation (19)) (Dameshghi and Refan, 2019)

Kurtosis = \frac{\frac{1}{n} \sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{4}}{{(\frac{1}{n} \sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{2})}^{2}}

(19)

Analysis tools

Two test groups are designed. The first group is based on a real wind turbine in the MAPNA power plant. The data collected from the real wind turbine are used to evaluate the noise elimination algorithms. The second group test is based on the data collected from the 90-kW DFIG test rig. This test rig is used to simulate the fault and FD application. The diagnosis of the fault and the effective evaluation of the R-WT-LMS method are based on the data collected from the DFIG test rig.

The first analysis tool (2.5-MW DFIG wind turbine)

A 2.5-MW variable-speed pitch-regulated DFIG wind turbine owned by MAPNA Co. is used for the first test group. The characteristics of the real turbine that is used for the performance test of the noise cancelation algorithm are given in Table 1. The 5-minute data from the standard supervisory control and data acquisition (SCADA) system are collected. The noise elimination algorithms are evaluated and validated based on actual outputs of the MAPNA wind turbine. The turbine actual data are collected for 6 months from 18 June 2016 to 13 September 2016 (Mendeley dataset, 2017).

Table 1.

Parameters of MAPNA wind turbine (2.5-MW DFIG).

WT		DFIG
Wind speed	11.43 m/s	Rated power	2.5 MW
Power coefficient	0.43	Number of poles	Three pairs of poles
Air density	1.225 kg/m³	Speed	750–1310 r/min (50 Hz)
Turbine blade radius	53 m	Stator rated voltage	690 V
Tip speed ratio	9	Armature resistance	0.0014 Ω
Blade surface	8495	Rated frequency	50 Hz
Start generation	3.5/4 m/s	Stator resistance	0.0014 Ω
Stop generation	25 m/s	Rotor resistance	0.0014 Ω
Gearbox	Gear with three stages by 1:79.6	Stator leakage inductance	9.8e–5 H
Back-to-back converter		Rotor leakage inductance	8.6e–5 H
Switching frequency of the rotor	2.5 kHz	Magnetizing inductance	0.00169 H
Switching frequency of the stator	3 kHz	Stator/rotor turn ratio	0.3
DC link capacitor/DC link voltage	22 mF/1100 V	Line resistance	0.0001 Ω

DFIG: doubly fed induction generators; WT: wavelet transform; DC: direct current.

The second analysis tool (90-kW DFIG test rig)

The verification of the proposed FD method is carried out on a designed WT test rig by the authors; this test rig is shown in Figure 5. This test rig is used to test REA faults in a variable-speed WT and it maintains online communication with the CM module. The rotor circuit asymmetry is applied under two operating conditions: fixed and variable speed. This setup contains a 90-kW DFIG coupled to a sun gearbox with a transmission ratio of 1:3.33 (parameters shown in Table 2). The gearbox is rotated by an asynchronous 110-kW motor. The DFIG has eight poles and operates at 400 V and 50 Hz. The system comprises two voltage source inverters in back-to-back converter topology with a high power rate of 50 kW. In this topology, there are a gate drive circuit to trigger 12 gates of the insulated-gate bipolar transistor (IGBT) and a DFIG crowbar circuit to protect from short circuit current. The control system of the converter is designed based on the ARM/FPGA digital board with $100 kHz$ sampling frequency for the A/D multichannel. A vector control strategy is used for the back-to-back converter. Field-oriented control (FOC) with the support vector machine (SVM) method are employed for control of the converter. An encoder coupled to the shaft of the DFIG generator is used to measure the mechanical speed. The drive of the prime mover system is capable of receiving the wind pattern. The wind pattern emulated to the ABB-ACS800-31 motor drive using the torque–speed curve is based on the LabVIEW interface and using a PC. The test rig operates during the experiments under “healthy” and “faulty” conditions. Relevant signals are collected from the terminals of the generator and the converter. The fault types are applied electrically asymmetrically on the generator rotor, representing the effect of a rotor winding fault in the WT generator. Three systems for data collection in this test rig are used. A data acquisition system was used to obtain different electrical aspects of the machine. Another system is WT CMS (condition monitoring system), this system is used for the measurement of vibration and operational data of WT (power, generator speed, and wind speed). The control signal measurement is based on the logger FPGA interface module; it collects all data of the converter control system. The characteristics of the test rig and measurement systems are presented in Table 3. The general view of the data acquisition system and communication is depicted in Figure 6.

Figure 5.

DFIG wind turbine test rig.

Table 2.

Parameters of test rig components.

Drivetrain		Converter
Power	90	Filter resistance	$5 m Ω$
Speed	1488 r/min	Filter inductance	$800 μ H$
Stator voltage	400 V	Sampling frequency	100 kHz
DC link voltage	700 V	Switching frequency	2.5 kHz
Current	199 A	Grid side converter	FOC
Torque	578 N m	Rotor side converter	FOC
Number of pole pairs	2	Electrical measurement instrument
Magnetizing inductance	120.4 mH	Input channels	Voltage/current: four channels
cos Φ	0.88	Measurement line types	Three-phase three-wire
Stator resistance	24.8 mΩ	Sensors	Clamp-on sensors: 1000 A AC, 1000 A
Stator inductance	44 mH	Measurement current	2 MHz sampling
Rotor resistance	16.6 mΩ	Mechanical measurement instrument
Rotor inductance	33 mH	Measurement	32 kHz
Gearbox	Gear with one stage by 1:3.32	Input channels	Time processing command variables up to a maximum of four channels (power, pitch angle, wind speed, generator speed)/eight acceleration sensors (vibration channels)
Prime mover motor	Eight poles/100 kW/400 V/742 r/min

DC: direct current; FOC: field-oriented control; AC: alternate current.

Table 3.

Electrical asymmetry scenario applied to the DFIG test rig.

Time (s)	Description	$Δ R (%)$	Rotor resistance (mΩ)
0–50	Balanced	0	16.6
50–150	Low asymmetry	9	18.09
150–200	Balanced	0	16.6
200–300	Medium asymmetry	20	19.92
300–350	Balanced	0	16.6
350–450	High asymmetry	46	24.23
450–500	Balanced	0	16.6

DFIG: doubly fed induction generators.

Figure 6.

Data acquisition system configuration.

The power data and stator current data are filtered so that only values in the maximum power point tracking (MPPT) and fixed-speed operations are used in the CWT and FFT, respectively. Operating points of the DFIG test rig based on the power–generator speed curve are similar to Figure 7. Two operational areas are selected for REA diagnosis as follows (A&B):

Section A. The wind turbine works at the MPPT. Wind speed is roughly between 6 and 9 m/s, and the speed of the generator varies so that the optimum output power can be obtained. The back-to-back converter has a special role in this area. Fault estimation based on CWT is proper for this area of wind turbine operation, and this area is very noisy.

Section B. The speed of the generator in this region is constant. Of course, it has a slight slope. The generator speed is about 10% faster than the sync speed. The wind speed is roughly between 9 and 12 m/s. There is the least mechanical stress in this area. Fault estimation based on FFT is proper for this area of wind turbine operation.

Section C. There is a nominal power production in this area. The variation of wind speed is from more than 12 m/s to 25 m/s (cutoff speed). In this area, the power of the turbine is controlled with the pitch system. There is a lot of mechanical stress in this area of wind turbine operation. Generator speeds up to 20% faster than sync speed. The turbine dynamics is unstable due to mechanical motion of the pitch and blades. This area is not suitable for fault diagnosis.

Figure 7.

Power output–generator speed curve for the DFIG test rig.

Fault representation at the DFIG test rig

The electrical asymmetry is emulated on the DFIG by adjusting the phase variable resistances in the load bank externally connected to the rotor. Three levels of rotor asymmetry are applied to evaluate the effect of an incipient fault. The detail of the generator rotor circuit with external resistance is shown in Figure 8. This structure allows the rotor fault to be executed by adding a varying external resistor. The REA can be defined as (Zaggout et al., 2014)

δ R = | R_{AB} e^{i θ_{1}} + R_{BC} e^{i θ_{2}} + R_{CA} e^{i θ_{3}} |

(20)

where $δ R$ is the value of the added resistance due to effect of REA, $i = \sqrt[2]{- 1}$ , $θ_{1} = 0$ , $θ_{2} = 2 π / 3$ , and $θ_{3} = 4 π / 3$ . In the above equation, h denotes the healthy state and f denotes the faulty one. On the contrary, the amount of asymmetry is specified as follows (Zaggout et al., 2014)

Δ R (%) = \frac{δ R}{R_{AB}} \times 100 = \frac{δ R}{R_{BC}} \times 100 = \frac{δ R}{R_{CA}} \times 100

(21)

Figure 8.

Rotor circuit diagram.

Different levels of fault are exerted by varying the resistance. The fault percent is determined based on equation (21). The rotor rated phase resistance of the test rig generator is 16.6 mΩ. In this study, the percentages of faults are selected to be 7%, 23%, and 46%. The additional resistances are added with variable resistances, and this is for creating a different percentage of REA faults.

Experimental results

The experimental results are investigated based on two case studies. In the first case study, the real data of a healthy 2.5-MW DFIG wind turbine is used and the second case study is based on the real data collected from a faulty 90-kW DFIG test rig. The first case study as the first analysis tool is used for the evaluation of signal processing methods and the second analysis tool is used for the evaluation of the proposed FD strategy.

Results based on the first analysis tool: noise cancelation

The data of the stator current signal and power output in different operating ranges are collected from the MAPNA wind turbine control system. In Figure 9, the wind speed data received from the anemometer are shown. The power curve (power–generator speed) is illustrated in Figure 10. As can be seen from the figure, the turbine had been operating under varying wind speeds. The performance of LMS, wavelet, and R-LMS-WT algorithms is evaluated by applying them to the real signals of the wind turbine at varying speeds.

Figure 9.

Wind speed data received from the MAPNA 2.5-MW wind turbine.

Figure 10.

Power curve for the MAPNA 2.5-MW wind turbine.

The raw signal of one phase of the wind turbine stator is shown in Figure 11(a). As can be seen, this signal is very noisy. The total output power signal of the wind turbine is shown in Figure 11(b), and this signal is also very noisy. CMS and FD based on weak signals with low SNR values are very difficult.

Figure 11.

Input signals of noise elimination algorithms: (a) single-phase current signal of the stator and (b) output power.

Based on the collected power data, convergence results of LMS, WT, and R-LMS-WT are simulated; for increasing the convergence of LMS, the step size of LMS is assumed as 0.01. Figure 12 shows the results of these three methods. As shown in Figure 12(a), although the step size of LMS is high, the convergence does not occur before 2500 iterations, while in the case of R-LMS-WT (Figure 12(c)) convergence occurs at iteration 200.

Figure 12.

Investigating the convergence of noise elimination algorithms: (a) LMS, (b) wavelet, and (c) R-LMS-WT.

The effectiveness of the three algorithms is evaluated with the mean square error (MSE) index. Figure 13(a) and (b) shows the MSE index graph for the stator current data and power output data, respectively. It is clear from Figure 13(a) that the R-LMS-WT algorithm convergence based on the MSE index with the stator current input signal is better than the other two methods. This simulation result is also achieved in Figure 13(b) with the power signal input, and the MSE values of R-LMS-WT are lower than those of LMS and WT. On the contrary, in all the simulation results based on real data of the experimental setup, the wavelet performance is better than that of the LMS adaptive filter.

Figure 13.

Investigating the effectiveness of LMS, wavelet, and R-LMS-WT based on the MSE index: (a) evaluation based on the stator current signal and (b) evaluation based on the power output signal.

The output results of noise cancelation of these three algorithms based on the input signal of the stator current are presented in Figure 14. As can be seen, LMS and wavelet output still have a high-amplitude noise, while the output of R-LMS-WT is very sharp and smooth and its SNR is high. The method of R-LMS-WT is simple and effective. For wavelet denoising, it is important to consider the level of decomposition of the signal and the parameter selection of LMS has some influence on errors of convergence.

Figure 14.

Results of noise cancelation for LMS, wavelet, and R-LMS-WT.

The previous simulation shows the reliability of diagnosis procedure based on R-LMS-WT denoising method. Now, the influence of individual denoising methods is studied based on the value of kurtosis. Different tests are conducted on a set of rotor winding currents to determine the indicator. Each signal is processed by the three denoising methods in a frequency range of 0–32 kHz. Figure 15 shows the kurtosis values without and with denoising methods. Among the three studied denoising methods, namely, LMS, R-LMS-WT, and wavelet, the R-LMS-WT gives the most conclusive results.

Figure 15.

Evaluation of noise elimination algorithms based on kurtosis index, in the frequency range of 0–32 kHz, with the denoising algorithms (LMS, wavelet, and R-LMS-WT) and without the denoising algorithm.

Results based on the second analysis tool: REA detection

The stator current and power output of the test rig are passed through the R-LMS-WT denoising block and then the output signal is used as an input of FD for tracking the fault frequency (according to Figure 16). Based on the operation of the wind turbine, two signal processing methods are used for fault estimation: FFT and CWT.

Figure 16.

Block diagram of REA detection.

Analysis under fixed-speed operation of the wind turbine

The test rig has been implemented in B-part operation (as shown in Figure 8) of 1630 to 1660 r/min with the generator delivering 44–86 kW, under healthy or faulty conditions. The operating speed of the test rig is chosen at 1650 r/min $(s \approx - 0.098)$ . The input of the test rig (wind speed) is based on the drive of the prime mover motor; this drive is operated based on the turbine model, developed by the authors of this article. The goal of this experiment is to maintain the speed of the test rig constant. In fact, the speed of the rig test cannot be exactly constant because of turbulence of the turbine model. The healthy rotor resistance, including internal winding resistance, is 16.6 mΩ per phase and additional resistance up to 3.32 mΩ is successively added to one phase to give 23% unbalance. Higher levels of noise are incorporated into the measured signals based on different source including grid frequency fluctuation, grid voltage unbalance, and high vibration due to misalignment of the gearbox shaft. Electrical signals are used to estimate the rotor asymmetry fault with and without the R-LMS-WT noise reduction block. The analysis is based on the stator current and power output. Signals are transferred to the frequency domain after passing through the noise cancelation block. The harmonic spectra are obtained by applying an FFT. All signal spectra are converted to 0 dB at the highest harmonic. The stator current harmonic spectra after passing through the R-LMS-WT block are presented in Figure 17(a) (healthy) and Figure 17(b) (faulty). The magnitude of the faulty harmonic is −47 dB for the stator current at 59.8 Hz (1 – 2s)f. This experiment with visible amplitude of spectra indicates the effectiveness of R-LMS-WT in noise reduction.

Figure 17.

Healthy and faulty measured spectra for single stator current signals: (a) stator current—healthy condition and (b) stator current—faulty condition.

The total power harmonic spectra are presented in Figure 18(a) (healthy) and Figure 18(b) (faulty). The faulty harmonic component magnitude at 9.8 Hz (2sf) is −60 dB. These experimental results confirm that the use of the R-LMS-WT denoising block is more effective for FD for every signal and at any frequency component. Experiments showed that the power signal is better than the other signals such as stator current. This signal has higher faulty component magnitudes at the frequency of 2sf.

Figure 18.

Healthy and faulty measured spectra for the total power signal: (a) total power—healthy condition and (b) total power—faulty condition.

For a signal, being appropriate for detecting a specified fault is not merely related to the algorithm and harmonic amplitude; however, it is related to signal sensitivity. For calculating the value of sensitivity, equation (22) is used (Leung and Yang, 2012)

s = 10 \log (\frac{A_{f} - A_{h}}{A_{h}})

(22)

where S denotes the sensitivity and A_f and A_h are the faulty and healthy harmonic amplitudes, respectively. Figure 19 shows the sensitivity curve. The results have been obtained from the DFIG test rig in a 1600-r/min steady-state condition at various fault severities. As can be seen, the sensitivity of the power signal with R-LMS-WT is higher than that of stator current signals for REA FD. This experiment showed a decreased sensitivity result without R-LS-WT because of the noise in the measured signals.

Figure 19.

Signal sensitivity to REA fault.

Analysis under variable-speed operation of the wind turbine

The electrical asymmetry (representing the effect of a rotor winding fault, brush imbalance, or air gap eccentricity in the WT generator) is simulated on the rotor of DFIG by adding the variable resistance. Different levels of rotor asymmetry are applied to investigate the effect of an incipient fault based on Table 3. The experiments are performed at variable speeds of the operational wind turbine and proportional to those in Figure 7 at a speed of 1220–1600 r/min. This rotational speed of the generator is derived by the wind speed pattern; Figure 20 shows the speed of the prime mover motor rotor and generator speed in about 3 days of testing. In this article, the specific parameters are used for the implementation of the experiment. The $ω_{c}$ value is 2sf for the power signal and (1 – 2sf) for the stator current signal. The $ω_{f}$ parameter based on the model of wind turbine is selected to be 0.6sf.

Figure 20.

The overview of the test rig operation in terms of rotational speed.

The time waveforms of the signals collected in this experiment are shown in Figure 21, and it can be seen that, due to the effect of the varying generator speed, the fault symptom cannot be observed clearly from either the generator stator current or the total power. The rotational speed of the generator, mechanical torque, single-phase stator current, and total power signals are measured from the test rig based on the topology of Figure 6. The important observations of raw signal measurements in Figure 21 are as follows:

The variable-speed operational area of the wind turbine includes disturbance and noisy signal.

The FD process in this operational area for the diagnosis algorithm is very difficult.

The rotor fault symptom cannot be observed clearly from raw signal measurements.

The signal behaviors of power, generator speed, and torque are similar, but the main difference is the noise that is modulated on signals with different amplitudes.

Figure 21.

Electrical asymmetry applied to a DFIG rotor: (a) stator current signal in small abnormal REA; (b) mechanical drive shaft torque signal based on the REA scenario of Table 3; (c) rotational speed signal based on the REA scenario of Table 3; and (d) generator total power signal based on the REA scenario of Table 3.

The experimental results of REA detection under variable speeds of the generator are shown in Figure 22. The experiments are based on the use and non-use of the R-LMS-WT noise elimination block, and a new CWT index has been used to detect the fault.

Figure 22.

Detecting an electrical asymmetry fault from the power signal and stator current signal: (a) frequency graph from the power signal; (b) frequency graph from the stator current signal; (c) energy CWT index of the power signal without R-LMS-WT; (d) energy CWT index of the power signal with R-LMS-WT; (e) energy CWT index of the stator current signal without R-LMS-WT; and (f) energy CWT index of the stator current signal with R-LMS-WT.

The important observations of the experimental results shown in Figure 22 are as follows:

(a) and (b) The fault-related frequency (1 – 2s)f for stator current and the fault-related frequency 2sf for the total power are extracted. The behavior of these two signals is similar to the behavior of the generator’s rotational speed signal, and the degradation of the generator fraction changes the frequency-associated symptom fault.

(c) The CWT technique is applied to extract the energy at 2sf frequency. It is illustrated that the small asymmetry fault is not detected, so the CWT algorithm is poor in this case. This lack of tracking is due to overcoming the noise on the signal. Although the increase in energy in the medium fault time is clearly visible, the proximity of the signal energy in the time interval of 450–500 s to the signal energy of large asymmetry fault in the time interval 350–450 s makes it difficult to monitor the condition.

(d) The CWT energy tracking with R-LMS-WT for the power signal has been able to distinguish between all levels of fault. This shows that the proposed technique with the noise cancelation block (R-LMS-WT) has the potential to detect electrical asymmetry fault on a DFIG WT generator.

(e) It is clear in this experiment that CWT energy tracking based on the stator signal without R-LMS-WT succeeded only for a high asymmetry rotor fault.

(f) Using the noise reduction block, REA FD based on the stator current signal succeeded for medium and high asymmetry rates, but detectability of this signal with the presence of the noise reduction block is weak. Based on Figure 19, the signal sensitivity of stator current to REA fault in the low percentage of asymmetries is also low.

Conclusion

This article presented the application of the R-LMS-WT algorithm for amplifying a weak signal of the wind turbine. The capabilities of this algorithm were measured by the test rig. In this article, instead of vibration signals, the electrical signals were used. The electrical data included power and stator current signals. This led to the reduction of the operation and maintenance (O&M) cost. General results of this study are as follows:

The noise elimination method utilized in this study had the advantages of both adaptive filter and WT at once. In addition, it has high speed and rate of convergence. This method allowed very weak electrical signals, which have low SNRs, to be used for CM of the wind turbine without requiring sensors and hardware.

Fault frequencies were extracted from different signals. The common frequencies $1 - 2 sf$ and $2 sf$ were used for stator current and power signals, respectively.

Fault tracking was performed using FFT and CWT for different percentages of REA based on the operational area of the wind turbine.

The algorithm of FD was used in the entire operational conditions of the wind turbine. With regard to varying speed of the turbine under study, the ability for processing unstable electrical signals was one of the obvious aspects of CWT and R-LMS-WT.

The results showed that the proposed method has the required competence for being used in the wind turbine industry.

Based on the simulation and experiment in this article, it can be concluded that energy tracking of CWT is powerful and has low time cost in comparison to DWT.

In this article, it was shown that both the current and power signals are usable for REA detection. The current signal has some advantages; for example, its availability and its data are sufficient for FD. On the contrary, the power signal has a high sensitivity to fault compared to the current signal. Signatures in a current phase are only sensible to the fault of that phase. The power signal contains the data of all the electrical signals and, furthermore, considers the operational conditions of the turbine. Power has a higher spectral quality than current and eliminates the 50 Hz frequency, which is the dominant spectrum in current.

The authors are planning to use this noise reduction block in detecting other wind turbine generator faults, including the stator and bearing defects; the noise reduction block is the primary block in fault diagnosis and is very important. The authors have decided to use R-LMS-WT in the wind turbine fault diagnostic structure based on multiple fusion strategies. It is also recommended to use the proposed method to reduce noise of vibration signals in CMS with applications other than wind turbines.

Footnotes

Appendix 1 Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Mohamad Hossein Refan

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