A Diagnostic Method for the Saturable Reactor Core Looseness Degree of Thyristor Converter Valves

Abstract

During the long-term operation of thyristor converter valves, the saturable reactor vibration (mainly caused by magnetostriction) will lead to core looseness faults. In order to accurately evaluate the fault degradation degree, this paper proposes a vibration signal recognition model for iron core looseness based on synchrosqueezed wavelet transforms and a convolutional neural network. Firstly, vibration experiments are conducted on saturable reactors to obtain signals under different core looseness degrees. Then, the spectrogram features of vibration signals are extracted using synchrosqueezed wavelet transform. Finally, based on the high-dimensional learning ability of convolutional neural networks, the fault characteristics of the spectrogram are mined to accurately identify the core looseness degree. The research results indicate that the model in the paper has higher recognition accuracy than some other methods, which provides convenience for the monitoring and maintenance of saturable reactors.

1. Introduction

Saturable reactors are the core components of converter valves. Their functions include sharing voltage, suppressing the rate of current change and ensuring the normal opening and closing of thyristors. In practical engineering, the converter valve operates online for a long time in the valve hall of the converter station. The complex internal stress and external factors will gradually erode the working performance of the converter valve components. During this process, the tension belt of the saturable reactor will undergo plastic deformation, which leads to changes in the tension and looseness of the iron core [1]. Subsequently, there may be increased iron loss or overheating, which may even cause the shutdown of the converter valve [2]. Therefore, timely monitoring of the looseness of the saturable reactor core has important engineering value for the maintenance of the converter valve.

The saturable reactor is located inside the converter valve tower. Conventional visual inspection and infrared detection cannot effectively detect whether the iron core inside the saturable reactor is loose. However, during the operation of a saturable reactor a magnetostrictive effect will make the iron core vibrate [3]. The vibration signals generated by iron cores with different fault levels have different characteristics. Therefore, iron core looseness faults can be identified by analyzing these vibration signals.

The research on vibration signals is relatively rich, but there are few studies on the vibration characteristics of saturable reactors [4,5,6]. These saturable reactors operate in variable operating conditions. Therefore, the vibration characteristics also change. However, there is no current measurement device installed on the bridge arm of the converter valve. It fails to obtain the operating conditions of the converter valve. Therefore, it is not feasible to identify the vibration signal of the saturable reactor core looseness degree based on the independent operating conditions. The extraction and recognition of vibration features based on variable operating conditions is an important goal of this study. Traditional time and frequency domain analyses and machine learning algorithms cannot realize accurate identification of core looseness. Because the data features under varying operating conditions are mixed, misjudgments can occur. In recent years, convolutional neural networks (CNNs) have been widely used in the field of power equipment, including for feature extraction, pattern recognition, parameter prediction, etc. [7,8,9]. A convolutional neural network can effectively avoid the problem of the exponentially increased number of neurons by reducing the dimensions of input features through convolution, pooling and other processes. By constructing a deep-level network structure, the feature information contained in the input data can be effectively learned and beneficial features can be retained. Therefore, this paper builds a multi-layered convolutional neural network to deeply study the vibration characteristics of the saturable reactor core and effectively overcomes the problem of misjudgments.

In addition, research on vibration signals mainly focuses on feature extraction in the time and frequency domains, such as signal decomposition, spectrum analysis, etc. [10,11]. In order to extract richer feature information, Y. Sun et al. constructed a two-dimensional image with rich time–frequency information [12]. The image was based on the vibration signal of bearings, which applied continuous wavelet transform (CWT). M. Ahsan et al. transformed the vibration dataset of bearings and gears into two-dimensional grayscale images to improve the diagnosis accuracy of proposed models [13]. According to the above research, this paper also converts the one-dimensional signals into a 2D spectrogram image and takes the image as the direct input of a CNN. Synchrosqueezed wavelet transform (SST) is an improved method of wavelet transform with a better compression rate [14]. J. Yuan et al. applied SST to extract gear fault features and improved the resolution of time–frequency representation through multi-step dual kernel denoising [15]. S. Wang et al. improved the SST algorithm to extract the rapidly changing intermediate frequency signal of aviation generator vibration [16]. C. Zhou et al. compared the feature expression effects of SST and HHT, verifying the effectiveness of SST in extracting fault features from non-stationary signals in rotating machinery [17]. This article uses the algorithm to convert the vibration signal of the loose iron core into a time–frequency image.

Above all, this paper proposes a vibration signal recognition model of iron core looseness based on SST and a CNN. The model consists of two parts. One is generating a spectrogram of the vibration signal based on SST. The second is to construct a model for identifying the iron core looseness degree based on a CNN. The vibration signals with different degrees of looseness under variable working conditions are taken as the original data. Through synchrosqueezed wavelet transform, the vibration signals are converted into a time–frequency spectrum and image compression is realized at the same time. A CNN model is constructed to learn the characteristics of the spectrogram to identify the iron core looseness degree.

In this paper, Section 2 analyzes the vibration mechanism of saturable reactors. Section 3 introduces the experimental platform and experimental approach. A visual display of some experimental data is also provided. Section 4 provides a detailed explanation of the diagnostic method. Section 5 validates the performance of the proposed method through several experiments and comparative cases. Section 6 provides a summary of the whole paper.

2. Vibration Mechanism of Saturable Reactors

The structure of a saturable reactor is shown in Figure 1. It mainly consists of windings, iron cores, cover plates and screws. A single iron core is fixed as a whole by two U-shaped laminated silicon steel sheets through tensioning straps. According to reference [18], the voltage borne by a saturable reactor is as follows:

$$U={{\displaystyle \sum }}_{k=0,1,2,\cdots }^K{U}_k\sin \left(k\omega t+{\phi }_k\right)$$

(1)

where $U_k$ and ${\phi }_k$ are the voltage amplitude and phase of the k-th harmonic, respectively, $\omega =50 \mathrm{Hz}$ and $K$ is the total harmonic number.

The small deformations of saturable reactor components caused by magnetostriction satisfies the following relationship:

$$\frac{\Delta L}{L}·\frac{1}{\mathrm{d}H}=\frac{2{\epsilon }_s}{H_c^2}\left|H\right|$$

(2)

where $\Delta L$ is the deformation and expansion amount of silicon steel sheet, $L$ is the original size of the silicon steel sheet, ${\epsilon }_s$ is the saturated magnetostriction rate of the silicon steel sheet, $H_c$ is the coercive force and $H$ is the magnetic field strength in the iron core.

Therefore, the vibration formula of the saturable reactor core is as follows:

$$a=\frac{d^2\Delta L}{d{t}^2}=\gamma \left\{{{\displaystyle \sum }}_{1}2U_k^2\cos \left(2k\omega t+2{\phi }_k\right)+{{\displaystyle \sum }}_2{q}_1\cos \left[\left(k_1+k_2\right)\omega t+{\phi }_{k1}+{\phi }_{k2}\right]+{{\displaystyle \sum }}_2{q}_2\cos \left[\left(k_1-k_2\right)\omega t+{\phi }_{k1}-{\phi }_{k2}\right]\right\}$$

(3)

$$q_1=\frac{{\left(k_1+k_2\right)}^2{U}_{k1}{U}_{k2}}{k_1{k}_2}$$

(4)

$$q_2=\frac{{\left(k_1-k_2\right)}^2{U}_{k1}{U}_{k2}}{k_1{k}_2}$$

(5)

where $U_k$ and ${\phi }_k$ are the voltage amplitude and phase of the k-th harmonic, respectively, and $\omega$ is the angular frequency of 50 Hz voltage. ${\displaystyle \sum }_1\ast ={{\displaystyle \sum }}_{k=1,2,3,\cdots }^K\ast$, ${\displaystyle \sum }_2\ast ={{\displaystyle \sum }}_{k_1\ne k_2=1,2,3,\cdots }^K\ast$. $\gamma$ is related to the saturation magnetic flux density of the iron core, winding turns, saturation magnetostriction rate of the silicon steel sheet, cross-sectional area of the iron core, original size of the silicon steel sheet and other parameters.

According to the mechanism analysis process mentioned above, magnetostriction is the core factor causing the vibration of a saturable reactor [19]. The voltage borne by the saturable reactor during operation contains many higher-order harmonics. Resonance occurs when the natural frequency of the iron core approaches the excitation frequency. In addition, the material and structure of the iron core can affect its nonlinear characteristics. These factors will further affect the vibration mechanism of the iron core [20].

3. Saturable Reactor Core Looseness Experiment

3.1. Experiment Platform

The iron core looseness experiment platform is shown in Figure 2. The platform consists of three parts, a power circuit, a saturable reactor, and vibration acquisition equipment. The structural diagram of the experimental platform is shown in Figure 3. The power circuit provides power, control and protection for the entire experiment platform. It includes a power supply, control switch and H-bridge module. The power supply provides the required DC and AC power for the entire experimental platform. The control switch is responsible for controlling the start and stop activities of the experiment and also has the function of protection. The H-bridge module mainly includes IGBT devices to achieve rectification and provide voltage excitation to the saturable reactor. The saturable reactor is the experimental object. The iron core in it will be artificially set to loosen during the experiment, which is to simulate iron core failure. The vibration acquisition device includes a vibration sensor, optical fiber, acquisition board, upper computer, etc. The sensor is adhered to the surface of the saturable reactor. The collected vibration signals will be uploaded through optical fibers. In the entire experimental platform, the power circuit emits voltage excitation that simulates the two pulse voltages generated by the switch instantaneously. Equivalent stray capacitance is used to regulate the voltage peaks and simulate the actual operating conditions. The vibration signal generated by the saturable reactor is received through a sensor, transmitted through optical fibers, processed by the acquisition board and finally input into the upper computer for analysis.

3.2. Experimental Process and Data Collection

The iron core looseness experiment simulates different looseness degrees by adjusting the tension belt screw torque and includes five modes: normal state (NS), slight looseness (SL), extreme looseness (EL), total looseness (TL) and screw bolt off (SO). The specific experimental parameters are shown in

Table 1. Test parameters.

Parameter	Value
Current peak	270 A, 335 A, 465 A, 600 A, 730 A, 865 A, 1000 A, 1130 A, 1280 A
Vibration sensor frequency response range	3 Hz~30 kHz
Data collection sampling frequency	1 MHz
a. screw bolt off (SO)	Tension belt screw removed
b. total looseness (TL)	Tension belt screw torque: 0 N·m
c. extreme looseness (EL)	Tension belt screw torque: 6 N·m
d. slight looseness (SL)	Tension belt screw torque: 8 N·m
e. normal state (NS)	Tension belt screw torque: 10 N·m

. The nine current peaks in the table represent nine different operating conditions. That is, in engineering applications, saturable reactors usually operate under these nine operating conditions. In order to be as close to engineering practice as possible, this experimental platform directly provides corresponding currents for the saturable reactor under nine operating conditions. Each looseness mode is tested under the mixed action of nine operating conditions.

Three typical operating conditions are selected. Figure 4 shows the vibration signals with different iron core looseness degrees under these operating conditions. The horizontal axis corresponds to the sampling time for three different working conditions. The vertical axis represents the amplitude of the vibration signals. From the graph, it can be observed that there are many differences between the same looseness modes under the three working conditions. However, the differences in the different looseness modes under the same working conditions are not obvious. Their shapes are similar and only have differences in amplitude. However, this difference is not intuitive enough. It is difficult to accurately identify the iron core looseness degrees using vibration data directly.

A method is needed to extract the features of vibration signals. It should meet the following two basic requirements: (1) the differences under different working conditions should be preserved and (2) the differences in different looseness modes under the same working condition should be extracted and made more obvious. Only in this way can the diagnostic effect for the iron core looseness degree be improved.

4. Diagnostic Method for Saturable Reactor Core Looseness Degrees

4.1. Synchrosqueezed Wavelet Transform

Synchrosqueezed wavelet transform is the redistribution of the time and frequency domains based on wavelet transform [21]. It uses synchronous compression to transform the energy of the time scale plane into the energy of the time frequency plane, which makes the curve expressing frequency more concentrated.

For a given signal $s\left(t\right)$, its continuous wavelet transform $W_s$ is defined as:

$$W_s\left(a,b\right)=\int s\left(t\right)a^{-\frac{1}{2}}\overline{\mathsf{\Psi }\left(\frac{t-b}{a}\right)}dt$$

(6)

where $\mathsf{\Psi }$ is the selected mother wavelet, $a$ and $b$ are the scale parameter and translation parameter of the mother wavelet transform, respectively, and $\overline{\mathsf{\Psi }\left(t\right)}$ represents the complex conjugation of $\mathsf{\Psi }\left(t\right)$. For any $\left(a,b\right)$ satisfying $W_s\left(a,b\right)\ne 0$, the instantaneous phase and frequency of signal $s\left(t\right)$ is:

$$W_s\left(a,b\right)=-i{\left(W_s\left(a,b\right)\right)}^{-1}\frac{\partial }{\partial b}{W}_s\left(a,b\right)$$

(7)

According to the mapping relationship $\left(b,a\right)\to \left(b,W_s\left(a,b\right)\right)$, the transformation information $W_s\left(a,b\right)$ is transformed from the time–scale plane of the wavelet transform to the time–frequency plane; this process is called synchronous compression. $a$ and $\omega$ are divided into several small boxes, with $a_k-a_{k-1}={\left(\Delta a\right)}_k, {\omega }_l-{\omega }_{l-1}=\Delta \omega$. The synchronous compression transformation $T_s\left(\omega ,b\right)$ is only determined by $W_s\left(a,b\right)$ in a box with a continuous center ${\omega }_l$ and a width $\Delta \omega$:

$$T_s\left( {\omega }_l,b\right)=\Delta {\omega }^{-1}{{\displaystyle \sum }}_{a_k:\left|\omega \left(a_k,b\right)-{\omega }_l\right|\le \Delta \omega /2}{W}_s\left(a_k,b\right)a_k^{-\frac{3}{2}}{\left(\Delta a\right)}_k$$

(8)

where $a_k$ is the k-th discrete scale and ${\omega }_l$ is the first discrete angular frequency. Through the above transformation, the wavelet factor spectrum can be squeezed along the scale axis and the energy distribution of the spectrogram can be more concentrated. Therefore, the spectrogram of the SST has a higher aggregation and resolution than the general wavelet factor spectrum.

SST is applied to convert the vibration signal in Figure 4 into a 2D figure, and CWT was also used for comparison with SST; these data are shown in Figure 5 and Figure 6.

In terms of the comparison between the CWT and SST methods, the mother wavelet functions they use are all Morlet wavelet functions. The original spectrogram directly obtained through calculation can only highlight the main frequency components. In order to improve the ability to reflect the non-main frequency components, the original spectrogram is logarithmically treated as $T_{st}=\log \left(T_s+\alpha \right)$. For the spectrogram of the wavelet transform, the value of parameter $\alpha$ is taken as $\alpha =0.05$. For the SST spectrogram, the value of parameter $\alpha$ is $\alpha =0.0005$. Figure 5 and Figure 6 are the vibration spectrogram spectra of the two methods under three typical working conditions, which correspond to Figure 4. It can be seen from the two figures that the working conditions and the iron core looseness will affect the color and shape of the time spectrum, such as the brightness, holes, vortices, etc. The SST time–frequency figures are generally clearer than the wavelet transform time–frequency map, with more obvious boundaries. When viewed with the naked eye, the spectrogram spectrum of wavelet transform is fuzzy. Dark spots, holes and other features can be clearly seen in the SST spectrogram; this is more beneficial for identifying the iron core looseness.

4.2. Convolutional Neural Network

This paper designs a new CNN model; its structure is shown in Figure 7. The model includes an input layer, an output layer, seven convolutional pooling layers, a DropOut layer and two fully connected layers. The vibration signal of the iron core is converted into a two-dimensional time–frequency spectrum using SST, and these images are used as input data to enter the input layer of the CNN. The seven convolutional pooling layers have similar structures, including convolutional layers, batch normalization layers, maximum pooling layers and Relu activation layers. They differ in size. The seven convolutional pooling layer groups convert the original spectrogram characteristics into feature maps and realize the dimension reduction. The characteristics of the time–frequency spectrum of iron core vibrations are extracted through the seven convolutional pooling layers. These features are input into the DropOut layer for further processing to obtain a set of one-dimensional sequences. Then, this set of sequences passes through two fully connected layers. All features are compressed into the final five features and input into the SoftMax layer. Finally, the SoftMax layer is set to achieve the output of a recognition result.

4.3. Diagnosis Process for Iron Core Looseness

The basic idea of the entire diagnostic process is to first train the model, then validate the model and then to finally use the model that meets the requirements for testing. The saturable reactor experimental platform is used to obtain datasets and their looseness level labels under various operating conditions and iron core looseness modes. These data face the issues analyzed in Section 3.2 and therefore cannot be directly used. Further extraction of beneficial features is needed. At this point, the SST algorithm is applied to convert the vibration signals into two-dimensional images. The vibration characteristics are sharpened and highlighted. Moreover, the image is input into a CNN network with set basic parameters for learning and training. The obtained model needs to be confirmed through the validation set, otherwise the parameters of the CNN network will continue to be optimized. The final model (the one that meets the requirements) will be truly used to test its diagnostic performance.

The specific steps for constructing a diagnosis method for the saturable reactor core looseness degree based on the SST and CNN are as follows:

(1)

Set different core looseness degrees on the experimental platform. Collect vibration signals under varying operating conditions and denoise them.

(2)

Select appropriate mother wavelet functions and related parameters. SST is used to convert the vibration signals into two-dimensional images. These images are divided into training sets, validation sets and testing sets.

(3)

Construct a CNN model using the time–frequency spectrum of iron core vibration signals under different looseness degrees as input and construct a class matrix of iron core looseness as output. Configure the network parameters for training.

(4)

Use the validation set to test the trained CNN model. If it does not meet the recognition accuracy requirements, return to step 3 and change the parameters.

(5)

Finally, the testing sets are used to verify the performance of the trained model.

5. Experiment Validation and Discussion

5.1. Identification Results for the Iron Core Looseness Degree

According to the iron core looseness degree, the experiment data are divided into five groups. The data in each group are collected under various operating conditions. Matlab 2022a with Deep Learning Toolbox is used in this study. The original data are cut and resampled, and each set of data is divided into a training set, verification set and test set. All data sets are converted into two-dimensional spectrogram figures using SST and used to train and validate the CNN model. As shown in Figure 8, at the 130-th iteration, the model accuracy of the validation sets reaches its peak of 99.73%, where the model is taken as the recognition model. The testing sets are applied in the model and the identified results are summarized to build a confusion matrix, which is shown in Figure 9. The vertical axis of the confusion matrix represents the actual looseness state. The horizontal axis represents the results of the model diagnosis. The letters a~e represent the five degrees of iron core looseness. According to the definition, when the diagnostic results of the model are completely correct, the samples should be concentrated on the diagonal of the confusion matrix. When there are errors in the diagnostic results, some samples will be distributed off the diagonal.

In Figure 9, each mode has 300 test samples. It can be seen that misclassification is mainly concentrated in the extreme looseness mode, where it is misjudged as slight looseness and has an accuracy rate of only 84.33%. The recognition accuracies of the other patterns is above 92%. The diagnostic results are mainly concentrated on the diagonal and the dispersion of misjudgments is not high.

5.2. Recognition Effects Comparison for Different Methods

This section adopts different methods to conduct a comparative analysis. On the one hand, the feature extraction method has been replaced and, on the other hand, the model construction method has been replaced. However, the basic steps are consistent with the content in Section 4.3. The purpose of this is to compare the effectiveness of different feature extraction algorithms and learning models and ultimately demonstrate the superiority of the proposed method.

Training and testing the recognition model based on the CWT and SST features is performed.

Table 2. Recognition results comparison of different methods.

Methods	Parameter Scale	Average F1 Value	Minimum F1 Value
SST + CNN	44.1 k	0.9306	0.8569
CWT + CNN	44.1 k	0.8946	0.8139
SST + LeNet	61.8 k	0.9014	0.8335
SST + AlexNet	56.8 M	0.9182	0.7922
SST + VggNet	134.2 M	0.8176	0.5882
SST + ResNet	23.5 M	0.7737	0.5571

shows the recognition results for the different methods. The F1 value represents a comprehensive indicator of the recall rate and accuracy [22]. The larger the F1 value, the higher the accuracy of the method and the lower the miss rate. The average F1 value represents the average of all test results. The minimum F1 value represents the smallest value among the F1 values obtained after multiple tests. Therefore, a high average F1 value indicates that the overall recognition effect of the method is good, whereas a high minimum F1 value indicates that the single recognition effect of the method is reliable. From the table, the superiority of our algorithm is demonstrated; its precision and recall are better than those for CWT. Moreover, the parameter scale of the CWT algorithm is similar to that of the algorithm in this paper. Furthermore, under the same resources, the proposed algorithm can better reflect the changes in the iron core looseness degree than the features extracted using CWT. The detection accuracy for the algorithm from this paper has higher reliability in multiple tests.

Table 2 also shows the scheme of using synchrosqueezed wavelet transform to extract image features when using other diagnostic methods. The method proposed in this article has the smallest parameter size and the best diagnostic performance. In contrast, LeNet’s diagnostic results are slightly worse [23]. However, AlexNet [24], VggNet [25] and ResNet [26] not only have lager parameter sizes but also have a significant difference between the average F1 value and the minimum F1 value. This indicates that their diagnostic results have strong volatility and that there are extreme situations during multiple testing processes. Therefore, the reliability of these algorithms is relatively low and cannot always provide convincing diagnostic results. Figure 10 is a comparison diagram of the confusion matrices for the four algorithms. From the figure, it can be seen that LeNet and VggNet have some misjudgments regarding extreme looseness. AlexNet has large diagnostic errors in both the total looseness and slight looseness modes. ResNet does not perform well in diagnosing extreme looseness and total looseness. Further comparison between Figure 9 and Figure 10 shows that the diagnostic accuracies of LeNet, VggNet and ResNet are relatively low, whereas the diagnostic results for AlexNet are more extreme. Either all recognition is correct or there is a large misjudgment. Its stability is poor. The above comparison results indicate that the algorithm proposed in this paper has both diagnostic accuracy and stability for identifying the iron core looseness degree. From Figure 10, it can be concluded that most misjudgments occur in adjacent looseness modes. By analyzing the original data and time–frequency spectrum of the vibration signals, the main reasons for this phenomenon are identified as follows: (1) In adjacent modes, the vibration signals have partially similar features, which leads to misjudgments in the diagnostic model. (2) The four algorithms did not fully extract the features of the iron core looseness in the time–frequency figures. Due to the incomplete extraction and learning of the iron core looseness features hidden in the vibration signals, the diagnostic performance of these four comparative models is poor. Compared with these four algorithms, the model in this paper can more effectively learn the iron core looseness fault characteristics. It can also effectively distinguish between different iron core looseness degrees.

6. Conclusions

During long-term operation, the degradation of the iron cores in saturable reactors may become more and more severe, especially in terms of the looseness degree. This will have a negative impact on the healthy operation of the converter valve. Therefore, how to accurately identify the saturable reactor core looseness degree under complex operating conditions is of great significance for achieving condition-based maintenance of the converter valve. To solve this problem, this paper proposes a vibration signal recognition model for iron core looseness based on synchrosqueezed wavelet transform and a convolutional neural network. The advantages of this model are as follows: (1) It can cope with the challenges of complex variable operating conditions. (2) The method of time–frequency analysis plus a CNN can effectively identify the looseness degree of the iron core. (3) Compared with some other methods, this method has better diagnostic ability.