Figure
1.
Topology of the CRAFT magnet high-power supply.
| Citation: |
Chong GAO, Zhongjian KANG, Dajian GONG, Yang ZHANG, Yufang WANG, Yiming SUN. Novel method for identifying the stages of discharge underwater based on impedance change characteristic[J]. Plasma Science and Technology, 2024, 26(4): 045503. DOI: 10.1088/2058-6272/ad0d56
|
It is difficult to determine the discharge stages in a fixed time of repetitive discharge underwater due to the arc formation process being susceptible to external environmental influences. This paper proposes a novel underwater discharge stage identification method based on the Strong Tracking Filter (STF) and impedance change characteristics. The time-varying equivalent circuit model of the discharge underwater is established based on the plasma theory analysis of the impedance change characteristics and mechanism of the discharge process. The STF is used to reduce the randomness of the impedance of repeated discharges underwater, and then the universal identification resistance data is obtained. Based on the resistance variation characteristics of the discriminating resistance of the pre-breakdown, main, and oscillatory discharge stages, the threshold values for determining the discharge stage are obtained. These include the threshold values for the resistance variation rate (K) and the moment (t). Experimental and error analysis results demonstrate the efficacy of this innovative method in discharge stage determination, with a maximum mean square deviation of Scr less than 1.761.
The Comprehensive Research Facility for Fusion Technology (CRAFT) is intended to test the major tokamak components, such as the magnet power supply, which is vital for providing energy to the superconducting magnet. During the operation of the power supply, several anomaly conditions may occur, posing possible system dangers. As a result, it is critical to diagnose the anomalous state in a timely manner so that staff can locate and repair the fault.
Traditional diagnosis approaches are based on empirical and physical models, however, they have several drawbacks.
(1) Empirical model-based approach.
This method primarily depends on the expertise and information gained by professionals over time. Although the empirical model-based method can replicate human experts to solve some problems, it still relies too heavily on the domain’s fuzzy set of system features and expert system rules to explain themselves.
(2) Physical model-based method.
The physical model-based method has more stringent requirements for device modeling. Most mathematical models based on device mechanisms are static. The static model’s parameters are fixed, and it is difficult to use the original mathematical model to forecast adequately after altering the prediction aim, therefore universality is limited.
In recent years, the traditional data driven method has been widely used in the field of power load forecasting [1]. As an important deep learning model, LSTM is widely used in a variety of prediction, detection, and classification tasks due to the excellent time series processing capabilities.
References [2–6] explored various applications of LSTM-based models in power load forecasting, including small-scale systems, medium and long-term forecasting frameworks, decomposition-based models, and machine learning approaches combining factor analysis for specific load predictions. Its prominence extends to the fields of large-scale grid load forecasting, small hydropower development, power deficit prediction post-disturbance, convolutional LSTM models for energy forecasting.
References [7–13] introduced innovative LSTM-based models, including an MP-LSTM optimized with an improved particle swarm algorithm, an SSA-LSTM hybrid leveraging singular spectrum analysis for load prediction, and an adaptive clustering LSTM network integrating clustering and forecasting processes. Further research compared LSTM and bidirectional LSTM for univariate time series forecasting [14], proposed deterministic differential equation-based LSTM models for arc furnace cycles [15], and introduced algorithms for load-based peak reduction and valley filling [16].
The robustness of LSTM in sequence processing has also led to applications in stability prediction, such as multi-parameter battery system forecasting [17], anomaly detection frameworks using LSTM auto-encoders [18], and transient stability evaluation methods [19]. Additionally, LSTM networks have been employed in electric vehicle battery state of charging prediction [20], digital twin simulations for high-voltage batteries [21], and power reserve strategies in hybrid electric vehicles [22].
In plasma science and technology, fault detection advancements include frequency-domain fault diagnosis for diodes [23], ultrasonic signal detection using multi-physical models [24], and liquid metal current limiters combining fast switches and current-limiting reactors [25]. Reference [26] further detailed neutron flux monitoring systems for ITER using fission chamber detectors and advanced controllers.
Due to the particularity of the fusion field and its power system, there is an urgent demand for safety and stability. Therefore, it is necessary to adopt effective methods to strengthen identification, improve work efficiency, and ensure the safety of power and personnel. During the operation of high-power power supplies, there are abnormal states that are difficult for individuals to identify, making it difficult to find the cause. After conducting multiple experiments on the testing platform, common abnormal states include the following aspects: (a) Current signal interruption, (b) Overcurrent, (c) Transformer arcing, (d) Protective make switch (PMS, which is activated mistakenly during normal operation), (e) Unbalance of parallel thyristors, (f) Arm short, (g) Bridge short, (h) Firing drift, (i) Overvoltage, and (j) Thyristor fuse drop.
The test output of individual converter is reaching up to 30 kA, while test platform output of two converters (CU1&CU2 or CU3&CU4) can reach up to 55 kA. Furthermore, there is bypass configured in reverse parallel with the converter, and protective make switch operates in parallel with the superconducting magnet. The dummy load is superconducting coil, whose inductance value is around 2.5 mH. When fault is occurred, converter firing is set to inverting state, so converter output voltage is reversed and the bypass device adopting thyristor and protective make switch is activated to bear the load current, the topology is depicted in figure 1.
The structure of CRAFT magnet high-power supply is shown in figure 2, which mainly includes the input filter, the thyristor rectifier bridge, ux (x = a, b, c) is three-phase input voltage, Lx are the input inductance and resistance, respectively. According to the experiment requirements of testing platform, thyristor converter needs to realize long pulse charging of load.
The current sensors are located on bypass, the DC side of each converter and the load side to measure the converter current and load current, and timely feedback to the control system to adjust and send command signals to compensate or eliminate the load current, so that it can follow the given preset current by upper computer.
Under normal operating conditions, the direct current of the dummy load, as shown in figure 3, exhibits a trapezoidal waveform. This shape results from the preset waveform from the upper computer of the control system, and the stable-state current is adjustable.
If the current signal is interrupted on the output side of certain converter, the current output sampling Idc1 is false signal 0. In the experiment, to simulate branch current signal interruption, the signal wire is removed. As proportional-integral-derivative (PID) feedback control is adopted in the power control system, as shown in figure 4, when the branch current signal interruption happened, the branch current signal 0 is sent to the comparator in the local controller to calculate the error between the half reference current and Idc1, then error signal is sent to the PID controller, and the referent voltage is increased and firing is changed, resulting in the increase of load current Idc. When the load current Idc reaches the threshold, the inverting mode starts and the load current Idc decreases, as shown in figure 5.
If the total current signal is interrupted, the current output sampling Idc of the converter is false signal 0. Total current signal interruption is simulated when the current is up to 6000 A, and Idc is set to false signal 0 at 31.8 s, in this case, Idc1+Idc2−Idc = 6000+6000−0 > 3000 A. The disparity between the combined output currents of the two converters and the total current on the DC side exceeds 3000 A, due to the fault detection and protection control in Programmable Logic Controller (PLC) in the CRAFT power supply, secondary protection measures will be implemented and the thyristor firing will be forced to invert, then the load current decreases, as shown in figure 6.
When the load current reaches the protection threshold 5900 A of control system, Idc > 5900, the inverting mode starts, then the load current decreases, as shown in figure 7. Unlike the impact of load current sensor failure shown in the figure 6, once the current reaches the threshold, the relevant protection is performed immediately.
The dust particles at the test platform leads to reduction in the insulation performance of the rectifier transformer, which results in arcing on the primary side during power testing, and the phenomenon of peak current lasts 1.534 ms until it reaches protection threshold current, as shown in figure 8.
The PMS is activated mistakenly due to the error caused by human factors, and it may exhibit abnormal and oscillating current, as shown in figure 9.
When bridge short circuit fault occurs, the three-phase current is shown in figure 10, due to the phase difference, the instantaneous voltages of phase A and phase B are different. At the moment of the short circuit, the voltage of phase A is higher instantaneous value, which leads to different short-circuit currents. But after transient process, the system gradually reaches a new steady state. Under steady-state conditions, the transient response gradually disappears due to the symmetry of the three-phase power supply, the currents of phase A and phase B tend to be balanced.
Firing drift fault means that the firing angle of the thyristor is delayed and not fired according to the expected phase.
It is assumed that the normal trigger angle is α1, thyristor 1 and thyristor 2 are switched on as planned, and thyristor 3 should be fired at the commutation time. At this time, near the commutation moment, the firing angle suddenly changes to α2, where α2 > α1, which leads to the failure of thyristor 3 to be fired in time, and the load current cannot be immediately transferred to the thyristor 3, but it is maintained in the original thyristor.
At the initial moment of firing angle changes, the impact of exponential decay is significant, and the current adjustment is rapid. As time increases, the exponential decay term tends to zero, the system reaches steady state, and only periodic oscillation terms remain in the current. The oscillation amplitude is related to the load impedance and voltage source characteristics, and the superposition effect of the actual current waveform will be between these two characteristics.
At the end of the commutation, the thyristor 3 is fired and the current enters the new conduction path. At this time, the load current gradually returns to normal commutation period from the previous delayed state, and the change of firing angle causes the voltage applied at the on-time to be different. Thyristor current is shown in figure 11, described by
| id(t)=(id0−RLUmR2L+(ωLd)2)e−RLLdt+ωLdUmR2L+(ωLd)2sin(ωt)+RLUmR2L+(ωLd)2cos(ωt). | (1) |
Where the Um represents the maximum value of the three-phase voltage，RL represents the resistor on the line, and the Ld represents the load inductance, ω represents the frequency of the power system, id0 represents the initial load current.
When the AC side switch is open and the current can not naturally cross zero, it will cause the sudden release of inductive energy storage, resulting in transient overvoltage in the AC side, as shown in figure 12.
When the thyristor fuse drop occurred in phase A, the thyristor circuit was open and phase A current loss occured as shown in figure 13.
LSTM consists of an input layer, a hidden layer and an output layer. LSTM adds a memory unit to each neural unit of the hidden layer, enabling the selective output of characteristic information of the time series. The long-term memory problem of RNN in practical application was solved. The memory unit structure of LSTM is shown in figure 14.
The cell state is updated through three gated structures: the input gate, the forget gate, and the output gate. At time t, the cell state can be calculated as follows:
| {ft=sig(Wfg[ht−1,xt]+bf)it=sig(Wfg[ht−1,xt]+bi)Ci=tanh(Wcg[ht−1,xt]+bc)Ct=ft×Ct−1+it×Ctot=sig(Wog[ht−1,xt]+bo)ht=ot×tanh(Ci) | (2) |
Where ft, it and ot are the calculation results of three gating structures respectively; xt is input at time t; ht is the LSTM output at time t; Ct showed cell state at time t. Ci is a new candidate value vector. Wf and Wo are the weight matrix of the corresponding gating structure respectively. bf, bi and bo are the bias vectors. Wc is the weight matrix of the candidate value vector, whose bias is represented by bc, and tanh represents the activation functions. The process of the proposed algorithm is outlined in table 1.
| Algorithm1 |
| Input: Sequence of input vectors xt and initial cell state C0, initial hidden state h0 Output: Sequence of input vectors ht 1: Initialization: set the initial cell state C0 and initial hidden state h0. 2: For each time step t from 1 to T: 3: Calculate ft, it and Ct , ot , ht based on equation (1) 4: Repeat step 3 for each time step t. 5: Output the sequence of hidden states ht End |
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The abnormal state prognostics method is introduced in details in figure 15. Firstly, the experimental data are acquired by sensors; secondly, the data are normalized according to normalized formula, then normal data and abnormal data are annotated and shuffled meanwhile; thirdly, all data are separated to training and test sets, and the training set is input to train LSTM neural network model.
(a) Data acquisition
A large amount of operational data have been collected at sampling frequency of 20 kHz from high-power converter systems, covering various signals under normal and fault conditions. Different types of faults require different input signals. All data include the following signals.
i. Total current (Idc);
ii. Branch current: converter output current (Idc1/Idc2); thyristor branch current; bypass current;
iii. Three-phase AC voltage (Ua, Ub, Uc).
(b) Data normalization
Since the data frequently manifest at different levels, z-score is employed to standardize the data. The number of standard deviations that a raw score deviates from or exceeds the mean value of the observed or measured object is known as the z-score in statistics. The formula for calculating the z-score is z=x−μθ, where μ represents the average value of the data and θ denotes the standard deviation.
(c) Data shuffling
The training model may be able to learn the time order feature if the data are input in the same order, since the data’s order will also be a feature of the network. Order features, however, are not actual model features. In order to improve generalization ability and shuffle the order of the entire dataset, the shuffling method is necessary.
Normal and fault signals are separated, the training and test sets are split in 8:2 ratios, and the model is then trained and tested. The LSTM model is adopted to process time-series data. LSTM is particularly suitable for processing time series data, such as current and voltage signals, as it can capture patterns of signal variation over time.
Four Nvidia P100 GPUs were used in a multi-GPU configuration in MATLAB during the fault detection system's training phase. The ability of processing data speeds up the training process and allows the model to process large datasets efficiently.
Initialization of weights and biases. Meticulous initialization of weights and biases was carried out during the training phase. The Xavier initialization method, which gives the weights suitable values, was used to initialize the weights. The neural network’s stability and convergence are aided by this initialization technique.
Optimization algorithm. The Adam optimizer, which is essential for updating parameters, helped with the optimization process. Adam is an advanced optimization algorithm that stands for “Adaptive Moment Estimation”. It combines aspects of momentum-based and Root Mean Square (RMS) approaches, which makes it very efficient for a variety of deep learning tasks.
Gradient clipping. Gradient clipping was used to address possible problems like gradient explosion and gradient vanishing. This method prevents gradients from growing unduly large or small by limiting their magnitude during the back-propagation phase. It guarantees more stable and efficient training.
Model training. The dataset is divided into a training set and a testing set. During the training phase, the model adjusts its internal parameters by traversing the training set multiple times (known as epochs) to enable it to recognize features of different types of faults. In our experiment, the model was trained for a total of 131 epochs, which means that the model fully traversed the training dataset 131 times. The entire model training process lasted about 15 h. This time is mainly spent on the model repeatedly learning a large amount of data to ensure that it can provide accurate detection in various fault situations and model’s pertinent parameters are given in table 2.
| Explanation | Best value |
| Learning rate | 0.005 |
| Loss function type | Binary cross-entropy loss |
| Optimizer scheme | Adam |
| Dropout probability | 0.1 |
| Epoch | 131 |
| Gradient threshold | 1 |
| Batch size | 150 |
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The model loss training curve with different epochs is shown in figure 16. The model accuracy is beyond 99.83%, which indicates that the accuracy of the model is good.
The confusion matrix is often used to measure the performance of classification model on test samples, as shown in the table 3. The confusion matrix of training of branch current signal interruption, total current signal interruption, overcurrent, transformer arcing, PMS closed mistakenly, unbalance of parallel thyristors, arm short, bridge short, firing shifting and overvoltage is shown in the figure 17.
| Classification | True class | ||
| Positive | Negative | ||
| Predicted class |
Positive | True positive (TP) | False positive (FP) |
| Negative | False negative (FN) | True negative (TN) | |
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The proposed fault diagnosis contains data sampling, date preprocessing, and LSTM feature extraction and classification. To verify the performance of the LSTM, the experiment platform is established under operation conditions, and is shown in figure 18. The test platform enters the line from 35 kV, drops to 197 V to the converter. The control and protection logic are completed by the control system, and the PMS is used to achieve first-level fault protection, with each dummy load of 5 mH. During the test, two dummy loads run in parallel, which is 2.5 mH. The main control board is based on the digital signal processor TMS320F28335. The fault diagnosis method of LSTM runs on the host computer of the system. The current sensor is to sample the input three-phase currents and the output current for convenience.
When the trained LSTM model is imported into the processor and using it for fault feature extraction, it is observed that the model efficiently detects the above-mentioned faults after processing 8 ms of signal data which are an encouraging result.
In the proposed algorithm, “1” represents the normal state signal flag and “0” represents the fault state signal flag. Under situations of current sensors failure, overcurrent, transformer arcing, PMS activated, the detections are performed as shown in figure 19, and test times are summarized in the table 4.
| Fault types | Fault time (s) | Delay time (ms) |
| Branch current signal interruption | 48.510 | 33.6 |
| Total current signal interruption | 31.750 | 7.2 |
| Overcurrent | 34.350 | 7.5 |
| Transformer arcing | 35.3930 | 2.0 |
| PMS mistakenly activated | 78.350 | 2.1 |
| Unbalance of parallel thyristors | 4.010 | 12.3 |
| Arm short | 4.010 | 15.5 |
| Bridge short | 4.000 | 10.8 |
| Firing drift | 3.800 | 5.4 |
| Overvoltage | 10.591 | 6.7 |
| Thyristor fuse drop | 9.200 | 5.5 |
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Figure 19 gives the waveforms of different fault current, the fault flag (0 & 1), and fault diagnosis delay time for four different fault times. The prediction of the neural network model is based on the sample in the training set, and model only focuses on predicting the two states of “normal” and “fault”.
Signal fluctuations caused by different types of faults vary. These signals are transmitted to the model through sensors, resulting in differences in the detection time of the model. For example, branch current signal interruption causes more significant signal changes, which may result in longer detection delays.
The characteristics and complexity of different types of faults vary, which may result in different times required for the model to process and confirm fault states. For some complex or inconspicuous faults, the model may require more time to accurately identify and confirm.
As demonstrated by formulas (3)–(6), four key metrics are used to evaluate the performance of a model: True Positives (TP), True Negatives (TN), False Positives (FP), and False Negatives (FN). True Positives (TP) are the instances where the model correctly predicts the positive class, meaning both the actual class and the predicted class are positive. True Negatives (TN) are the instances where the model correctly predicts the negative class, meaning both the actual class and the predicted class are negative. False Positives (FP) occur when the model incorrectly predicts the positive class, meaning the actual class is negative, but the prediction is positive. False Negatives (FN) occur when the model incorrectly predicts the negative class, meaning the actual class is positive, but the prediction is negative. These metrics form the foundation for calculating other important evaluation metrics such as Accuracy, Precision, Recall, and F1-score. One of the most prevalently utilized evaluation indicators is accuracy, which is defined as the ratio of correct classifications. However, a high accuracy rate does not signify that the classification algorithm is reliable when the sample distribution for each category is highly imbalanced. The precision can be defined as the proportion of predicted positive data that are actually positive. The recall represents the proportion of actual positive data that were expected to be positive. Recall and precision are incompatible metrics. The F1-score is the harmonic mean of the two indicators.
| Accuracy = TP + TNTP + FP + FN + TN | (3) |
| Precision = TPTP + FP | (4) |
| Recall=TPTP + FNμX | (5) |
| F1-score = 2Precision−1 + Recall−1 | (6) |
The accuracy, precision, recall, and F1-score value are shown in table 5, the lowest accuracy, recall, and F1-score are 0.9867 and 0.9752, 0.9832 respectively, indicating that the performance of the model is good.
| Fault type | Accuracy | Recall | F1-score |
| Branch current signal interruption | 0.9948 | 0.9956 | 0.9832 |
| Total current signal interruption | 0.9867 | 0.9752 | 0.9921 |
| Overcurrent | 0.9956 | 0.9956 | 0.9843 |
| Transformer arcing | 0.9941 | 0.9773 | 0.9871 |
| PMS mistakenly activated | 0.9987 | 0.9975 | 0.9974 |
| Unbalance of parallel thyristors | 0.9875 | 0.9875 | 0.9825 |
| Arm short | 0.9855 | 0.9958 | 0.9975 |
| Bridge short | 0.9962 | 0.9985 | 0.9991 |
| Mis-firing | 0.9978 | 0.9987 | 0.9991 |
| Overvoltage | 0.9997 | 0.9925 | 0.9858 |
| Thyristor fuse drop | 0.9889 | 0.9898 | 0.9968 |
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The receiver operating characteristic (ROC) curve depicts a false positive rate (FPR) on the X-axis and a true positive rate (TPR) on the Y-axis. The ROC curve can be produced by constantly adjusting the “threshold” of the classifier. The calculation formulas of FPR and TPR are respectively demonstrated by formulas (7) and (8).
The nearer the ROC curve is to the upper left corner of the graph, the higher the sensitivity of the test and the lower the false positive rate, the lower the false positive rate, the better the diagnostic effect. Figure 20 presents the ROC curve of the neural network model.
| FPR = FPFP + TN | (7) |
| TPR = TPTP + FN | (8) |
The research focuses on solving the fault detection and health monitoring of high-power thyristor converters in nuclear fusion. The neural network of LSTM is applied in the power supply to diagnose different faults and the health status preventing potential crisis. By analyzing diagnosis results, LSTM models can identify failure patterns. This approach allows for operations personnel can identify problems more quickly and make more timely maintenance decisions. In addition, ability of the model to adapt to new data ensures continuous improvement in fault diagnosis and health assessment capabilities, which are critical in the nuclear fusion.
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Figures(13) / Tables(3)
Supported by: Beijing Renhe Information Technology Co., Ltd. 
| Algorithm1 |
| Input: Sequence of input vectors xt and initial cell state C0, initial hidden state h0 Output: Sequence of input vectors ht 1: Initialization: set the initial cell state C0 and initial hidden state h0. 2: For each time step t from 1 to T: 3: Calculate ft, it and Ct , ot , ht based on equation (1) 4: Repeat step 3 for each time step t. 5: Output the sequence of hidden states ht End |
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| Explanation | Best value |
| Learning rate | 0.005 |
| Loss function type | Binary cross-entropy loss |
| Optimizer scheme | Adam |
| Dropout probability | 0.1 |
| Epoch | 131 |
| Gradient threshold | 1 |
| Batch size | 150 |
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| Classification | True class | ||
| Positive | Negative | ||
| Predicted class |
Positive | True positive (TP) | False positive (FP) |
| Negative | False negative (FN) | True negative (TN) | |
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| Fault types | Fault time (s) | Delay time (ms) |
| Branch current signal interruption | 48.510 | 33.6 |
| Total current signal interruption | 31.750 | 7.2 |
| Overcurrent | 34.350 | 7.5 |
| Transformer arcing | 35.3930 | 2.0 |
| PMS mistakenly activated | 78.350 | 2.1 |
| Unbalance of parallel thyristors | 4.010 | 12.3 |
| Arm short | 4.010 | 15.5 |
| Bridge short | 4.000 | 10.8 |
| Firing drift | 3.800 | 5.4 |
| Overvoltage | 10.591 | 6.7 |
| Thyristor fuse drop | 9.200 | 5.5 |
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| Fault type | Accuracy | Recall | F1-score |
| Branch current signal interruption | 0.9948 | 0.9956 | 0.9832 |
| Total current signal interruption | 0.9867 | 0.9752 | 0.9921 |
| Overcurrent | 0.9956 | 0.9956 | 0.9843 |
| Transformer arcing | 0.9941 | 0.9773 | 0.9871 |
| PMS mistakenly activated | 0.9987 | 0.9975 | 0.9974 |
| Unbalance of parallel thyristors | 0.9875 | 0.9875 | 0.9825 |
| Arm short | 0.9855 | 0.9958 | 0.9975 |
| Bridge short | 0.9962 | 0.9985 | 0.9991 |
| Mis-firing | 0.9978 | 0.9987 | 0.9991 |
| Overvoltage | 0.9997 | 0.9925 | 0.9858 |
| Thyristor fuse drop | 0.9889 | 0.9898 | 0.9968 |
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