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Abstract
Severe icing of transmission lines causes power failures, tower collapses, and other adverse events, which hinders the normal operation of society. Existing icing monitoring methods have problems of irregular monitoring and poor accuracy. In this study, we propose a comprehensive model for predicting hard rime and glaze ice using temperature, humidity, and historical icing data. The results of the experimental verification conducted for nine icing cycles in different years and geographic locations demonstrate that the proposed technique can effectively predict multiple types of icing while ensuring correlation coefficients > 0.99 and mean squared error < 4%.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Atmospheric icing poses a serious threat to the operation of overhead transmission lines. When the transmission line is covered with ice or wet snow, it increases the overall weight and internal stress of the wire, consequently increasing the vertical load on line conductors and their surface area, which is exposed to wind loads. This may lead to tower collapse [1]. Severe icing can cause not only serious damage, but may also loss of lives. The worst known severe impact was the 2008 snow disaster in China, where the affected population exceeded 100 million and caused a direct economic loss of more than RMB 150 billion.
A highly effective approach to address icing hazards is to realize real-time monitoring and prediction of ice thickness in key icing areas. In overhead transmission lines, information on the icing of lines can be obtained using several means depending on different observation methods, measuring instruments, and equipment [2,3]. However, the existing monitoring methods have numerous problems. For example, although manual line inspection has high precision, it incurs a high labor cost and requires considerable material resources. Moreover, it is difficult to reach remote mountainous areas under rainy and snowy conditions. Furthermore, electronic sensors have the following disadvantages: they are inherently subject to electromagnetic interference, have an unsustainable energy supply, etc. The 2008 snow disaster is a typical case that illustrates the limitations of relying on electronic ice thickness measurements. These deficiencies highlight the importance of reliable method for monitoring icing of transmission lines.
There exists an increasing need for long-term reliable micrometeorological data during icing cycles as it helps determine the conditions and characteristics of various icing patterns. We used a passive fiber Bragg grating (FBG) sensor as the principal measurement instrument to ensure stable and continuous data acquisition for icing of a tower. FBG sensors have proven their reliability in various fields owing to their advantages such as absolute measurement, high robustness, and high-voltage insulation performance [4–9]. In the field of power grid, FBGs are used in many fields including temperature and humidity monitoring of high-voltage switch cabinets in substations, meteorological monitoring of overhead lines, galloping monitoring and other fields. There are few researches on line icing monitoring based on FBG. The main method is to install the FBG tension sensor on the wire to measure the tension change of the wire when the line is icing and calculate the corresponding ice thickness. [9–11].
Icing is a result of the combined effects of various physical processes, among which, micrometeorology mainly affects the type and extent of icing. It includes air temperature, humidity, wind speed, wind direction, hydrometeor phase, morphology, mass flux, and size distribution, which are immediate environmental factors in which the transmission lines are located [12]. Some indirect factors are equally important. These mainly include the characteristics of the wire itself, such as size and torsional stiffness, and the line direction. These findings confirm the correlation between micrometeorology and icing on overhead transmission lines. Therefore, it is feasible to use meteorological conditions for icing prediction. Artificial neural networks (ANNs) are parallel-distributed computing networks capable of learning new associations, functional dependencies, and patterns [13]. Thus, ice thickness can be better monitored via ANN-based prediction rather than through observations and measurements alone. ANNs function as parallel distributed computing networks and can learn new associations, functional dependencies, and patterns [13]. Moreover, the number of ANN-based applications has significantly increased in recent years [14]. Originally introduced as a tool for computer vision and image processing [15,16], ANNs have expanded to several other fields, such as complex structure prediction [17], transmission and distribution [18,19], and optics [20]. In optical fiber sensing, ANNs have mainly been used for the advanced analysis of measurement data, such as pattern recognition and event classification in distributed acoustic sensing applications [21–23]. Despite their growing popularity, ANN are mostly used in smart grid, smart distribution nerwork, power system security, only a few studies have investigated ANNs for icing-detection applications [24–26]. Most of the existing methods for ice-cover detection using machine learning perform image recognition on pictures of ice-covered lines captured using a camera to calculate the ice-cover thickness. However, this method is limited by the sharpness of the shooting equipment and calculation algorithm. Because a camera cannot guarantee power supply and shooting clarity in rainy and snowy weather conditions, the actual application effect of machine learning is unsatisfactory.
This study presents icing forecasting techniques devised for use in power transmission lines and evaluates their performance. In this study, we aimed to examine the joint distribution of air temperature, humidity, historical icing data, wind speed, and wind direction to determine the spatiotemporal characteristics of line icing. We demonstrated that an ANN can effectively predict various types of icing using micrometeorological monitoring data. If the icing model is combined with meteorological data, large-scale icing prediction can be achieved. This will significantly reduce the cost of line patrols during winter and ensure normal operation of transmission lines.
The remainder of this paper is organized as follows. Section 2. introduces the FBG monitoring system and the neural network architecture. The ANN training and implementation methods are discussed in Section 3. The development and validation of the ANN-based prediction model is detailed in Section 4. Finally, the conclusions are drawn in Section 5.
2. System design and principles
In this experiment, we selected overhead transmission lines in various climates to ensure that the widest possible range of icing conditions can be collected efficiently. Fiber sensors for temperature, humidity, rainfall, illumination, wind speed, and wind direction were installed 20 m above the ground, and real-time micrometeorological data were stored in the substation server. The monitoring system is illustrated in Fig. 1. As shown, the FBG sensors are installed above the cross arm under the tower, and all sensors are welded in series in a splice closure. The division and multiplexing technology transmits all FBG information using one fiber core in the OPGW optical cable. The optical sensing interrogator in the substation emits broad-spectrum light in the C-band, which is injected into various sensors through an OPGW optical cable. Owing to the different FBG wavelengths of the various sensors, the light of the corresponding wavelength was reflected back to the optical sensing interrogator. The optical sensing interrogator demodulates the wavelengths reflected back from each FBG at a frequency of 1 kHz (a high sampling rate is beneficial for obtaining more accurate wavelength changes) and transfers wavelength information to the server database for storage. The server then calculates the corresponding micrometeorological data according to the mathematical models of various sensors.
Figure 1 shows a schematic of a neural network with one input layer, $k$ hidden layers, and one output layer. A neural network is a hierarchical structure comprising numerous neurons. The first layer, which directly accepts the original input data, is called the input layer, and its units are called input units. The number of input units is determined by the number of features and data types in the dataset. In this study, the input units are the temperature, humidity, wind speed, wind direction, rainfall, illumination, and historical icing data. For the hidden layer, an intelligent algorithm was used to determine the number of hidden layers from one to five. These layers operate as fully connected layers, meaning that any two nodes between adjacent layers are interconnected. For a given input, the network output is determined by the network connection method, weight value, and the excitation function.
3. ANN training
3.1 Datasets
In this experiment, to measure icing conditions under various conditions, the Jiangxi 220 kV Qinwu Line (low-altitude tuyere), Jiangxi 220 kV Miaolu Line (located on Lushan Mountain at approximately 1000 m), Hunan 220 kV Qianping Line (low-altitude hill), and Hubei 110 kV Songbo Line (high-altitude valley at approximately 2000 m) were selected. Fig. 2 illustrates nine complete icing cycle curves collected, including hard rime (Fig. 2(a) to (c)) and glaze ice (Fig. 2(d) to (i)). In this study, the icing data collected were the thickness of ice cover on the analog wire, which was considered as the true ice thickness. It is a reliable and easy-to-operate method for measuring equivalent ice thickness. The details of the nine datasets are listed in Appendix Table 3.
A typical icing cycle comprises three stages: accumulation, persistence, and melting (dropping off). Fig. 3(a) shows the evolution of a hard rime on the conductors of the 220 kV Miaolu transmission line in 2020/01, which corresponds to dataset (Fig. 3(b)). In this figure, the period between 1/10 and 1/12 is the accumulation stage. During this period, as the temperature decreased, the humidity increased and the effect of the wind load escalated the transmission line icing process. When the temperature was below 0 $^{\circ }$C and the humidity was above 90 RH$\%$, and the ice began to accumulate on the line. The period between 1/12 and 1/14 corresponds to icing persistence. During this period, as the temperature decreased and the humidity increased within a small range, and hence, the icing increased. Subsequently, icing decreased as the temperature increased and humidity decreased (the temperature remained lower than 0 $^{\circ }$C). The entire transmission line was covered with ice until the temperature rose above zero on 1/15, and the humidity fell below 90 RH$\%$. This was accompanied by a certain degree of wind, and finally, the ice fell off; which indicates the final shedding.
Fig. 3. (a) Various monitoring data under the same icing cycle. (b) FBG wavelength shift of sensors in the ice-coating cycle.
Figure 3(b) illustrates the working principle of the FBG sensor. Because the wavelength change of the FBG is only affected by the variation in temperature and stress, the change in the micrometeorological parameters to be measured can be converted into the variations in FBG wavelength. It can be clearly observed in Fig. 3(b) that the variation in wavelength corresponding to temperature and illumination is highly similar to that in the measured temperature and illumination. This is because the two types of sensors use a single change in the temperature and stress of the FBG. The illumination sensor uses double-grating temperature compensation to eliminate the influence of temperature variation. A clear correlation was observed between the change in illumination and temperature during this period (the rising and declining patterns were similar). The wavelength change of the humidity sensor is affected by both temperature and stress; hence, the trends of the wavelength change and the measured value are different. Thus, an algorithm to eliminate the interference of temperature change is required. Fig. 3(b) shows the wavelength change of the wind speed sensor in one day. The principle of the wind speed sensor is to use the number of revolutions of the wind cup per minute to calculate the wind speed. Moreover, a wavelength exceeding 0.055 nm jumps into an effective count once. Therefore, we used a 1 kHz optical sensing interrogator, which can record 1000 wavelengths per second for precise measurements.
3.2 Algorithm of ANN
Data preparation and the complete training process of ANN consist of the following parts:
Step 1. Identifying the input and output variables of ANN.
It is crucial to choose the appropriate input variables so that the ANN can produce an ideal output. Efficient selection of input variables is critical for successful neural network training. Absence of key input variables and the addition of redundant extraneous inputs results in reduced prediction accuracy of the model. Selectable input parameters included micrometeorological parameters (ambient temperature, humidity, wind speed, and wind direction) and historical data for ice thickness. Considering the needs of practical applications, the number of input parameters should be minimized while ensuring high accuracy, which not only helps improve the computing efficiency but also improves the possibility of applying the prediction system in engineering application at reduced cost. The need for fewer input parameters implies that fewer sensors can be installed to make predictions. In this study, various combinations of input variables were examined through theoretical analysis and practical tests. For example, illumination can be considered to be highly related to temperature; hence, removal of light intensity from the input parameters should have negligible effect on the prediction results.
Step 2. Dataset preprocessing.
First, the data of the dataset were normalized to ensure that the input variables were in the same range. The next step was to use cross-validation to divide the training and test datasets. All data were then batch-processed. The neural network first processed each batch and calculated the error. After all the batches were completed, the results of each batch were integrated. Then, the error of each layer was calculated, and the weight was adjusted according to the sum of the errors. The goal of training was to minimize the total error value.
Step 3. Optimizing the ANN parameters.
The prediction effect of a neural network is primarily determined by the activation function. We verified the different numbers of layers and nodes in dataset (a). The results are presented in Fig. 4. The number of layers has a significant impact on the prediction effect. To improve the prediction results, we used automatic optimization, which can traverse these variables as required to determine the best prediction model. the parameters selected in this study and their ranges are listed in Table 1. A maximum of 100 iterations were performed for a neural network consisting of one–five layers, and the number of neurons in each layer ranged from 1 to 500. A single activation function is used for each layer of each prediction model. It was either ReLU, tanh, sigmoid, or none. In the table, "Glorot" indicates that the weights are initialized using the Glorot initializer [27]. The Glorot initializer samples from a distribution with zero mean and variance $2/(I+O)$ for each layer independently, where $I$ and $O$ denote the input and output sizes, respectively. Similarly, "He" indicates that the weights are initialized with the He initializer [28]. For each layer, the He initializer samples from a normal distribution with zero mean and variance $2/I$. For the LayerBiases initializer, 0 and 1 are the initial bias values for each fully connected layer.
Table 1. Specifics of the functions used in this study.
Step 4. Identifying the parameter required for ANN convergence.
The mean squared error (MSE) between the predicted and true values is defined as:
where, ${\mathop {{y_i}}^ \wedge }$ and ${y_i}$ are the predicted and true values, respectively. The mean absolute percentage error (MAPE), which has the range of $[0,\infty )$, was calculated as follows:A well-trained network should have minimal MSE and MAPE values.
Step 5. Loss function minimization.
The role of the loss function is to evaluate the extent to which the model predictions differ from the actual values. The smaller the loss value, the better is the model. For the optimization, the objective function is log(1 + cross-validation loss). Because there is a single, deterministic variable ${\rm {f}}(x)$, the training model is a full-batch, deterministic model. Limited-memory Broyden–Fletcher–Goldfarb–Shanno quasi-Newton (LBFGS) algorithm is a common optimization algorithm with the advantages of fast convergence and low memory overhead. We chose this as the loss function minimization technique for the model Because these methods are advantageous for solving problems involving big data. In this case, the Hessian matrix calculation consumes a significant amount of computing power and cannot be calculated. Unlike storing fully dense $n*n$ approximations, these methods maintain simple and compact approximations of the Hessian matrices. They save only a few vectors of length $n$ which represents the simplicity of the approximation [29].
Step 6. Validating the trained and tested ANN models
Prediction models are used on new datasets (on which ANNs have not been trained) to effectively measure the accuracy and robustness of the actual model predictions. Only by passing the verification test can the model be considered as universally applicable. In this study, ten percent of a certain dataset was used as the training set, the remaining part was used as the validation set, and the remaining eight datasets (different years or regions) were used as the test set to ensure the reliability of the experimental results.
4. Experimental results
This section discusses the optimal input parameters for the comprehensive model. The model was trained using different datasets and parameter sets, and the MSE, MAPE, and correlation coefficients were used to verify its accuracy.
4.1 Determining the best input parameters
Meteorological conditions are known to be the main factor in the formation of icing. However, to predict transmission-line icing more accurately and efficiently, it is necessary to analyze the input parameters because they directly determine the prediction accuracy. In our input, there are some direct factors (such as temperature and humidity) that cause icing on transmission lines, and some indirect factors (such as illumination and rainfall). Hence, we first considered removing rainfall and illumination at the input end for the prediction. It was observed that there was no significant difference in the prediction results, which proved that rainfall and illumination could be replaced by temperature and humidity. Different icing types originate from diverse climatic and geographical environments, and differences in these conditions directly affect changes in micrometeorological parameters. This causes the results of one type of predictive model to disagree with those of the other. This is exactly the problem encountered by the author of a previous study [30]. Figure 5 clearly illustrates the difficulty in predicting results caused by different icing types. Models for one type of icing struggle to correctly predict another type of icing.
To determine a comprehensive model that can predict accurately in multiple icing conditions including glaze ice and hard rime, it is necessary to introduce a parameter that is related to icing but not sensitive to the environment. Generally, one may consider the icing time; however, this parameter changes with the icing situation of the line and is not universal. Therefore, we chose historical icing data as the new input parameter. The historical ice thickness is directly related to the current ice thickness, and the correlation of the ice thickness with the time dimension compensates for the differences caused by the wide spatial distribution. In this study, we chose the historical icing times from 1 min to 1 h as follows: 1 min, 2min, 3 min, 5 min, 7 min, 10 min, 13 min, 30 min, and 1 h. The historical icing data refers to the icing value before the current moment in an icing cycle, as shown in Fig. 6, if the current time t is 01:30, and the icing value is w1, all icing value at the previous moment is the historical icing data, and the 13minute historical icing data is the icing value thirteen minute before the current moment. 1h historical icing data is the icing value one hour before the current moment.
After training the model on each of these nine datasets, we found that dataset (e) was the most sensitive to the input of historical time (possibly because it had the largest time span). Accordingly, Fig. 7 shows the prediction results for various historical times as input parameters in dataset (e); the other inputs were temperature, humidity, and wind speed and direction. After determining the best single icing input parameter (1 min, 3 min, and 10 min all showed good performance, among which the best was 1min), we simultaneously used multiple historical icing times with good effects as additional inputs for testing, and the results showed that the prediction effect of multiple historical data was not as good as that of single historical data. This may be because multiple historical data provide the prediction function with more feature information of the training data; therefore, it is not conducive for use in icing prediction in different environments.
4.2 Determining the best input parameters
A power transmission line can form different types of icing during different periods. In the absence of an effective classification, using a single prediction model affects prediction accuracy. Therefore, a model that can comprehensively predict multiple icing conditions would significantly improve the prediction accuracy, which would improve the prediction and safety of transmission lines. Considering that historical data are the parameter that is least sensitive to space and closely related to icing, this will greatly improve the prediction accuracy of the comprehensive model. Moreover, to broaden the application scenarios of the prediction model and meet the purpose of wide-area icing prediction, wind speed and wind direction values with greater regional differences, were excluded. Finally, we considered a comprehensive prediction model that uses only the temperature, humidity, and historical event data. After using any of the nine datasets and their combinations as the training set, with all all the remaining data as the test set, we obtained an optimal predictive model using dataset (b), which was derived from the training set. In order to measure the generalization and transferability, we evaluate gaussian process regression (GPR), support vector machine (SVM) and random forest (RF) regression models with the same input and training set. The parameter range of the GPR model is the same as the previous article. The parameters of these models also used the optimization algorithm to obtain the best results. The final determined optimal value of $\sigma$ was 0.13852 and the value of $\log (1 + loss)$ was 0.02499 in GPR model. The specific parameter ranges of SVM and RF are shown in Appendix Table 4, the best model parameters are shown in Appendix Table 5. The final comprehensive prediction model parameters and results of ANN are shown in Fig. 10. This model uses a sigmoid activation function with a network of [1 35 79 116].
Figure 8 shows the performance of other mainstream models used to predict hard rime and glaze ice on nine datasets. It can be seen that these three models have good effects on the dataset (b) where the train set is located and the dataset (a) which the icing period before dataset (b), but the generalization ability on other datasets is obviously insufficient, among them the SVM effect is the worst. It did not perform well on long-period icing data such as the datasets (d)-(g), while the performance of the GPR and RF model on these datasets is acceptable, and can predict the trend of the icing cycle more accurately. The performance of the RF was the best, but it still lacking in accuracy. The comparison of the effect of the GPR model with our previous article can prove that the introduction of historical icing data can help enhance the generalization ability of the model and improve the accuracy of the model.
In Fig. 9, the similarity in MSE values of the training and validation sets and the observation that test error obeys a normal distribution with 0 mean confirms the suitability of the proposed model. Figure 10 shows the performance of ANN model used to predict hard rime and glaze ice on nine datasets. Our ANN model outperforms the others for predicting. The icing prediction curve (blue) reflects the features of the icing episode; the forecast perfectly matches the observations on dataset (b) for training and also with the observations on eight other field data points in the case of both hard rime and glaze ice. It can be seen that the model has the best results in the dataset (a) (b), because the training set is part of the dataset (b), which is expected to have the best performance, and the dataset (a) is the same tower in the previous icing cycle, it is expected that the model performed well on this, and the prediction error in dataset (c) is mainly due to the fact that the tower is located in the tuyere, and it will be more affected by the wind, while the wind has been removed from the input features in the model, dataset (h) is also located in a tuyere similarly. The good performance in the dataset Fig. 10(d), (e), and (f) demonstrates the important role of historical icing data, and the temporal correlation information makes up for the negative effects of spatial differences.
It can be seen from the prediction results of the model on datasets (d) and (e) that the initial predicted values are both 0, which are quite different from the actual values, but the results subsequently improve. Because datasets (d) and (e) are the only ones in which the ice thickness is not an icing cycle that increases from 0 mm, these two datasets were selected to test whether the prediction model will perform well if the prediction starts in the icing growth period. Second, owing to the introduction of 1 min of historical data, for the dataset starting from the icing period, the historical data in the input of the initial predicted value are 0 mm, which also reduces the accuracy of the initial predicted value. However, as the prediction accumulates, the predicted results gradually approach the true values. In addition, in practical applications, the icing time interval that the disaster prevention department is concerned about is 10–30 min. Therefore, the result corresponding to the initial predicted value of only 1 min will not result in incorrect guidance for practical applications. Table 2 reports the MSE, MAPE, and R in nine datasets. These parameters can be used to effectively evaluate the validity and accuracy of the model.
Table 2. Predictive evaluation index for different datasets.
5. Conclusion
The experimental results from the models indicate good potential for the quantitative detection of icing using current ANN models with meteorological parameterizations. The model was tested in nine groups of six different locations in four provinces. The model performed satisfactorily under glaze ice and hard rime conditions, and the accuracy of handling complex icing conditions was significantly improved compared to trained models include GPR, SVM and RF. Finally, this study proposes a new prediction model that can predict a variety of icing events using only temperature and humidity values and 1 min of historical icing data. Tests were performed on historical icing data with satisfactory results within R $>0.99$ and MSE $<4\%$. It is believed that the model combined with weather forecasts can provide strong support for the qualitative analysis of large-scale transmission line icing.
Appendix
Data were obtained from FBG sensors installed in the transmission lines of Jiangxi, Hunan, and Hubei provinces. The specifics are provided in Table 3. The specifics of functions and best model parameter on SVM and Random Forest are provided in Table 4,5, respectively.
Table 3. Specific information of the datasets.
Table 4. Specific information of the SVM and Random Forest functions.
Table 5. The best model parameters of SVM and Random Forest
Funding
National Natural Science Foundation of China (62075017).
Acknowledgments
The authors thank the Jiangxi Power Supply Company for their practical test support.
Disclosures
The authors declare that they have no conflicts of interest.
Data availability
The data underlying the results presented in this paper are not publicly available currently but may be obtained from the authors upon reasonable request.
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