- Email: [email protected]
Predicting lightning outages of transmission lines using generalized regression neural network
Applied Soft Computing Journal 78 (2019) 438–446
Contents lists available at ScienceDirect
Applied Soft Computing Journal journal homepage: www.elsevier.com/locate/asoc
Predicting lightning outages of transmission lines using generalized regression neural network ∗
Yunyun Xie a , Chaojie Li b , , Youjie Lv c , Chen Yu d a
School of Automation, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu Province, China School of Engineering, Royal Melbourne Institute of Technology University, Melbourne, VIC, Australia c State Grid Wuxi Power Supply Company, Wuxi 214062, China d State Grid Electric Power Research Institute/ NARI Group Corporation, Nanjing 211106, China b
article
info
Article history: Received 12 February 2018 Received in revised form 30 July 2018 Accepted 8 September 2018 Available online 1 February 2019 Keywords: Transmission line Lightning outage Outage prediction Generalized regression neural network
a b s t r a c t Lightning is the major cause of transmission line outages, which can result in large area blackouts of power systems. One effective method to prevent catastrophic consequences is to predict lightning outages before they occur. The abundance of recorded lightning and lightning outage data in power system makes it possible to predict lightning outages of transmission lines. This paper proposes an artificially intelligent algorithm using general regression neural networks (GRNN) to predict lightning outages of transmission lines. First, the data that can be obtained from the operation and management system of a power company are analyzed, and the features that can be used as input parameters of GRNN are extracted. The prediction model based on GRNN is then built to perform lightning outage prediction. Finally, the effectiveness of the proposed method is validated by comparing it with (Back Propagation) BP and (Radial Basis Function) RBF neural networks using actual lightning data and lightning outage data. The simulation results show that the proposed method provides much better prediction performance. © 2019 Elsevier B.V. All rights reserved.
1. Introduction Lightning is the major cause of transmission line outages. More than 45% of transmission line outages are caused by lightning according to the statistics of one provincial power grid from 2005 to 2014 in China [1]. A lightning outage can impact the reliability of power supply and can result in catastrophic blackout consequences, such as the Brazil blackout in 2009 that was caused by lightning [2]. To enhance the reliability of power supplies and prevent catastrophic consequences, some efforts have been undertaken to improve the lightning protection design of transmission lines [3,4]. However, the improvement of lightning protection design cannot completely prevent lightning outages. It is necessary to predict lightning outages to adjust the operation mode beforehand, consequently reducing the loss of lightning outages. One cause of transmission line outages is lightning flashover of overhead lines resulting from conductor overvoltage due to lightning directly striking the conductor or transmission tower. To predict lightning outages, some efforts have been undertaken to predict lightning areas. Lightning is mainly predicted based on Doppler weather radar data and ground-based atmospheric electric field meter data. Because the electrification process within ∗ Corresponding author. E-mail addresses: [email protected] (Y. Xie), [email protected] (C. Li), [email protected] (Y. Lv), [email protected] (C. Yu). https://doi.org/10.1016/j.asoc.2018.09.042 1568-4946/© 2019 Elsevier B.V. All rights reserved.
a growing thunderstorm returns large reflectivity echoes, the reflectivity data of Doppler weather radar can be used to identify a growing thunderstorm [5]. The characteristics of radar reflectivity echoes related to lightning have been researched in many studies to predict thunderstorm areas [5–7]. Because the electrical field in a thunderstorm will change before lightning strikes, the electrical field data of a ground-based atmospheric electric field meter can also be employed to predict lightning according to the change of the electric field [8,9]. Though both Doppler weather radar and ground-based atmospheric electric field meters can identify the lightning area, they have some drawbacks in predicting lightning. The thunderstorm area given by Doppler weather radar is a large area greater than one hundred kilometers, which makes it challenging to predict the lightning around transmission lines. A single atmospheric electric field can cover areas within only 10–20 km. To protect long-distance transmission lines, it is necessary to build up an atmospheric electric field network, which increases the cost of operation and the difficulty of lightning identification. Furthermore, in addition to the lightning area, the location of lightning and number of lightning strikes are important parameters for lightning outage prediction that cannot be obtained from Doppler weather radar data or ground-based atmospheric electric field meter data. To enhance operational efficiency, lightning location systems (LLS) have been installed to monitor lightning activities by electric power companies across the world, including companies in the U.S., the U.K., and China [10]. An LLS can observe the parameters of
Y. Xie, C. Li, Y. Lv et al. / Applied Soft Computing Journal 78 (2019) 438–446
lightning such as lightning location and peak current. The collected lightning data are usually applied to estimate the ground-flash density, assess the line performance, classify the faults, etc. [11]. In [12], a lightning outage prediction method based on LLS data is proposed based on real-time measured lightning information. The real-time measured lightning is divided into many time steps. Areas with lightning in each time step are then collected to identify the lightning area. The multi-step lightning areas are adopted to extrapolate the lightning area in the next time step. The predicted lightning area and the amount of lightning in the past time step are employed to calculate the lightning outage rate in the next time step. This method uses the real-time data only to predict the lightning outage rate of transmission lines; it cannot clearly predict whether a lightning outage will occur. Plenty of lightning and lightning outage data have been accumulated by the LLS and in the operation of power systems. More than 3 million lightning strikes per year are observed by the European LLS [13], and hundreds of lightning outages are collected by a province level grid [14]. However, this large amount of historical lightning and lightning outage data has not been utilized for predicting lightning outages. With the development of data mining, (Artificial Intelligent) AI-based methods can describe the relation between input and output data from historical data via non-statistical approaches such as support vector machines and artificial neural networks, which have demonstrated good performance in power system operations such as wind power forecasting [15,16], health evaluation of power transformers [17], and short-term power load forecasting [18], prediction of power load profile [19]. Because of the large amount of lightning from LLS and the lightning outage data in the power system, data mining methods are very suitable to find relationships between recorded lightning and lightning outages. Lightning outage prediction of transmission lines is a classification problem that is suitable for artificial neural networks. Therefore, this paper focuses on identifying the relationship between the lightning outages of transmission lines and the recorded lightning of LLS by an artificial neural network that can predict lightning outages with real-time lightning data. To satisfy this demand, a reliable, precise, and fast method is required. The general regression neural network (GRNN) developed by Specht [20] is a type of radial basis function neural network that has good nonlinear approximation ability, excellent anti-interference performance, fast convergence speed and autonomous learning [21]. Most required parameters of GRNN can be derived from the input data. Moreover, GRNN can control the complexity of its interpolation based on the information conveyed by the training samples, and it has a simple algorithm to implement and fast calculation speed [17]. Due to the above advantages, GRNN has been widely applied in short-term power load forecasting [21], wind power prediction [22], and transient stability evaluation of power systems [23]. Because the relationship between the lightning outages of transmission lines and the recorded lightning of LLS is strongly nonlinear, the prediction of lightning outage requires the method to have good nonlinear approximation ability, fast convergence speed which is the characteristic of GRNN. Therefore, GRNN is suitable for the prediction of lightning outage. In this work, we investigate the idea of predicting lightning outages of transmission lines using GRNN. This method utilizes the historical lightning data of LLS and historical lightning outage data in power systems to build the GRNN model, which can identify the relation between lightning and lightning outages of transmission lines. Furthermore, the GRNN model can be employed to predict lightning outages according to real-time lightning data. The innovations of this paper are the following: (1) GRNN is employed to predict lightning outages and, to the best of our knowledge, is the first lightning outage prediction method based on artificial
439
neural networks; (2) some features that can reflect the probability of lightning strikes of transmission lines are constructed based on the lightning data and transmission tower data. This paper is organized as follows: Section 2 analyzes the necessary data for predicting lightning outages and constructs the input parameters of GRNN. Section 3 describes the GRNN method and its application to predict lightning outages of transmission lines. Section 4 demonstrates the simulation results and comparisons with BP and RBF neural network methods. Finally, the conclusion is presented in Section 5. 2. The input feature for lightning outage prediction In this section, the mechanism of lightning outages is first reviewed to analyze the necessary data for predicting lightning outages. The data directly collected by the LLS and the operation system of the power system are then introduced. Furthermore, the parameters that can be employed as the input feature of GRNN are constructed based on the lightning data and transmission tower data. 2.1. Security indices and reliability Lightning outages of transmission lines can be caused by the lightning strikes on a transmission tower (back flashover) or lightning passing an overhead ground line to strike a transmission line (shielding failure). When lightning strikes a transmission tower, the insulator between the transmission conductor and transmission tower can endure a certain range of overvoltage, which is called the lightning resistance level and can be expressed as [24]
I1 =
U50%
(1 − k) β Rch +
(
ha hgt
) ( L − k β 2gt.6 + 1 −
hb k hd 0
)
hd 2 .6
(1)
where U50% is the 50% flashover voltage of insulator strings; k is the coupling coefficient between the overhead ground line and transmission line; k0 is the coupling coefficient between the line and the ground; ha , ht , hav and hg v are the height of the crossarm, the height of the tower, the height of the line and the height of the ground line, respectively; β is the shunt coefficient; and Rsu and L1 are the earth resistance and equivalent inductance of the tower, respectively. If the lightning current is greater than the lightning resistance level, the insulation of the insulator strings may be broken down. The probability can be calculated by the probability of the lightning current: P1 (I0 > I1 ) = 10−I1 /88
(2)
where I0 is the lightning current amplitude. When lightning strikes a transmission line, the lightning resistance level of the transmission line can be expressed as I2 =
4U50% z
≈
U50% 100
(3)
where z is the wave impedance of conductor. The approximately value of wave impedance is 400 in simplified calculation. The shielding failure probability can be expressed as P2 (I0 > I2 ) = 10−I2 /88
(4)
When lightning strikes a transmission line, it may strike either the conductor or the tower. When the lightning current is greater than the lightning resistance level, the insulator may break down. Therefore, the probability of lightning outage can be expressed as P = η (gP1 + Pa P2 )
(5)
440
Y. Xie, C. Li, Y. Lv et al. / Applied Soft Computing Journal 78 (2019) 438–446
Table 1 Information collected by LLS and power system operation and management system. Information source
Information type
Data type
LLS
Lightning
PMIS EMS
Transmission tower Lightning outage of transmission line
Longitude, latitude, peak lightning current Longitude, latitude, voltage level Name of outage transmission line, time of outage, location of lightning outage
where η is the probability to produce an electric arc; g is the probability to strike the transmission tower; and Pa is the probability to bypass the overhead ground line. The parameters in (1)–(5) will be different for different types of transmission lines, terrains and regions. For example, the value of Pa in flat regions is less than that in hilly regions. The above lightning outage model can quantitatively assess the probability of transmission line outage when lightning strikes the transmission line. However, the lightning prediction always predicts the lightning area, which cannot tell us whether there will be a lightning strike on the transmission lines. This is why the lightning prediction method cannot be used in lightning outage prediction. From the above lightning outage model, we can summarize that the main impact factors of lightning outages are the peak lightning current and the probability of lightning strikes on transmission lines. Because the insulator parameters of transmission lines in one voltage level are similar, the transmission line parameters are neglected in this paper. 2.2. The information collected by LLS and power system operation Most existing LLSs, such as EUCILD [13], GDLLS [14], are based on the magnetic direction method and the time-of-arrival method to locate lightning discharges. There are three major parts of LLS: combined magnetic direction and time-of-arrival finders (DTFs), naval process apparatus, and lightning location information analysis and display system. The main parts of DTF are the orthogonal loop magnetic field antenna, electric-field antenna, global positioning system (GPS) receiving antenna, GPS pulse-timing board, and CPU board. The DTFs can distinguish lightning based on the preset waveform discrimination criteria. Once a lightning strike is detected by a DTF, the lightning data are transmitted to the control center. The naval process apparatus in the control center records the lightning data and combines the data from multiple DTFs to provide the location, time, and peak current of the lightning in real time. Finally, the lightning information is stored in a permanent database and displayed in the control center. Therefore, the information that LLS can provide is the location, time, and peak current of lightning. For the operation of the power system, the location of the transmission tower is stored in the Project Management Information System (PMIS) of power companies for daily maintenance and service. In the operation of the power system, the outages of transmission lines due to different causes are labeled and recorded in the Energy Management System (EMS) for repair and analysis. The information that can be directly collected from LLS and the power system operation and management system is illustrated in Table 1. The information collected by LLS and power system operation is historical data, which cannot directly predict lightning. However, the historical lightning data can reflect the lightning intensity in a given area, which is highly correlated to lightning outages.
2.3. The features of lightning outage prediction From the analysis in Section 2.1, the main impact factors of lightning outages are peak lightning current and the probability of lightning striking transmission lines. The first factor can be directly obtained from the lightning information collected by LLS, but the second factor cannot be collected directly. Therefore, it is necessary to construct some parameters that can reflect the probability that lightning will strike transmission lines. According to our experience, the more abundant the lightning around a transmission line and the closer the lightning to the transmission line, the greater the probability that lightning will strike the transmission lines. Based on the location information of lightning and the transmission tower, the distance between the lightning and the transmission line is easy to calculate. The number of lightning strikes around the transmission line can then be counted for a given distance away from the transmission line. The given distance is defined as the lightning corridor in this paper. In summary, the parameters that can be used for lightning outage prediction in this paper are the number of lightning strikes in the lightning corridor, the nearest distance between the line and the lightning, the average lightning current intensity in the lightning corridor, and the peak current of the nearest lightning strike. 3. GRNN-based lightning outage prediction method In this section, a lightning outage prediction model is established based on GRNN, and the prediction method employing the prediction model is presented. 3.1. General regression GRNN is a network that can be employed to estimate a dependent variable from an independent variable through a finite dataset. The theoretical foundation of GRNN is kernel regression, which is non-linear regression analysis. The function f (x, y) is defined as the joint probability density function (PDF) of two random variables x and y. x is a vector random variable representing the input, and y is a scalar random variable representing the output. When f (x, y) is known, the condition mean of y on a given x0 can be calculated by ∧
∫∞ −∞
y(x0 ) = E(y|x0 ) = ∫ ∞
yf (x0 , y)dy
−∞
f (x0 , y)dy
(6)
This means that we can predict the value of y according to the input x0 when f (x, y) is known. However, f (x, y) is usually unknown in many systems, such as the joint PDF of lightning parameters and the lightning outage of transmission lines. Therefore, it is necessary to estimate f (x, y) for the output parameter calculation. GRNN uses a group of measured x and y values to estimate f (x, y) based on the consistent estimators proposed by Parzen [20]. For a given measured sample data point {xi , yi |i = 1, 2, . . ., N }, the estimated PDF can be expressed as
⎧ n ∑ ∧ ⎪ 1 ⎪ ⎪f (x, y) = eD(xi ) · eD(yi ) ⎪ (p+1)/2 σ (p+1) ⎪ n(2 π ) ⎪ ⎨ i=1 (x − xi )2 D(xi ) = − ⎪ ⎪ ⎪ 2σ 2 ⎪ 2 ⎪ ⎪ ⎩D(yi ) = − (y − yi ) 2 2σ
(7)
where n is the number of measured samples, p is the dimension of vector random variable x, and σ is the smooth parameter of the Gauss function (also called the spread factor).
Y. Xie, C. Li, Y. Lv et al. / Applied Soft Computing Journal 78 (2019) 438–446
441
basis function and affects the network output. If σ is too large, the predicted value y0 will be close to the mean output of all training samples. If σ is too small, y0 will be close to the output of the training sample, which has the minimal Euclidean distance from x0 . Therefore, it is necessary to select the value of the smooth parameter. Because the absolute value of the smallest mean absolute error (MAE) in (11) is greater than the other indexes [18], such as the mean absolute percentage error (MAPE) and mean-square error (MSE), it is employed to evaluate the effectiveness of the smooth parameter in this paper. MAE = Fig. 1. Structure of GRNN.
∑n
y(x0 ) = ∑i=n1
yi eD(xi )
i=1
eD(xi )
(8)
The estimated condition mean can be visualized as a weighted average of all observed values yi , where each observed value is weighted exponentially according to its Euclidean distance from x0 . 3.2. GRNN model GRNN consists of four layers: the input layer, the pattern layer (also called the latent regression layer), the summation layer and the output layer, as shown in Fig. 1. Each layer has a specific computational function for performing non-linear regression. The function of the input layer is to receive information. There are p neurons in the input layer, which correspond to the p dimension input characteristics of the samples. We assume that one input sample is x0 = [x01 , x02 , . . . , x0p ]T . The input neurons then transmit the data to the second layer. Every neuron in the pattern layer is a cluster center, which calculates the exponential form of the Euclidean distance between the prediction sample x0 and training sample xi ; the output of neuron i is eD(xi ) . The number of neurons in the pattern layer is equal to the number of training samples. The training sample that is closer to x0 is given a greater weight when predicting the output. The neurons of the third layer (summation layer) receive the outputs of the pattern neurons. This layer includes two units. The second unit calculates the sum of the output. The summation layer has two neurons (SD and SN ) to sum the output of the pattern layer with different weights shown in (9)– (10). The weight of the first neuron SD is 1, and the weight of the second neuron SN is the output yi of the corresponding training sample. SD =
n ∑
eD(xi )
(9)
i=1 n
SN =
∑
yi eD(xi )
(11)
i=1
By substituting the estimated PDF in (7) into the condition mean in (6) and interchanging the order of integration and summation, the desired condition mean of y for a given x0 can be yielded: ∧
n ∑ ⏐ ⏐ ⏐yˆ (xi ) − y(xi )⏐ /N
(10)
i=1
The two outputs of the summation layer are divided by the output layer to obtain the final output. 3.3. Smooth parameter selection In formula (7), σ is the smooth parameter of the radial basis function, which has great influence on the shape of the radial
The procedure to select the smooth parameter is shown as follows. Step (1) Select a value in increments of 0.001 from the range [0, 0.1] as the candidate smooth parameter. Step (2) Initialize MAE0 with large values (e.g., 100). Step (3) Train GRNN with the training samples and the candidate smooth parameter σi , and compute MAEi . Step (4) If MAEi < MAE0 , store the value of the smooth parameter. Step (5) Repeat Steps (3)–(4) until all values of the smooth parameter are tested. Step (6) If the smallest smooth parameter is obtained in the upper bound, the actual smallest MAE has not been found. Add 0.1 to the candidate range of the smooth parameter, and repeat (3)–(5). Step (7) The last stored smooth parameter is the selected smooth parameter for the prediction of the test dataset. 3.4. Lightning outage prediction based on GRNN After the lightning data and the information on the transmission tower and historical lightning outages are obtained from the operation and management system, the lightning outage prediction can be implemented by the method introduced above. Before the application of GRNN, some preparation works are necessary. The detailed procedure to predict lightning outages is shown as follows. Step (1) Divide the lightning data into groups according to time. From the time of first lightning strike, the lightning strikes in every 15 min period are collected into a group. Step (2) Construct the sample set. According to the analysis in Section 1, the input parameters of the sample are the number of lightning strikes in lightning corridor, the nearest distance between the line and the lightning, the average lightning current intensity in the lightning corridor, and the peak current of the nearest lightning strike. The input parameters in every sample are calculated by the lightning data in every group and the location of the transmission tower. The output data represent the occurrence of lightning outages in the next time period (if an outage occurs, yi = 1, or yi = 0). Step (3) Select the training samples and test samples. Because the number of lightning outage cases is much less than the number of normal operation cases, the normal operation cases are randomly selected as the normal operation sample to form the balanced normal and outage samples. The lightning outage cases are all selected as outage samples. Eighty percent of the total sample is selected as the training samples, and the others are the test samples. Step (4) Optimize the smooth parameter. According to the method introduced in Section 3.3, the optimal smooth parameter is selected, and at the same time, GRNN is trained. Step (5) Employ the trained GRNN to predict lightning outages in the test samples. After obtaining the prediction sample output
442
Y. Xie, C. Li, Y. Lv et al. / Applied Soft Computing Journal 78 (2019) 438–446
Table 2 Statistics of lightning trip information. Line
X1
X2 (km)
X3 (kA)
X4 (kA)
JJ SJ DB BJ WH YH YM FY GL WY
18 1 25 17 65 25 3 6 18 45
0.1017 0.6254 0.0588 0.1301 0.0549 0.1244 0.4929 0.0436 0.091 0.0064
75.42 40.20 46.96 51.22 44.04 49.90 145.26 53.30 30.13 39.53
80.0 40.2 44.5 52.0 40.8 50.4 76.9 30.2 28.1 37.3
y0 , this paper takes 0.5 as a threshold to classify the sample. If y0 is greater than 0.5, the sample is classified as a lightning outage sample. Step (6) Verify the effectiveness of test samples. Compare the prediction status of the transmission line with the recorded data to confirm the accuracy of prediction.
Fig. 2. MAE of different candidate smooth parameters.
4. Experiments and results In this section, the GRNN lightning outage prediction method is verified by actual lightning data, transmission data and lightning outage data. The result of GRNN is compared with the results of the BP network and RBF network. 4.1. Dataset
Fig. 3. Prediction error of training samples by GRNN.
The data in this paper are from the LLS and operation and management system of a power system in an eastern province of China. There are 150 recorded lightning outages. In this paper, 120 fault samples and 120 normal samples are used as training samples. The remaining 30 fault samples and 30 normal samples are employed as the test samples. According to the above analysis, the input parameters of GRNN in this article are the number of lightning strikes within 1.5 km of lightning corridor x1 , the nearest distance between the line and lightning x2 , the average lightning current intensity within the 1.5 km lightning corridor x3 , and the peak current of the nearest lightning strike x4 . The input parameters of partial lightning outage samples are shown in Table 2. 4.2. Performance evaluation index
Table 3 The statistics of training samples by GRNN. Outage sample Normal sample
Classified as outage
Classified as normal
120 7
0 113
4.3. Value of smooth parameter According to the method of smooth parameter selection, the candidate smooth parameter values are the increments of 0.001 in the range [0, 0.1]. The training samples are employed to train GRNN with different candidate smooth parameters. MAE of the candidate smooth parameters is shown in Fig. 2. When the smooth parameter is 0.05, MAE is minimized. Therefore, the smooth parameter in the next prediction is 0.05. 4.4. Prediction results of GRNN
The fault detection rate (FDR), false alarm rate (FAR), and total prediction accuracy (PA), which are the common indexes to evaluate the prediction performance, are employed to evaluate the performance of the prediction methods in this paper. FDR =
FAR = PA =
FN FP + FN
× 100%
TN × 100% TP + TN FN + TP
FP + FN + TP + TN
(12)
(13)
× 100%
(14)
where FP and FN are the numbers of outage samples classified as normal and outage, respectively. TP and TN are the numbers of normal samples classified as normal and outage, respectively.
In the training samples, there are 120 lightning outage samples (output y = 1) and 120 normal samples (y = 0). The errors of prediction output and actual output for the training samples are shown in Fig. 3. In Fig. 3, the red line represents a prediction error of 0.5. Because the threshold to classify the occurrence of lightning outage is 0.5, the prediction will be inaccurate when the prediction error is greater than 0.5. The number of inaccurate samples for training samples is illustrated in Table 3. The performance evaluation indexes of training samples are shown in Table 4. FDR is 100.00%, which means that all lightning outage cases are detected. FAR is 5.83%, which means that 5.83% of the normal cases are false positives. PA is 97.08%, which means that 97.08% of all cases are correctly predicted. The results show that GRNN has good training effectiveness.
Y. Xie, C. Li, Y. Lv et al. / Applied Soft Computing Journal 78 (2019) 438–446 Table 4 The performance evaluation indexes of training and test samples by GRNN. Training sample Test sample
FDR
FAR
PA
100.00% 76.70%
5.83% 11.30%
97.08% 81.70%
Fig. 4. Prediction errors of test samples by GRNN.
In the test samples, there are 30 lightning outage samples and 30 normal samples. The prediction error of the test samples is shown in Fig. 4. The performance evaluation indexes of test samples are also shown in Table 4. Fig. 4 and Table 4 show that the FDR of the test samples is 76.70%, FAR is 11.30%, and PA is 81.70%, which are all worse than the training samples. From the input parameters, the reason why lightning outages are not predicted successfully is that there are very few lightning strikes around the line. Similarly, the reason why the normal cases are predicted inaccurately is that there are many lightning strikes around the line. 4.5. Comparison with other methods To verify the effectiveness of GRNN, the most popular BP neural network is employed for comparison with GRNN. Because GRNN is derived from RBF, it is also employed for comparison with GRNN. The BP neural network in this paper has a single hidden layer. There are 5 neurons in the input layer: a neuron designed to introduce the threshold of the hidden layer and the four neurons corresponding to the same input features as GRNN. The results of the BP neural network with different numbers of neurons in the hidden layer are provided in Table 5. When the number of neurons is 8, the training and test results are best with the minimal number of neurons. Consequently, 8 neurons are selected in the hidden layer, including a neuron designed to provide the threshold of the output layer. The output layer is a single neuron related to lightning outage. The sigmoid function is used as an activation function in both the hidden and output layers. The network is trained by the standard backpropagation algorithm, and the training samples are selected randomly to generate the connection weights between the output layer and the hidden layer. The input layer of the RBF neural network has 4 neurons related to the same four features as GRNN. The results of the RBF neural network with different numbers of neurons in the hidden layer are provided in Table 6. When the number of neurons is 21, the training and test results are best. Consequently, 21 neurons are selected in the hidden layer, including a neuron designed to provide the threshold of the output layer. The output layer is a single neuron related to the lightning outage. The Gauss radial basis function is used as the activation function in the hidden layer. The k-means clustering algorithm is employed to determine the radial basis function center of 20 hidden layer neurons. The smooth parameter
443
Table 5 The performance of the BP neural network with different numbers of neurons in the hidden layer. No. of neural in hidden layer
Training results
Test results
FDR
FAR
PA
FDR
FAR
PA
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
80.00% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67%
13.33% 4.17% 3.33% 4.17% 5.83% 4.17% 3.33% 3.33% 3.33% 3.33% 4.17% 3.33% 4.17% 3.33% 3.33% 3.33% 3.33% 4.17% 3.33% 3.33%
83.33% 91.25% 91.67% 91.25% 90.42% 91.25% 91.67% 91.67% 91.67% 91.67% 91.25% 91.67% 91.25% 91.67% 91.67% 91.67% 91.67% 91.25% 91.67% 91.67%
83.33% 63.33% 63.33% 66.67% 66.67% 66.67% 66.67% 63.33% 63.33% 63.33% 66.67% 66.67% 66.67% 63.33% 66.67% 66.67% 66.67% 66.67% 66.67% 66.67%
26.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67%
78.33% 73.33% 73.33% 75.00% 75.00% 75.00% 75.00% 73.33% 73.33% 73.33% 75.00% 75.00% 75.00% 73.33% 75.00% 75.00% 75.00% 75.00% 75.00% 75.00%
Table 6 The performance of the RBF neural network with different numbers of neurons in the hidden layer. No. of neural in hidden layer
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Training results
Test results
FDR
FAR
PA
FDR
FAR
PA
80.00% 80.00% 73.33% 80.00% 80.00% 86.67% 80.00% 80.00% 80.00% 80.00% 93.33% 93.33% 93.33% 93.33% 93.33% 93.33% 100.00% 100.00% 100.00% 100.00% 100.00%
21.67% 7.50% 7.50% 10.00% 11.67% 11.67% 7.50% 4.17% 4.17% 4.17% 9.17% 8.33% 8.33% 8.33% 10.83% 11.67% 10.00% 9.17% 8.33% 9.17% 9.17%
79.17% 86.25% 82.92% 85.00% 84.17% 87.50% 86.25% 87.92% 87.92% 87.92% 92.08% 92.50% 92.50% 92.50% 91.25% 90.83% 95.00% 95.42% 95.83% 95.42% 95.42%
63.33% 63.33% 66.67% 70.00% 76.67% 73.33% 73.33% 66.67% 70.00% 66.67% 73.33% 76.67% 76.67% 76.67% 76.67% 76.67% 73.33% 73.33% 76.67% 76.67% 76.67%
33.33% 16.67% 20.00% 20.00% 20.00% 23.33% 16.67% 16.67% 20.00% 16.67% 20.00% 20.00% 20.00% 20.00% 20.00% 20.00% 16.67% 16.67% 16.67% 16.67% 16.67%
65.00% 73.33% 73.33% 75.00% 78.33% 75.00% 78.33% 75.00% 75.00% 75.00% 76.67% 78.33% 78.33% 78.33% 78.33% 78.33% 78.33% 78.33% 80.00% 80.00% 80.00%
of each function is then determined by the distance between each center. The output layer uses the linear activation function. The connection weights of the hidden layer and the output layer are determined by the pseudo-inverse method. The prediction errors of the training samples in the two neural networks are illustrated in Figs. 5 and 6. Comparing Fig. 3 with Figs. 5 and 6, the training effectiveness of the BP neural network is worse than those of GRNN and the RBF neural network because the latter two methods have accurate function approximation from sparse data and robustness to noise and outliers. The performance evaluation indexes of the test samples in the two methods are shown in Table 7. The same test samples are employed to test the BP and RBF neural networks. The prediction errors of the test samples in the two neural networks are illustrated in Figs. 7 and 8. The performance evaluation indexes of the test samples in the two methods are shown in Table 8.
444
Y. Xie, C. Li, Y. Lv et al. / Applied Soft Computing Journal 78 (2019) 438–446 Table 7 The performance evaluation indexes of the training samples in BP and RBF neural networks. BP RBF GRNN
FDR
FAR
PA
Training time
86.67% 100.00% 100.00%
3.33% 8.33% 5.83%
91.67% 95.83% 97.08%
61.00 2.25 0.11
Table 8 The performance evaluation indexes of the test samples in BP and RBF neural networks. BP RBF GRNN
FDR
FAR
PA
66.7% 76.7% 76.7%
16.7% 16.7% 11.3%
75.0% 80.0% 81.7%
Fig. 5. Prediction error of training samples in BP neural network.
Fig. 9. Prediction results when the width of the lightning corridor is 1 km. Fig. 6. Prediction error of training samples in RBF neural network.
Fig. 7. Prediction error of test samples in BP neural network.
In Table 7, the training results show that GRNN has the best prediction accuracy. Meanwhile, the training time is the fastest. In Table 8, the FDR of BP and RBF for the test samples are 66.7% and 76.7%, respectively, while the FDR of GRNN is 76.7%. GRNN achieves better prediction than BP and similar prediction to RBF. The FAR values of BP and RBF are all 16.67%, while the FAR of GRNN is 11.3%. GRNN achieves better prediction than BP and RBF. The PA values of BP and RBF are 75.0% and 80.0%, respectively, while the PA of GRNN is 81.7%. The prediction of GRNN is better than that of the BP and RBF neural networks. This is because BP neural networks need large sample sets to achieve sufficient accuracy. While GRNN and RBF can quickly learn the underlying function from a limited set of training samples, the prediction effect of BP is worse than that of GRNN and RBF. Because the RBF neural network must determine three parameters during training, while GRNN must determine only one parameter, GRNN has better approximation ability and better ability to quickly learn the underlying function of highdimensional measurements from a limited set of training samples. 4.6. The impact of input parameters
Fig. 8. Prediction errors of test samples in RBF neural network.
The values of input parameters are varied with the width of the lightning corridor and the time step for dividing the lightning data into groups, which can affect the prediction result. To verify the result of the above simulation, the effectiveness of input parameters with different widths and time steps is compared in Figs. 9–13. The prediction results will fluctuate with increasing time steps. The statistics of average prediction results with different time steps are shown in Table 9. The time step with the best prediction accuracy is 15 min. Therefore, the time step selected in the above simulation is adequate. When the time step is 15 min, the prediction results with different lightning corridor widths are shown in Fig. 14. With increasing
Y. Xie, C. Li, Y. Lv et al. / Applied Soft Computing Journal 78 (2019) 438–446
445
Table 9 The average prediction results with different time steps. Time step
Average prediction results FDR
FAR
PA
5 10 15 20 30
61% 61% 71% 64% 62%
6% 8% 9% 9% 12%
78% 77% 81% 78% 75%
Fig. 10. Prediction results when the width of the lightning corridor is 1.5 km.
Fig. 14. Prediction results when the time step is 15 min.
width, the prediction accuracy deteriorates. The results of 1 km, 1.5 km and 2 km are similar. Therefore, the lightning corridor width in the above simulation is acceptable. Fig. 11. Prediction results when the width of the lightning corridor is 2 km.
Fig. 12. Prediction results when the width of the lightning corridor is 3 km.
5. Conclusions Lightning outage prediction has great significance in the security and reliability of power system operation. Considering that large historical lightning and lightning outage datasets have not been utilized in lightning prediction, this paper employed GRNN to identify the relationship between lightning and the lightning outages of transmission lines, which can be used to predict lightning outages via real-time lightning data. The method is trained and tested through actual lightning data and lightning outage data from a power company. The prediction of the proposed method is compared with BP and RBF neural networks. The simulation results show that the proposed method has higher accuracy and a lower false alarm rate than the other methods. This method can provide a reference of lightning outage prediction for power companies. In this paper, the prediction accuracy of the proposed method is 81.7%. The prediction error is derived from two aspects: (1) the GRNN cannot classify all samples; (2) the lightning outage in the first time step cannot be identified. Therefore, it is necessary to employ new prediction methods and input features and integrate the data from other information collection devices to improve the prediction accuracy of lightning outages in further research. Acknowledgments This work is supported by the National Natural Science Foundation of China (51507080, 61673213), the Fundamental Research Funds for the Central Universities, China (30918011330). The authors also would like to thank the editor and anonymous reviewers for their comments, which improved this paper. References
Fig. 13. Prediction results when the width of the lightning corridor is 5 km.
[1] J. Lu, T. Zhou, C. Wu, B. Li, Fault statistics and analysis of 220 kV and above power transmission line in province-level power grid, High Voltage Eng. 42 (1) (2016) 200–207.
446
Y. Xie, C. Li, Y. Lv et al. / Applied Soft Computing Journal 78 (2019) 438–446
[2] A. Boston, Delivering a secure electricity supply on a low carbon pathway, Energy Policy 52 (2013) 55–59. [3] C. Yao, Y. Long, H. Wu, Q. Wang, Y. Ma, Y. Shen, L. Wang, Study of magnetic fields from different types of lightning faults on a multi-tower system, IEEE Trans. Dielectr. Electr. Insul. 21 (4) (2014) 1866–1874. [4] P. Karampelas, L. Ekonomou, S. Panetsos, G.E. Chatzarakis, LPAT: An interactive simulation tool for assessing the lightning performance of Hellenic high voltage transmission lines, Appl. Soft Comput. 11 (1) (2011) 1380–1387. [5] B.R. Vincent, L. Carey, D. Schneider, R. Gonski, Using WSR-88D reflectivity data for the prediction of cloud-to-ground lightning: A central North Carolina study, Natl. Wea. Dig. 27 (2004) 35–44. [6] J. Wang, S. Zhou, B. Yang, X. Meng, B. Zhou, Nowcasting cloud-to-ground lightning over Nanjing area using S-band dual-polarization Doppler radar, Atmos. Res. 178–179 (1) (2016) 55–64. [7] G.S. Zepka, A.C.V. Saraiva, Lightning forecasting in southeastern Brazil using the WRF model, Atmos. Res. 135 (2014) 344–362. [8] T.N.G. Trinh, O. Scholten, A. Bonard, S. Buitink, A. Corstanje, U. Ebert, J.E. Enriquez, H. Falcke, J.R. Hörandel, B.M. Hare, P. Mitra, K. Mulrey, A. Nelles, J.P. Ranchen. L. Rossetto, C. Rutjes, P. Schellart, S. Thoudam, S. ter Veen, T. Winchen, Thunderstorm electric fields probed by extensive air showers through their polarized radio emission, Phys. Rev. D 95 (8) (2017) 083004. [9] A. Fort, M. Mugnaini, V. Vignoli, S. Rocchi, F. Perini, J. Monari. M. Schiaffino, F. Fiocchi, Design, modeling, and test of a system for atmospheric electric field measurement, IEEE Trans. Instrum. Meas. 60 (8) (2011) 2778–2785. [10] W. Schulz, G. Diendorfer, S. Pedeboy, D.R. Poelman, The European lightning location system EUCLID–Part 1: Performance analysis and validation, Natl. Hazards Earth Syst. Sci. 16 (2) (2016) 595–605. [11] S.M. Chen, Y. Du, L.M. Fan, H.M. He, D.Z. Zhong, A lightning location system in China: its performances and applications, IEEE Trans. Electromagn. Compat. 44 (4) (2002) 555–560. [12] Y. Xie, Y. Xue, H. Wang, T. Xu, Z. Dong, X. Jin, Space–time early-warning of power grid fault probability by lightning, Automat. Electr. Power Syst. 37 (17) (2013) 44–51. [13] D.R. Poelman, W. Schulz, G. Diendorfer, M. Bernardi, The European lightning location system EUCLID-Part 2: Observations, Natl. Hazards Earth Syst. Sci. 16 (2) (2016) 607–616.
[14] J. He, X. Wang, Z. Yu, R. Zeng, Statistical analysis on lightning performance of transmission lines in several regions of China, IEEE Trans. Power Deliv. 30 (3) (2015) 1543–1551. [15] A.S. Qureshi, A. Khan, A. Zameer, A. Usman, Wind power prediction using deep neural network based meta regression and transfer learning, Appl. Soft Comput. 58 (2017) 742–755. [16] X. Ma, Y. Jin, Q. Dong, A generalized dynamic fuzzy neural network based on singular spectrum analysis optimized by brain storm optimization for shortterm wind speed forecasting, Appl. Soft Comput. 54 (2017) 296–312. [17] M.M. Islam, G. Lee, S.N. Hettiwatte, K. Williams, Calculating a health index for power transformers using a subsystem-based GRNN approach, IEEE Trans. Power Deliv. 33 (4) (2018) 1093–1912. [18] E.E. Elattar, J. Goulermas, Q.H. Wu, Electric load forecasting based on locally weighted support vector regression, IEEE Trans. Syst. Man Cybern. C Appl. Rev. 40 (4) (2010) 438–447. [19] S. Brodowski, A. Bielecki, M. Filocha, A hybrid system for forecasting 24-h power load profile for Polish electric grid, Appl. Soft Comput. 58 (2017) 527– 539. [20] D.F. Specht, A general regression neural network, IEEE Trans. Neural Netw. 2 (6) (1991) 568–576. [21] R. Hu, S. Wen, Z. Zeng, T. Huang, A short-term power load forecasting model based on the generalized regression neural network with decreasing step fruit fly optimization algorithm, Neurocomputing 221 (19) (2017) 24–31. [22] E.E. Elattar, Prediction of wind power based on evolutionary optimised local general regression neural network, IET Gener. Transm. Distrib. 8 (5) (2014) 916–923. [23] A.M.A. Haidar, M.W. Mustafa, F.A.F. Ibrahim, I.A. Ahmed, Transient stability evaluation of electrical power system using generalized regression neural networks, Appl. Soft Comput. 11 (4) (2011) 3558–3570. [24] N. Balijepalli, S.S. Venkata, C.W. Richter, R.D. Christie, V.J. Longo, Distribution system reliability assessment due to lightning storms, IEEE Trans. Power Deliv. 20 (3) (2005) 2153–2159.
Contents lists available at ScienceDirect
Applied Soft Computing Journal journal homepage: www.elsevier.com/locate/asoc
Predicting lightning outages of transmission lines using generalized regression neural network ∗
Yunyun Xie a , Chaojie Li b , , Youjie Lv c , Chen Yu d a
School of Automation, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu Province, China School of Engineering, Royal Melbourne Institute of Technology University, Melbourne, VIC, Australia c State Grid Wuxi Power Supply Company, Wuxi 214062, China d State Grid Electric Power Research Institute/ NARI Group Corporation, Nanjing 211106, China b
article
info
Article history: Received 12 February 2018 Received in revised form 30 July 2018 Accepted 8 September 2018 Available online 1 February 2019 Keywords: Transmission line Lightning outage Outage prediction Generalized regression neural network
a b s t r a c t Lightning is the major cause of transmission line outages, which can result in large area blackouts of power systems. One effective method to prevent catastrophic consequences is to predict lightning outages before they occur. The abundance of recorded lightning and lightning outage data in power system makes it possible to predict lightning outages of transmission lines. This paper proposes an artificially intelligent algorithm using general regression neural networks (GRNN) to predict lightning outages of transmission lines. First, the data that can be obtained from the operation and management system of a power company are analyzed, and the features that can be used as input parameters of GRNN are extracted. The prediction model based on GRNN is then built to perform lightning outage prediction. Finally, the effectiveness of the proposed method is validated by comparing it with (Back Propagation) BP and (Radial Basis Function) RBF neural networks using actual lightning data and lightning outage data. The simulation results show that the proposed method provides much better prediction performance. © 2019 Elsevier B.V. All rights reserved.
1. Introduction Lightning is the major cause of transmission line outages. More than 45% of transmission line outages are caused by lightning according to the statistics of one provincial power grid from 2005 to 2014 in China [1]. A lightning outage can impact the reliability of power supply and can result in catastrophic blackout consequences, such as the Brazil blackout in 2009 that was caused by lightning [2]. To enhance the reliability of power supplies and prevent catastrophic consequences, some efforts have been undertaken to improve the lightning protection design of transmission lines [3,4]. However, the improvement of lightning protection design cannot completely prevent lightning outages. It is necessary to predict lightning outages to adjust the operation mode beforehand, consequently reducing the loss of lightning outages. One cause of transmission line outages is lightning flashover of overhead lines resulting from conductor overvoltage due to lightning directly striking the conductor or transmission tower. To predict lightning outages, some efforts have been undertaken to predict lightning areas. Lightning is mainly predicted based on Doppler weather radar data and ground-based atmospheric electric field meter data. Because the electrification process within ∗ Corresponding author. E-mail addresses: [email protected] (Y. Xie), [email protected] (C. Li), [email protected] (Y. Lv), [email protected] (C. Yu). https://doi.org/10.1016/j.asoc.2018.09.042 1568-4946/© 2019 Elsevier B.V. All rights reserved.
a growing thunderstorm returns large reflectivity echoes, the reflectivity data of Doppler weather radar can be used to identify a growing thunderstorm [5]. The characteristics of radar reflectivity echoes related to lightning have been researched in many studies to predict thunderstorm areas [5–7]. Because the electrical field in a thunderstorm will change before lightning strikes, the electrical field data of a ground-based atmospheric electric field meter can also be employed to predict lightning according to the change of the electric field [8,9]. Though both Doppler weather radar and ground-based atmospheric electric field meters can identify the lightning area, they have some drawbacks in predicting lightning. The thunderstorm area given by Doppler weather radar is a large area greater than one hundred kilometers, which makes it challenging to predict the lightning around transmission lines. A single atmospheric electric field can cover areas within only 10–20 km. To protect long-distance transmission lines, it is necessary to build up an atmospheric electric field network, which increases the cost of operation and the difficulty of lightning identification. Furthermore, in addition to the lightning area, the location of lightning and number of lightning strikes are important parameters for lightning outage prediction that cannot be obtained from Doppler weather radar data or ground-based atmospheric electric field meter data. To enhance operational efficiency, lightning location systems (LLS) have been installed to monitor lightning activities by electric power companies across the world, including companies in the U.S., the U.K., and China [10]. An LLS can observe the parameters of
Y. Xie, C. Li, Y. Lv et al. / Applied Soft Computing Journal 78 (2019) 438–446
lightning such as lightning location and peak current. The collected lightning data are usually applied to estimate the ground-flash density, assess the line performance, classify the faults, etc. [11]. In [12], a lightning outage prediction method based on LLS data is proposed based on real-time measured lightning information. The real-time measured lightning is divided into many time steps. Areas with lightning in each time step are then collected to identify the lightning area. The multi-step lightning areas are adopted to extrapolate the lightning area in the next time step. The predicted lightning area and the amount of lightning in the past time step are employed to calculate the lightning outage rate in the next time step. This method uses the real-time data only to predict the lightning outage rate of transmission lines; it cannot clearly predict whether a lightning outage will occur. Plenty of lightning and lightning outage data have been accumulated by the LLS and in the operation of power systems. More than 3 million lightning strikes per year are observed by the European LLS [13], and hundreds of lightning outages are collected by a province level grid [14]. However, this large amount of historical lightning and lightning outage data has not been utilized for predicting lightning outages. With the development of data mining, (Artificial Intelligent) AI-based methods can describe the relation between input and output data from historical data via non-statistical approaches such as support vector machines and artificial neural networks, which have demonstrated good performance in power system operations such as wind power forecasting [15,16], health evaluation of power transformers [17], and short-term power load forecasting [18], prediction of power load profile [19]. Because of the large amount of lightning from LLS and the lightning outage data in the power system, data mining methods are very suitable to find relationships between recorded lightning and lightning outages. Lightning outage prediction of transmission lines is a classification problem that is suitable for artificial neural networks. Therefore, this paper focuses on identifying the relationship between the lightning outages of transmission lines and the recorded lightning of LLS by an artificial neural network that can predict lightning outages with real-time lightning data. To satisfy this demand, a reliable, precise, and fast method is required. The general regression neural network (GRNN) developed by Specht [20] is a type of radial basis function neural network that has good nonlinear approximation ability, excellent anti-interference performance, fast convergence speed and autonomous learning [21]. Most required parameters of GRNN can be derived from the input data. Moreover, GRNN can control the complexity of its interpolation based on the information conveyed by the training samples, and it has a simple algorithm to implement and fast calculation speed [17]. Due to the above advantages, GRNN has been widely applied in short-term power load forecasting [21], wind power prediction [22], and transient stability evaluation of power systems [23]. Because the relationship between the lightning outages of transmission lines and the recorded lightning of LLS is strongly nonlinear, the prediction of lightning outage requires the method to have good nonlinear approximation ability, fast convergence speed which is the characteristic of GRNN. Therefore, GRNN is suitable for the prediction of lightning outage. In this work, we investigate the idea of predicting lightning outages of transmission lines using GRNN. This method utilizes the historical lightning data of LLS and historical lightning outage data in power systems to build the GRNN model, which can identify the relation between lightning and lightning outages of transmission lines. Furthermore, the GRNN model can be employed to predict lightning outages according to real-time lightning data. The innovations of this paper are the following: (1) GRNN is employed to predict lightning outages and, to the best of our knowledge, is the first lightning outage prediction method based on artificial
439
neural networks; (2) some features that can reflect the probability of lightning strikes of transmission lines are constructed based on the lightning data and transmission tower data. This paper is organized as follows: Section 2 analyzes the necessary data for predicting lightning outages and constructs the input parameters of GRNN. Section 3 describes the GRNN method and its application to predict lightning outages of transmission lines. Section 4 demonstrates the simulation results and comparisons with BP and RBF neural network methods. Finally, the conclusion is presented in Section 5. 2. The input feature for lightning outage prediction In this section, the mechanism of lightning outages is first reviewed to analyze the necessary data for predicting lightning outages. The data directly collected by the LLS and the operation system of the power system are then introduced. Furthermore, the parameters that can be employed as the input feature of GRNN are constructed based on the lightning data and transmission tower data. 2.1. Security indices and reliability Lightning outages of transmission lines can be caused by the lightning strikes on a transmission tower (back flashover) or lightning passing an overhead ground line to strike a transmission line (shielding failure). When lightning strikes a transmission tower, the insulator between the transmission conductor and transmission tower can endure a certain range of overvoltage, which is called the lightning resistance level and can be expressed as [24]
I1 =
U50%
(1 − k) β Rch +
(
ha hgt
) ( L − k β 2gt.6 + 1 −
hb k hd 0
)
hd 2 .6
(1)
where U50% is the 50% flashover voltage of insulator strings; k is the coupling coefficient between the overhead ground line and transmission line; k0 is the coupling coefficient between the line and the ground; ha , ht , hav and hg v are the height of the crossarm, the height of the tower, the height of the line and the height of the ground line, respectively; β is the shunt coefficient; and Rsu and L1 are the earth resistance and equivalent inductance of the tower, respectively. If the lightning current is greater than the lightning resistance level, the insulation of the insulator strings may be broken down. The probability can be calculated by the probability of the lightning current: P1 (I0 > I1 ) = 10−I1 /88
(2)
where I0 is the lightning current amplitude. When lightning strikes a transmission line, the lightning resistance level of the transmission line can be expressed as I2 =
4U50% z
≈
U50% 100
(3)
where z is the wave impedance of conductor. The approximately value of wave impedance is 400 in simplified calculation. The shielding failure probability can be expressed as P2 (I0 > I2 ) = 10−I2 /88
(4)
When lightning strikes a transmission line, it may strike either the conductor or the tower. When the lightning current is greater than the lightning resistance level, the insulator may break down. Therefore, the probability of lightning outage can be expressed as P = η (gP1 + Pa P2 )
(5)
440
Y. Xie, C. Li, Y. Lv et al. / Applied Soft Computing Journal 78 (2019) 438–446
Table 1 Information collected by LLS and power system operation and management system. Information source
Information type
Data type
LLS
Lightning
PMIS EMS
Transmission tower Lightning outage of transmission line
Longitude, latitude, peak lightning current Longitude, latitude, voltage level Name of outage transmission line, time of outage, location of lightning outage
where η is the probability to produce an electric arc; g is the probability to strike the transmission tower; and Pa is the probability to bypass the overhead ground line. The parameters in (1)–(5) will be different for different types of transmission lines, terrains and regions. For example, the value of Pa in flat regions is less than that in hilly regions. The above lightning outage model can quantitatively assess the probability of transmission line outage when lightning strikes the transmission line. However, the lightning prediction always predicts the lightning area, which cannot tell us whether there will be a lightning strike on the transmission lines. This is why the lightning prediction method cannot be used in lightning outage prediction. From the above lightning outage model, we can summarize that the main impact factors of lightning outages are the peak lightning current and the probability of lightning strikes on transmission lines. Because the insulator parameters of transmission lines in one voltage level are similar, the transmission line parameters are neglected in this paper. 2.2. The information collected by LLS and power system operation Most existing LLSs, such as EUCILD [13], GDLLS [14], are based on the magnetic direction method and the time-of-arrival method to locate lightning discharges. There are three major parts of LLS: combined magnetic direction and time-of-arrival finders (DTFs), naval process apparatus, and lightning location information analysis and display system. The main parts of DTF are the orthogonal loop magnetic field antenna, electric-field antenna, global positioning system (GPS) receiving antenna, GPS pulse-timing board, and CPU board. The DTFs can distinguish lightning based on the preset waveform discrimination criteria. Once a lightning strike is detected by a DTF, the lightning data are transmitted to the control center. The naval process apparatus in the control center records the lightning data and combines the data from multiple DTFs to provide the location, time, and peak current of the lightning in real time. Finally, the lightning information is stored in a permanent database and displayed in the control center. Therefore, the information that LLS can provide is the location, time, and peak current of lightning. For the operation of the power system, the location of the transmission tower is stored in the Project Management Information System (PMIS) of power companies for daily maintenance and service. In the operation of the power system, the outages of transmission lines due to different causes are labeled and recorded in the Energy Management System (EMS) for repair and analysis. The information that can be directly collected from LLS and the power system operation and management system is illustrated in Table 1. The information collected by LLS and power system operation is historical data, which cannot directly predict lightning. However, the historical lightning data can reflect the lightning intensity in a given area, which is highly correlated to lightning outages.
2.3. The features of lightning outage prediction From the analysis in Section 2.1, the main impact factors of lightning outages are peak lightning current and the probability of lightning striking transmission lines. The first factor can be directly obtained from the lightning information collected by LLS, but the second factor cannot be collected directly. Therefore, it is necessary to construct some parameters that can reflect the probability that lightning will strike transmission lines. According to our experience, the more abundant the lightning around a transmission line and the closer the lightning to the transmission line, the greater the probability that lightning will strike the transmission lines. Based on the location information of lightning and the transmission tower, the distance between the lightning and the transmission line is easy to calculate. The number of lightning strikes around the transmission line can then be counted for a given distance away from the transmission line. The given distance is defined as the lightning corridor in this paper. In summary, the parameters that can be used for lightning outage prediction in this paper are the number of lightning strikes in the lightning corridor, the nearest distance between the line and the lightning, the average lightning current intensity in the lightning corridor, and the peak current of the nearest lightning strike. 3. GRNN-based lightning outage prediction method In this section, a lightning outage prediction model is established based on GRNN, and the prediction method employing the prediction model is presented. 3.1. General regression GRNN is a network that can be employed to estimate a dependent variable from an independent variable through a finite dataset. The theoretical foundation of GRNN is kernel regression, which is non-linear regression analysis. The function f (x, y) is defined as the joint probability density function (PDF) of two random variables x and y. x is a vector random variable representing the input, and y is a scalar random variable representing the output. When f (x, y) is known, the condition mean of y on a given x0 can be calculated by ∧
∫∞ −∞
y(x0 ) = E(y|x0 ) = ∫ ∞
yf (x0 , y)dy
−∞
f (x0 , y)dy
(6)
This means that we can predict the value of y according to the input x0 when f (x, y) is known. However, f (x, y) is usually unknown in many systems, such as the joint PDF of lightning parameters and the lightning outage of transmission lines. Therefore, it is necessary to estimate f (x, y) for the output parameter calculation. GRNN uses a group of measured x and y values to estimate f (x, y) based on the consistent estimators proposed by Parzen [20]. For a given measured sample data point {xi , yi |i = 1, 2, . . ., N }, the estimated PDF can be expressed as
⎧ n ∑ ∧ ⎪ 1 ⎪ ⎪f (x, y) = eD(xi ) · eD(yi ) ⎪ (p+1)/2 σ (p+1) ⎪ n(2 π ) ⎪ ⎨ i=1 (x − xi )2 D(xi ) = − ⎪ ⎪ ⎪ 2σ 2 ⎪ 2 ⎪ ⎪ ⎩D(yi ) = − (y − yi ) 2 2σ
(7)
where n is the number of measured samples, p is the dimension of vector random variable x, and σ is the smooth parameter of the Gauss function (also called the spread factor).
Y. Xie, C. Li, Y. Lv et al. / Applied Soft Computing Journal 78 (2019) 438–446
441
basis function and affects the network output. If σ is too large, the predicted value y0 will be close to the mean output of all training samples. If σ is too small, y0 will be close to the output of the training sample, which has the minimal Euclidean distance from x0 . Therefore, it is necessary to select the value of the smooth parameter. Because the absolute value of the smallest mean absolute error (MAE) in (11) is greater than the other indexes [18], such as the mean absolute percentage error (MAPE) and mean-square error (MSE), it is employed to evaluate the effectiveness of the smooth parameter in this paper. MAE = Fig. 1. Structure of GRNN.
∑n
y(x0 ) = ∑i=n1
yi eD(xi )
i=1
eD(xi )
(8)
The estimated condition mean can be visualized as a weighted average of all observed values yi , where each observed value is weighted exponentially according to its Euclidean distance from x0 . 3.2. GRNN model GRNN consists of four layers: the input layer, the pattern layer (also called the latent regression layer), the summation layer and the output layer, as shown in Fig. 1. Each layer has a specific computational function for performing non-linear regression. The function of the input layer is to receive information. There are p neurons in the input layer, which correspond to the p dimension input characteristics of the samples. We assume that one input sample is x0 = [x01 , x02 , . . . , x0p ]T . The input neurons then transmit the data to the second layer. Every neuron in the pattern layer is a cluster center, which calculates the exponential form of the Euclidean distance between the prediction sample x0 and training sample xi ; the output of neuron i is eD(xi ) . The number of neurons in the pattern layer is equal to the number of training samples. The training sample that is closer to x0 is given a greater weight when predicting the output. The neurons of the third layer (summation layer) receive the outputs of the pattern neurons. This layer includes two units. The second unit calculates the sum of the output. The summation layer has two neurons (SD and SN ) to sum the output of the pattern layer with different weights shown in (9)– (10). The weight of the first neuron SD is 1, and the weight of the second neuron SN is the output yi of the corresponding training sample. SD =
n ∑
eD(xi )
(9)
i=1 n
SN =
∑
yi eD(xi )
(11)
i=1
By substituting the estimated PDF in (7) into the condition mean in (6) and interchanging the order of integration and summation, the desired condition mean of y for a given x0 can be yielded: ∧
n ∑ ⏐ ⏐ ⏐yˆ (xi ) − y(xi )⏐ /N
(10)
i=1
The two outputs of the summation layer are divided by the output layer to obtain the final output. 3.3. Smooth parameter selection In formula (7), σ is the smooth parameter of the radial basis function, which has great influence on the shape of the radial
The procedure to select the smooth parameter is shown as follows. Step (1) Select a value in increments of 0.001 from the range [0, 0.1] as the candidate smooth parameter. Step (2) Initialize MAE0 with large values (e.g., 100). Step (3) Train GRNN with the training samples and the candidate smooth parameter σi , and compute MAEi . Step (4) If MAEi < MAE0 , store the value of the smooth parameter. Step (5) Repeat Steps (3)–(4) until all values of the smooth parameter are tested. Step (6) If the smallest smooth parameter is obtained in the upper bound, the actual smallest MAE has not been found. Add 0.1 to the candidate range of the smooth parameter, and repeat (3)–(5). Step (7) The last stored smooth parameter is the selected smooth parameter for the prediction of the test dataset. 3.4. Lightning outage prediction based on GRNN After the lightning data and the information on the transmission tower and historical lightning outages are obtained from the operation and management system, the lightning outage prediction can be implemented by the method introduced above. Before the application of GRNN, some preparation works are necessary. The detailed procedure to predict lightning outages is shown as follows. Step (1) Divide the lightning data into groups according to time. From the time of first lightning strike, the lightning strikes in every 15 min period are collected into a group. Step (2) Construct the sample set. According to the analysis in Section 1, the input parameters of the sample are the number of lightning strikes in lightning corridor, the nearest distance between the line and the lightning, the average lightning current intensity in the lightning corridor, and the peak current of the nearest lightning strike. The input parameters in every sample are calculated by the lightning data in every group and the location of the transmission tower. The output data represent the occurrence of lightning outages in the next time period (if an outage occurs, yi = 1, or yi = 0). Step (3) Select the training samples and test samples. Because the number of lightning outage cases is much less than the number of normal operation cases, the normal operation cases are randomly selected as the normal operation sample to form the balanced normal and outage samples. The lightning outage cases are all selected as outage samples. Eighty percent of the total sample is selected as the training samples, and the others are the test samples. Step (4) Optimize the smooth parameter. According to the method introduced in Section 3.3, the optimal smooth parameter is selected, and at the same time, GRNN is trained. Step (5) Employ the trained GRNN to predict lightning outages in the test samples. After obtaining the prediction sample output
442
Y. Xie, C. Li, Y. Lv et al. / Applied Soft Computing Journal 78 (2019) 438–446
Table 2 Statistics of lightning trip information. Line
X1
X2 (km)
X3 (kA)
X4 (kA)
JJ SJ DB BJ WH YH YM FY GL WY
18 1 25 17 65 25 3 6 18 45
0.1017 0.6254 0.0588 0.1301 0.0549 0.1244 0.4929 0.0436 0.091 0.0064
75.42 40.20 46.96 51.22 44.04 49.90 145.26 53.30 30.13 39.53
80.0 40.2 44.5 52.0 40.8 50.4 76.9 30.2 28.1 37.3
y0 , this paper takes 0.5 as a threshold to classify the sample. If y0 is greater than 0.5, the sample is classified as a lightning outage sample. Step (6) Verify the effectiveness of test samples. Compare the prediction status of the transmission line with the recorded data to confirm the accuracy of prediction.
Fig. 2. MAE of different candidate smooth parameters.
4. Experiments and results In this section, the GRNN lightning outage prediction method is verified by actual lightning data, transmission data and lightning outage data. The result of GRNN is compared with the results of the BP network and RBF network. 4.1. Dataset
Fig. 3. Prediction error of training samples by GRNN.
The data in this paper are from the LLS and operation and management system of a power system in an eastern province of China. There are 150 recorded lightning outages. In this paper, 120 fault samples and 120 normal samples are used as training samples. The remaining 30 fault samples and 30 normal samples are employed as the test samples. According to the above analysis, the input parameters of GRNN in this article are the number of lightning strikes within 1.5 km of lightning corridor x1 , the nearest distance between the line and lightning x2 , the average lightning current intensity within the 1.5 km lightning corridor x3 , and the peak current of the nearest lightning strike x4 . The input parameters of partial lightning outage samples are shown in Table 2. 4.2. Performance evaluation index
Table 3 The statistics of training samples by GRNN. Outage sample Normal sample
Classified as outage
Classified as normal
120 7
0 113
4.3. Value of smooth parameter According to the method of smooth parameter selection, the candidate smooth parameter values are the increments of 0.001 in the range [0, 0.1]. The training samples are employed to train GRNN with different candidate smooth parameters. MAE of the candidate smooth parameters is shown in Fig. 2. When the smooth parameter is 0.05, MAE is minimized. Therefore, the smooth parameter in the next prediction is 0.05. 4.4. Prediction results of GRNN
The fault detection rate (FDR), false alarm rate (FAR), and total prediction accuracy (PA), which are the common indexes to evaluate the prediction performance, are employed to evaluate the performance of the prediction methods in this paper. FDR =
FAR = PA =
FN FP + FN
× 100%
TN × 100% TP + TN FN + TP
FP + FN + TP + TN
(12)
(13)
× 100%
(14)
where FP and FN are the numbers of outage samples classified as normal and outage, respectively. TP and TN are the numbers of normal samples classified as normal and outage, respectively.
In the training samples, there are 120 lightning outage samples (output y = 1) and 120 normal samples (y = 0). The errors of prediction output and actual output for the training samples are shown in Fig. 3. In Fig. 3, the red line represents a prediction error of 0.5. Because the threshold to classify the occurrence of lightning outage is 0.5, the prediction will be inaccurate when the prediction error is greater than 0.5. The number of inaccurate samples for training samples is illustrated in Table 3. The performance evaluation indexes of training samples are shown in Table 4. FDR is 100.00%, which means that all lightning outage cases are detected. FAR is 5.83%, which means that 5.83% of the normal cases are false positives. PA is 97.08%, which means that 97.08% of all cases are correctly predicted. The results show that GRNN has good training effectiveness.
Y. Xie, C. Li, Y. Lv et al. / Applied Soft Computing Journal 78 (2019) 438–446 Table 4 The performance evaluation indexes of training and test samples by GRNN. Training sample Test sample
FDR
FAR
PA
100.00% 76.70%
5.83% 11.30%
97.08% 81.70%
Fig. 4. Prediction errors of test samples by GRNN.
In the test samples, there are 30 lightning outage samples and 30 normal samples. The prediction error of the test samples is shown in Fig. 4. The performance evaluation indexes of test samples are also shown in Table 4. Fig. 4 and Table 4 show that the FDR of the test samples is 76.70%, FAR is 11.30%, and PA is 81.70%, which are all worse than the training samples. From the input parameters, the reason why lightning outages are not predicted successfully is that there are very few lightning strikes around the line. Similarly, the reason why the normal cases are predicted inaccurately is that there are many lightning strikes around the line. 4.5. Comparison with other methods To verify the effectiveness of GRNN, the most popular BP neural network is employed for comparison with GRNN. Because GRNN is derived from RBF, it is also employed for comparison with GRNN. The BP neural network in this paper has a single hidden layer. There are 5 neurons in the input layer: a neuron designed to introduce the threshold of the hidden layer and the four neurons corresponding to the same input features as GRNN. The results of the BP neural network with different numbers of neurons in the hidden layer are provided in Table 5. When the number of neurons is 8, the training and test results are best with the minimal number of neurons. Consequently, 8 neurons are selected in the hidden layer, including a neuron designed to provide the threshold of the output layer. The output layer is a single neuron related to lightning outage. The sigmoid function is used as an activation function in both the hidden and output layers. The network is trained by the standard backpropagation algorithm, and the training samples are selected randomly to generate the connection weights between the output layer and the hidden layer. The input layer of the RBF neural network has 4 neurons related to the same four features as GRNN. The results of the RBF neural network with different numbers of neurons in the hidden layer are provided in Table 6. When the number of neurons is 21, the training and test results are best. Consequently, 21 neurons are selected in the hidden layer, including a neuron designed to provide the threshold of the output layer. The output layer is a single neuron related to the lightning outage. The Gauss radial basis function is used as the activation function in the hidden layer. The k-means clustering algorithm is employed to determine the radial basis function center of 20 hidden layer neurons. The smooth parameter
443
Table 5 The performance of the BP neural network with different numbers of neurons in the hidden layer. No. of neural in hidden layer
Training results
Test results
FDR
FAR
PA
FDR
FAR
PA
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
80.00% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67% 86.67%
13.33% 4.17% 3.33% 4.17% 5.83% 4.17% 3.33% 3.33% 3.33% 3.33% 4.17% 3.33% 4.17% 3.33% 3.33% 3.33% 3.33% 4.17% 3.33% 3.33%
83.33% 91.25% 91.67% 91.25% 90.42% 91.25% 91.67% 91.67% 91.67% 91.67% 91.25% 91.67% 91.25% 91.67% 91.67% 91.67% 91.67% 91.25% 91.67% 91.67%
83.33% 63.33% 63.33% 66.67% 66.67% 66.67% 66.67% 63.33% 63.33% 63.33% 66.67% 66.67% 66.67% 63.33% 66.67% 66.67% 66.67% 66.67% 66.67% 66.67%
26.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67% 16.67%
78.33% 73.33% 73.33% 75.00% 75.00% 75.00% 75.00% 73.33% 73.33% 73.33% 75.00% 75.00% 75.00% 73.33% 75.00% 75.00% 75.00% 75.00% 75.00% 75.00%
Table 6 The performance of the RBF neural network with different numbers of neurons in the hidden layer. No. of neural in hidden layer
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Training results
Test results
FDR
FAR
PA
FDR
FAR
PA
80.00% 80.00% 73.33% 80.00% 80.00% 86.67% 80.00% 80.00% 80.00% 80.00% 93.33% 93.33% 93.33% 93.33% 93.33% 93.33% 100.00% 100.00% 100.00% 100.00% 100.00%
21.67% 7.50% 7.50% 10.00% 11.67% 11.67% 7.50% 4.17% 4.17% 4.17% 9.17% 8.33% 8.33% 8.33% 10.83% 11.67% 10.00% 9.17% 8.33% 9.17% 9.17%
79.17% 86.25% 82.92% 85.00% 84.17% 87.50% 86.25% 87.92% 87.92% 87.92% 92.08% 92.50% 92.50% 92.50% 91.25% 90.83% 95.00% 95.42% 95.83% 95.42% 95.42%
63.33% 63.33% 66.67% 70.00% 76.67% 73.33% 73.33% 66.67% 70.00% 66.67% 73.33% 76.67% 76.67% 76.67% 76.67% 76.67% 73.33% 73.33% 76.67% 76.67% 76.67%
33.33% 16.67% 20.00% 20.00% 20.00% 23.33% 16.67% 16.67% 20.00% 16.67% 20.00% 20.00% 20.00% 20.00% 20.00% 20.00% 16.67% 16.67% 16.67% 16.67% 16.67%
65.00% 73.33% 73.33% 75.00% 78.33% 75.00% 78.33% 75.00% 75.00% 75.00% 76.67% 78.33% 78.33% 78.33% 78.33% 78.33% 78.33% 78.33% 80.00% 80.00% 80.00%
of each function is then determined by the distance between each center. The output layer uses the linear activation function. The connection weights of the hidden layer and the output layer are determined by the pseudo-inverse method. The prediction errors of the training samples in the two neural networks are illustrated in Figs. 5 and 6. Comparing Fig. 3 with Figs. 5 and 6, the training effectiveness of the BP neural network is worse than those of GRNN and the RBF neural network because the latter two methods have accurate function approximation from sparse data and robustness to noise and outliers. The performance evaluation indexes of the test samples in the two methods are shown in Table 7. The same test samples are employed to test the BP and RBF neural networks. The prediction errors of the test samples in the two neural networks are illustrated in Figs. 7 and 8. The performance evaluation indexes of the test samples in the two methods are shown in Table 8.
444
Y. Xie, C. Li, Y. Lv et al. / Applied Soft Computing Journal 78 (2019) 438–446 Table 7 The performance evaluation indexes of the training samples in BP and RBF neural networks. BP RBF GRNN
FDR
FAR
PA
Training time
86.67% 100.00% 100.00%
3.33% 8.33% 5.83%
91.67% 95.83% 97.08%
61.00 2.25 0.11
Table 8 The performance evaluation indexes of the test samples in BP and RBF neural networks. BP RBF GRNN
FDR
FAR
PA
66.7% 76.7% 76.7%
16.7% 16.7% 11.3%
75.0% 80.0% 81.7%
Fig. 5. Prediction error of training samples in BP neural network.
Fig. 9. Prediction results when the width of the lightning corridor is 1 km. Fig. 6. Prediction error of training samples in RBF neural network.
Fig. 7. Prediction error of test samples in BP neural network.
In Table 7, the training results show that GRNN has the best prediction accuracy. Meanwhile, the training time is the fastest. In Table 8, the FDR of BP and RBF for the test samples are 66.7% and 76.7%, respectively, while the FDR of GRNN is 76.7%. GRNN achieves better prediction than BP and similar prediction to RBF. The FAR values of BP and RBF are all 16.67%, while the FAR of GRNN is 11.3%. GRNN achieves better prediction than BP and RBF. The PA values of BP and RBF are 75.0% and 80.0%, respectively, while the PA of GRNN is 81.7%. The prediction of GRNN is better than that of the BP and RBF neural networks. This is because BP neural networks need large sample sets to achieve sufficient accuracy. While GRNN and RBF can quickly learn the underlying function from a limited set of training samples, the prediction effect of BP is worse than that of GRNN and RBF. Because the RBF neural network must determine three parameters during training, while GRNN must determine only one parameter, GRNN has better approximation ability and better ability to quickly learn the underlying function of highdimensional measurements from a limited set of training samples. 4.6. The impact of input parameters
Fig. 8. Prediction errors of test samples in RBF neural network.
The values of input parameters are varied with the width of the lightning corridor and the time step for dividing the lightning data into groups, which can affect the prediction result. To verify the result of the above simulation, the effectiveness of input parameters with different widths and time steps is compared in Figs. 9–13. The prediction results will fluctuate with increasing time steps. The statistics of average prediction results with different time steps are shown in Table 9. The time step with the best prediction accuracy is 15 min. Therefore, the time step selected in the above simulation is adequate. When the time step is 15 min, the prediction results with different lightning corridor widths are shown in Fig. 14. With increasing
Y. Xie, C. Li, Y. Lv et al. / Applied Soft Computing Journal 78 (2019) 438–446
445
Table 9 The average prediction results with different time steps. Time step
Average prediction results FDR
FAR
PA
5 10 15 20 30
61% 61% 71% 64% 62%
6% 8% 9% 9% 12%
78% 77% 81% 78% 75%
Fig. 10. Prediction results when the width of the lightning corridor is 1.5 km.
Fig. 14. Prediction results when the time step is 15 min.
width, the prediction accuracy deteriorates. The results of 1 km, 1.5 km and 2 km are similar. Therefore, the lightning corridor width in the above simulation is acceptable. Fig. 11. Prediction results when the width of the lightning corridor is 2 km.
Fig. 12. Prediction results when the width of the lightning corridor is 3 km.
5. Conclusions Lightning outage prediction has great significance in the security and reliability of power system operation. Considering that large historical lightning and lightning outage datasets have not been utilized in lightning prediction, this paper employed GRNN to identify the relationship between lightning and the lightning outages of transmission lines, which can be used to predict lightning outages via real-time lightning data. The method is trained and tested through actual lightning data and lightning outage data from a power company. The prediction of the proposed method is compared with BP and RBF neural networks. The simulation results show that the proposed method has higher accuracy and a lower false alarm rate than the other methods. This method can provide a reference of lightning outage prediction for power companies. In this paper, the prediction accuracy of the proposed method is 81.7%. The prediction error is derived from two aspects: (1) the GRNN cannot classify all samples; (2) the lightning outage in the first time step cannot be identified. Therefore, it is necessary to employ new prediction methods and input features and integrate the data from other information collection devices to improve the prediction accuracy of lightning outages in further research. Acknowledgments This work is supported by the National Natural Science Foundation of China (51507080, 61673213), the Fundamental Research Funds for the Central Universities, China (30918011330). The authors also would like to thank the editor and anonymous reviewers for their comments, which improved this paper. References
Fig. 13. Prediction results when the width of the lightning corridor is 5 km.
[1] J. Lu, T. Zhou, C. Wu, B. Li, Fault statistics and analysis of 220 kV and above power transmission line in province-level power grid, High Voltage Eng. 42 (1) (2016) 200–207.
446
Y. Xie, C. Li, Y. Lv et al. / Applied Soft Computing Journal 78 (2019) 438–446
[2] A. Boston, Delivering a secure electricity supply on a low carbon pathway, Energy Policy 52 (2013) 55–59. [3] C. Yao, Y. Long, H. Wu, Q. Wang, Y. Ma, Y. Shen, L. Wang, Study of magnetic fields from different types of lightning faults on a multi-tower system, IEEE Trans. Dielectr. Electr. Insul. 21 (4) (2014) 1866–1874. [4] P. Karampelas, L. Ekonomou, S. Panetsos, G.E. Chatzarakis, LPAT: An interactive simulation tool for assessing the lightning performance of Hellenic high voltage transmission lines, Appl. Soft Comput. 11 (1) (2011) 1380–1387. [5] B.R. Vincent, L. Carey, D. Schneider, R. Gonski, Using WSR-88D reflectivity data for the prediction of cloud-to-ground lightning: A central North Carolina study, Natl. Wea. Dig. 27 (2004) 35–44. [6] J. Wang, S. Zhou, B. Yang, X. Meng, B. Zhou, Nowcasting cloud-to-ground lightning over Nanjing area using S-band dual-polarization Doppler radar, Atmos. Res. 178–179 (1) (2016) 55–64. [7] G.S. Zepka, A.C.V. Saraiva, Lightning forecasting in southeastern Brazil using the WRF model, Atmos. Res. 135 (2014) 344–362. [8] T.N.G. Trinh, O. Scholten, A. Bonard, S. Buitink, A. Corstanje, U. Ebert, J.E. Enriquez, H. Falcke, J.R. Hörandel, B.M. Hare, P. Mitra, K. Mulrey, A. Nelles, J.P. Ranchen. L. Rossetto, C. Rutjes, P. Schellart, S. Thoudam, S. ter Veen, T. Winchen, Thunderstorm electric fields probed by extensive air showers through their polarized radio emission, Phys. Rev. D 95 (8) (2017) 083004. [9] A. Fort, M. Mugnaini, V. Vignoli, S. Rocchi, F. Perini, J. Monari. M. Schiaffino, F. Fiocchi, Design, modeling, and test of a system for atmospheric electric field measurement, IEEE Trans. Instrum. Meas. 60 (8) (2011) 2778–2785. [10] W. Schulz, G. Diendorfer, S. Pedeboy, D.R. Poelman, The European lightning location system EUCLID–Part 1: Performance analysis and validation, Natl. Hazards Earth Syst. Sci. 16 (2) (2016) 595–605. [11] S.M. Chen, Y. Du, L.M. Fan, H.M. He, D.Z. Zhong, A lightning location system in China: its performances and applications, IEEE Trans. Electromagn. Compat. 44 (4) (2002) 555–560. [12] Y. Xie, Y. Xue, H. Wang, T. Xu, Z. Dong, X. Jin, Space–time early-warning of power grid fault probability by lightning, Automat. Electr. Power Syst. 37 (17) (2013) 44–51. [13] D.R. Poelman, W. Schulz, G. Diendorfer, M. Bernardi, The European lightning location system EUCLID-Part 2: Observations, Natl. Hazards Earth Syst. Sci. 16 (2) (2016) 607–616.
[14] J. He, X. Wang, Z. Yu, R. Zeng, Statistical analysis on lightning performance of transmission lines in several regions of China, IEEE Trans. Power Deliv. 30 (3) (2015) 1543–1551. [15] A.S. Qureshi, A. Khan, A. Zameer, A. Usman, Wind power prediction using deep neural network based meta regression and transfer learning, Appl. Soft Comput. 58 (2017) 742–755. [16] X. Ma, Y. Jin, Q. Dong, A generalized dynamic fuzzy neural network based on singular spectrum analysis optimized by brain storm optimization for shortterm wind speed forecasting, Appl. Soft Comput. 54 (2017) 296–312. [17] M.M. Islam, G. Lee, S.N. Hettiwatte, K. Williams, Calculating a health index for power transformers using a subsystem-based GRNN approach, IEEE Trans. Power Deliv. 33 (4) (2018) 1093–1912. [18] E.E. Elattar, J. Goulermas, Q.H. Wu, Electric load forecasting based on locally weighted support vector regression, IEEE Trans. Syst. Man Cybern. C Appl. Rev. 40 (4) (2010) 438–447. [19] S. Brodowski, A. Bielecki, M. Filocha, A hybrid system for forecasting 24-h power load profile for Polish electric grid, Appl. Soft Comput. 58 (2017) 527– 539. [20] D.F. Specht, A general regression neural network, IEEE Trans. Neural Netw. 2 (6) (1991) 568–576. [21] R. Hu, S. Wen, Z. Zeng, T. Huang, A short-term power load forecasting model based on the generalized regression neural network with decreasing step fruit fly optimization algorithm, Neurocomputing 221 (19) (2017) 24–31. [22] E.E. Elattar, Prediction of wind power based on evolutionary optimised local general regression neural network, IET Gener. Transm. Distrib. 8 (5) (2014) 916–923. [23] A.M.A. Haidar, M.W. Mustafa, F.A.F. Ibrahim, I.A. Ahmed, Transient stability evaluation of electrical power system using generalized regression neural networks, Appl. Soft Comput. 11 (4) (2011) 3558–3570. [24] N. Balijepalli, S.S. Venkata, C.W. Richter, R.D. Christie, V.J. Longo, Distribution system reliability assessment due to lightning storms, IEEE Trans. Power Deliv. 20 (3) (2005) 2153–2159.