AbstractâIn this study, a new approach is proposed for fault estimation in high voltage direct current transmission lines using discrete wavelet transform and ...
A Fault Location Technique for HVDC Transmission Lines using Extreme Learning Machines Fatih ÜNAL1, Sami EKİCİ1, 1
Email: {funal, sekici}@firat.edu.tr Dept. of Energy Systems Engineering, Faculty of Technology, Firat University, Elazig, Turkey
Abstract—In this study, a new approach is proposed for fault estimation in high voltage direct current transmission lines using discrete wavelet transform and extreme learning machine. Recently, signal processing and intelligent systems have gained importance to ease very different tasks such as fault location and estimation, load estimations, reactive power compensation, the risk of blackouts. Therefore, a fast, accurate and reliable protection algorithms have a major interest in the extended usage of high voltage direct current systems for many areas. In this study, single phase-ground faults on DC lines examined and a new machine learning approach also discussed. The virtual faults obtained from Matlab simulation is utilized in the course of feature extraction of the wavelet transform. Furthermore, for identifying steady state and faulted condition, Shannon entropy and signal’s energy values have been calculated by using coefficients of the wavelet transform. After that, the coefficients normalized between [-1,1]. Finally, the extreme learning machine used to fault estimation and location process. Index Terms--Discrete wavelet transform, extreme learning
machines, machine learning methods, high voltage direct current. I. INTRODUCTION High Voltage Direct Current (HVDC) systems have become an excellent option in recent years, especially for offshore renewable energy source and different grid frequency applications. DC power transmission can perform better than AC transmission considering power transfer at a single voltage level. Some of the advantages of DC transmission are higher power transmission (up to 30%) at the same copper size and less net losses compared to counterpart [1], smaller transmission corridor (right of way), absence of skin effect on overhead lines and less dielectric losses in case of cables [2], not necessary to line compensation, transmission of bulk power over long distance [3] , interconnection to different frequencies of AC systems, limitations of faults, power flow and voltage control. Although AC transmission preferred for distances less than the breakeven distance, ıt is more expensive for longer distances. Therefore, considering the per unit line costs DC systems are more economical than AC systems. The breakeven distance can vary between 400 to 700 km of overhead lines and between 25 to 50 km with a cable system [2].
There are also some issues which are an obstacle in front of utilization in common applications. The high cost of converter stations [23], the complexity of control [24], generation of harmonics during conversion AC to DC and requirements of reactive power at converter stations [25], operational difficulties in the multi-terminal structure are the major problems in DC transmission [26 ],[27]. While HVDC transmission main protection scheme is traveling wave protection, derivative and differential protection are background protection. When a fault occurs on DC line, traveling wave produces at fault point to propagate along DC line, and reflects between converter station equipment which are DC filters and smoothing reactors. This traveling high-frequency signal contains useful information about fault location. Therefore, traveling wave protection utilizes the transient information of traveling wave at the beginning of faults to determine fault point. During to fault on DC line, DC voltage at rectifier side decreases rapidly and DC current at rectifier side increases. These transient characteristics also used in derivative protection. Because of derivative and traveling wave protection cannot perform well under faults with high impedance, differential protection is used as backup protection. As mentioned before this study mostly focuses on the DC side faults and proposes a novel protection algorithm that will be an alternative to classical traveling wave dispersion. A. Literature Survey Currently, HVDC protection techniques are classified into three categories; traveling wave protection, signal processing approaches and machine learning. In [4] to detect a fault on DC transmission line and improve the stability of traveling wave protection, modulus maxima of wavelet transform is used. In [5] to isolate the effect of fault impedance and create a novel traveling wave protection which is using common mode and differential mode, polarity comparison of forward and reflected traveling waves are used. In [6] to discriminate both external and internal faults on DC transmission line protection zone, uses the attenuation effect of boundary equipment on the highfrequency component and fault impedance. In [7] uses wavelet transform and entropy principle to protect for commutation failures in HVDC systems. Similarly, In [8] proposes an
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approach which can distinguish between external and internal faults using the voltage traveling wave polarity comparison based on wavelet transform and energy distribution. In [9] proposes a line fault location algorithm based on singular value decomposition and generalized regression neural network which can extract the feature of traveling wave and determine line fault position. In [10] takes advantage of genetic algorithm principle for low sampling rates when traditional traveling wave technique does not perform in limited time intervals and to estimate the amplitude of the non-periodic components. In [11] mentions the implementation of singular value decomposition, support vector machine combination for fault type identification and detection of commutation failures in HVDC systems.
II. SIMULATION STUDY AND SYSTEM IDENTIFICATION In the study, a monopolar HVDC system is used to obtain virtually DC voltage and current signals from the simulation in Matlab/Simulink environment. The system is shown in (1) is 500kV, 1000MW HVDC interconnection with 12 pulse converters on both rectifier and inverter side. DC line is 300 km long and transmits power from a 500kV, 5000MVA, 60 Hz network to 345kV, 1000MVA,50 Hz network. There are two 0.5 H reactors and DC filters positioned at the side of rectifier and inverter to eliminate distortions caused by DC side. The control system of converter stations consisted of mainly three sub-modules which composed of the model as master, rectifier and inverter control.
Figure 1. Simulation model of monopolar HVDC transmission system.
At the beginning of simulation and control strategy, the predefined simulation parameters are chosen so as to describe system properties and DC voltage and current values. After that, the fault current and voltage signals obtained from each km of 300 km DC line decomposed by signal processing techniques which in here Discrete Wavelet Transform (DWT) to attain considerable information about fault location. Also in Obtaining fault current and voltage signals from simulation (Id ve Vd) Segmentation
Discrete wavelet transform (DWT)
this stage feature extraction and normalization of parameters adjusted respectively signal energy and Shannon entropy, and normalization between [-1,1]. Finally, Extreme Learning Machine (ELM) method is used to fault estimation and location by input data which consist of fault current and voltage parameters at each km of DC line. In figure 2 shows that overall process of fault estimation using DWT and ELM techniques.
Feature Extraction (Signals energy, Shannon Enthropy etc.) Normalızation between [-1 1]
Training and testing stages of Extreme Learning Machine (ELM)
Fault Estimation and location
Figure 2. Overall processes of fault estimation on DC line.
In this study, simulation time is 1.6 sec. and the sampling frequency is 20 kHz. Fault current and voltage signals obtained from the simulation recorded at each km of 300 km between the 15th and 285th. Fault resistance and fault duration are kept constant for each km and appeared between [0.7-0.8] seconds after the simulation start. Also, the fault current and voltage signals obtained from simulation are recorded only on DC side without considering the noise effects or any other distortions. III. WAVELET TRANSFORM The ability of Wavelet Transform (WT) in time-frequency domain makes it possible to determine transients simultaneously and localization of their occurrence [12], [13]. Also, the WT enables us to understand how the parameters of the signal are varying over the sampling time and how ıt can be composed of different frequency bands like a low-pass filter or
a high-pass filter. Unlike Fourier Transform, The WT decomposes a signal into different frequency levels using a shifted and scaled mother wavelet. The summation of each different frequency levels represent the original signal and can be constructed vice versa [14]. While Continuous Wavelet Transform (CWT) uses the whole dataset, some undesirable situations such as the need for more memory requirement or incremental calculation time especially at shifting and scaling process might occur. In the DWT, this process carried out into dyadic windows or exponential coefficients of 2 [15],[19]. The CWT and DWT’s mathematical expression are given respectively in (1) and (2) as.
126
,
∗
= ,
=
,
(1)
√
is mother wavelet, b and a respectively are In (1), ∗ , shifting and scaling parameter, represents the wavelet transform of the original signal.
,
∑
= ,
=
∗
(2)
In (2), mathematical representation of DWT expressions are , = , = , where , , ∈ respectively; = ℤ.. The multiresolution of DWT decomposes a given signal into its detail and approximation coefficients, and this process can keep going to desired decomposition level [16]. While the wavelet coefficients of different levels can be preferred to analysis the signal, determination of appropriate properties which represents the feature of the signal instead of coefficients is more reasonable [19]. For such reasons ın this paper, wavelet entropy theorem and signals energy parameters are preferred to represent the entire signal and used as input values in the process of training ELM. The wavelet entropy theorem helps us to understand the uncertainty in the signal [17], [18]. When considering a signal which is randomly distributed in the time or frequency domain, the observed uncertainty state and entropy of signal is high. In contrast to this phenomenon, if a signal does not change at certain time intervals, ıts entropy is zero. Furthermore, the energy distribution of the voltage and current transient signal at decomposition scales represent their energy in the frequency domain [8], [19]. By WT theory, the wavelet energy of j decomposition level is defined as in (3). =∑
= 1,2,3, … . ,
approximate coefficient obtained. Since the approximate coefficients in the 12. level contain low-frequency components are not considered a distinguishing feature and removed from the data set. Thus, in total 22 feature vectors are obtained from the current and voltage signals for each km of fault point. IV. EXTREME LEARNING MACHINES ELM was introduced by Huang, [20] for single layer feedforward neural networks (SLFNs) which randomly chosen hidden layers and numerically determines the output weights of SLFN. In [21] ıt is proved that the input weights and the hidden layer biases can be chosen randomly and SLFN simply considered as a linear system and outputs of SLFN can be analytically determined by generalized inverse operation of hidden layer output matrix in case of activation functions in the hidden layer are infinitely differentiable [22]. Considering a data set which contains N different sample , ; = , , ,…., ∈ and corresponding = , , ,…., ∈ , N represents outputs are hidden layer and activation function, SLFN’s can mathematically modeled as [20], [21], ∑
=∑
= − ∑ p log p
,…., + ⋮ +
=
(5)
In (5), measures the complex interactions in different frequency components with the original signal to detect any changes in voltage and current signals. There are many commonly used entropy calculation methods and some of those; Shannon, Threshold, Norm, Logarithmic Energy and Sure criteria. In this study, Shannon entropy values are derivated to represent for each fault location by using fault current and voltage signals At the decomposition process of virtual faults obtained from simulation, ‘Daubechies (db4) wavelet family’ is used and analyzed the first 20 ms after the fault has started. When applying DWT to the fault current and voltage signals, 13 feature vectors in total, including 12 details and one
.
(6)
In the ELM method, mathematical representation of the network in a different manner can be considered as a multiplication of data matrices = [21]. Assuming that the output matrix of the hidden layer of the SLFN is , the weight vector is and the T matrix expresses the real outputs vectors and can mathematically written as shown in (7).
(3)
(4)
=
Where = , , ,…… is the randomly chosen weight vectors connecting th hidden layer and input layer, = , , ,….., is the weight vectors connecting th hidden layer and output layer. Also, represents the threshold value of the th hidden layer.
In (3), represents the DWT’s detail coefficients. So the energy of the signal and wavelet energy entropy values are respectively given by (4) and (5). =∑
+
⋮
,
,…., ⋯ ⋯ ⋯
= ×
,
,…., + ⋮ +
⋮
= (7) ×
(8) ×
The main goal of ELM method is to specify optimal values. If the number of hidden layer is equal to N training sample = , H matrix is a square matrix and and hidden layer invertible. Thereby, the input weight biases can be easily determined. However, in most cases, H is a nonsquare matrix, and this approach is not useful. To overcome this problem, Huang and his colleagues [21] rearranged the = equation using the generalized Moore-Penrose inverse matrix transformation in ELM method. The inverse transformation of nonlinear H matrix is given in (8). =
(9)
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V. TRAINING AND TESTING PROCESS OF ELM In the simulation, The DWT analysis of the fault voltage and current signals is the first 20 ms after the fault starts. This range covers between 14000 − 14400 samples from the data set of current and voltage signals.As a result, the data set will be very large, Shannon entropy and signals energy values determined to reduce datasets without any changes in features. Fig. 3 shows the first five levels of DWT’ s of the fault currentvoltages signals at 15. km by the rectifier.
The equation of = is also one of the least squares solutions of generalized = linear system and in other words the lowest training error can be achieved with this particular solution. The minimum training error criterion is also mathematically expressed in (9). −
=
−
0.25
‖
=
0.5
− ‖
0.75
1.0
(10)
1.25
0.25
1.50
0.5
0.75
1.0
Time (s)
Time (s)
(a)
(b)
1.25
1.50
Figure 3. The first five decomposition level of DWT (a) fault current (b) fault voltage.
In ELM method, the regularization parameter is 1 × 10 . In the DWT-ELM application, the size of training data matrix is 22 × 163 and in the testing and validation stage, the size of the feature matrix is 22 × 54 . The number of hidden layer neuron is determined as (n=100). After training process, the
regression value obtained from the ELM is (R= 0.99443). Fig. 4 shows the regression value of ELM application and the estimated fault location in the testing process.
Estimated fault location of ELM (red line),actual fault location (blue line)
: R=0.99432 Data Fit Y=T
250
200
200
Fault location (km)
Output ~= 1*Target + -1.1
250
150
100
150
100
50 50
0 0
5 0
50
100
150 (a)
200
250
10
15
20
25 30 Samples (b)
35
40
45
50
Figure 4. The testing process of ELM (a) regression value, (b) estimated and actual fault location
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VI.
CONCLUSION
In this study, a new machine learning algorithm is discussed and applied to estimate fault location on DC line. In the feature extraction and signal processing stage, DWT applied to fault signals. Obtained from Matlab simulation, the fault current and voltage signals are not exposed any other external effects (such as noise and different fault resistance) After that, calculation of Shannon entropy and signals energy parameters used for input layer of ELM in training stage. The ELM method can progress with fewer training steps in a shorter time than other neural networks using back propagation algorithm. However, this approach also will able to cause memorizing of ELM in training and can increase the training error. In literature, there are some implementations to overcome this problem using some adjustable parameters and equations like Regularized ELM (RELM), but in this study, the RELM results obtained close to ELM results did not mention in Section 4. In the future study, different signal processing techniques and more accurate feature parameters can be investigated to improve the ability of ELM in the estimation of single phaseground faults DC lines. Also, ıt is possible to implement these methods on bipolar HVDC lines and multi-terminal DC interconnection systems which are preferred commonly in HVDC applications. REFERENCES
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