New energy grid-connected line fault localization method based on improved VMD-MUSIC

In view of the limitations of the traditional double-ended traveling wave ranging method in new energy grid-connected transmission lines and the inability to effectively extract the deep characteristics of the traveling wave intrinsic frequency. This paper proposes a new energy grid-connected line fault localization method based on the fusion of Variational Mode Decomposition (VMD) and Multiple Signal Classification (MUSIC). Firstly, the fault traveling wave signal is decomposed into multiple intrinsic modal components by improving VMD; then, the spectrograms under the corresponding modes are obtained by using MUSIC to realize the accurate extraction of the intrinsic frequency of the traveling wave; Finally, the fault distance is calculated based on the relationship between the fault distance at the monitoring points at each end and the known line length. Simulation results show that the method can overcome the influence of spectral aliasing on the extraction of the principal component of the intrinsic frequency, and can accurately determine the fault interval, and the localization results are not affected by the fault distance, the fault type, and the fault resistance, which has good adaptability and high localization accuracy.


Introduction
With the development of the power system, new energy grid-connected will be more and more, the power system structure is more and more complex.Nowadays, fault localization of power system is mostly applied to simple lines, and rarely applied to complex new energy grid-connected lines, so it is very necessary to study the fault localization of new energy grid-connected lines.At present, the transient traveling wave fault localization methods mainly include time domain analysis method [1][2] and frequency domain analysis.Time domain analysis method traveling wave head arrival time is difficult to determine, resulting in large ranging error, while the traveling wave frequency domain method does not need to identify the traveling wave head, so it has strong applicability in new energy grid-connected line fault location.The key problem of the frequency domain analysis method is to carry out the fault traveling wave intrinsic frequency extraction.[3] The key problem of the frequency domain analysis is the extraction of the principal component of the intrinsic frequency of the faulty traveling wave, due to the propagation process of the faulty traveling wave at the connection point will occur in the folding reflection phenomenon, resulting in spectral aliasing, thus increasing the difficulty of the principal component of the intrinsic frequency extraction.Literature [4][5][6] Empirical modal decomposition algorithm (EMD), ensemble empirical modal decomposition (EEMD), variational modal decomposition (VMD) and other methods are proposed, which inhibit the spectral aliasing to a certain extent, but the effect is not ideal.In this paper, we propose to apply the improved (VMD) to decompose the faulty traveling wave signal, after multi-signal classification (MUSIC) The principal component of the traveling wave intrinsic frequency is extracted; then the distance of each end bus from the fault point is calculated using the intrinsic frequency method.

Variational modal decomposition and its improvement
The VMD algorithm corresponds to the variational problem of finding the K Intrinsic Mode Function (IMF) that minimizes the sum of the estimated bandwidths.The variational problem is transformed to obtain the augmented generalization equation and the multiplicative operator alternating direction method is used to solve this equation to obtain the solution of the modal function taking value problem.The variational modal decomposition requires a predetermined number of decompositions of the modal components when processing the signal, K.A large value of K will cause the signal with a frequency concentrated in one range to be decomposed into a number of modal components, which will make their center frequencies closer together, resulting in frequency aliasing; a smaller value of K will result in a lack of information, as the VMD algorithm is equivalent to an adaptive Wiener filter bank, and some key information in the original signal will be filtered out by the filter, resulting in a missing information.

Key IMF Component Determination
In this paper, a method for determining the number of modes based on the correlation coefficient is proposed.Under the premise that the maximum center frequency appears in the components, the correlation coefficient between modal components is calculated to determine whether there is frequency aliasing between each modal component, so as to determine the number of modes K.The correlation coefficients of signal x(n) and signal y(n) are defined as.

Traveling wave intrinsic frequency extraction method based on MUSIC algorithm
The basic idea of the MUSIC algorithm, on the other hand, is to eigen-decompose the covariance matrix of the output data of an arbitrary array, so as to obtain the signal subspace corresponding to the signal components and the noise subspace orthogonal to the signal components, and then use the orthogonality of these two subspaces to estimate the parameters of the signal.

Fault localization method based on traveling wave intrinsic frequency
The fault traveling wave propagating on a lossy transmission line undergoes reflexion between the fault point and the end of the bus, which is manifested in the frequency domain as a series of harmonic forms of specific frequencies, called the traveling wave intrinsic frequency.The component with the smallest frequency value and the largest corresponding amplitude energy is called the principal component of the traveling wave intrinsic frequency.The formula for calculating the distance to fault: In the formula, 1 and represent the reflection angle between the measuring end of the busbar and the fault point, is the intrinsic frequency, and corresponds to the wave speed, which is calculated by the formula: = 2 / • .The fault traveling wave signal detection device is installed at each end bus, and the length of each branch line is known.After the fault occurs, assuming that the intrinsic frequency of the fault traveling wave detected at each measurement point is , , , , the distance of the fault at the corresponding frequency is calculated according to equation ( 2), which is the distance from the bus at each end to the point of the fault, and it is divided into three cases.
(1) When the fault occurs on a branch line, it can be seen that only the fault distance calculated from the faulty branch measurement point is less than the distance from the faulty branch bus to the nearest node, while the opposite is true for non-faulty branches.When the fault occurs between A-F , the distance measured at bus A 1 < ,bus B, C, D are greater than the distance from the corresponding bus to the nearest node, both 1 > , 1 > , 1 > .select the distance measured at the faulty branch measuring point as the final fault distance.
(2) When the fault occurs at node F, there will always be one end of the measurement point calculated fault distance is equal to this end of the bus to the nearest node, at the same time, the remaining ends of the calculated fault distance is equal to the bus to the corresponding node, both = , = , = , = .When the fault travelling wave needs to pass through other nodes to propagate to the bus, select the propagation path of all the fault travelling wave through the least number of nodes can be reached to the bus end to get all the propagation paths to satisfy The fault distance of the bus end corresponding to all the satisfied propagation paths is obtained, and the minimum distance is compared, which is the final fault distance.
(3) When the fault occurs between two nodes, firstly, take end A as the beginning to increase the number of nodes one by one to compare it with the calculated fault distance, and when the fault distance satisfies between the distance from end A to the ith node and the distance from end A to the ith + 1 node, then stop the comparison and initially consider that the fault occurs between the ith node and the ith + 1 node; and then, take each of the remaining ends as the beginning to carry out the test.If the fault distance calculated at each end is between the distance from this end to 2 nodes, then the fault point is between 2 nodes.When the fault occurs between E and F, > 2 > , > 2 > , > 2 > , > 2 > .select the propagation path of the fault traveling wave that can reach the bus end only through the least number of nodes to get the fault distance of the bus end corresponding to all the satisfied propagation paths.The closest distance for localization is selected as the final fault distance.

Simulation Model
PSCAD is applied to simulate the electromagnetic transient process of 220kV transmission line model.The power supply at each end is an ideal voltage source, i.e., Zs = 0.The positive and zero sequence parameters of the line are r 1 = 0.0348Ω/km , x 1 = 0.425Ω/km , b 1 = 2.725μs/km , r 0 = 0.303Ω/ km , x 0 = 1.147Ω/km , and 0 = 1.938/km , respectively.The sampling frequency of the system is MHz  The fault occurs at the MT1 branch.Assuming that a single-phase metallic grounding fault occurs 30km away from the M end at 0.1s , the inherent frequency principal components are extracted by combining the improved VMD with the MUSIC algorithm.The spectra of the measurement points at the M, P1, P2,N ends are shown in Fig. 3, and the results of the ranging at the time of the fault are shown in Table 1.The localization result is that the fault occurs 30km away from the bus at M end, and the localization error is 83m.
The fault occurs at T1, T2 branch.Assuming that a single-phase metallic grounding fault occurs at 0.1s at a distance of 20km from the M terminal, the principal components of the intrinsic frequency are extracted (the spectrogram is not listed due to space reasons), and the ranging results are shown in Table 2.The fault occurs between T1 and T2 nodes, and the monitoring points M, P1, P2 and N pass through a node to the fault point, so the shortest distance of localization is chosen as the final localization result, which is both 30.086m, with a localization error of 86m.
The fault occurs at node T2.Assuming that a single-phase metallic grounding fault occurs at 0.1s, the intrinsic frequency principal components are extracted as shown in Table 3. N, P2 bus to the fault point are not through the node, compare the distance between the two, select the distance of the closest for the localization results, both 20.079km, localization error of 79m.

Applicability analysis
In order to verify the adaptability of the proposed method in new energy grid-connected lines.The localization results are given for different fault types at 10km from the measurement point M, as shown in Table 4.The localization results are given for different fault resistance conditions at 10km from the measurement point M, as shown in Table 5. .09393 Comprehensively, the above tables show that the change of fault location, fault type and fault resistance did not affect the accuracy of fault localization, therefore, the method has good adaptability and high localization accuracy.

Conclusion
In this paper, a new energy grid-connected transmission line fault localization method based on traveling wave intrinsic frequency is proposed.The method combines the improved VMD algorithm with the MUSIC algorithm, which solves the defect that the traditional method cannot accurately extract the principal component of the intrinsic frequency due to the complexity of the line structure.And it is not affected by fault location, fault type and fault resistance, and has strong adaptability.

Figure 1 .
Figure 1.Topography of new energy grid-connected lines.

1 and
the fault occurrence moment is 0.1s .

Figure 2 .
Figure 2. Simulation line.The fault occurs at the MT1 branch.Assuming that a single-phase metallic grounding fault occurs 30km away from the M end at 0.1s , the inherent frequency principal components are extracted by combining the improved VMD with the MUSIC algorithm.The spectra of the measurement points at the M, P1, P2,N ends are shown in Fig.3, and the results of the ranging at the time of the fault are shown in Table1.

Table 1 .
Faults occurring between M and TI node.

Table 3 .
Faults occurring at the T2 node.

Table 4 .
Localization results in case of different fault types.

Table 5 .
Localization results for different grounding resistances.