A new method for single‐phase high resistance grounding fault protection in low resistance grounded distribution networks

The neutral point of the distribution network is grounded with low resistance, which can quickly remove single‐phase grounding fault and effectively suppress overvoltage. However, the existing zero‐sequence overcurrent protection has a high setting value. In the case of large fault resistance and weak fault current, the existing protection methods may refuse to operate. Based on the waveform characteristics of the zero‐sequence current of each outgoing line in the distribution network, this article proposes a new method for single‐phase high resistance grounding fault protection in low resistance grounded distribution network, which combines cosine distance and improved K‐means algorithm. First, the cosine distance between zero‐sequence current of every two outgoing lines is obtained, and the cosine distance matrix used to describe the fault characteristics is constructed. Then the improved K‐means algorithm is used to cluster the row vectors of the cosine distance matrix to obtain the convergent cluster center and cluster label, so that the fault line can be determined. This protection method does not need to set the threshold value manually, and has strong ability to handle large fault resistance. It can effectively deal with noise interference and intermittent arc grounding fault, and still has good adaptability in scenarios such as change of fault initial phase angle, change of fault location, access of distributed generations and occurrence of two outgoing lines in phase to grounding fault. Finally, a model is built, and the effectiveness of the proposed method is proved by the simulation of grounding fault.

to the ground, the capacitance current to the ground is high when the fault occurs.At this point, using arc suppression coil compensation method is inconvenient for installation of underground cables, and the configuration speed of arc suppression coils can no longer keep up with the expansion speed of cable lines in the distribution network.The low resistance grounding method can overcome large capacitive current, quickly remove faults, and fundamentally suppress the generation of resonance overvoltage.Therefore, the low resistance grounding method is increasingly widely used in urban distribution networks with rapidly expanding cable lines. 1 In China Southern Power Grid, the low resistance grounding method has been widely used in the distribution network.][4] There are also some difficulties in relay protection for low resistance grounded distribution networks, with high resistance grounding faults being the most significant.At present, in low resistance grounded distribution networks, zero sequence overcurrent protection is often used to handle grounding faults, which often sets a protection threshold based on avoiding the maximum capacitive current of non-fault lines.Taking the commonly used zero sequence overcurrent protection setting value of 60 A in the field as an example, 5 the maximum fault resistance it can handle is only about 100 Ω. Due to the deep penetration of the distribution network into the load center, the environment in which it operates is complex and variable.Faults often occur through non-ideal conductors such as tree branches, soil, ponds, or cement buildings, that is single-phase high resistance grounding faults.The fault resistance is often thousands of ohms, and the fault current is very weak.Therefore, the existing overcurrent protection will refuse to operate.If the fault is not removed for a long time, it may break through the insulation layer between the lines, leading to the development of phase to phase short circuits, further inducing intermittent arc overvoltage, and causing irreversible damage to electrical equipment.More seriously, during the fault, the step voltage around the grounding point can even reach several thousand volts, and the temperature of the grounding point can generally reach several thousand degrees Celsius, which is prone to causing fire and posing a serious threat to the lives of nearby residents. 6omestic and foreign scholars have proposed some practical and feasible protection methods for high resistance grounding faults.For example, Reference 7 proposed a high resistance grounding fault protection method based on zero sequence voltage ratio restraint, which adaptively changes the protection setting value by utilizing the characteristic that the bus voltage can reflect the size of the fault resistance.This can increase the protection's ability to handle fault resistance to 1000 Ω, but the setting method is relatively complex.Reference 8 also utilizes the characteristic that bus voltage can reflect the size of fault resistance to correct the zero sequence current amount.Without changing the protection threshold, it amplifies the fault current and improves the protection's ability to handle fault resistance to 1000 Ω. References 9, 10 proposed a single-phase high resistance grounding protection method for low resistance grounded networks based on composite power, which can handle fault resistance up to 2000 Ω, but the construction idea of the criterion is complex.Reference 11 proposed a fault location method for low resistance grounded networks based on zero sequence admittance, which improves the fault location ability by using two terminal information, and the resistance to fault resistance can reach 2000 Ω. Reference 12 proposed a highly sensitive zero sequence stage overcurrent protection method, which decomposes the existing zero sequence overcurrent protection into multiple fixed time limit overcurrent protection, which can ensure the sensitivity of protection during high resistance grounding and the selectivity of protection during low resistance grounding, with the resistance to fault resistance of up to 1500 Ω. Reference 13 proposed a high resistance fault detection method for low resistance grounded networks based on integrated inner product transformation.The inner product principle is used to highlight the difference between fault outgoing line and non-fault outgoing line, but the neutral point current needs to be measured.Reference 14 proposed an interval slope to describe waveform distortions and detect high-impedance faults.Reference 15 detected high-impedance faults in a neutral isolated network by estimating the zero-sequence grid capacitance.Reference 16 uses the zero-sequence current and voltage to propose a protection principle.However, this method requires additional installation of voltage transformer.The methods proposed in References 17-20 all utilize the comparison of the zero sequence current amplitude or phase of each outgoing line to achieve protection, requiring communication means.However, such methods often require the setting of auxiliary criteria, is difficult to set the protection setting value, and cannot handle situations of multi-point grounding faults and distributed power supply connections.
After modeling and fault analysis of the low resistance grounded distribution network, this article found that there is a significant difference in the waveform of the zero sequence current flowing through the fault and non-fault outgoing lines after the occurrence of a single-phase grounding fault.The method proposed in this article uses cosine distance to describe this difference.The cosine distance between zero sequence current flowing through different outgoing lines constitutes a cosine distance matrix used to describe the fault characteristics.The fault outgoing line can be identified by running the improved K-means clustering analysis for row vectors in the cosine distance matrix.Through simulation verification, this method is practical and feasible, and does not need to set the threshold value manually.It has strong ability to handle fault resistance and still has good applicability in various situations such as intermittent arc grounding, noise interference, changes in initial phase angle of faults, and changes in fault location.Especially in terms of large-scale access of distributed generations, multi-point grounding faults, and the speed of protection, it has significant advantages compared to traditional protection methods.

2.1
The structure of low resistance grounded distribution network and the establishment of equivalent circuits As shown in Figure 1, it is a typical structure of a low resistance grounded distribution network.Using the equivalence principle similar to Reference 21, ignoring the impedance of the non-fault line and the line after the fault point, a zero sequence network when a single-phase grounding fault occurs in a low resistance grounded distribution network can be obtained as shown in Figure 2. 22,23 F I G U R E 1 The typical structure of a low resistance grounded distribution network.
F I G U R E 2 Grounding fault zero-sequence network of low resistance grounded distribution network.
The research object of this article is a low resistance grounded distribution network with a 10 kV voltage level.Therefore, the bus voltage in Figures 1 and 2 should be 10 kV.For the rated voltage of underground cables, in China's distribution network, according to national standards, the rated voltage of underground cables is often divided into phase to phase rated voltage and phase to ground rated voltage.In the AC system, the rated voltage between phases of the cable core should be greater than the rated voltage of the local power grid.For the 10 kV voltage level distribution network studied in this article, the rated voltage of the selected cable should be greater than or equal to 10 kV.In the AC system, the rated voltage (phase to ground voltage) between the cable core and the insulation layer or metal layer is determined by the neutral point grounding mode and the fault removal time.In the neutral point grounding system through low resistance, since the fault removal time of the grounding protection does not exceed 1 min, the working phase voltage of the circuit is selected as the rated voltage.In systems where the neutral point is not grounded or grounded through high resistance, the rated voltage should be the line voltage of the circuit.
In the above two figures: E A , E B , E C represent the electromotive force of the three-phase power supply, R n represents the neutral grounding resistance, and R f represents the fault resistance of the fault point.R N represents three times the neutral grounding resistance.u f = U m sin( 0 t + ) is the virtual power supply at the fault point, where, U m is the amplitude of the fault phase voltage during normal system operation,  0 is the power frequency angular frequency, and  is the fault initial phase angle.R represents the sum of the resistance of the upstream line at the fault point and three times the fault resistance, L represents the zero sequence inductance of the upstream line at the fault point, and C  represents the zero sequence distributed capacitance to ground of the upstream line at the fault point.C j represents the zero sequence distributed capacitance to ground of the jth non-fault line.u C n represents the zero sequence capacitive current to ground of the upstream line at the fault point, u C j represents the zero sequence capacitive current to ground of the jth non-fault line, u C  represents the zero sequence current flowing through the fault line, u C f represents the zero sequence current flowing through the fault point, and u C n represents the zero sequence current flowing through the neutral grounding resistance.

Mathematical Derivation of zero sequence current expression for each outgoing line
The composite sequence network 24 of low resistance grounding system in case of single-phase grounding fault is shown in Figure 3.
Where, the capacitance C  in the equivalent circuit is the total distributed capacitance to the ground of the system, and the inductance L is the series connection of the 1, 2, and 0 mode inductance of the upstream line at the fault point; The resistance R is the sum of the grounding fault resistance value of the upstream line of the fault point, which are connected in series with the 1, 2, and 0 mode resistance, and then connected in series with three times the grounding resistance of the fault point.The resistance R N is three times the neutral grounding resistance.
The fault virtual power supply is: F I G U R E 3 Single-phase grounding fault composite sequence network of the low resistance grounded distribution network.
According to Figure 3, when a single-phase grounding fault occurs, the general formula of the equivalent circuit is: ( From the above formula, we can get the following second-order non-homogeneous constant coefficient linear differential equation: Using mathematical methods to obtain the characteristic roots as: According to the values of the characteristic roots, the system is divided into two situations: over damping and under damping: , it belongs to the case of over damping; When 0 < R < , it belongs to the case of under damping.
As this article mainly studies the case of high resistance grounding, only the over damping case is considered below.After mathematical derivation, the following expression can be obtained.
The capacitance current of the jth non-fault outgoing line is: The zero sequence current flowing through the fault outgoing line is: Among them,

Similarity analysis of zero sequence current of each outgoing line
The first two terms of formulas ( 5) and ( 6) are transient components, while the last two terms are steady-state components.From formula (5), it can be found that the difference in steady-state zero sequence current flowing through different non-fault outgoing lines is that the phase is theoretically similar, but the amplitude is different.This is caused by the different capacitance distribution to the ground of different lines, while the length difference of distribution lines is not significant, so the difference in waveform amplitude is not significant.From formulas ( 5) and ( 6), it can be concluded that the zero sequence current flowing through the non-fault and fault outgoing lines is not similar in amplitude or phase.
In summary, the waveform similarity characteristics of the zero sequence current flowing through the non-fault and fault outgoing lines can be used to determine the fault outgoing line.Due to the difference in amplitude between the zero sequence currents flowing through non-fault outgoing lines, the calculated similarity is not high.Therefore, choosing an algorithm that ignores amplitude and only uses phase information to characterize similarity can more accurately select fault outgoing lines.

Cosine distance
The cosine distance, also known as cosine similarity, is the cosine value of the angle between two vectors in the vector space as a measure of the difference between two individuals.The specific calculation method is shown in formula (8).
Among them, vector x a = {x a (1), x a (2), … , x a (n)} is the sampling value of the zero sequence current in outgoing line a; vector y b = {y b (1), y b (2), … , y b (n)} is the sampling value of the zero sequence current sampling value in outgoing line b; r ab is the cosine value of the angle between two high-dimensional vectors, which is used to characterize the similarity of the zero sequence current in outgoing line a and outgoing line b.The range of r ab is [−1, 1], the closer the cosine value is to 1, the closer the angle is to 0 degree, and the more similar the two vectors are; The closer the cosine value is to −1, the closer the two vector waveforms are to completely opposite. 25

Establishment of cosine distance matrix
The cosine distance matrix can be established by analyzing the similarity of the zero sequence current flowing through every two outgoing lines in the distribution network and calculating its cosine distance.Taking the low resistance grounded distribution network with five outgoing cables in the simulation model of this article as an example, the cosine distance matrix shown in formula (9) can be obtained, which contains the fault characteristics of single-phase grounding fault and can be used as the basis for the protection method in this article.
where r represents the cosine distance matrix obtained through correlation analysis.Each element r ij represents the cosine distance between the zero sequence current in outgoing line i and outgoing line j.

Advantages and disadvantages of cosine distance algorithm
First, from the formula of cosine distance, it can be found that cosine distance needs to normalize the length of two high-dimensional vectors, and then measure the direction of the two vectors.Therefore, the calculation result is independent of the length of the vectors.As long as the two vectors have the same direction, regardless of their length, they can be considered "similar", that is, "cosine similarity is not sensitive to the absolute value of specific values."When not paying attention to the size of high-dimensional vectors, cosine distance is usually used.The traditional Euclidean distance and dynamic time warping distance (DTW) algorithms 26 focus on the numerical differences of vectors, measuring the absolute distance between two high-dimensional vectors.In the case of high resistance grounding faults, the fault current is relatively weak.In this case, the cosine distance algorithm is more effective.The comparison of zero sequence current similarity among various outgoing lines proposed in this article actually refers to the steady-state zero sequence current similarity.However, after a high resistance grounding fault occurs in a low resistance grounded distribution network, there is a relatively obvious transient process.Due to different fault initial phase angles, the severity of transient processes can be affected, thereby affecting the magnitude of the cosine distance threshold value.In addition, noise interference, intermittent arc grounding, distributed generations connection, and multi-point grounding can all cause changes in the threshold value.Therefore, in order to balance the reliability and sensitivity, it is often necessary to adaptively set the threshold value according to changes in the situation, which poses great difficulties in engineering.If a protection method that does not require setting the threshold value can be found based on the calculated cosine distance, it will greatly simplify the protection process.

Principle of improved K-means algorithm
K-means algorithm is a unsupervised learning method in machine learning, which can mine the similarity of data objects without any experience to achieve the purpose of data grouping. 27his algorithm requires pre specifying the number of clusters K and K initial clustering centers, calculating the distance between the given data object and the initial clustering center, and dividing each data object into the closest cluster.After all data objects are allocated, the average value of data objects for each type of cluster is recalculated as the new clustering center.Repeat the iteration for data object classification and cluster center update until the specified number of iterations is met or the cluster center changes within a small range, that is, the sum of squares of errors no longer changes or the objective function converges.
Each row vector in the cosine distance matrix is taken as a data object.Since only the fault outgoing line has faults, the number of clusters is 2, that is, the fault cluster and the non-fault cluster.
The traditional K-means algorithm usually randomly selects clustering centers, and the final clustering result is affected by the initial clustering center, and the speed of executing clustering tasks is slower.This article adopts an improved K-means clustering algorithm. 28Compared to traditional algorithms, the initial clustering centers in this article are no longer randomly selected, but rather K initial clustering centers as far away as possible.This not only increases the running speed, but also avoids classification errors caused by improper selection of initial clustering centers.

Protection algorithm process
According to the above algorithm, collect the zero sequence current data of half cycle (10 ms) in each outgoing line after the fault, respectively, calculate the cosine distance of zero sequence current in every two outgoing lines, and generate the cosine distance matrix.The cosine distance matrix is taken as the input of the improved K-means algorithm, and all row vectors in the matrix are clustered to obtain the cluster center and cluster label.The fault identification results are output according to the cluster label.The specific protection algorithm process is shown in Figure 4.

SIMULATION VERIFICATION ANALYSIS
In MATLAB/Simulink, build a single-phase grounding simulation model of the typical 10 kV low resistance grounded distribution network as shown in Figure 5.The five outgoing lines are cable lines, the neutral point grounding resistance R n = 10 Ω, and the grounding transformer is represented by a capital letter Z.The triggering time of faults is set at 0.1 s, the fault initial phase angle is set at 0

Simulation analysis of the applicability of protection methods
In order to verify the influence of the transient process on the protection method within the 10 ms data window, both filtered and unfiltered cases are considered in the following adaptive simulation analysis.

The influence of fault resistance
Assuming that a single-phase grounding fault occurs in phase A (F 1 ) at the midpoint of outgoing line 1, and the fault resistance is linear.In this section, simulations are conducted separately with fault resistance R f of 100, 1000, 2000, and 2500 Ω.The triple zero sequence current waveform of each outgoing line obtained in the first two cases is shown in Figures 6 and 7.
The half cycle in the dashed box represents the unfiltered data window, while the data window for filtering out the transient process is shown in the thumbnail in the upper left corner.In addition, the zero sequence current simulated in this article is three times the actual zero sequence current.The above content will not be further elaborated in the following text.
By observing the zero sequence current waveforms of each outgoing line under different fault resistance conditions, it is not difficult to find that after filtering, the waveform similarity of zero sequence current between non-fault outgoing lines in the data window is relatively high, while the waveform similarity of zero sequence current between non-fault outgoing lines and fault outgoing lines is relatively low.Due to the short 10 ms data window selected, the transient process will reduce the similarity between non-fault lines without filtering.
Through formula (8) and formula ( 9), the cosine distance matrix with and without filtering can be obtained, respectively.According to the principle introduced in Section 3.4, after the improved K-means clustering analysis of the cosine distance matrix above, the clustering center and clustering label can be obtained.

Clustering parameters Cluster results
Cosine distance matrix Due to space limitation, only cosine distance matrix and cluster center are given when the fault resistance is 100 Ω, as shown in Tables 2 and 3.In the applicability analysis of protection below, only clustering labels and fault discrimination results are provided.
By comparing each row vector in the cosine distance matrix and clustering centers, the clustering label characterizing the cluster where each outgoing line belongs can be obtained, so that the fault outgoing line can be determined.The specific results are shown in Table 4.
From Tables 2 and 3, it can be found that due to the influence of the transient process, the cosine distance between the zero sequence current of non-fault outgoing lines before filtering is significantly lower than that after filtering.However, as shown in Table 4, regardless of filtering or not, the method proposed in this article can correctly select the fault outgoing line under high fault resistance conditions.

Clustering parameters
Cluster results

The influence of intermittent arc grounding faults
When a single-phase grounding fault occurs in the actual system, the possibility of intermittent arc grounding is high, and the harm is also the most serious.When a single-phase metallic grounding fault occurs in the distribution network, the power grid is allowed to operate with the fault for 2 h, while arc grounding fault needs to be quickly removed.This is because the state of the arc is very unstable, and the ignition and extinguishing of the arc have a certain degree of randomness.Due to the presence of a large number of inductive components and distributed capacitance in the distribution system, the high-frequency components brought by the arc can cause electromagnetic oscillations in the inductance and capacitance, which can easily form overvoltage and cause serious harm to the entire power grid.Aiming at intermittent arc grounding faults, the cybernetics model is used to model the arc.
The mathematical expression of cybernetics model 23 is shown in formula (8).
where g is the arc conductivity; G s is the steady-state conductivity of the arc;  s is the arc time constant; t is the time; I p is the amplitude of the steady-state current when a metallic grounding fault occurs;  is a constant that affects the zero break time of the arc; U s0 characterizes the voltage drop per centimeter of the arc gap; and l arc characterizes the arc length.When an intermittent arc grounding fault occurs, repeat the above simulation process.Assuming that the single-phase grounding fault occurs in phase A (F 1 ) at the midpoint of outgoing line 1, simulations are conducted with fault resistance R f .arc of 100, 1000, 2000, and 2500 Ω.Among them, when the fault resistance is 100 Ω, the triple zero sequence current waveform of each outgoing line is shown in Figure 8.
By observing the waveform shown in Figure 8, it is not difficult to find that when an intermittent arc grounding fault occurs, due to the zero break phenomenon of the arc, the waveform of the zero sequence current of each outgoing line has been distorted.However, the zero sequence current in non-fault outgoing lines still maintains high similarity, and  the zero sequence current of the non-fault outgoing line and the fault outgoing line are still not similar.Therefore, the protection method described in this article is still applicable.The clustering labels and fault identification results obtained through similarity calculation and clustering analysis are shown in Table 5.

TA B L E 5 Fault diagnosis results in case of intermittent arc
From Table 5, it can be found that regardless of filtering or not, the protection method proposed in this article can reliably select the fault outgoing line under intermittent arc grounding faults, and has strong ability to handle large fault resistance.

4.1.3
The influence of noise Take the case where the linear fault resistance in Section 4.1.1 is 100 Ω as an example, add Gaussian white noise with signal-to-noise ratio (SNR) of −1, 10, and 25 dB to the zero sequence current.Figure 9 shows the waveform of the zero sequence current of each outgoing line under SNR = 25 dB noise interference.It can be seen from the figure that although the noise interference causes waveform distortion, the overall similarity characteristics have not changed.The clustering labels and fault identification results obtained by the method proposed in this article under the influence of noise are shown in Table 6.

Cluster labels SNR/dB
Before filtering After filtering Identification results From Table 6, it can be found that regardless of filtering or not, the protection method proposed in this article can select fault outgoing lines under noise interference of different signal-to-noise ratios, indicating that this method has strong noise tolerance ability.

4.1.4
The influence of fault initial phase angle The simulation results in Sections 4.1.1-4.1.3were obtained under the condition of the fault initial phase angle of 0 • .When the fault resistance is set to 100 Ω and the fault initial phase angle is changed to 90 • , the zero sequence current waveform of each outgoing line can be obtained as shown in Figure 10.
When the fault initial phase angle is taken as 45 • and 90 • , respectively, repeating the method proposed in this article can obtain the fault identification results shown in Table 7.
From Figure 9, it can be found that due to the more obvious transient process under the fault initial phase angle of 90 • compared to 0 • , the overall waveform similarity will decrease.In the calculation, it can also be observed that the cosine distance is significantly reduced.However, from Table 7, it can be found that the method proposed in this article can correctly select the fault outgoing line regardless of whether it is filtered or not.It can be found that the method proposed in this article has strong adaptability to changes in the fault initial phase angle.

Fault initial phase angle
Before filtering After filtering Identification results

Cluster labels
Fault location  Fault resistance () Before filtering After filtering Identification results

The influence of fault location and comprehensive simulation
The fault in the above simulation all occurs in phase A at F 1 .When the grounding fault occurs in phase A at F 2 and F 3 , a series of simulation work was conducted in this section.Considering the situation of linear high resistance grounding and intermittent arc high resistance grounding, respectively, set different initial fault phase angles, and add SNR = 15 dB Gaussian white noise in the zero sequence current of each outgoing line.Taking the above situation into account, the clustering labels and fault identification results obtained through similarity calculation and clustering analysis are shown in Table 8.

F I G U R E 11
Triple zero sequence current waveform when two outgoing lines are in phase to grounding fault.
From Table 8, it can be found that regardless of whether it is filtered or not, the protection method proposed in this article can correctly select fault outgoing lines in different fault locations, indicating that this method is not affected by the fault location.

The novelty and advantages of the method proposed in this article
The existing protection methods for high resistance grounding faults in low resistance grounding distribution networks are achieved by comparing the zero sequence current of each outgoing line.The main advantage is that in the case of high resistance faults, the amplitude difference between the fault and non-fault outgoing lines is significant, and there is also a common pattern in phase difference.For example, References 17-20 both utilize the criterion that the amplitude of the zero sequence current in the fault outgoing line is more than 10 times that of the zero sequence current in the non-fault outgoing line to determine the fault outgoing line.The method proposed in this article has the following four advantages compared to existing protection methods.

4.2.1
When the system experiences a grounding fault with two outgoing lines in the same phase When two outgoing lines are grounded in the same phase in the distribution network, their fault characteristics change compared to single point grounding.Taking outgoing line 1 and outgoing line 3 as examples, grounding faults occur in phase A at the same time (with fault resistance of 1000 and 800 Ω, respectively).The zero sequence current waveform of each outgoing line is obtained through simulation, as shown in Figure 11.
From Figure 11, it can be found that when two outgoing lines are grounded in the same phase, the phase of the zero sequence current of the two fault outgoing lines is similar, and the amplitude is much greater than that of the non-fault outgoing line.In this case, it is not possible to obtain the rule that "the amplitude of the zero sequence current of one outgoing line is more than ten times that of the zero sequence current of other outgoing lines" and "the fixed relationship between a certain outgoing line and other outgoing lines in phase."Therefore, the traditional schemes based on amplitude comparison and phase comparison are no longer applicable and often require retuning and adding additional criteria.The logic is more complex.The method proposed in this article is free of setting the threshold, so it is also suitable for two outgoing lines to be grounded in the same phase or even at multiple points.Through simulation, the clustering result is (1 2 1 2 2), which can quickly determine that outgoing lines 1 and 3 are the fault lines.

4.2.2
When there are distributed generations connected in the system When a distributed generation (DG) is connected to the outgoing line, the amplitude and phase relationship between the zero sequence currents of each outgoing line will change significantly.Taking DG connected to outgoing line 2 and outgoing line 4 as examples, when the fault occurs at outgoing line 1 and the fault resistance is 1000 Ω, the zero sequence current waveform of each outgoing line is obtained as shown in Figure 12.
From Figure 12, it can be found that due to the connection of DGs, the zero sequence current of the non-fault outgoing lines 2 and 4 significantly increases, and the amplitude of the zero sequence current is greater than that of the non-fault outgoing lines 3 and 5 without DGs connection.The amplitude ratio of the zero sequence current to the fault outgoing line 1 is also much less than 10 times.From Figure 12, it can be seen that the amplitude of the zero sequence current in fault outgoing line 1 is 10.46 A, while the amplitude of the non-fault outgoing line 2 with DGs connection reaches 6.614 A. The amplitude of the zero sequence current in fault outgoing line is only 1.58 times that in the non-fault outgoing line.At this point, using the amplitude comparison method in References 14,15 will result in protection malfunction, and if the times threshold in the original criterion of "the zero sequence current amplitude of the fault outgoing line is more than 10 times that of the non-fault outgoing line" is adjusted based on the connection of DGs, it will greatly lose the sensitivity of protection, and may cause protection rejection when a large number of DGs are connected to the non-fault outgoing line.
At the same time, due to the connection of DGs, the phase of zero sequence current in non-fault outgoing lines 2 and 4 also changes.The different selection of the grounding resistance of the neutral point of the DG grounding transformer can also cause the phase offset for the two outgoing lines with DGs connection.Therefore, using the criterion in Reference 14 that "a certain outgoing line exceeds all other outgoing lines by more than 90 • is a fault outgoing line" will also cause the protection to fail to operate.
Using the algorithm proposed in this article, the clustering number is changed to 3, and the outgoing lines are divided into fault outgoing lines, non-fault outgoing lines with DGs connection, and non-fault outgoing lines without DGs connection.The clustering label is (1 2 3 2 3), indicating that the fault occurs in the outgoing line 1.

4.2.3
Speed analysis of the proposed method The traditional protection method based on amplitude and phase usually adopts the full cycle Fourier filtering algorithm, with a data window length of 20 ms, which is one cycle; The data window length of the method proposed in this article is only 10 ms, which is half a cycle, and the filtering process is omitted.After the data window is determined, the traditional protection method needs to use Fourier algorithm to calculate and compare the amplitude and phase of zero sequence current.The method proposed in this article is also to calculate the cosine distance of zero sequence current of every two outgoing lines and generate the cosine distance matrix.In terms of workload, the two methods are equivalent.In addition, the improved K-means algorithm used in this article takes approximately 10 ms to execute clustering tasks.Therefore, compared to traditional methods, the method proposed in this article has better rapidity.Therefore, the method proposed in this article does not require setting the threshold value and other auxiliary criteria manually, and replaces the complex protection setting process with the clustering algorithm.This method has moderate computational complexity, accurate fault identification, and better speed performance.In the event of two outgoing lines being grounded in the same phase and a large number of distributed generations connected to the distribution network, the protection can still operate correctly.

4.2.4
Exemption from setting the protection value manually For traditional protection methods, the operation of the protection device largely depends on the setting of the protection setting value.For high resistance grounding faults, the current itself is very weak.In order to achieve correct protection operation, it is necessary to reduce the setting value of the protection.However, a too small setting value may cause the protection to misoperation when there is unbalanced current in the system.Therefore, how to set the protection setting value is the key to existing protection methods, and it is also a challenge that often restricts the ability of the protection method to handle the fault resistance.The method proposed in this article does not require manual setting of the protection setting value, fundamentally solving this problem.

PERFORMANCE ANALYSIS OF PROTECTION METHODS
1.In China's low resistance grounded distribution network, the premise for the correct operation of mainstream relay protection devices is the setting of protection setting values.The method proposed in this article does not need to set protection setting values, and can automatically determine the fault outgoing line and cut off the fault based on the fault characteristics.If the method proposed in this article can be applied to the device, the feature of exemption from setting the protection value manually will be the biggest advantage compared to existing protection devices.2. The simulation part of this article was validated in both filtered and unfiltered cases, and it was found that although unfiltered reduces the similarity of zero sequence current between non-fault lines, it can still reliably cut off fault lines.Therefore, from the perspective of engineering applications, the method proposed in this article does not require filtering and has certain economic benefits.3. The existing high resistance grounding fault protection methods often use zero sequence voltage and zero sequence current information to construct protection criteria, which requires additional installation of voltage transformer on the line.The method proposed in this article only uses zero sequence current information, and only needs to extract the information of the current transformers installed at the line outlet, without the need to install other measurement equipments.The application scenario is relatively flexible.4.This article has demonstrated the adaptability of protection methods in situations such as noise interference, initial phase angle changes, fault resistance changes, and intermittent arc grounding faults through simulation.The effectiveness of this method was verified based on fault recording data from on-site artificial grounding short circuit tests.

CONCLUSIONS
By comparing the similarity of the zero sequence current waveform of outgoing lines, this article proposes a new method for single-phase high resistance grounding fault protection in low resistance grounded distribution networks, which is combined cosine distance with improved K-means algorithm.The main conclusions are as follows: 1.This article uses cosine distance to characterize the similarity of zero sequence current in each outgoing line.It takes advantage of the insensitivity of cosine distance to vector size, and can also compare the similarity even when the vector modulus is small.2. The improved K-means algorithm adopted in this article can mine the valuable information hidden in the cosine distance matrix representing the fault characteristics, classify outgoing lines accurately, and quickly select the fault line.It is free of setting the threshold value, and solves the problem of how to set the setting values in traditional high resistance grounding protection.3. The method proposed in this article does not require voltage information and the zero sequence current used is full information without filtering process.4.Under the condition equipped with high-precision current transformers, the method proposed in this article can handle fault resistance up to 2500 Ω, which greatly improves the reliability of traditional zero sequence overcurrent protection.It is also applicable in intermittent arc grounding situations. 5.The method proposed in this article is equally applicable in various situations such as changes in the faults initial phase angle, changes in fault location, noise interference and so on.It has significant advantages compared to traditional protection methods, especially in the cases of large-scale distributed generations connected to the distribution network, multi-point grounding faults, and the speed of protection.

F I G U R E 4 F I G U R E 5
Clustering analysis and protection algorithm flow chart.Simulation model of a low resistance grounded distribution network.

F I G U R E 7
Triple zero sequence current waveform (R f = 1000 Ω).

F I G U R E 8
Triple zero sequence current waveform (R f .arc= 100 Ω).

F I G U R E 9
Triple zero sequence current waveform of each outgoing line (SNR = 25 dB, R f = 100 Ω).

F
I G U R E 10 Triple zero sequence current waveform of each outgoing line ( = 90 • , R f = 100 Ω).

F
I G U R E 12Triple zero sequence current waveform of each outgoing line when the outgoing line is connected with DGs.
r 11 r 12 r 13 r 14 r 15 r 21 r 22 r 23 r 24 r 25 r 31 r 32 r 33 r 34 r 35 r 41 r 42 r 33 r 44 r 45 r 51 r 52 r 53 r 54 r 55 Cluster labels and fault identification results in case of different fault resistance