Direct-current distribution network fault detection method based on inflection point dense area concave-convex wave fluctuation characteristics

Abstract

The application discloses a DC distribution network fault detection method based on inflection point dense area concave-convex fluctuation characteristics, and aims at each feeder zero-mode current i FC_k (n) in a distribution network s_k (n) is obtained by using a variational mode decomposition algorithm, the correlation strength of the intrinsic mode component and the zero-mode current is calculated by using a Pearson correlation coefficient, and the intrinsic mode component IMF q_k (n) with the highest correlation strength with the zero-mode current is selected as a characteristic component i IMFq_k (n); secondly, the second derivative of each feeder characteristic component is calculated, and an inflection point dense area is selected; then, the second derivative in the inflection point dense area of each feeder is normalized, and the concave-convex fluctuation in the inflection point dense area of the zero-mode current is judged; finally, if the concave-convex fluctuation of the zero-mode current corresponding to all feeders in the inflection point dense area is the same, it is determined that a single-pole grounding fault occurs at the bus; if the concave-convex fluctuation of the zero-mode current corresponding to the jth feeder in the inflection point dense area is opposite to that of other feeders, it is determined that the jth feeder is a fault feeder.

Description

Technical Field

[0001] This invention belongs to the field of relay protection technology for power system distribution networks, specifically relating to a fault detection method for DC distribution networks based on the undulating characteristics of inflection point dense areas. Background Technology

[0002] In recent years, due to the rapid development of distributed energy and power electronics technology, and the advantages of DC distribution systems such as low line loss, facilitating the integration of distributed energy, and reducing the number of AC-DC conversions, DC distribution networks have gradually become a research hotspot both domestically and internationally. Flexible DC distribution networks based on modular multilevel converters (MMCs) have the characteristics of independent control of reactive and active power, no commutation failure, and fewer commutation stages, and their proportion in future DC distribution networks will gradually increase. However, MMC-based DC distribution systems have characteristics such as low inertia, weak damping, and no current zero-crossing point. This can lead to rapid rise and high peak values ​​of fault current after a single-pole ground fault, making it difficult for circuit breakers to clear the fault. Since the power electronic devices in the converter have limited ability to withstand transient inrush currents, failure to clear the fault in time can cause significant impacts on devices such as diodes in the system, thereby damaging other distribution equipment. Therefore, after a fault occurs in a DC distribution system, it is necessary to quickly select and isolate the faulty feeder. Rapid and reliable fault identification is a crucial foundation for protection actions; typically, protection schemes need to identify faults within 3ms, which is a problem that urgently needs to be solved in DC distribution networks. Summary of the Invention

[0003] The purpose of this invention is to provide a DC distribution network fault detection method based on the concave-convex fluctuation characteristics of dense inflection point areas, which can improve the accuracy of fault line identification.

[0004] The technical solution adopted in this invention is a DC distribution network fault detection method based on the undulating characteristics of dense inflection point areas, which is implemented according to the following steps:

[0005] Step 1: Collect the zero-mode current of each feeder, and use the variational mode decomposition algorithm to perform variational mode decomposition on the zero-mode current of each feeder to obtain the intrinsic mode components.

[0006] Step 2: Calculate the zero-mode current i of each feeder. FC_k (n) and intrinsic mode components IMF s_k The Pearson correlation coefficient r of (n) is used to determine the characteristic component i. IMFq_k (n);

[0007] Step 3: Calculate the characteristic component i IMFq_k The second derivative of f(n);

[0008] Step 4: Select the dense inflection point region for each feeder based on the second derivative f(n);

[0009] Step 5: Within the dense inflection point area, determine the specific fault type based on the zero-mode current fluctuation of each feeder.

[0010] The invention is further characterized by:

[0011] Step 1 is as follows:

[0012] Step 1.1: Use a signal detection device to collect the zero-mode current i of each feeder. FC_k (n), k represents the number of feeders, k = 1, 2, ..., j, ..., l, l represents the total number of feeders, n represents the number of sampling points, n = 1, 2, ..., N, N represents the total number of sampling points;

[0013] Step 1.2: Use the variational mode decomposition algorithm to perform variational mode decomposition on the zero-mode current of each feeder to obtain the intrinsic mode components (IMFs). s_k (n), where s represents the number of intrinsic modes, s = 1, 2, ..., q, ..., M, and M represents the total number of intrinsic modes.

[0014] Step 2 involves calculating the zero-mode current i of each feeder. FC_k (n) and intrinsic mode components IMF s_k The Pearson correlation coefficient r of (n) is expressed as follows:

[0015]

[0016] The relationship between the range of the correlation coefficient r and the correlation strength is shown in the following formula.

[0017]

[0018] When the qth intrinsic mode component IMF q_k (n) and zero-mode current i FC_k When the calculated Pearson correlation coefficient r corresponding to (n) is within the interval [0.8, 1], it indicates that the intrinsic mode component (IMF) is within the range [0.8, 1]. q_k (n) and zero-mode current i FC_k If the overall trend of (n) is the same, then the intrinsic mode components (IMF) will be... q_k (n) is denoted as characteristic component i IMFq_k (n).

[0019] In step 3, the characteristic component i is calculated. IMFq_k The second derivative f(n) of n is calculated as follows:

[0020]

[0021] In the formula: h represents the difference between n+1 and n.

[0022] Step 4 is as follows:

[0023] When the sampling point n satisfies f(n)∈[-δ,δ], δ is a local minimum, and the data point (n,i) IMFq_k (n) is an inflection point. When four or more consecutive second derivatives f(n) are detected that are within the threshold interval [-δ,δ], then g sampling points near the region of consecutive second derivatives are selected as the inflection point dense region, and f(w)f(g-w+1)<0, w=1,2,…,[g / 2], [·] represents the floor function. Otherwise, the detected inflection point is discarded.

[0024] Step 5 is as follows:

[0025] If the zero-mode current of all feeders has the same undulation in the dense inflection point area, then the busbar is determined to have a single-pole grounding fault.

[0026] If the zero-mode current of the j-th feeder exhibits the opposite undulation characteristics to other feeders in the dense inflection point region, then the j-th feeder is determined to be a faulty feeder.

[0027] The beneficial effects of this invention are:

[0028] 1) The time window used in this invention is 3ms after the fault, but the line selection algorithm only selects 7 sampling points for line selection. The algorithm is simple, the calculation time is short, and it meets the requirements of DC distribution network for protection speed.

[0029] 2) This invention processes data within a dense inflection point region, a microscopic method. Within this region, the zero-mode current fluctuations of faulty feeders and healthy feeders are opposite, and the impact of transition resistance is minimal. It can accurately identify faulty feeders under different fault distances and MMC grounding methods, demonstrating high applicability. Attached Figure Description

[0030] Figure 1 This is a flowchart of the DC distribution network fault detection method based on the concave-convex fluctuation characteristics of the inflection point dense area according to the present invention.

[0031] Figure 2 This is a schematic diagram of the dense inflection point region of the present invention;

[0032] Figure 3 This is a schematic diagram illustrating the concavity and convexity of the curve and the inflection point of the present invention;

[0033] Figure 4 This is a schematic diagram illustrating the concave-convex wave pattern of the present invention;

[0034] Figure 5 This is a schematic diagram of a DC distribution network model according to an embodiment of the present invention;

[0035] Figure 6 This is a schematic diagram of the zero-mode current waveform of each feeder in the distribution network according to an embodiment of the present invention;

[0036] Figure 7 The IMF of zero-mode current for each feeder in the embodiments of the present invention k_1 (n) Schematic diagram;

[0037] Figure 8 This is a schematic diagram showing the selection range of densely populated feeder inflection points in each embodiment of the present invention. Detailed Implementation

[0038] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0039] This invention relates to a DC distribution network fault detection method based on the undulating characteristics of densely populated inflection point regions, such as... Figure 1 As shown, please follow these steps:

[0040] Step 1: Collect the zero-mode current of each feeder, and use the Variational Mode Decomposition (VMD) algorithm to perform variational mode decomposition on the zero-mode current of each feeder to obtain the intrinsic mode components; the specific process is as follows:

[0041] Step 1.1: Use a signal detection device to collect the zero-mode current i of each feeder. FC_k (n), k represents the number of feeders, k = 1, 2, ..., j, ..., l, l represents the total number of feeders, n represents the number of sampling points, n = 1, 2, ..., N, N represents the total number of sampling points;

[0042] Step 1.2: Use the variational mode decomposition algorithm to perform variational mode decomposition on the zero-mode current of each feeder to obtain the intrinsic mode components (IMFs). s_k (n), where s represents the number of intrinsic modes, s = 1, 2, ..., q, ..., M, and M represents the total number of intrinsic modes.

[0043] Step 2: Calculate the zero-mode current i of each feeder. FC_k (n) and intrinsic mode components IMF s_k The Pearson correlation coefficient r of (n) is used to determine the characteristic component i. IMFq_k (n); The specific process is: calculate the zero-mode current i of each feeder. FC_k (n) and intrinsic mode components IMF s_k The Pearson correlation coefficient r of (n) is expressed as follows:

[0044]

[0045] The relationship between the range of the correlation coefficient r and the correlation strength is shown in the following formula.

[0046]

[0047] When the qth intrinsic mode component IMF q_k (n) and zero-mode current i FC_k When the calculated Pearson correlation coefficient r corresponding to (n) is within the interval [0.8, 1], it indicates that the intrinsic mode component (IMF) is within the range [0.8, 1]. q_k (n) and zero-mode current i FC_k If the overall trend of (n) is the same, then the intrinsic mode components (IMF) will be... q_k (n) is denoted as characteristic component i IMFq_k (n).

[0048] Step 3: Calculate the characteristic component i IMFq_k The second derivative of f(n);

[0049] Calculate the characteristic component i IMFq_k The second derivative f(n) of n is calculated as follows:

[0050]

[0051] In the formula: h represents the difference between n+1 and n.

[0052] Step 4: Select the dense inflection point region for each feeder based on the second derivative f(n); the specific process is as follows:

[0053] When the sampling point n satisfies f(n)∈[-δ,δ], δ is a local minimum, and the data point (n,i) IMFq_k (n) is an inflection point. When four or more consecutive second derivatives f(n) are detected that are within the threshold interval [-δ,δ], then g sampling points near the region of consecutive second derivatives are selected as the inflection point dense region, and f(w)f(g-w+1)<0, w=1,2,…,[g / 2], [·] represents the floor function. Otherwise, the detected inflection point is discarded.

[0054] The second derivatives within the dense inflection point region of each feeder are normalized. The normalization formula is as follows:

[0055]

[0056] In the formula, f max f min G represents the maximum and minimum values ​​of the second derivative within the dense region of inflection points. max g min y(g) represents the maximum and minimum values ​​of sampling points g within the dense inflection point region, and y(g) represents the normalized value corresponding to the g-th sampling point.

[0057] The zero-mode current ripple characteristics of each feeder can be determined by the normalized value of the second derivative of each feeder in the dense region of inflection points.

[0058] The zero-mode current fluctuation of each feeder can be determined by the normalized value of the second derivative of each feeder in the dense region of inflection points.

[0059] Feature component i IMFq_k (n) During the process of the inflection point changing from concave (convex) to convex (concave), the absolute value of the second derivative in the dense region of the inflection point decreases from large to small until it becomes zero, and then increases again. Numerically, this reflects the characteristic component i IMFq_k The curvature of (n) is a dynamic process of change from sharp to gentle and then back to sharp; the sign of the second derivative changes from positive (negative) to negative (positive) within the dense region of inflection points, reflecting the characteristic component i IMFq_k (n) The overall trend of changing from concave (convex) to convex (concave) within the dense region of inflection points. Zero-mode current concavity / convexity ripple refers to the characteristic component i corresponding to the zero-mode current. IMFq_k (n) The dynamic change process of the feeder changing from concave (convex) to convex (concave) and then back to concave (convex) within the dense region of inflection points. The zero-mode current concavity and convexity fluctuation of each feeder can be determined based on the normalized value of the second derivative of each feeder within the dense region of inflection points.

[0060] Step 5: Within the dense inflection point region, determine the specific fault type based on the zero-mode current fluctuation characteristics of each feeder. The specific process is as follows:

[0061] If the zero-mode current of all feeders has the same undulation in the dense inflection point area, then the busbar is determined to have a single-pole grounding fault.

[0062] If the zero-mode current of the j-th feeder exhibits the opposite undulation characteristics to other feeders in the dense inflection point region, then the j-th feeder is determined to be a faulty feeder.

[0063] The working principle of the DC distribution network fault detection method based on the concave-convex fluctuation characteristics of the inflection point dense area in this invention is as follows:

[0064] 1. Dense areas of inflection points on the curve

[0065] The second derivative of the discrete function f(k) is calculated using the following formula:

[0066]

[0067] In the formula: k represents the sampling point, k = 1, 2, ..., N, N represents the total number of sampling points, and h represents the difference between k and k+1.

[0068] When f(k) satisfies the threshold interval [-δ, δ], this point is an inflection point. If there are four or more consecutive second derivatives that satisfy the threshold interval [-δ, δ], then n sampling points near this second derivative region are taken as the inflection point dense region, and f(w)f(n-w+1)<0, w=1,2,…,[n / 2], where [·] represents the floor function. Otherwise, the detected inflection point value is discarded, and this region is defined as the inflection point dense region.

[0069] like Figure 2 As shown, sampling points 23, 24, 57–62, and 117 that meet the threshold range were detected on the second derivative curve. By defining the dense inflection point region, it can be seen that although the magnitudes of the second derivative values ​​in regions ① and ③ meet the settings, the number is less than 4. Therefore, these two regions are discarded and not analyzed. Furthermore, individual values ​​exhibit strong randomness and are easily affected by waveform and external factors; this processing reduces the impact of random values ​​on the overall trend. It is evident that the magnitude and number of values ​​in region ① meet the settings, so the region containing these values ​​belongs to the dense inflection point region. This dense region reflects the period with the richest transient information in f(x).

[0070] 2. The concavity and undulation of the curve

[0071] The concavity and inflection points of a function f(x) in an interval I can be determined by the sign of its second derivative. If f' ...

[0072] The concavity or convexity of a curve can be determined using the second derivative, such as... Figure 3 As shown: Within the interval (t0, t2), the slope of the tangent line l1 to l2 of the curve gradually changes from positive to negative, and the first derivative of the curve exhibits a monotonically decreasing trend, meaning the change in the slope of the tangent line weakens. Therefore, the second derivative is less than zero, indicating a convex arc. At time t2, the curve reaches a stationary point. Within the interval (t2, t4), the tangent line changes from l3 to l4, and the slope gradually changes from negative to positive. The first derivative of the curve exhibits a monotonically increasing trend, meaning the change in the slope of the tangent line becomes more drastic. Therefore, the second derivative is greater than zero, indicating a concave arc. Thus, the second derivative is used to describe the changing trend of the tangent slope (first derivative) at a point on the curve. When the curve changes from concave (convex) to convex (concave), this characteristic is the concavity / convexity of the curve.

[0073] like Figure 4 As shown, the original curve f(x) exhibits continuous bending characteristics. The process of the original curve changing from concave (convex) to convex (concave) and then back to concave (convex) within a certain range is defined as the concavity-convexity undulation of the curve.

[0074] 3. Variational Mode Decomposition (VMD)

[0075] Variational mode decomposition (VM) is a signal decomposition and estimation method. This method determines the frequency center and bandwidth of each component by iteratively searching for the optimal solution of the variational model during the acquisition of decomposed components. This enables adaptive frequency domain partitioning of the signal and effective separation of its components. The intrinsic mode function (IMF) is defined as an amplitude-frequency modulated (AM-FM) signal, and can be expressed as:

[0076]

[0077] The VMD algorithm can be divided into two parts: constructing and solving the variational problem.

[0078] 1) Construction of variational problems

[0079] Assuming each "mode" is a finite bandwidth with a center frequency, the variational problem is described as seeking k mode functions u. k (t) is constructed to minimize the sum of the estimated bandwidths of each mode, with the constraint that the sum of the bandwidths of all modes equals the input signal f. The specific construction steps are as follows:

[0080] Step 1: Obtain each mode u through Hilbert transform. k The analytic signal of (t) is obtained by its one-sided spectrum:

[0081]

[0082] Step 2: Estimate the center frequency by mixing the analytical signals of each mode. Modulate the spectrum of each mode to the corresponding baseband:

[0083]

[0084] Step 3: Calculate the square L of the demodulated signal gradient. 2 Norms are used to estimate the bandwidth of each mode signal, and a variational problem is constructed:

[0085]

[0086] Among them, {u k}={u1,…,u K},{ω k}={ω1,…,ω K},

[0087] 2) Solving variational problems

[0088] Step 1: Introduce the quadratic penalty factor α and the Lagrange multiplier operator λ(t) to transform the constrained variational problem into an unconstrained variational problem. The quadratic penalty factor ensures the reconstruction accuracy of the signal in the presence of Gaussian noise, and the Lagrange operator keeps the constraints strict. The extended Lagrange expression is as follows:

[0089]

[0090] Step 2: VMD employs the Alternating Direction Multiplication Method (ADMM) to solve the above variational problem, through alternating updates. and λ n+1 Seeking "saddle points" for extended Lagrange expressions.

[0091] in The problem of the value of can be expressed as:

[0092]

[0093] In the formula: ω k Equivalent to Equivalent to Using the Parseval / Plancherel Fourier isometric transform, the equation is transformed to the frequency domain:

[0094]

[0095] Example

[0096] Create such in PSCAD Figure 5 The simulation model of the ±10kV single-source flexible DC radial distribution system shown has five feeders. Figure 5 The main parameters of the model are shown in Table 1.

[0097] Table 1

[0098] System simulation parameters numerical values Rated DC voltage / kV ±10 DC reactor / mH 5 Control strategy Constant DC voltage, reactive power MMC submodule capacitor / mF 4.5 Clamping resistor / MΩ 1 <![CDATA[L1 / km]]> 20 <![CDATA[L2 / km]]> 16 <![CDATA[L3 / km]]> 14 <![CDATA[L4 / km]]> 17 <![CDATA[L5 / km]]> 10

[0099] A positive ground fault is set at K1 10km after feeder L1, with a transition resistance of 500Ω. Taking the fault occurrence time of 2s as an example, the zero-mode current of each feeder is measured at the beginning of the feeder as follows: Figure 6 As shown.

[0100] VMD decomposition was performed on the zero-mode currents of each feeder to filter out high-order harmonics and noise present in the original waveforms. The characteristic components obtained after VMD decomposition of the zero-mode current waveforms of feeders L1, L2, L3, and L4 are as follows: Figure 7 As shown.

[0101] The Pearson correlation coefficient r between the characteristic components of each feeder and the zero-mode current waveform was calculated, and the results are shown in Table 2.

[0102] Table 2

[0103] feeder <![CDATA[L1]]> <![CDATA[L2]]> <![CDATA[L3]]> <![CDATA[L4]]> <![CDATA[L5]]> r 0.837 0.851 0.821 0.863 0.801

[0104] There is a strong correlation coefficient between the zero-mode current and the characteristic component of each feeder. The overall trend of the characteristic component is similar to that of the zero-mode current, which reduces abrupt spikes and makes the zero-mode current curve smoother and more representative.

[0105] The second derivative of the characteristic components of each feeder is calculated. Based on this, the inflection point density region of each feeder is selected for analysis, and the inflection point density region of each feeder is obtained as follows: Figure 8 As shown in the figure. Analysis of line L1 reveals that the second derivative exhibits consecutive values ​​satisfying the threshold range between 66 and 70, with a number greater than or equal to 4. Therefore, the range of 65 to 71 near 66 to 70 is selected as the inflection point density region. Inflection points 24 and 29 to 31 also appear in the figure, but these data do not meet the criteria for the inflection point density region, so these values ​​are discarded. The selected inflection point density regions for lines L1, L2, L3, L4, and L5 are shown in Table 3.

[0106] Table 3

[0107] line <![CDATA[L1]]> <![CDATA[L2]]> <![CDATA[L3]]> <![CDATA[L4]]> <![CDATA[L5]]> Select sampling point range 65～71 66～72 64～70 68～74 63～69

[0108] The values ​​of the second derivative in the dense region of each feeder inflection point are shown in Table 4.

[0109] Table 4

[0110] <![CDATA[L1(10 -9 )]]> <![CDATA[L2(10 -9 )]]> <![CDATA[L3(10 -8 )]]> <![CDATA[L4(10 -9 )]]> <![CDATA[L5(10 -8 )]]> 1 -328.99 90.992 9.2557 83.737 6.6903 2 -223.59 63.324 5.5292 55.843 3.9358 3 -114.70 33.760 1.7860 24.805 1.2215 4 -4.4849 2.8663 -1.8681 -8.7624 -1.3788 5 104.78 -28.701 -5.3306 -44.083 -3.7954 6 210.75 -60.228 -8.5063 -80.244 -5.9660 7 311.12 -90.962 -11.311 -116.23 -7.8377

[0111] The second derivative values ​​of each feeder in Table 4 were normalized to eliminate the differences caused by small order of magnitude and sign of the data. The normalization results are shown in Table 5.

[0112] Table 5

[0113]

[0114] Feeder L1 exhibits a trend of changing from convex to concave within the dense inflection point area, while feeders L2 to L5 exhibit a trend of changing from concave to convex. Since the concave-convex fluctuation of feeder L1 differs from that of the other feeders, feeder L1 is determined to be a faulty feeder. Analysis shows that the protection scheme proposed in this invention can accurately identify faulty lines.

[0115] Through the above-described method, this invention provides a DC distribution network fault detection method based on the undulating characteristics of inflection point dense areas. The method selects feeders based on the differences in zero-mode current waveforms between faulty and healthy feeders. First, VMD transformation is performed on the zero-mode current of each feeder to obtain its intrinsic mode components. Second, the Pearson correlation coefficient between the zero-mode current and the intrinsic mode components is calculated, the correlation strength is determined, and characteristic components are selected. Third, the second derivative of the characteristic components is calculated, inflection point dense areas are selected, and the second derivative of the inflection point dense areas is normalized. Finally, the undulating characteristics of the zero-mode current of each feeder within the inflection point dense areas are determined, thereby achieving accurate feeder selection for a single-source radial flexible DC distribution network based on modular multilevel circuits.

Claims

1. A DC distribution network fault detection method based on the undulating characteristics of densely populated inflection point regions, characterized in that, Specifically, according to one Next steps: Step 1: Collect the zero-mode current of each feeder, and use the variational mode decomposition algorithm to perform variational mode decomposition on the zero-mode current of each feeder to obtain the intrinsic mode components. Step 2: Calculate the Pearson correlation coefficient r between the zero-mode current iFC_k(n) and the intrinsic mode component IMFs_k(n) of each feeder, and determine the characteristic component iIMFq_k(n) based on the Pearson correlation coefficient r. Step 3: Calculate the second derivative f(n) of the eigencomponent i IMFq_k(n); Step 4: Select the dense inflection point region for each feeder based on the second derivative f(n); Step 5: In the dense inflection point area, determine the specific fault type based on the zero-mode current fluctuation of each feeder; Step 4 is as follows: When the sampling point n satisfies f(n)∈ [-δ,δ], δ is a local minimum value, and the data point (n,i IMFq_k (n)) is an inflection point. When four or more consecutive second derivatives f(n) are detected that are within the threshold interval [-δ,δ], then g sampling points near the region of consecutive second derivatives are selected as the inflection point dense region, and f(w)f(g-w+1)<0, w=1,2,… ,[g / 2], [·] represents the floor function. Otherwise, the detected inflection points are discarded. Step 5 is as follows: The second derivatives within the dense inflection point region of each feeder are normalized. The normalization formula is as follows: ； In the formula, fmax and fmin represent the maximum and minimum values ​​of the second derivative within the dense region of inflection points, gmax and gmin represent the maximum and minimum values ​​of the sampling point g within the dense region of inflection points, and y(g) represents the normalized value corresponding to the g-th sampling point. The zero-mode current ripple characteristics of each feeder can be determined by the normalized value of the second derivative of each feeder in the dense region of inflection points. If the zero-mode current of all feeders has the same undulation in the dense inflection point area, then the busbar is determined to have a single-pole grounding fault. If the zero-mode current of the j-th feeder exhibits the opposite undulation characteristics to other feeders in the dense inflection point region, then the j-th feeder is determined to be a faulty feeder.

2. The DC distribution network fault detection method based on the concave-convex fluctuation characteristics of dense inflection point areas according to claim 1, characterized in that, Step 1 is as follows: Step 1.1: Use a signal detection device to collect the zero-mode current iFC_k(n) of each feeder, where k represents the number of feeders, k = 1, 2, ..., j, ..., l, l represents the total number of feeders, and n represents the sampling point, n = 1, 2, ..., N, N represents the total number of sampling points; Step 1.2: Use the variational mode decomposition algorithm to perform variational mode decomposition on the zero-mode current of each feeder to obtain the intrinsic mode components IMFs_k(n), where s represents the number of intrinsic modes, s=1,2,… ,q,… ,M, and M represents the total number of intrinsic modes.

3. The DC distribution network fault detection method based on the concave-convex fluctuation characteristics of dense inflection point areas according to claim 1, characterized in that, Step 2 involves calculating the Pearson correlation coefficient r between the zero-mode current iFC_k(n) and the intrinsic mode components IMFs_k(n) of each feeder. The expression for the Pearson correlation coefficient r is as follows: ； The relationship between the range of the correlation coefficient r and the correlation strength is shown in the following formula; ； When the calculated Pearson correlation coefficient r between the q-th intrinsic mode component IMFq_k(n) and the zero-mode current iFC_k(n) is within the interval [0.8,1], it indicates that the overall variation trend of the intrinsic mode component IMFq_k(n) and the zero-mode current iFC_k(n) is the same. Then, the intrinsic mode component IMFq_k(n) is denoted as the characteristic component iIMFq_k(n).

4. The DC distribution network fault detection method based on the concave-convex fluctuation characteristics of dense inflection point areas according to claim 1, characterized in that, The calculation of the second derivative f(n) of the eigencomponent i IMFq_k(n) in step 3 is as follows: ； In the formula: h represents the difference between n+1 and n.

Images