Fault location method for subsea direct current power supply system based on time domain characteristics of multi-element fault current

Abstract

The submarine direct-current power supply system fault positioning method based on the multi-element fault current time domain characteristics provided by the application first acquires the current signal in real time by the protection device, judges whether overcurrent exists at the branch unit, marks the current time as the fault time when overcurrent exists, and acquires the current data within 5 ms after the fault by each protection device; then the initial value of the fault current slope, the initial value of the curvature, the initial peak time and the initial peak size at each branch unit are acquired; then the initial value of the fault current slope, the initial value of the curvature, the initial peak time and the initial peak size are input into the support vector machine regression algorithm trained in advance, and the distance y from the fault point to each branch unit is obtained respectively n ; finally, the fault position is determined, the fault position is sent to the shore base station, and the monopolar grounding fault positioning is completed. The application can quickly and accurately distinguish the monopolar grounding fault line and the fault distance of the submarine observation network direct-current power supply system, the application has a small amount of transmission information, and has a low requirement for the transmission information synchronization.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of power system relay protection technology, and in particular to a submarine DC power supply system fault location method based on multi-element fault current time domain characteristics. BACKGROUND

[0002] The submarine observation network power supply system is the basis for the operation of the submarine observation network and is the source of power for the observation equipment. The submarine observation network power supply system is mainly a mesh-shaped or ring-shaped power supply network connected by submarine optical fiber composite cables, and mostly adopts a monopolar constant voltage DC power supply method. The normal operation of the submarine observation network power supply system is directly related to the operation of the submarine observation network equipment and the collection and transmission of information. However, due to the unique geographical location of the submarine observation network, the operating environment of the submarine cable is very harsh, and is also affected by crustal movement, marine microorganisms, and other corrosion, as well as human activities such as ship anchoring and resource development, so the failure rate of the submarine cable is high. In addition, the fault current of the submarine observation network DC power supply system rises rapidly, and the fault impact current is huge, which poses a significant threat to the safety of the power equipment. Therefore, accurate fault location and corresponding protection are the guarantee for the safe and reliable operation of the submarine observation network power supply system.

[0003] The transmission of power and information of the entire submarine observation network relies on submarine optical fiber composite cables, but the communication of the submarine optical fiber composite cables may be affected during a fault. In order to improve the accuracy of fault location, a fault location method with less transmission information and less synchronization requirement for transmission information is needed. At present, fault distance measurement of flexible DC transmission systems on land is mainly divided into traveling wave type distance measurement and parameter identification type distance measurement. The traveling wave type distance measurement highly depends on wave head identification and wave speed estimation, and has high requirements for the synchronization of communication, which is not suitable for fault distance measurement of the submarine observation network. For the parameter identification method, due to the great difference in fault topology between the submarine observation network DC power supply system and the land DC transmission system, and the limited size of the branch unit of the submarine observation network, the commonly used RL model positioning method on land is not applicable, so a distance measurement method suitable for the submarine observation network power supply system needs to be proposed. SUMMARY

[0004] The technical problem to be solved by the present application is to provide a submarine DC power supply system fault location method based on multi-element fault current time domain characteristics. Under this method, when single-pole grounding fault occurs in the grounding of the submarine observation network DC power supply, the single-sided protection device of the protected line can quickly and accurately determine the fault line and the fault distance. This method not only has less transmission information, but also has less synchronization requirement for transmission information.

[0005] To solve the above technical problems, the present application adopts the following technical method: a submarine DC power supply system fault location method based on multi-element fault current time domain characteristics, comprising:

[0006] Step S1, the protection device at each branch unit of the seabed observation network DC power supply system acquires current signals in real time, judges whether the current position is overcurrent, and when overcurrent exists, marks the current time as the fault time, each protection device acquires current data within 5 ms after the fault, and enters step S2;

[0007] Step S2, the initial value of the fault current slope, the initial value of the curvature, the initial peak time and the initial peak value of each branch unit are extracted from the current data within 5 ms after the fault acquired by each protection device;

[0008] Step S3, the obtained initial value of the fault current slope, the initial value of the curvature, the initial peak time and the initial peak value are input into the pre-trained support vector machine regression algorithm, and the distance y n from the fault point to each branch unit is obtained, n is the serial number of the branch unit, the fault position is determined, the fault position is sent to the shore base station, and the single-point grounding fault positioning is completed;

[0009] Step S4, the fault current data and the fault position under the current working condition are recorded and added to the training set of the support vector machine regression algorithm.

[0010] Further, in step S1, the criterion for judging whether each branch unit is overcurrent is:

[0011] Δi dc > 0.3I N (1)

[0012] In the formula, Δi dc is the current mutation, which is obtained from the difference between the sampled current data and the steady-state DC current, and I N is the rated current.

[0013] Further, in step S3, the training process of the support vector machine regression algorithm is as follows:

[0014] S31, the training set of the current data is {(X1, y1), (X2, y2)…(Xt, y t )}, where t is the sample number; X ∈ RN is the input value, that is, the fault current feature, N = 4 is the dimension of the input value; y ∈ R is the corresponding output value, that is, the fault distance from the fault point to each branch unit; the training set data is mapped to a high-dimensional linear space through a nonlinear function Φ(X), and a sample regression function is obtained, as shown in the following formula (2):

[0015] {f(X) = w T Φ(X) + b | w ∈ R N}(2)

[0016] In the formula, w is the weight vector, and b is a constant;

[0017] S32, introduce the insensitive loss function, as follows (3):

[0018]

[0019] S33, regression problem is equivalent to constrained optimization problem, as follows (4):

[0020]

[0021] In the formula, ζ i ,ζ i * Relaxation factor for the existence of the solution of the optimization problem, i is the serial number of the sample in the training set, i=1,2,…t, ε is the insensitive loss function, C is the penalty coefficient;

[0022] S34, using the Lagrange function and the dual principle to transform formula (4) into dual form, as follows (5):

[0023]

[0024] In the formula, α i ,α i * Lagrange coefficient, i is the serial number of the sample in the training set; X i , X j The input value of the i, j sample in the training set, i=1, 2,…t, j=1, 2,…t, and i≠j; l is the Lagrange multiplier; C is the penalty coefficient;

[0025] S35, the value of Lagrange coefficient α is obtained from formula (5), and the value of bias b is obtained by using KKT condition, and the expression of the regression function is obtained by training:

[0026]

[0027] The selection of kernel function K(X i ,X j )=Φ T (X)Φ(X I ) satisfies the Merce condition, and is selected from the following kernel functions:

[0028]

[0029] Further, in step S3, the initial value of the fault current slope, the initial value of the curvature, the initial peak time, and the initial peak value obtained in step S2 are substituted into the regression function (6) trained by the training set, and the distance y nIf the fault current collected by the protection device at the nth branch unit is from the branch unit to the system end, the fault point is downstream of the branch unit, at this time if y n is less than the length of the downstream line of the branch unit, it is determined that the fault occurs at a position y n distance from the head end of the downstream line, otherwise the fault does not occur on the downstream line; if the fault current collected by the protection device at the nth branch unit is from the branch unit to the system head, the fault point is upstream of the branch unit, at this time if y n is less than the length of the upstream line of the branch unit, it is determined that the fault occurs at a position y n distance from the head end of the upstream line, otherwise the fault does not occur on the upstream line; the determined fault position is sent to the shore station, and the single-pole grounding fault positioning is completed.

[0030] The submarine direct current power supply system fault positioning method based on the multi-element fault current time domain characteristics provided by the application can ensure that the single-pole grounding fault of the submarine observation network direct current power supply grounding can be quickly and accurately determined by the single-side protection device of the protected line. Specifically, after the single-pole grounding fault of the submarine observation network direct current power supply grounding occurs, the MMC sub-module capacitor and the LLC input side capacitor rapidly discharge to generate a fault current to feed into the fault point. The initial slope, curvature, and fault current first peak value size and peak time of the fault current waveform are jointly affected by the fault distance and the fault resistance. The application analyzes the different influences of the fault distance and the fault resistance on the fault characteristics, and uses a support vector machine regression algorithm to construct a mapping between the multi-element fault current time domain characteristics and the fault position, thereby eliminating the influence of the fault resistance on the positioning accuracy and accurately determining the fault line and the fault distance. The ranging method based on single-end information quantity proposed by the application has small communication data quantity and low communication bandwidth requirement. Since the protection is based on single-end information quantity, the synchronization requirement of communication is also not high. In addition, because the submarine observation network direct current power supply system has small inertia and weak damping, the fault current usually rises to the first peak value within 5ms, so the application can complete the determination of the fault line and the fault distance within 5ms after the fault, thereby greatly shortening the protection action time. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 The flowchart of the submarine direct current power supply system fault positioning method based on the multi-element fault current time domain characteristics according to the application is shown in the figure.

[0032] Figure 2 The structure diagram of a typical submarine observation network direct current power supply system (the submarine instrument interface module and the scientific observation instrument are not shown in the figure) is shown in the figure.

[0033] Figure 3Figure for equivalent model of fault of direct current power supply system of seafloor observation network; wherein, (a) is an equivalent model of MMC; (b) is an equivalent model of LLC; (c) is an equivalent model of seafloor optical cable;

[0034] Figure 4 Figure for equivalent circuit of fault of direct current power supply system of seafloor observation network; wherein, (a) is an equivalent Laplace fault circuit of direct current power supply system of seafloor observation network; (b) is an equivalent circuit of fault of direct current power supply system of seafloor observation network after decoupling at fault resistance; (c) is an equivalent circuit of fault of direct current power supply system of seafloor observation network after decoupling at common branch. DETAILED DESCRIPTION

[0035] For the convenience of understanding of those skilled in the art, the present application is further described below in combination with examples and drawings, and the content mentioned in the embodiments is not a limitation on the present application.

[0036] In order to quickly and accurately judge the fault line and fault distance, the present application first analyzes the relationship between the transient fault current characteristics of the seafloor observation network power supply system and the fault distance in detail, and then proposes a fault positioning method for the seafloor direct current power supply system based on the time domain characteristics of the multi-element fault current, as follows.

[0037] I. Analyzing the relationship between the transient fault current characteristics of the seafloor observation network power supply system and the fault distance.

[0038] Referring to Figure 2 , a typical seafloor observation network direct current power supply system mainly includes a shore station, a seafloor optical and electrical composite cable, a branch unit, a main and secondary connection box, a seafloor instrument interface module and scientific observation instruments and the like. The shore station power supply provides a stable 10kV direct current voltage through a modular multilevel converter (MMC) and its control system, the 10kV voltage at the main connection box is converted into a 375V direct current voltage through a resonant converter (LLC), and each converter at the secondary connection box converts the 375V direct current voltage into an alternating current or direct current voltage required by the observation equipment. In order to simplify the description, as shown in Figure 2 , the shore station of the seafloor observation network direct current power supply system in the present embodiment is divided into a shore station 1 at the first end of the system and a shore station 2 at the end of the system, the seafloor optical and electrical composite cable is divided into LINE1, LINE2 and LINE3, and the branch unit is divided into a No. 1 branch unit and a No. 2 branch unit.

[0039] Due to the limitation of one-way LLC, when a single-pole ground fault occurs in the seafloor observation network direct current power supply system, each level of converter and equipment after the main connection box does not form a fault overcurrent loop, and the fault current is mainly composed of the discharge current of the MMC sub-module capacitor and the discharge current of the input side capacitor of LLC.

[0040] For constant voltage controlled MMCs, when a single-pole ground fault occurs on the DC side, its fault response can be decomposed into AC and DC components. Meanwhile, the current fed into the three-phase symmetrical AC power supply line is almost negligible, and the DC component of the fault current is mainly the discharge current of the submodule capacitors. For example... Figure 3 As shown in (a), the fault model can be equivalent to an RLC series circuit, and its resistance, inductance, and capacitance can be calculated using the following formula:

[0041]

[0042] In the formula, N is the number of individual bridge arm submodules in the MMC, R, L, and C are the bridge arm resistance, bridge arm reactance, and submodule capacitance, respectively, and R on L is the IGBT switching resistor. T It is a series current-limiting reactor.

[0043] For a phase-shift controlled unidirectional LLC with series input and parallel output, due to the unidirectional conduction characteristic of its diodes, the output current cannot be fed into the DC bus. Therefore, the fault current fed into the bus from each stage of the network starting from the main junction box is mainly determined by the input capacitance of the LLC converter. Figure 3 As shown in (b), the LLC fault model can be equivalent to a single capacitor, the size of which can be calculated by equation (14), where C in M represents a single LLC input capacitor, and M is the number of LLC capacitors connected in series on the input side.

[0044]

[0045] While the parametric distributed model can analyze the reflection and refraction process of traveling waves in detail for modeling submarine optical cables, the calculations are too complex, and the traveling wave location method is not applicable to submarine DC power supply systems. Therefore, a lumped parameter model is used to model submarine optical cables. Although it cannot reflect the weak oscillations during the current rise process in detail, it can reflect the overall trend of fault current changes, and the calculation results still meet the accuracy requirements. As shown in Table 1, the parameters of submarine optical cables differ significantly from those of terrestrial DC cables. The resistance and inductance of submarine optical cables, especially the resistance, are very high, which greatly affects the rise process of fault current. At the same time, the distributed capacitance of submarine optical cables is much smaller than that of the LLC input capacitor directly connected in parallel and can be ignored. The fault equivalent model of submarine optical cables is as follows: Figure 3 As shown in (c), its resistance and the size of the cable are calculated by formula (10), where x represents the distance from the fault point to the branch unit where the protection is installed.

[0046]

[0047] Table 1

[0048] Direct current cable resistance r0 (Ω / km) Inductance L0 (mH / km) Low voltage (0.12 - 1.5 kV) 0.04-0.2 >0.5 Medium voltage (1.5 - 30 kV) 0.02-0.1 0.3-0.5 High voltage (30 - 600 kV) 0.01-0.05 0.1-0.3 Opto-electric composite cable 1 1

[0049] Based on the above analysis, for Figure 2 As shown in the typical direct current power supply system of the ocean bottom observation network, when the fault occurs on LINE2 (the case of the fault occurring on LINE1 or LINE3 is similar to that on LINE2, and therefore only the case of the fault occurring on LINE2 is analyzed in the present embodiment), in order to simplify the complex derivative operation into simple algebraic operation, the fault current is calculated after Laplace transformation of the fault model, and the transformed fault equivalent model is shown in Fig. Figure 4 (a). In the figure, B F is the fault point, and the distance y1 between B F and B1 is defined as the distance from the fault point to the position of the first branch unit.

[0050] As can be seen from Figure 4 (a), the currents on the left and right sides of the fault point are coupled at the fault resistance, and therefore even if the impedance of the seawater is very small, the fault resistance R F ≈0 cannot be ignored. The fault resistance on both sides of the fault loop is decoupled, and the fault resistance on both sides of the decoupled loop is:

[0051]

[0052] As shown in Fig. Figure 4 (b), two independent fault loops are obtained after decoupling of the fault resistance. The impedance of each branch is:

[0053] 1 / sC1=1 / sC LLC1 ;

[0054] 1 / sC2=1 / sC LLC2 ;

[0055] R3+sL3+1 / sC3=(R MMC1 +R LINE1 )+(sL MMC1 +sL LINE2 )+1 / sC MMC1 ;

[0056] R4+sL4+1 / sC4=(R MMC2 +R LINE3 )+(sL MMC2 +sL LINE3 )+1 / sC MMC2 ;

[0057] Taking the left fault loop for analysis, the fault currents I1 and I3 are in the common branch B1B FThe left fault loop is decomposed into two independent discharge loops of I1 and I3 by using the parallel impedance shunt principle Figure 4 (c) shown, wherein B1B F The branch impedance is decomposed into two loops with the following sizes:

[0058]

[0059] The fault current I F1 The fault current I dc is the superposition of two non-oscillating discharge currents. Because the model has a high order, the time-domain analytical expression cannot be directly obtained by Laplace inverse transform. However, because the per-kilometer resistance of the submarine optical cable is as high as 1 Ω, which is several tens or even hundreds of times higher than that of the land cable, and the equivalent capacitance of the MMC and LLC is much larger than the equivalent fault capacitance of the flexible DC transmission system, unlike the DC system on land, the fault current of the submarine observation network DC power supply system is the superposition of two non-oscillating discharge currents, and the time-domain general formula of the non-oscillating current of the RLC series circuit is:

[0060]

[0061]

[0062] In the formula, i is the fault current, U dc is the steady-state DC bus voltage of LINE2, I dc is the steady-state DC current of LINE2, L is the inductance size of the RLC series circuit, R is the resistance size of the RLC series circuit, and C is the capacitance size of the RLC series circuit.

[0063] Because the fault current of the submarine DC power supply system is a non-oscillating discharge, it does not have a fixed oscillation frequency, and the frequency domain characteristics of the waveform are not obvious, the time domain characteristics of the fault current are extracted as the protection criterion.

[0064] The first-order and second-order derivatives of the current expression (13) are obtained by derivation, and the first-order and second-order derivatives of the fault current of the submarine observation network DC power supply system are as follows:

[0065]

[0066]

[0067] As can be seen from formula (15), the first-order derivative of the fault current monotonically decreases and reaches the maximum value at the initial fault time, that is, the slope of the current waveform is the largest at the initial fault time, and the rising speed is the fastest, and there is:

[0068]

[0069] As shown in equation (2), A is the initial value of the fault current slope, the magnitude of which is related to the resistance R and the inductance L, and due to the steady-state DC current I of LINE2. dc The initial value of the fault current slope is very small, mainly depending on the inductance L, which is the magnitude of the fault distance y1. When the fault distance y1 is constant, the change in resistance R is also affected by the fault resistance R. F The influence of this factor is significant, therefore the latter term cannot be ignored. Differentiating the initial fault current slope with respect to inductance L and resistance R respectively, we obtain:

[0070]

[0071]

[0072] From equation (18), we can obtain that when the fault resistance R F For a given fault distance y1, the larger the fault distance y1, the smaller the initial value of the fault current slope. From equation (19), it can be seen that when the fault distance y1 is constant, the fault resistance R F The larger the value, the smaller the initial value of the fault current slope, but the rate of change is not large. The initial value of the fault current slope mainly depends on the fault distance y1.

[0073] Since the influence of fault resistance cannot be completely ignored due to the waveform slope characteristics, and the change in the initial value of the fault current slope is small when the fault distance y1 is large, using the fault distance as a single protection criterion cannot meet the requirements of positioning accuracy. Considering that curvature can characterize the degree of bending of the fault waveform, the initial value B of the fault current curvature is calculated as follows:

[0074]

[0075] Because the non-oscillatory discharge process of the submarine DC power supply system satisfies And the fault slope satisfies Equation (20) can be simplified to:

[0076]

[0077] Differentiating the simplified initial value of the fault current curvature with respect to inductance L and resistance R respectively, we get:

[0078]

[0079]

[0080] From equation (22), we can obtain that when the fault resistance R F For a given fault distance y1, the larger the fault current curvature, the larger the initial value of the fault current curvature. From equation (23), it can be seen that when the fault distance y1 is constant, the fault resistance R FThe larger the value, the larger the initial value of the fault current curvature. Furthermore, the initial value of curvature does not change very little with increasing fault distance y1.

[0081] When the initial values ​​of the fault current slope and curvature are extracted together as protection criteria, the problem of changes in fault distance and protection quantity can be solved. However, since the initial values ​​of the fault current slope and curvature change the same with the fault distance and fault resistance, they cannot offset the influence of the fault resistance on fault distance measurement. Therefore, it is considered to extract the first peak time and peak value of the fault current at the same time.

[0082] For the two fault circuits B1B after the disassembly of the submarine DC power supply system F With B3B F Because of B1B F Both the capacitance and resistance values ​​are less than B3B. F Therefore, the first peak time and magnitude of the fault current mainly depend on loop B1B. F For non-oscillating discharge current, its peak time and peak magnitude can be expressed as:

[0083]

[0084]

[0085] Regarding the magnitude of the fault current peak, whether it is due to an increase in fault distance y1 or fault resistance R... F As R increases, its value decreases. However, at the peak time, due to R... 2 C>>4L, equation (24) can be simplified to:

[0086]

[0087] Differentiating the simplified equation (26) with respect to inductor L and resistance R respectively, we get:

[0088]

[0089]

[0090] From equation (27), we can obtain that when the fault resistance R F For a given fault distance y1, the larger the fault distance y1, the longer the time it takes for the fault current to reach its first peak value. From equation (28), it can be seen that when the fault distance y1 is constant, the fault resistance R F The larger the value, the shorter the time it takes for the fault current to reach its first peak value. The time it takes for the fault current to reach its first peak value varies with the fault distance and the fault resistance. Therefore, by simultaneously selecting the magnitude of the first peak value of the fault current and the time when it reaches the first peak value, the impact of the fault resistance on the positioning accuracy can be reduced.

[0091] In summary, since the initial value of the fault current slope and the initial value of the curvature mainly depend on the loop inductance, i.e. the size of the fault distance y1 from the fault point to the first branch unit, the application can roughly determine the range of the fault distance y by the initial value of the fault current slope and the initial value of the curvature, eliminate the influence of the fault resistance and improve the positioning accuracy based on the characteristics that the size of the first peak of the fault current and the time to reach the first peak change with the fault distance and the fault resistance. The changes of the initial value of the fault current slope, the initial value of the curvature, the peak time and the peak size with the fault distance and the fault resistance are shown in Table 2.

[0092] Table 2

[0093] Initial slope Initial curvature Peak time Peak size Fault distance↑ ↓ ↑ ↑ ↓ Fault resistance↑ ↓ ↑ ↓ ↓

[0094] Since the sample amount of the fault data of the submarine DC observation network power supply system is small, and the application intends to establish the mapping between the initial value of the fault current slope, the initial value of the curvature, the peak time, the peak size and the fault distance, rather than the mapping between the fault current time sequence and the fault distance, it is best to use a regression algorithm with less sample requirement, simple calculation and high accuracy for fault positioning. In view of this, the application intends to use a support vector machine regression algorithm (SVR) for fault ranging, and proposes a submarine DC power supply system fault positioning method based on the multi-element fault current time domain characteristics as follows.

[0095] II. Submarine DC power supply system fault positioning method based on multi-element fault current time domain characteristics

[0096] As shown in Figure 1 , the submarine DC power supply system fault positioning method based on the multi-element fault current time domain characteristics provided by the application has the following specific steps:

[0097] Step S1, the protection device at each branch unit of the submarine observation network DC power supply system collects current signals in real time and stores 5ms of current data, and the sampling frequency is set to 10kHz.

[0098] As can be known from the foregoing analysis, the current rises rapidly at the fault time of the submarine DC power supply system. In order to prevent protection misoperation caused by load fluctuation, noise interference and the like, the application sets the criterion for whether the current at the branch unit is overcurrent as follows:

[0099] Δi dc > 0.3I N (1)

[0100] In the formula, Δi dc is the current mutation, which is obtained from the difference between the sampled current data and the steady-state DC current, and I N is the rated current.

[0101] When the overcurrent criterion shown in equation (1) is satisfied, each protection device will start the protection algorithm, mark the current time as the fault time, and obtain the current data within 5ms after the fault, and proceed to step S2.

[0102] Step S2: Extract the initial values ​​of the fault current slope, curvature, initial peak time, and initial peak value at each branch unit from the current data acquired by each protection device within 5ms after the fault. It is worth noting that the initial peak time and initial peak value are directly obtained from the acquired current data, while the initial values ​​of the fault current slope and curvature are calculated according to their respective definitions.

[0103] Step S3: Use the Support Vector Machine Regression (SVR) algorithm to locate the fault and determine its location.

[0104] 1) The Support Vector Machine (SVM) regression algorithm, based on VC dimension theory and the structural risk minimization criterion, uses minimum training error as a constraint, unlike traditional neural network algorithms which aim to minimize training error. It possesses strong generalization ability and is computationally simple and highly accurate in regression analysis of small-sample, nonlinear, and high-dimensional data. Before fault location, this invention requires training the SVM regression algorithm, as follows:

[0105] S31, the training set for the given current data is {(X1,y1), (X2,y2)...(Xt,y...} t )}, where t is the number of samples; X∈R N The input value is the fault current characteristic, and N = 4 is the dimension of the input value; y ∈ R is the corresponding output value, that is, the fault distance from the fault point to each branch unit; the training set data is mapped to the high-order linear space through the nonlinear function Φ(X) to obtain the sample regression function, as shown in the following equation (2):

[0106] {f(X)=w T Φ(X)+b|w∈R N} (2)

[0107] In the formula, w is the weight vector and b is a constant;

[0108] S32, introduce the insensitive loss function as shown in equation (3):

[0109]

[0110] S33, the regression problem is equivalent to the constrained optimization problem, as shown in equation (4):

[0111]

[0112] In the formula, ζ i ,ζ i* wherein, i is the serial number of the sample in the training set, i = 1, 2, … t, ε is the insensitive loss function, and C is the penalty coefficient;

[0113] In S34, the formula (4) is converted into a dual form by using the Lagrange function and the dual principle, as shown in the following formula (5):

[0114]

[0115] wherein, α i , α i * is the Lagrange coefficient, i is the serial number of the sample in the training set; X i , X j are the input values of the i-th and j-th samples in the training set, i = 1, 2, … t, j = 1, 2, … t, and i ≠ j; l is the Lagrange multiplier; and C is the penalty coefficient;

[0116] In S35, the value of the Lagrange coefficient α is obtained from the formula (5), and the value of the bias b is obtained by using the KKT condition, and the expression of the regression function is obtained by training as follows:

[0117]

[0118] wherein the kernel function K(X i , X j ) = Φ T (X) Φ(X I ) is selected from the following kernel functions.

[0119]

[0120] As can be seen from the formula (5), (6) and (7), the support vector machine regression algorithm only needs to calculate the kernel function when calculating the regression function, without the need to specifically clarify and calculate the nonlinear function Φ(X), thereby effectively avoiding the calculation difficulty problem in the high-dimensional space.

[0121] 2) The initial value of the fault current slope, the initial value of the curvature, the initial peak value time and the initial peak value size obtained in the step S2 are substituted into the regression function (6) trained by the training set, to obtain the distance y n from the fault point to each branch unit, wherein n is the serial number of the branch unit; if the fault current collected by the protection device at the n-th branch unit is from the branch unit to the system terminal, the fault point is downstream of the branch unit, and if y n is smaller than the length of the downstream line of the branch unit, it is determined that the fault occurs at the distance y nIf the protection device at the n-th branch unit collects the fault current flowing from the branch unit to the system head, the fault point is on the upstream of the branch unit, and if y n is smaller than the length of the upstream line of the branch unit, it is determined that the fault occurs at a position y n distance from the head of the upstream line, otherwise the fault does not occur on the upstream line; and the determined fault position is sent to the shore station, and the single-pole grounding fault positioning is completed.

[0122] In step S4, the fault current data and the fault position under the current working condition are recorded, and are added to the training set of the support vector machine regression algorithm, so as to further improve the positioning accuracy.

[0123] The above embodiment is a preferred implementation scheme of the present application, and in addition thereto, the present application can be implemented in other manners, and any obvious replacement without departing from the concept of the technical scheme is within the protection scope of the present application.

[0124] In order to make the ordinary skilled in the art more convenient to understand the improvement of the present application relative to the prior art, some of the drawings and descriptions of the present application have been simplified, and some other elements have been omitted in the present application file for the sake of clarity, and the ordinary skilled in the art should realize that these omitted elements can also constitute the content of the present application.

Claims

1. A method for fault location of a submarine DC power supply system based on the time domain characteristics of multi-element fault current, characterized in that, Comprise: Step S1, the protection device of each branch unit of the submarine observation network DC power supply system acquires current signal in real time, judges whether the current position is over current, when there is over current, marks the current time as fault time, each protection device acquires the current data within 5 ms after fault, enters step S2; Step S2, the initial value of the fault current slope, the initial value of the curvature, the initial peak time and the initial peak value of each branch unit are extracted from the current data within 5 ms after fault acquired by each protection device; Step S3, inputting the obtained initial value of fault current slope, initial value of curvature, initial peak time and initial peak value into the pre-trained support vector machine regression algorithm to obtain the distance from the fault point to each branch unit , is the serial number of the branch unit, the fault position is determined, the fault position is sent to the shore-based station, and the single-pole grounding fault positioning is completed; The training process of the support vector machine regression algorithm is as follows: S31, the training set of the given current data is wherein is the number of samples; X ∈ R N is the input value, i.e. the fault current feature, N = 4 is the input value dimension; is the corresponding output value, i.e. the fault distance from the fault point to each branch unit; through a nonlinear function the training set data is mapped to a high-dimensional linear space to obtain a sample regression function, as shown in the following formula (2): (2) wherein is a weight vector, is a constant; S32, introduce insensitive loss function, as follows (3): (3) S33, the regression problem is equivalent to the constrained optimization problem, as follows (4): (4) In the formula, a relaxation factor for the existence of a solution to the optimization problem, a serial number of a sample in the training set, = 1, 2, … t, an insensitive loss function, a penalty coefficient; S34, use Lagrange function and dual principle to convert formula (4) into dual form, as follows (5): (5) In the formula, , is a Lagrange coefficient, is the serial number of the sample in the training set; , are input values of the first , samples in the training set, respectively, =1,2,…t, =1,2,…t, and ; is a Lagrange multiplier; is a penalty coefficient; S35, the value of Lagrange coefficient a is solved from formula (5), and the value of bias is solved by KKT condition The expression of the regression function obtained by training is: (6) where the kernel function is chosen to satisfy the Mercer condition from the following kernel functions: (7) Substituting the initial values ​​of the fault current slope, curvature, initial peak time, and initial peak magnitude obtained in step S2 into the regression function (6) trained using the training set, the distances from the fault point to each branch unit are obtained respectively. ;if The fault current collected by the protection device at branch unit number 1 flows from that branch unit to the end of the system, so the fault point is downstream of that branch unit. If in this case... If the distance is less than the length of the downstream line of the branch unit, then the fault is determined to occur at a distance from the beginning of the downstream line. If the fault is located far away, otherwise it means the fault did not occur on the downstream line; if the fault current collected by the protection device at branch unit n flows from that branch unit to the beginning of the system, then the fault point is upstream of that branch unit. If the distance is less than the length of the upstream line of the branch unit, then the fault is determined to occur at a distance from the beginning of the upstream line. If the fault is located at a distant location, it indicates that the fault did not occur on the upstream line; otherwise, the determined fault location is sent to the shore base station to complete the location of this single-pole grounding fault.

2. The method for fault locating of a subsea DC power supply system based on the time domain characteristics of multi-element fault current according to claim 1, characterized in that: In step S1, the criterion for judging whether each branch unit is over current is: (1) wherein is the current jump, which is derived from the difference between the sampled current data and the steady state direct current, is the rated current.

3. The method for fault locating of a subsea DC power supply system based on multi-element fault current time domain features according to claim 1 or 2, characterized in that: It also includes step S4, record the fault current data and fault position under this working condition, and add it to the training set of the support vector machine regression algorithm.

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