Method for locating single-pole grounding faults in DC distribution networks

Abstract

A method for single-pole grounding fault location in a DC distribution network belongs to the technical field of DC power distribution networks. Aiming at the problems of difficult fault location caused by the unclear fault characteristics and the great influence of the fault characteristics on the control strategy of power electronic devices in the distribution network when a single-pole grounding fault occurs in a flexible DC distribution network, a method for single-pole grounding fault location in a DC distribution network based on the sparsity of fault zero-mode current is proposed. First, an equivalent model of MMC and DC / DC converters and an equivalent circuit of a single-pole grounding fault in the system are established under the zero-mode network, and on this basis, the sparse characteristics of the fault zero-mode current are analyzed. Then, the zero-mode voltage at the distribution measurement points is extracted to form a node zero-mode voltage equation, and the sparse quantity of the fault zero-mode current is reconstructed through a compressive sensing algorithm to achieve fast and accurate fault location. A large number of simulation results show that the method proposed in the present invention can quickly and accurately identify the fault line without being affected by the converter control strategy, has a low requirement for the number of measurement points, and has good tolerance to transition resistance and load changes at the same time.

Description

Technical Field

[0001] The present invention belongs to the technical field of DC power distribution networks. Background Art

[0002] Distributed generation (DG) mainly based on clean and renewable energy sources such as solar energy and wind energy has become the core component of the new generation of power distribution networks due to its advantages such as reliable power supply and environmental friendliness. Under the trend of increasing penetration of new energy generation and the increasing number of new types of loads, the insufficient acceptance capacity of traditional AC power grids has become a bottleneck restricting the large-scale access of new energy to the power grid. Compared with AC power distribution networks, DC power distribution networks have flexible operation control and obvious advantages in efficiently accepting "sources", "loads", and "energy storage".

[0003] With the rapid development of modern power systems, the structure of DC power distribution networks has become increasingly complex, and distribution lines are subject to the influence of harsh environments, resulting in frequent random faults, among which single-pole grounding faults are the most frequent. When a single-pole grounding fault occurs, the equivalent circuit and parameters of the distribution network system become complex, the fault characteristic quantities become unclear, the positive and negative pole voltages are asymmetric, and at the same time, a DC bias phenomenon will occur in the AC side voltage, which will seriously threaten the safe and stable operation of the system. Moreover, the DC fault characteristics are affected by the control strategy of the converter station and are difficult to analyze linearly by equivalent, which will affect the accuracy of fault location. Therefore, it is necessary to conduct in-depth research on the single-pole grounding fault location of DC power distribution networks.

[0004] At present, scholars at home and abroad have carried out a large number of studies on the single-pole grounding fault location in DC distribution networks. It is mainly divided into the traveling wave method, the active injection method, and the fault analysis method. Among them, the traveling wave method estimates the fault location according to the propagation time of the fault transient traveling wave along the grounding electrode line. It has a short positioning time and high accuracy and is widely used in transmission lines. However, its positioning accuracy is affected by the multiple branches of the distribution network, so it is not applicable in the distribution system. The active injection method realizes fault location by detecting and obtaining additional signals through additional devices, but additional equipment needs to be invested, reducing the economy of the system, and at the same time, the positioning accuracy is greatly affected by noise. The fault analysis method refers to combining system parameters and analyzing the internal relationship between fault electrical quantities and fault distances by solving circuit equations to achieve fault location. However, it is related to the fault characteristics of the DC distribution network, and the positioning accuracy is affected by the converter control strategy. Some literature proposes a fault location method that uses current fiber optic sensors to be arranged at multiple points along the line. The fault is detected by comparing the differential current on adjacent sensors, but the positioning accuracy is limited by the control strategy of the converter MMC. Some literature identifies faults based on the difference in the Pearson correlation coefficients of the transient voltages of the positive and negative poles of the line during internal and external faults. This method is not affected by the transition resistance and can reliably identify single-pole grounding faults. However, this method requires installing reactors, which increases a large amount of cost, and there is still no relatively perfect and systematic calculation method for the parameters of DC reactors and the boundary setting values. To avoid the influence of the fault pole on the non-fault pole due to the coupling effect during a single-pole grounding fault and effectively distinguish normal electrical quantities from fault electrical quantities, some scholars propose to analyze the zero-mode characteristics obtained by phase-mode transformation of the fault components to achieve single-pole grounding fault location. Some literature proposes a fault location method based on the frequency difference of the zero-mode current transient components from the frequency domain perspective, which overcomes the influence of the arc suppression coil in principle, but poses a high requirement for the computing performance of the digital processing chip. Some literature uses a standard fitting function to fit the fault zero-mode current collected after the fault occurs to achieve adaptive traveling wave protection for high-resistance grounding faults. However, its parameters depend on the prior estimation of the range of the transition resistance, and the uncertainty of parameter changes is relatively large. Some literature establishes mathematical models for internal and external faults based on the zero-mode network and identifies the fault line by comparing the similarity between the measured value of the zero-mode differential current and the pre-calculated values through the internal and external mathematical models. The protection setting is simple, but it is still affected by the transition resistance and the fault location.

[0005] Based on the above analysis, at present, the single-pole grounding fault in the DC distribution system is easily affected by the transition resistance and the converter control strategy. Summary of the Invention

[0006] The object of the present invention is to propose a single-pole grounding fault location method for a DC distribution network, which is a single-pole grounding fault location scheme for a flexible DC distribution system based on the sparsity of fault zero-mode current, targeting a small-current grounded DC distribution network.

[0007] The steps of the present invention are as follows:

[0008] S1. Fault node zero-mode voltage equation

[0009] Write the zero-mode node voltage equation as Equation (16):

[0010] (16)

[0011] In the formula, the matrix Y M×M ( ω ) is the node zero-mode admittance matrix. That is, when the system is operating normally, the zero-mode current vector is zero, that is, no node has zero-mode current to the ground;

[0012] If it is assumed that node l is the fault point, then only the element in the zero-mode current vector is non-zero; if a fault occurs between certain nodes, then only the zero-mode current values of the 2 nodes connected to this fault line in the zero-mode current vector are non-zero;

[0013] The node zero-mode impedance matrix in the zero-mode network is obtained by inverting the node zero-mode admittance matrix, that is:

[0014] (17)

[0015] In the formula: Z ii ( ω ) is the self-impedance of node i in the zero-mode network, Z ij ( ω ) is the mutual impedance between node i and node j in the zero-mode network;

[0016] The zero-mode current vector is the quantity to be solved, and the zero-mode voltage vector is the known measured value; Combining Equation (16) and Equation (17) is changed to Equation (18), that is:

[0017] (18)

[0018] When zero-mode voltage measuring devices are installed only on S ( S << M ) nodes, the corresponding node zero-mode voltage is U 1( ω ), U 2(ω ), …, U S ( ω );

[0019] Excluding the zero-mode voltage outside the measurement points and the impedance values of the rows where the measurement points are located in the nodal zero-mode impedance matrix, then only S equations can be listed in Equation (18). Since the number of unknowns is more than the number of equations in the system, this system of equations is an underdetermined system of equations. Thus, partial sparse nodal equations are obtained as shown in Equations (19) to (20):

[0020] (19)

[0021] (20)

[0022] To eliminate the angle calculation brought by the phasor, the modulus value of the zero-mode component is usually taken for calculation. Therefore, Equation (20) can be expressed as a modulus equation:

[0023] (21)

[0024] Solving the fault zero-mode current according to Equation (21) and using the sparsity of the vector to be solved, the unique solution can be determined, and the fault location can be accurately located;

[0025] S2. Compressive Sensing Algorithm

[0026] The sparse representation of the original compressive sensing signal is shown in Equation (22):

[0027] (22)

[0028] Where: y ∈ R S is the observation vector, that is, the nodal zero-mode voltage vector ; ∈ R S×M ( S << M ) is the observation matrix, that is, the nodal zero-mode impedance matrix Z S×M ( ω ); x ∈ R S is the sparse vector to be reconstructed, that is, the nodal zero-mode current vector ; e ∈ R S obeys N (0, σ 2 ) Gaussian white noise;

[0029] Reconstruct the underdetermined system of equations using the OMP algorithm;

[0030] The established observation matrix When the isometry property requirement is satisfied, the compressive sensing theory can first solve the sparse coefficient s for the inverse problem of the above formula (22), and then the signal with sparsity K x Can be correctly recovered from the M-dimensional measurement projection value y; By The norm regularization formula to find the optimal sparse solution is:

[0031] (23)

[0032] Restore the compressed and observed signal to the initial signal form through formula (23), thereby completing signal reconstruction;

[0033] In the reconstructed zero-mode current signal, judge according to the number and position of the largest reconstruction values, and the final result is the location where the fault occurs;

[0034] S3. Measuring point distribution design

[0035] The number of observation points r Should satisfy formula (24) with the sparsity and the length of the signal to be reconstructed:

[0036] (24)

[0037] Where: r Is the number of measuring points; q Is the sparsity of the signal to be reconstructed; p Is the length of the reconstructed signal;

[0038] S4. Fault location method flow

[0039] Step 1: Obtain the node zero-mode admittance matrix according to the topological structure and line parameters of the multi-node DC distribution network, then perform an inverse operation and take its modulus value to obtain the observation matrix Z' S×M ( ω )

[0040] Step 2: After the fault occurs, collect the fault transient voltage signal waveforms of the distribution measuring points before the MMC sub-module is blocked, obtain the fault zero-mode voltage component through the phase-mode transformation method, and calculate the zero-mode voltage signal of a continuous window length U S ( ω )

[0041] Step 3: Combine the observation matrix Z' S×M ( ω ) and the zero-mode voltage signal US ( ω ) is imported as a parameter into the compressive sensing reconstruction algorithm for calculation, and a sparse vector composed of the zero-mode current amplitudes of each node is reconstructed. I S ( ω );

[0042] Step 4: According to the reconstructed sparse vector I S ( ω ), determine the number of relatively large amplitude values and the corresponding nodes in its vector, and judge and locate the fault location.

[0043] The method proposed by the present invention can quickly and accurately identify the fault line without being affected by the converter control strategy, has low requirements for the number of measurement points, and at the same time has good tolerance to transition resistance and load changes. Description of the Drawings

[0044] Figure 1 is a diagram of the change of zero-mode electrical quantity;

[0045] Figure 2 is a topological structure diagram of MMC;

[0046] Figure 3a is a zero-mode current path diagram of MMC;

[0047] Figure 3b is a series-parallel circuit diagram of RLC;

[0048] Figure 4a is a structural diagram of a full-bridge DC / DC sub-module;

[0049] Figure 4b is a structural diagram of a DAB-type sub-module;

[0050] Figure 5a is a zero-mode current path diagram of DC / DC;

[0051] Figure 5b is an equivalent circuit diagram of DC / DC;

[0052] Figure 6 is a diagram of zero-mode voltage sag;

[0053] Figure 7 is an equivalent circuit diagram of the fault;

[0054] Figure 8 is a fault location flow chart;

[0055] Figure 9 is a model diagram of an IEEE 32-node DC distribution network;

[0056] Figure 10 is a schematic diagram of the zero-mode electrical quantity fault location result;

[0057] Figure 11 It is a schematic diagram of the transient electrical quantity fault location result;

[0058] Figure 12 It is a schematic diagram of the fault location results for different transition resistances;

[0059] Figure 13 It is a schematic diagram of the fault location results for different loads;

[0060] Figure 14 It is a schematic diagram for comparing the fault location results of different measuring points. Specific implementation manner

[0061] The present invention takes a small current grounded DC distribution network as the object. First, by constructing a zero-mode impedance equivalent model of a modular multilevel converter (MMC) and a DC / DC converter through the zero-mode current loop, a fault zero-mode equivalent circuit is established to analyze the sparsity characteristics of the zero-mode current. Then, the zero-mode voltages at distributed measuring points are extracted to form a node zero-mode voltage equation, which is combined with the compressed sensing theory to solve the sparse quantity of the zero-mode current, and a single-pole grounding fault location scheme for a flexible DC distribution system based on the sparsity of the fault zero-mode current is proposed. The simulation results of PSCAD / EMTDC show that the proposed method can quickly and accurately identify the fault line on the basis of significantly reducing the difficulty of extracting and processing fault characteristic quantities.

[0062] 1. Analysis of fault current characteristics under the zero-mode network

[0063] When a single-pole grounding fault occurs in a flexible DC distribution network, the electrical quantities of the positive and negative poles become asymmetric due to the coupling effect of the line. Through the phase-mode transformation method, it is transformed into independent zero-mode components for analysis, making the fault electrical quantity characteristics obvious. Therefore, first, the impedance equivalent model of the converter under the zero-mode network is analyzed. On this basis, the sparsity of the fault zero-mode current is analyzed according to the fault equivalent circuit.

[0064] The structure of the DC distribution network is becoming increasingly complex and has more branches. When a single-pole grounding fault occurs on the line, traveling waves will be generated at the fault point and propagate to both ends of the line. Due to the coupling effect of factors such as the transient capacitance and transient inductance of the line, induced fault electrical components will appear on the non-fault pole line, causing asymmetry in the electrical quantities of the positive and negative poles. To facilitate the analysis of the DC distribution network lines, the phasors are usually transformed into moduli to eliminate the influence caused by the coupling effect of the positive and negative poles of the line. In the literature, a phase-mode transformation method suitable for the electrical quantities of DC lines is constructed, and a decoupling matrix is introduced to decompose the fault electrical components of the line. The decoupling matrix is shown in Equations (1) and (2). Through phase-mode transformation, the asymmetric positive and negative pole electrical quantities are transformed into independent first-mode and zero-mode components, where the reference directions of the positive and negative pole currents are both from the bus to the line

[0065] (1)

[0066] (2)

[0067] Wherein: S is the decoupling matrix; S -1 is the inverse decoupling matrix; X P, X N are the electrical quantities of the positive and negative poles of the DC line; X 1, X 0 are the electrical quantities of the first mode and the zero mode.

[0068] By combining Equation (1) and Equation (2), we can obtain

[0069] (3)

[0070] (4)

[0071] It can be seen from Equation (3) and Equation (4) that the zero-mode electrical quantity is obtained by adding the electrical quantities of the positive and negative poles. This means that when the DC distribution network is in normal operation or a bipolar short-circuit fault occurs, there will be no zero-mode component on the line, and the zero-mode component will only appear when a single-pole grounding fault occurs in the system. As Figure 1 shown, when the single-pole grounding fault does not occur in the system, the zero-mode electrical quantity value is 0 at this time. After the fault occurs, the zero-mode value will show an obvious upward or downward trend. This method can clearly distinguish normal electrical quantities from fault electrical quantities.

[0072] 1.2 Zero-mode equivalent model of the DC distribution network converter

[0073] To meet the requirement that the zero-mode impedance model is convenient for calculation and thus accurately locate faults, the present invention is based on analyzing the switch states of the converter, and reasonably simplifies according to the actual parameters under the zero-mode network, and establishes a zero-mode impedance model of the MMC and DC / DC converters that is not affected by specific control strategies and system operating states.

[0074] 1.2.1 Zero-mode equivalent model of MMC

[0075] At present, the research on MMC in existing literature has been very in-depth, and various MMC sub-module structures have been proposed, such as Figure 2It is the equivalent model of the MMC, which consists of six symmetrical bridge arms in three phases. Each phase has N sub-modules and an arm inductor on the upper and lower bridge arms. The sub-module adopts a half-bridge structure and is composed of an arm reactance, a switching tube, and a sub-module capacitor. Among them, the arm reactance is a fixed value, and the on-resistance value of the switching tube is extremely small, both of which have little impact on the equivalent impedance derivation and are within the negligible range. Affected by the control algorithm and the system operation state, the number of sub-module capacitors put into operation is not fixed. Reasonable equivalence of it is the key to deriving the equivalent impedance of the MMC.

[0076] When a single-pole grounding fault occurs on the DC side of the MMC converter studied in this invention, due to the existence of a grounding resistance, there will be no overcurrent phenomenon in the system. The MMC converter can operate for a period of time in the fault state. Therefore, the zero-mode impedance of the MMC converter is the same as that in the normal operation state when a single-pole grounding fault occurs. The circulation path of the zero-mode current should take the ground as the loop. The dotted line in Fig. 3(a) represents the zero-mode current loop flowing through the sub-module. The fault zero-mode current flows in from the fault source through the ABC three-phase bridge arms, passes through the coupling transformer, and finally flows out through the large grounding resistance. Therefore, based on the principles of constant energy storage and constant total voltage of the sub-module capacitor, the zero-mode model of the MMC converter can be equivalently a series-parallel RLC lumped model, as shown in Fig. 3(b). In the figure, U s is the equivalent voltage of the coupling transformer, R L is the equivalent resistance of the line, L L is the equivalent reactance of the line

[0077] (5)

[0078] In the formula: R arm is the equivalent resistance of the arm, L m is the arm reactance, R s is the equivalent resistance of the coupling transformer, L s is the equivalent reactance of the coupling transformer, R 0 is the zero-mode resistance, L 0 is the zero-mode reactance.

[0079] According to the above analysis, combining Fig. 3(a) and Fig. 3(b), it can be seen that when a single-pole grounding fault occurs on the DC side, the lumped parameters of the MMC zero-mode equivalent are as shown in Eq. (6). Therefore, the mathematical expression of the MMC zero-mode impedance is:

[0080] (6)

[0081] (7)

[0082] In the formula: R $R_{0}$ is the zero-mode resistance, L $X_{0}$ is the zero-mode reactance, C $C_{0}$ is the zero-mode capacitance of the sub-module, R g $R_{g}$ is the grounding resistance of the AC side neutral point, N $N$ is the number of MMC sub-modules.

[0083] 1.2.2 DC / DC Zero-Mode Equivalent Model

[0084] The DC load and the photovoltaic power supply are connected to the flexible DC distribution network through the DC / DC converter. There are two common structures of the DC / DC converter. One is the full-bridge DC converter, which is usually used as a DC transformer in the DC distribution system, and the output voltage is jointly determined by the amplitude of the input voltage and the turns ratio of the transformer. The other is the dual-active bridge (DAB) DC / DC converter. When the DC distribution network operates stably, the current at the output end of the DAB converter has a constant proportional relationship with the current on its freewheeling inductor. The structures of its sub-modules are shown in Figures 4(a) and 4(b) respectively.

[0085] In the present invention, the DC / DC converter with a dual-active bridge structure is mainly adopted. The DAB-type sub-module structure is symmetrical. When it is used as a boost converter or a buck converter, only the positions of the high-voltage and low-voltage side voltage-stabilizing capacitors need to be swapped. When a single-pole grounding fault occurs on the DC side, the zero-mode current circulation path is shown in Figure 5(a). Since g 11 $S_{1}$ is turned on and g 12 $S_{2}$ is turned on, the loop parameters and structure are the same. Figure 5(b) shows its zero-mode impedance model (ignoring the loop resistance). Considering the actual values of the parameters of the converter in the zero-mode network, the inductive reactance of the inductor in its equivalent circuit will be much higher than the capacitive reactance of the output voltage-stabilizing capacitor. To simplify the calculation and unify the model when the DC / DC converter is used as a buck-boost converter, the branches with inductors and loads in the equivalent circuit are ignored. At this time, the zero-mode equivalent impedance model on the output side of the converter sub-module can be simplified to its output voltage-stabilizing capacitor model. In the figure, L $L_{1}$ 、L $L_{2}$ and L 12 $M$ are respectively the self-inductance of the low-voltage side, the self-inductance of the high-voltage side, and the mutual inductance between the primary and secondary sides of the isolation transformer equivalent to the high-voltage side; C h $C_{1}$ is the high-voltage side support capacitor; Z load $R_{L}$ is the DC load; k $n$ is the turns ratio of the isolation transformer.

[0086] As can be seen from the above analysis, when the fault source is injected from the series port of the sub-module, the zero-mode impedance of the overall DAB-type DC / DC converter can be approximately equivalent to the capacitive reactance of the capacitor connected to its DC port. In the Input-Parallel Output-Series (IPOS) system connection mode, the output terminals of each sub-module are in series. Therefore, the overall zero-mode equivalent impedance of the converter is n the series connection of the capacitive reactances of

[0087] (8)

[0088] where: N 2 is the number of DC / DC sub-modules, C h is the capacitive reactance value of the output capacitor.

[0089] 1.3 Analysis of Fault Zero-Mode Current

[0090] In a flexible DC distribution network, when a line fault occurs, the zero-mode voltage at the fault point drops instantaneously. As Figure 6 shown, it can be approximately equivalent to connecting a step signal source at the fault location.

[0091] Combined with the zero-mode equivalent model of the converter analyzed in Section 1.2, the corresponding fault zero-mode equivalent circuit can be obtained during the fault stage. As Figure 7 shown is the zero-mode equivalent circuit diagram of a fault occurring between two nodes in a DC distribution network.

[0092] Figure 7 where: Z L0 is the equivalent impedance of the reactor; Z mmc0 is the equivalent impedance of the MMC; Z dc0 is the equivalent impedance of the DC / DC converter; Z line0x is the equivalent impedance of the line; I 01 is the fault line current; I 02 is the non-fault line current; U f0 is the fault voltage source.

[0093] According to the fault equivalent circuit, series and parallel analyses are carried out in the complex frequency domain to obtain the equivalent impedance Z 1( s ) on the left side of the fault point, specifically:

[0094] (9)

[0095] (10)

[0096] Wherein: Z 01 ( s ) is the series zero-mode equivalent impedance of the MMC, reactor and line under the fault condition; Z 02 ( s ) is the series zero-mode equivalent impedance of the DC / DC, reactor and line under the fault condition.

[0097] By analyzing the fault circuit, the complex frequency-domain expression of the zero-mode current of the fault line can be further obtained I 01 as:

[0098] (11)

[0099] (12)

[0100] Wherein: U f0 is the fault voltage; L r is the inductance of the reactor in the DC distribution network; N 2 is the number of DAB modules in the DC / DC converter; r 0x and l 0x are the resistance and inductance of the line respectively.

[0101] If taking the fault occurring in Figure 7 as an example, from the above analysis, it can be known that the transient zero-mode current flowing through the fault line is I 01 ( s ). According to the circuit shunt principle, the current flowing through the non-fault line I 02 ( s ) and the current flowing into the DC / DC converter I dc0 ( s ) are:

[0102] (13)

[0103] (14)

[0104] Thus, the ratio of the zero-mode current flowing through the non-fault line to the zero-mode current flowing into the DC / DC converter can be further obtained as:

[0105] (15).

[0106] The zero - mode impedance of the MMC converter includes a large earthing resistor connected to the neutral point on the valve side of the coupling transformer R g. To reduce the threat of a single - pole earthing fault to the system, R g generally takes a relatively large value. In the present invention, 1 kΩ is selected. The DC / DC converter is approximately equivalent to an output voltage - stabilizing capacitor, and its value is very small after actual parameter calculation. Therefore, in the frequency band set in the present invention, the modulus values of the line zero - mode impedance, the DC reactor zero - mode impedance, and the MMC equivalent zero - mode impedance are much larger than the DC / DC converter equivalent zero - mode impedance value, that is, the denominator in Equation (15) is much larger than the numerator.

[0107] From the above analysis, it can be obtained that in fact, after the zero - mode component of the fault current flows out of the fault point, a large amount of it will flow into the DC / DC converter with a relatively small impedance modulus value, greatly reducing the zero - mode current component flowing into the non - fault line, almost to 0. Therefore, it can be shown that when a single - pole earthing fault occurs in a DC distribution network, the zero - mode fault current has sparsity.

[0108] 2. Fault location method based on the sparsity of zero - mode current

[0109] When a single - pole earthing fault occurs at a certain node of the DC distribution network line, the zero - mode current at this node is non - zero, and the zero - mode current at other nodes is zero; if a single - pole earthing fault occurs between two nodes, the fault zero - mode current can be equivalently non - zero at these two nodes and zero at the rest. Since node faults are simpler than inter - node faults, for the result to be more general, the subsequent analysis in the present invention takes the fault occurring between nodes as an example.

[0110] 2.1 Zero - mode voltage equation of the fault node

[0111] For a DC distribution network line with M nodes, after an inter - node fault occurs, only the fault point will generate a fault source. From the analysis in the first section above, it can be obtained that the zero - mode fault current has sparsity. The zero - mode node voltage equation is written as Equation (16):

[0112] (16)

[0113] In the formula, the matrix Y M×M ( ω ) is the node zero - mode admittance matrix. That is, when the system is operating normally, the zero - mode current vector is zero, that is, no node has a zero - mode current to the ground. If it is assumed that node l is the fault point, then only the in the zero - mode current vector I l ( ω ) element is non - zero. If a fault occurs between certain nodes, then the zero - mode current vector Only the zero-mode current values of the two nodes connected to this faulty line are non-zero values.

[0114] The node zero-mode impedance matrix in the zero-mode network can be obtained by inverting the node zero-mode admittance matrix, i.e.:

[0115] (17)

[0116] In the formula: Z ii ( ω ) is the self-impedance of node i under the zero-mode network, Z ij ( ω ) is the mutual impedance between node i and node j under the zero-mode network.

[0117] In the fault location method of the present invention, the zero-mode current vector is the quantity to be solved, and the zero-mode voltage vector is the known measured quantity. Combining Equation (16) and Equation (17) can be changed to Equation (18), i.e.:

[0118] (18).

[0119] When zero-mode voltage measuring devices are installed only on S ( S << M ) nodes, the corresponding node zero-mode voltages are U 1( ω ), U 2( ω ), …, U S ( ω ). Removing the zero-mode voltages other than the measurement points and the impedance values of the rows where the measurement points are located in the node zero-mode impedance matrix, then Equation (18) can only list S equations. Since the number of unknowns is more than the number of equations in the system, this system of equations is an underdetermined system of equations, so partial sparse node equations are obtained as shown in Equations (19) to (20):

[0120] (19)

[0121] (20).

[0122] In addition, to eliminate the angle calculation brought by phasors, the modulus values of the zero-mode components are usually taken for calculation. Therefore, Equation (20) can be expressed as a modulus equation:

[0123] (21).

[0124] Solve the fault zero-mode current according to Equation (21). However, this equation is an underdetermined system of equations, and there are usually infinitely many solutions under normal circumstances. The theory of compressive sensing proposes that when the signal to be solved is sparse enough, there exists a unique sparse solution. Therefore, by utilizing the sparsity of the vector to be solved, a unique solution can be determined, thereby accurately locating the fault position.

[0125] 2.2 Compressive Sensing Algorithm

[0126] Compressive sensing is a method of sampling sparse signals at a lower frequency to achieve high-probability accurate reconstruction. The sampling frequency requirement for the signal is much lower than the Nyquist sampling frequency. The signal is acquired and compressed. During the signal reconstruction process, the compressed signal is restored using a reconstruction algorithm to obtain enough of the original signal. Compared with other processing methods, it significantly reduces the data storage space and the requirements for collecting data.

[0127] Compressive sensing can be widely applied in the field of signals. The sparse representation of its original signal is shown in Equation (22):

[0128] (22)

[0129] In the formula: y ∈ R S is the observation vector (i.e., the node zero-mode voltage vector ); ∈ R S×M ( S << M ) is the observation matrix (i.e., the node zero-mode impedance matrix Z S×M ( ω )); x ∈ R S is the sparse vector to be reconstructed (i.e., the node zero-mode current vector ); e ∈ R S is N (0, σ 2 ) Gaussian white noise.

[0130] The above Equation (22) is an underdetermined equation, which has infinitely many solutions or no solution. The present invention uses the OMP algorithm to reconstruct the underdetermined system of equations.

[0131] The observation matrix has an important impact on the signal reconstruction accuracy. It can effectively reduce the data dimension and its storage amount, thereby achieving highly compressed signals. When a discrete signal of finite length is a sparse signal, the established observation matrix When the restricted isometry property (RIP) requirement is satisfied, the compressive sensing theory can first solve the sparse coefficient s for the inverse problem of Equation (22), and then correctly recover the signal with sparsity K from the M-dimensional measurement projection value y. By x using the norm regularization formula to find the optimal sparse solution:

[0132] (23).

[0133] The compressed and observed signal is restored to the initial signal form through Equation (23), thereby completing signal reconstruction. In the reconstructed zero-mode current signal, the final result obtained by judging according to the number and position of the maximum reconstruction values is the location where the fault occurs.

[0134] 2.3. Measuring point distribution design

[0135] According to the compressive sensing theory, to accurately obtain the reconstruction result, the number and position of the measuring points need to be reasonably arranged. The number of measuring points is determined by the minimum number of measuring points that can reflect the fault characteristics of the entire DC distribution network by the compressive sensing algorithm, that is, the number of observation points r should satisfy Equation (24) with the sparsity and the length of the signal to be reconstructed.

[0136] If it is less than this defined value, it is difficult to perform overall reconstruction

[0137] (24)

[0138] In the formula: r is the number of measuring points; q is the sparsity of the signal to be reconstructed; p is the length of the reconstructed signal.

[0139] The position of the measuring point is set according to the system network topology. The basis and minimum requirement for zero-mode voltage sag monitoring is that the fault information of each branch during a fault should be collected by at least 1 measuring point. Since the zero-mode equivalent impedance of the converter station in the DC distribution network is quite different from that of the line, and there are many power electronic devices in the converter station, and the control strategy affects its fault characteristics, therefore, in order to make the measurement result more accurate and the monitoring information can reflect the fault characteristics of the entire network, measuring points need to be set at the outlet of the converter station.

[0140] For the present invention, the sparsity q is taken as 5, and the signal length p is taken as 32, and then the number of measuring points r should be no less than 6. Combining with the design of the DC distribution network topology structure, the total number of measuring points finally selected is 7.

[0141] 2.4、Fault Location Method Flow

[0142] The fault location scheme proposed by the present invention is mainly divided into three parts: data acquisition, OMP algorithm reconstruction, and fault location. The detailed steps are as follows:

[0143] Step 1: Obtain the node zero-mode admittance matrix according to the topological structure and line parameters of the multi-node DC distribution network, then perform an inverse operation and take its modulus value to obtain the observation matrix Z' S×M ( ω )

[0144] Step 2: After a fault occurs, collect the fault transient voltage signal waveforms at the distributed measurement points before the MMC sub-module is blocked, obtain the fault zero-mode voltage component through the phase-mode transformation method, and calculate the zero-mode voltage signal of a continuous window length U S ( ω )

[0145] Step 3: Import the observation matrix Z' S×M ( ω ) and the zero-mode voltage signal U S ( ω ) obtained in the previous two steps as parameters into the compressive sensing reconstruction algorithm for calculation, and reconstruct the sparse vector composed of the zero-mode current amplitudes of each node I S ( ω )

[0146] Step 4: According to the reconstructed sparse vector I S ( ω ), determine the number of relatively large amplitude values and the corresponding nodes in the vector, and judge and locate the fault location.

[0147] Due to the inevitable errors in the algorithms used in the above steps, this will cause some points with non-zero ground current values in addition to the non-zero zero-mode current value at the fault point in the current vector. However, generally speaking, the zero-mode current value at the fault point is the maximum. Therefore, select the node corresponding to the maximum reconstructed value in the zero-mode current vector as the fault point. The fault location process is as Figure 8 shown

[0148] 3. Simulation Analysis

[0149] To verify the effectiveness of the above fault location method, the present invention uses the PSCAD / EMTDC platform to build as Figure 9The improved IEEE 32-node DC distribution network simulation model shown, where there is three-terminal power supply. The alternating current is converted into direct current by the MMC converter to supply power to the whole system, and the other two terminals are connected to distributed power sources, including photovoltaic power supply through the DC / DC converter and wind power supply through the MMC converter. According to Equation (25), it can be known that r ≥5.55. Considering the distribution network topology structure and the number of branch ends comprehensively, it is determined that at least 7 measurement points are required for the topology studied in the present invention. For example Figure 9 The nodes with boxes in are the measurement point positions. The line parameters and load parameters are shown in Table 1 as follows

[0150] Table 1 System simulation related parameters

[0151]

[0152] 3.1. Verification of fault location scheme (comparative analysis of similar algorithms)

[0153] To verify the superiority of the fault location method based on the sparsity of the zero-mode current between nodes proposed in the present invention, it is set in the present invention that at a frequency of 1000 Hz, a positive pole grounding fault occurs on branch 12 of the DC distribution network at 1 s, and the transition resistance is set to 1 Ω

[0154] In the fault location method proposed in the present invention, only the fault waveform information at the moment of fault needs to be extracted. However, to reflect the change process of the fault voltage and current, the transient electrical quantity change data within 5 ms before and after the fault occurrence is taken, and then it is transformed into independent zero-mode components through phase-mode transformation for analysis. The fault location results in two cases of using zero-mode electrical quantities and transient electrical quantities are analyzed and verified respectively below

[0155] 3.1.1 Zero-mode electrical quantity location results

[0156] When using zero-mode electrical quantities for fault location, first extract the transient voltages of the distributed measurement points within 5 ms before and after the fault occurrence, decouple the zero-mode voltage components to form the zero-mode voltage signals of the distributed measurement points, and then calculate the node zero-mode impedance matrix through the parameters of the DC distribution network. Combining with the OMP reconstruction algorithm, the zero-mode current values of each node are reconstructed. The location results are as Figure 10 shown

[0157] From Figure 10 it can be seen that in the DC distribution network, the reconstruction values of nodes 12 and 13 are relatively large. Within the allowable error range, the others are approximately 0. It can be determined that the fault occurs between nodes 12 and 13. Therefore, it can be known that the location result is accurate

[0158] 3.1.2 Transient electrical quantity location results

[0159] When using transient electrical quantities for fault location, the transient voltage waveforms at the distributed measurement points at the fault moment can be directly extracted and imported into the OMP reconstruction algorithm together with the node impedance matrix for calculation to solve for the transient current vector. The positioning results are as Figure 11 shown.

[0160] As Figure 11 can be seen, in the distribution network system, there are situations where the reconstruction values are relatively large at nodes 12 and 17. There are non-zero values at nodes 21, 24, and 32 connected to the power supply, and the values at the remaining nodes are all 0. It can be determined that the fault occurs in the area of nodes 12 - 17. Therefore, it can be known that using transient quantities can only locate to a certain area.

[0161] From the above analysis, it can be obtained that the fault location result using the zero-mode electrical quantity of the fault is more accurate than directly using the transient electrical quantity of the fault, and the fault line can be directly located. Because when a single-pole grounding fault occurs in a DC distribution network, when identifying the fault quantity, the change of the transient electrical quantity is not obvious, and the transient electrical quantity value at the power supply is almost unchanged, so it will affect the final location result. After using the zero-mode network, the transient electrical quantity of the fault becomes an independent zero-mode component for analysis, with obvious fault quantity characteristics and more accurate location results.

[0162] 3.2. Influence factor analysis

[0163] For the DC distribution network system, the main influencing factors on the zero-mode electrical quantity of the fault include transition resistance, signal noise, line parameters, and topological structure, etc. The DC distribution line belongs to a short line, and the distributed capacitance is very small. And this invention is aimed at single-pole grounding faults, and the size of the distributed capacitance has little influence on the zero-mode electrical quantity of the fault. Therefore, this invention does not consider the influence of the distributed capacitance. The influence of transition resistance, signal noise, load change, line parameters, and measurement points on the fault location accuracy is mainly considered.

[0164] 3.2.1. Influence of transition resistance

[0165] To study the influence of transition resistance on the fault location accuracy, considering that the maximum transition resistance in medium and low voltage DC distribution networks is generally only a dozen ohms, this invention respectively sets R f = 1Ω, 5Ω, 10Ω for fault analysis, and the simulation results are shown in Table 2.

[0166] Table 2 Analysis of location results with different transition resistances

[0167]

[0168] From the fault location results in Table 2, it can be obtained that: under different transition resistance conditions, the proposed scheme in this invention can accurately identify the fault line.

[0169] In the fault location algorithm proposed in the present invention, the value of the transition resistance does not affect the elements in the node zero-mode impedance matrix. It mainly affects the amplitude of the fault zero-mode electrical quantity column vector, as Figure 12 shown. In the sparse column vector of the node zero-mode current obtained by the OMP reconstruction algorithm, the reconstruction result of the fault branch is the largest, and the reconstruction results of the remaining nodes are still approximately 0. Therefore, the algorithm proposed in the present invention has strong tolerance to the influence of the transition resistance.

[0170] 3.2.2. Influence of signal noise

[0171] The amplitude of Gaussian white noise follows a normal distribution, and its influence on the power system is relatively random, which is one of the important factors affecting fault location. In the present invention, when the signal-to-noise ratio (SNR) is 20, 30, and 40 dB respectively, the fault location results are shown in Table 3. Signal noise will cause fluctuations in the sampled signals. After the original electrical quantity data collected at the sparse measurement points are processed by the moving average filtering algorithm, the fluctuations of the original sampled data are reduced, and at the same time, the overall change trend of the independent data is not affected, greatly reducing the influence of noise.

[0172] The fault location algorithm of the present invention also considers the influence of Gaussian white noise at the initial stage of equation construction. This algorithm has good resistance to a certain amount of noise. However, when the SNR reaches 20 dB, the noise has a greater impact on the location result, and it is difficult to obtain the optimal solution through the limited error during the solution of the algorithm.

[0173] Table 3 Analysis of fault location results under different noises

[0174]

[0175] 3.2.3. Influence of load change

[0176] The DC distribution network has relatively dense branches and many loads, and the load change has a great impact on the power flow distribution. In the present invention, the influence of load change on fault location is considered under three cases where the node load is 2 MW, 1 MW, and 0.5 MW respectively. The statistical results are shown in Table 4 for details.

[0177] Table 4 Analysis of fault location results under load change

[0178]

[0179] It can be concluded from the fault location results in Table 4 that the load change has little influence on the accuracy of the algorithm proposed in the present invention.

[0180] Since the load is much larger than the line impedance, in the self-admittance and mutual admittance, the proportion of the load is much smaller than that of the DC line impedance. Therefore, the influence of load change on the node zero-mode admittance matrix is negligible, that is, the load change has almost no influence on fault location, asFigure 13 as shown

[0181] 3.2.4, Influence of Line Parameter Variation

[0182] Since the accuracy of obtaining line parameters of the DC distribution network is generally not high, and the algorithm proposed in the present invention is directly related to the accuracy of the elements of the nodal zero-mode impedance matrix. Therefore, the accuracies of the DC distribution network line parameters are set to 94%, 96% and 98% respectively to verify the accuracy of fault location. The location results are shown in Table 5. It can be seen from the table that when the error is within 4%, the fault location algorithm proposed in the present invention can accurately judge the line of the DC fault.

[0183] Table 5 Analysis of Location Results of Line Parameter Variation

[0184]

[0185] 3.2.5, Influence of Measuring Points

[0186] The distribution and number of measuring points have a great influence on the accuracy of the reconstruction result, and the number of measuring points actually means the size of the investment. In order to minimize the investment cost without affecting the accuracy of fault location, it is necessary to know the specific influence degree of the number and distribution of measuring points on the location result. Figure 14 The fault location results under different numbers of measuring points are given. It can be seen from the figure that when the number of measuring points is less than the number of measuring points obtained by the compressive sensing theory, the accuracy rate of fault location drops sharply and the location result becomes unreliable. When the number of measuring points increases, the fault location result becomes more and more accurate, and this result is consistent with the compressive sensing theory.

[0187] The distribution of measuring points also has an impact on the probability of successful fault location. For the voltage data of the same number of measuring points, when there are voltage measurement devices both upstream and downstream of the fault, the accuracy rate of fault location is significantly higher than that when there is only a voltage measurement device on one side of the fault.

[0188] Conclusion

[0189] The present invention establishes an equivalent impedance model of MMC and DC / DC converters and a fault equivalent circuit in the zero-mode network for single-pole grounding faults in DC distribution networks, analyzes the sparse characteristics of fault zero-mode current, and proposes a method for fault location in combination with the compressive sensing theory. And there are the following conclusions:

[0190] 1) The transient electrical quantities are decoupled into zero-mode components by the phase-mode transformation method, avoiding the influence of the coupling effect of the fault line and making the fault characteristics obvious. The zero-mode impedance equivalent model of MMC and DC / DC converters can be constructed in the zero-mode network without being affected by the converter control strategy.

[0191] 2) Based on the sparse characteristics of the fault zero-mode current, a fault location method is proposed in combination with the compressed sensing theory. This method can quickly and accurately identify the fault location. It can achieve full-network fault location through a small number of distributed measuring points, the measurement information does not need to be synchronized, and the data required for location is short. It has a strong ability to withstand transition resistance, noise, and load changes. A large amount of simulation data shows that the fault location method proposed in the present invention has high location accuracy, but there are certain requirements for the number and location of distributed measuring points, and further research is needed.

Claims

1. A method for locating a single-pole grounding fault in a DC distribution network, characterized in that: The steps are as follows: S1. Zero-mode voltage equation of the fault node Write the zero-mode node voltage equation as shown in Equation (16): In the formula, matrix Y M×M (ω) is the zero-mode admittance matrix of nodes. That is, when the system is operating normally, the zero-mode current vector is zero, meaning that no node has zero-mode current to the ground; If it is assumed that node l is the fault point, then in the zero-mode current vector only the element I l (ω) is non-zero; If a fault occurs between certain nodes, then only the zero-mode current values of the two nodes connected to this faulty line in the zero-mode current vector are non-zero; The node zero-mode impedance matrix in the zero-mode network is obtained by inverting the node zero-mode admittance matrix, that is: Where: Z ii (ω) is the self-impedance of node i under the zero-mode network, and Z ij (ω) is the mutual impedance between node i and node j under the zero-mode network; Zero-mode current vector is the quantity to be determined, and the zero-mode voltage vector is the known measured quantity; Combining Equation (16) and Equation (17) is transformed into Equation (18), that is: When zero-mode voltage measuring devices are installed on only S nodes, the corresponding node zero-mode voltages are U1(ω), U2(ω), …, U S (ω); where S << M; Excluding the zero-mode voltage other than the measurement points and the impedance values of the rows where the measurement points are located in the node zero-mode impedance matrix, then only S equations can be listed in Equation (18). Since the number of unknowns is more than the number of equations in the system of equations, this system of equations is an underdetermined system of equations. Thus, partial sparse node equations are obtained as shown in Equations (19) - (20): To eliminate the angle calculation brought by phasors, usually the modulus value of the zero-mode component is taken for calculation. Therefore, Equation (20) can be expressed as a modulus equation: Solve the fault zero-mode current according to Equation (21). Using the sparsity of the vector to be solved, the unique solution can be determined, and thus the fault location can be accurately located; S2. Compressive sensing algorithm The sparse representation of the original signal in compressive sensing is shown in Equation (22): y = ψ·x + e (22) where: \(y\in R\) S is the observation vector, i.e., the node zero-mode voltage vector \(\psi\in R\) S×M is the observation matrix, i.e., the node zero-mode impedance matrix \(Z\) S×M (\(\omega\)); \(x\in R\) S is the sparse vector to be reconstructed, i.e., the node zero-mode current vector \(e\in R\) S is Gaussian white noise following \(N(0,\sigma\) 2 ); where \(S << M\); Use the OMP algorithm to reconstruct the underdetermined system of equations; When the established observation matrix ψ satisfies the requirements of the isometric property, the compressive sensing theory can first solve the sparse coefficient s for the inverse problem of the above Equation (22), and then correctly recover the signal x with sparsity K from the M-dimensional measurement projection value y; find the optimal sparse solution through the l1-norm regularization formula as: Restore the signal after compressive observation to the initial signal form through Equation (23), thereby completing signal reconstruction; In the reconstructed zero-mode current signal, judge according to the number and position of the maximum reconstructed values, and the final result obtained is the location where the fault occurs; S3. Design of measurement point distribution The number r of observation points, the sparsity, and the length of the signal to be reconstructed should satisfy Equation (24): In the formula: r is the number of measurement points; q is the sparsity of the signal to be reconstructed; p is the length of the reconstructed signal; S4. Flow chart of the fault location method Step 1: Obtain the node zero-mode admittance matrix based on the topological structure and line parameters of the multi-node DC distribution network, then perform an inverse operation and take its modulus value to obtain the observation matrix Z' S×M (ω); Step 2: After the fault occurs, collect the waveforms of the fault transient voltage signals at the distributed measuring points before the MMC sub-module is blocked, obtain the zero-mode voltage component of the fault through the phase-mode transformation method, and calculate the zero-mode voltage signal U of a continuous window length S (ω); Step 3: Import the observation matrix Z' S×M (ω) and the zero-mode voltage signal U S (ω) as parameters into the compressive sensing reconstruction algorithm for calculation, and reconstruct the sparse vector I S (ω) composed of the zero-mode current amplitudes of each node; Step 4: According to the sparse vector I S (ω) reconstructed, determine the number of relatively large amplitude values and the corresponding nodes in its vector, and judge and locate the fault location.

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