Complex multi-terminal flexible direct-current power distribution network single-pole grounding protection method based on phase space transient mapping trajectory

Abstract

The invention relates to a single-pole grounding protection method for a complex multi-terminal flexible direct current power distribution network based on a phase space transient mapping trajectory, which is suitable for a multi-terminal flexible direct current system comprising various converters. According to the method, phase space trajectories of currents at two ends of a fault line are constructed, a delay embedded vector is constructed by using dominant frequency, trajectory directivity and main axis offset are extracted, direction criteria and form criteria are formed respectively, and dual identification of internal and external faults is realized. And by combining a virtual breaking point theory and transfer impedance modeling, the universality and accuracy of fault modeling are ensured. The method does not depend on communication and synchronization, has good high-resistance adaptability and anti-noise performance, and is suitable for engineering deployment.

Description

Technical Field

[0001] This invention relates to the field of power system relay protection and flexible DC distribution technology, specifically to a method for single-pole grounding protection of complex multi-terminal flexible DC distribution networks based on phase space transient mapping trajectories. Background Technology

[0002] With the large-scale integration of new energy sources and the rapid development of DC loads, flexible DC distribution technology, with its advantages of flexible power flow control, diverse system structures, and parallel operation, has become an important direction for promoting the construction of new power systems. In multi-terminal flexible DC distribution networks, the safety and power supply continuity of the DC system depend on fast and reliable fault protection mechanisms. Among these, single-pole grounding faults, as the most common type of fault, are particularly critical in terms of identification and location. Most existing flexible DC system protection schemes draw on traditional high-voltage DC protection methods, widely adopting protection strategies that rely on boundary elements (such as current-limiting reactors). These methods identify faults within and outside the fault zone by measuring boundary response characteristics such as transient voltage or transient energy. However, in multi-terminal interconnected and complex mesh distribution systems, current-limiting reactors are usually only configured on the outgoing line side of the converter station, and some DC lines lack boundary elements or have unclear boundary characteristics, leading to the risk of failure for traditional boundary element-dependent protection strategies. To overcome the boundary condition dependence problem, some studies have introduced protection methods based on directional criteria such as current mutation, zero-mode current directionality, or correlation analysis. For example, fault direction identification criteria can be constructed using current wavefront amplitude ratio, zero-mode power direction, or waveform similarity. While these methods are effective in specific scenarios, in flexible DC power distribution systems, lines are generally short and have numerous branches, leading to rapid attenuation of high-frequency characteristics in fault signals and difficulty in accurately capturing traveling wave fronts. Simultaneously, transient oscillations caused by distributed capacitance result in strong nonlinear characteristics in the current signal, distorting correlation calculations and easily leading to misjudgments and failures to operate. Furthermore, flexible DC power distribution systems often use ungrounded neutral points or impedance-grounded systems, resulting in small fault current amplitudes and short durations during single-pole ground faults, making it difficult to establish significant amplitude differences. These "weak feature" faults are difficult to identify in traditional protection logic, especially in the presence of measurement noise or high-resistance grounding, further exacerbating the risk of fault criterion failure. Furthermore, existing research typically focuses on models with simple structures and a single converter type, failing to fully consider the differences in the impact of various converter grounding methods, such as MMC (Modular Multilevel Converter), VSC (Voltage Source Converter), and DCT (DC Transformer), on fault transient behavior. It lacks universal protection mechanisms for complex heterogeneous systems and is difficult to adapt to complex scenarios in engineering practice, such as multi-source access, multiple converter units, and asymmetric distributed parameters.

[0003] In summary, existing single-pole grounding protection technologies for flexible DC power distribution systems generally suffer from the following shortcomings: over-reliance on boundary elements, poor stability of directional criteria in complex networks, lack of effective identification capability for weak characteristic faults, lack of unified modeling and criterion construction methods for multi-converter and multi-structure networks, and significant degradation in protection performance under conditions of increased transition resistance or measurement signal noise, making it difficult to meet the requirements of new power distribution systems for high reliability and wide adaptability of protection. Summary of the Invention

[0004] In view of the shortcomings of the prior art, the purpose of this invention is to provide a single-pole grounding protection method for complex multi-terminal flexible DC distribution networks based on phase space transient mapping trajectory, aiming to solve the following key problems: Existing protection methods generally suffer from low identification accuracy, reliance on boundary elements, and poor protection applicability when facing weak fault characteristics, high transition resistance, strong noise disturbance, complex network topology, and multi-type converter access scenarios, making it difficult to meet the high requirements of the new generation of flexible DC distribution systems for speed, robustness, and universality.

[0005] To achieve the above objectives, the present invention provides the following technical solution: In one embodiment of the present invention, a method for single-pole grounding protection of complex multi-terminal flexible DC distribution networks based on phase space transient mapping trajectory is provided, comprising the following steps: S1. Fault initiation and signal acquisition: Detecting the positive and negative pole-to-ground voltages of the DC line; when the voltage difference exceeds a set threshold, determining that a single-pole grounding fault has occurred, initiating protection, and acquiring the fault transient current signals at both ends of the DC line to be protected; S2. Phase space trajectory construction: Extracting the dominant frequency of the fault transient current signal and determining the delay time based on the period corresponding to the dominant frequency; mapping the one-dimensional current sequence to a two-dimensional phase space coordinate sequence according to the delay time to form a phase space trajectory; S3. Trajectory feature extraction: Extracting geometric morphological features from the phase space trajectory, including trajectory direction features based on the initial quadrant distribution and trajectory morphological consistency features based on the principal axis offset; S4. Fault identification and determination: Performing direction criteria based on the trajectory direction features; when the current directions at both ends of the line are consistent, directly determining the fault type; when the directions are inconsistent, further performing principal axis offset difference criteria based on the trajectory morphological consistency features to distinguish between intra-zone faults and extra-zone faults.

[0006] Furthermore, in the process of extracting trajectory direction features in step S3, the following steps are included: selecting a preset time window in the two-dimensional phase space coordinate sequence, calculating the mean value of the sign function of the sampled values ​​within the window to obtain the direction criterion value; comparing the direction criterion values ​​at both ends of the line with preset positive and negative thresholds respectively, and determining the direction as positive when the criterion value is greater than the positive threshold and as negative when it is less than the negative threshold.

[0007] Furthermore, in step S4, during the process of executing the direction criterion based on the trajectory direction features, if the direction criterion values ​​at both ends of the line are both positive, it is determined to be an in-zone fault; if the direction criterion values ​​at both ends of the line are both negative, it is determined to be an out-of-zone fault; if the direction criterion values ​​are one positive and one negative or the directions are inconsistent, the spindle offset difference criterion is activated to continue the judgment.

[0008] Furthermore, in the process of extracting trajectory morphology consistency features in step S3, the following steps are included: initial segment removal and centering of the two-dimensional phase space coordinate sequence; principal component analysis (PCA) is performed on the centered data using a sliding time window to extract the principal axis direction angles within each window; and the standard deviation of the direction angle sequence is calculated as the principal axis offset characterizing the trajectory morphology consistency.

[0009] Furthermore, in the process of executing the spindle offset difference criterion in step S4, the following steps are included: calculating the spindle offset at the protection measuring points at both ends of the line; if the difference between the spindle offsets at both ends is greater than the preset setting value, it is determined to be an internal fault; otherwise, it is determined to be an external fault.

[0010] Preferably, when analyzing fault characteristics, a network equivalent decoupling model containing virtual breakpoints is constructed to characterize the transient response characteristics of the networks on both sides of the fault point; wherein, the location of the virtual breakpoint is determined by the line parameters, the fault location and the equivalent impedance of the connected converter, and is used to guide the analysis and criterion setting of trajectory characteristic differences.

[0011] In another embodiment of the present invention, a complex multi-terminal flexible DC distribution network single-pole grounding protection device for implementing the above method is provided, comprising: The signal acquisition and activation module is used to acquire the current signal and the positive and negative voltage signals to ground at both ends of the line, and to issue a protection activation signal when the voltage difference exceeds a set threshold; the data processing and trajectory construction module is connected to the signal acquisition and activation module, and is used to extract the dominant frequency of the fault current and construct a two-dimensional phase space trajectory based on the delay time; the feature extraction module is connected to the trajectory construction module, and is used to extract trajectory direction features and trajectory shape consistency features; the protection judgment module is connected to the feature extraction module, and is used to execute the direction criterion and the main shaft offset difference criterion, and output the judgment result of faults inside or outside the zone.

[0012] Alternatively, in another embodiment of the present invention, a complex multi-terminal flexible DC distribution network system is provided, including at least two interconnected DC lines and the aforementioned single-pole grounding protection device, wherein the protection device is configured on the DC line to be protected.

[0013] Compared with existing technologies, the method, device, and system for single-pole grounding protection of complex multi-terminal flexible DC distribution networks based on phase space transient mapping trajectories provided by this invention have the following significant technical advantages and beneficial effects: 1. Most existing protection strategies rely on the structural differences in current-limiting reactors or boundary converters at both ends of the line. If the system topology is a ring network, weak boundary, or no boundary configuration, the protection strategy will fail. This invention innovatively starts from the inherent dynamic characteristics of the fault current signal and extracts geometric features such as trajectory direction and shape based on phase space embedding mapping, without relying on any physical boundary components. This mechanism can be adapted to any converter grounding method and topology, significantly reducing construction and renovation costs, and solving the applicability bottleneck of existing methods after the increase in the complexity of flexible DC networks.

[0014] 2. Compared to traditional directional current protection or waveform matching protection, which are susceptible to noise interference and oscillation misjudgment, this invention maps the fault transient current to a two-dimensional phase space to construct a trajectory geometric analysis framework. First, the direction criterion is calculated through the initial quadrant distribution of the trajectory. This method, based on sampled symbol statistics, possesses good anti-distortion and anti-noise performance. Second, a "principal axis offset" index is further proposed. Based on principal component analysis (PCA), the trajectory morphological stability is extracted, effectively distinguishing between regular single RLC responses and multiple superimposed disturbances. The dual-criteria mechanism of this invention complements each other, significantly improving the identification accuracy and protection reliability under complex fault scenarios.

[0015] 3. In flexible DC systems, single-pole grounding faults often manifest as low-amplitude, short-lived signals under high resistance conditions, making it difficult for existing amplitude- or integral-based protection strategies to maintain operational sensitivity. This invention significantly enhances the ability to detect weak-feature faults by extracting trajectory features (rather than instantaneous values) that reflect dynamic structural characteristics. Even under conditions of transition resistance as high as 200Ω and a signal-to-noise ratio below 20dB, the trajectory direction and main axis shape remain identifiable. Simulation tests demonstrate that this method has good anti-interference capability and operational stability.

[0016] 4. Traditional protection strategies are typically only applicable to specific structures and struggle to explain the differences in converter combinations within complex ring networks. This invention analyzes the impact of different converter (MMC, VSC, DCT) grounding methods on transient response, innovatively introducing the concept of a "virtual break point" to construct a unified dynamic decoupling model, revealing the essential differences in direction and morphology between fault trajectories within and outside the fault zone. This theoretical model can be extended to complex heterogeneous DC systems, providing a unified analytical foundation for future diversified protection principles, and possesses strong theoretical value and methodological extensibility.

[0017] 5. This method requires a moderate amount of computation, and core modules such as Prony frequency extraction and PCA principal component analysis can be implemented in real time using embedded platforms such as DSPs or FPGAs. Furthermore, the method does not rely on communication networks or clock synchronization, allowing protection devices to operate independently on-site, demonstrating excellent distributed deployment capabilities. This characteristic makes it particularly suitable for next-generation flexible DC distribution systems or DC microgrid scenarios with flexible structures and diverse converters, enhancing system adaptability and reliability while improving response speed, thus meeting the higher intrinsic safety requirements of future power systems. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the complex multi-terminal flexible DC distribution network topology involved in this invention, used to illustrate the various types of converter stations and their connection relationships, as well as the configuration of multi-terminal DC lines.

[0019] Figure 2 The diagrams show typical grounding methods for different converters, where: (a) is the grounding method for the MMC converter; (b) is the grounding method for the VSC converter; and (c) is the grounding method for the DCT converter.

[0020] Figure 3 This is an equivalent circuit diagram for a positive ground fault, used to illustrate the current path and network coupling characteristics at the fault point after a single-pole ground fault occurs.

[0021] Figure 4 This diagram illustrates the additional network diagram for a single-pole grounding fault constructed after introducing a virtual break point, used to demonstrate the effect of the virtual break point on network decoupling.

[0022] Figure 5 This is a diagram of the decoupled network structure when the virtual break point is located within the faulty line.

[0023] Figure 6 for Figure 5 The equivalent analysis circuit shown is as follows: (a) is the overall coupled circuit; (b) is the decoupled equivalent circuit after eliminating the transition resistance coupling.

[0024] Figure 7 This is a diagram of the decoupled network structure when the virtual break point is located within a non-faulty line.

[0025] Figure 8 This is the decoupling equivalent circuit diagram when the virtual break point is located within the protected line (Line1) under the condition of an external fault.

[0026] Figure 9 This is the decoupling equivalent circuit diagram when the virtual break point is located within other lines under the condition of an external fault.

[0027] Figure 10The diagram shows the mapping trajectory of the transient response of a single RLC loop in two-dimensional phase space, where: (a) is the three-dimensional spiral convergence trajectory; and (b) is the two-dimensional planar elliptical trajectory.

[0028] Figure 11 This is a mapping trajectory diagram of the multi-RLC loop coupling response in two-dimensional phase space, used to illustrate the changes in principal axis direction and trajectory divergence.

[0029] Figure 12 The initial quadrant distribution diagram of the phase space trajectory under different current directions is used to illustrate the basis for the formation of the direction criterion.

[0030] Figure 13 This is a flowchart of the overall protection scheme proposed in this invention, which shows the complete logic of initiation judgment, feature extraction, criterion construction and protection decision.

[0031] Figure 14 The simulation results of the current waveform and phase space trajectory of the fault in the region under scenario C1 are shown.

[0032] Figure 15 This is a diagram showing the current waveform and phase space trajectory when there is a fault in the area (long line) under scenario C2.

[0033] Figure 16 This is a comparison of the spindle offset at both ends when there is a fault within the zone in scenario C2.

[0034] Figure 17 Simulation diagram of current waveform and phase space trajectory for faults outside the zone in scenario C1.

[0035] Figure 18 for Figure 17 A comparison chart of spindle offsets outside the indicated fault zone.

[0036] Figure 19 The simulation results of the external fault in scenario C2 are shown, including the current trajectory and direction criterion values. Detailed Implementation

[0037] To make the technical objectives, technical solutions, and beneficial effects of this invention clearer and more complete, the following detailed description of the method, device, and system for single-pole grounding protection of complex multi-terminal flexible DC distribution networks based on phase-space transient mapping trajectories, in conjunction with the accompanying drawings and specific embodiments, is provided. It should be understood that the specific embodiments described below are only for explaining the technical solutions of this invention and are not intended to limit the scope of protection of this invention. For those skilled in the art, equivalent substitutions or modifications made to the relevant embodiments without departing from the technical concept and scope of the claims should be included within the scope of protection of this invention.

[0038] Example 1:

[0039] In one embodiment of the present invention, a single-pole grounding protection method for complex multi-terminal flexible DC distribution networks based on phase-space transient mapping trajectories is proposed and applied to complex flexible DC distribution networks composed of various types of converters. To ensure the applicability of this method in practical engineering and the universality of the criterion construction, the network topology, typical converter grounding methods, and protection deployment methods must first be described in detail.

[0040] I. Topology of complex multi-terminal flexible DC distribution networks: such as Figure 1 As shown, the system includes multiple converter station nodes with different functions and several interconnected DC lines, forming a typical six-terminal ring network structure. Among them: The converter station includes: MMC1 (Modular Multilevel Converter), which uses constant DC voltage control; MMC2, which uses constant power control; VSC (Voltage Source Converter), which uses constant AC voltage control; and DCT (DC Transformer), which uses single-phase shift control.

[0041] DC lines: Marked as Line 1 to Line 6, connecting each converter node to achieve flexible power distribution. Current-limiting reactors: Current-limiting reactors (represented by L in the diagram) are configured on the outgoing side of some converter stations to control the short-circuit current amplitude and improve fault transient response. Protection measurement points Pij (i=1~6, j=1,2): Deployed at both ends of each DC line to collect transient current and voltage signals required for protection. This structure has typical "mesh-type" flexible DC characteristics, with high network coupling and complex fault propagation paths, placing higher demands on fault identification.

[0042] II. Typical grounding methods for converters: Different converters employ significantly different grounding methods in flexible DC systems, such as... Figure 2 As shown: Figure 2 (a): MMC converters typically use AC side grounding, that is, grounding through a series grounding resistor at point Yn of the converter transformer, while the DC side is not grounded; Figure 2 (b): The VSC converter is grounded on both the AC and DC sides, and a resistor is set on the DC side to improve zero-sequence stability; Figure 2 (c): Since DCT converters have no AC side, they are usually grounded by a grounding resistor connected in series after the clamping capacitor on the DC side in order to stabilize the potential and suppress high-frequency oscillations.

[0043] Due to differences in converter grounding paths, the feed path, capacitor discharge behavior, and their impact on transient response vary among converters during a single-pole ground fault. For example, the MMC converter primarily feeds indirectly through the AC side, resulting in a weaker fault response; the VSC converter has dual-side grounding paths, leading to a stronger transient response; and the DCT converter's discharge path mainly originates from its DC-side capacitor. This invention fully considers these differences and introduces a "virtual breakpoint" and dynamic impedance correction mechanism in modeling and protection logic construction to improve the universality and accuracy of the protection strategy.

[0044] III. Protection Deployment Strategy and Signal Acquisition Method: To achieve single-pole grounding fault identification for each DC line, the protection device described in this invention is deployed at both ends (Pij points) of each line. This device mainly consists of the following modules: The system comprises the following modules: a signal acquisition module for acquiring DC current and positive / negative voltage signals to ground at both ends of the line; a data processing and mapping module for performing Prony modeling, dominant frequency extraction, and phase space mapping; a protection criterion calculation module for dual discrimination based on initial quadrant distribution and trajectory principal axis offset; a control output module for outputting protection action commands when a fault occurs within the judgment zone; and an optional activation module for activating protection when the detected positive / negative voltage difference to ground exceeds a set threshold. A data sampling frequency of at least 20kHz, preferably 50kHz, is recommended to ensure effective capture of transient signal characteristics. Each module can be embedded using an embedded processor (such as a DSP or FPGA) to meet engineering deployment requirements.

[0045] Example 2:

[0046] I. Fault Modeling and Derivation of Virtual Breakpoint Location: In order to effectively identify single-pole grounding faults in flexible DC distribution systems and construct protection criteria that can be universally applied to various converters and complex topologies, this invention first establishes a fault equivalent model at the physical level and introduces a "virtual breakpoint" mechanism to achieve theoretical decoupling and mathematical modeling of complex networks.

[0047] 1.1 System Modeling of Unipolar Ground Faults ( Figure 3 ) like Figure 3 As shown, taking a positive ground fault at point f1 in Line 1 as an example, an equivalent system model is constructed for the initial stage of the fault. The following factors are mainly considered in the modeling: the equivalent impedance of the lines on both sides of the fault point: Z 11 Z 12 Sound circuit impedance: Z2~Z5; Transition resistance: R f Converter grounding equivalent impedance: R g1 R g2 R g3 ; Distributed capacitance of positive and negative lines to ground: Cijp C ijn .

[0048] Based on the above modeling, the fault current mainly consists of the following four paths: 1. DC-side capacitor discharge path of the converter; 2. Positive-to-ground capacitor discharge path of the faulty line itself; 3. Reverse feed path of non-faulty pole-to-ground capacitor coupled through the bridge arm; 4. AC-side grounding path of the MMC or VSC converter (contributing less). In this strongly coupled, weakly grounded, and complexly distributed network, traditional analysis methods based on equivalent models are difficult to accurately characterize the fault propagation behavior, thus requiring further decoupling analysis.

[0049] 1.2 Introduction and Correction of Virtual Breakpoints ( Figure 4 ) To achieve mathematical decoupling, this invention introduces the concept of a "virtual breakpoint (K-point)". For example... Figure 4 As shown, point K divides the ring network into two radial structures in terms of electrical equivalence, allowing the transient response of each branch to be analyzed independently.

[0050] In traditional models, point K is usually set at the midpoint of the faulty line (at a distance of (l / 2) from the fault point). However, under complex operating conditions, the location of point K is affected by the following factors: the specific location of the fault point on the line; the length of the line and the asymmetry of its parameters; the differences in the distribution of positive and negative capacitances and the discharge path; and the equivalent impedance characteristics of different converter arms.

[0051] Therefore, based on the traditional expression, this invention introduces a virtual breaking coefficient k to form formulas (1) to (3), and dynamically corrects the position of point K to make it more realistically reflect the network coupling behavior and fault propagation direction.

[0052] (1) It represents the change in positive and negative pole voltage to ground at a measuring point (P11) at one end of the protected DC line after a single-pole ground fault occurs. The unit is volt (V), which is used to characterize the fault voltage response amplitude at the measuring point. Z represents the change in transient fault current at the corresponding measuring point during the initial stage of the fault, expressed in amperes (A), and is used to characterize the fault current response characteristics; C The characteristic impedance of a DC line is determined by the inductance and capacitance per unit length of the line, and is measured in ohms (Ω). It reflects the impedance characteristics of the line to the propagation of transient traveling waves. The propagation constant of a DC line is a complex number that includes an attenuation coefficient and a phase constant. It describes the propagation and attenuation characteristics of transient fault signals in a DC line, and its unit is per meter (m). -1 ); This represents the equivalent electrical length from measuring point P11 to the end of the DC line or the reference node, in meters (m). The equivalent electrical distance from the fault point to the reference node is expressed in meters (m); sinh(⋅) and cosh(⋅) represent the hyperbolic sine function and hyperbolic cosine function, respectively, used to describe the exponential variation characteristics of transient quantities propagating along the line in a distributed parameter line.

[0053] (2) K is the ratio coefficient of the change in current at the beginning of the fault, which is used to characterize the difference in current amplitude between one end (P11) and the other end (P12) of the protected line at the beginning of the fault. It is dimensionless. The change in current at measuring point P11 after the fault occurs, expressed in amperes (A). The change in current at measuring point P12 after the fault occurs, in amperes (A).

[0054] (3) To consider the fault point transfer impedance expression under the condition of asymmetrical current at both ends, and to further improve the model's adaptability to non-ideal operating conditions.

[0055] The meanings of the newly added variables are as follows: k: as mentioned above, the ratio of the currents at both ends of the fault, reflecting the directionality of current propagation and the differences in converter characteristics; the meanings of the other variables are consistent with the definitions in formula (1), and will not be repeated here. This modified formula reveals that the offset direction of point K is always consistent with the direction of the main fault feed current, and the distance is closely related to the converter type, capacitor layout and topology connection.

[0056] 1.3 Decoupling Modeling of Multiple RLC Loops and Transfer Impedance ( Figure 6 ) To quantitatively model the current response behavior on both sides of point K, this invention uses the transfer impedance method to convert the complex system into multiple independent feed loops.

[0057] The specific modeling process is as follows: 1. Model the circuits on both sides of the fault point, using point K as the dividing line; 2. Each branch consists of the converter arm impedance, line impedance, and equivalent capacitance connected in series; 3. Calculate the equivalent impedance from each capacitor to the fault point using the branch transfer function solution method; 4. For common branches with coupling (such as shared paths for bridge arms or grounding resistance), introduce an impedance coupling coefficient k. Z Decoupling is performed, see formulas (4) to (9) for details.

[0058] like Figure 6 As shown in (a), the RLC branches in the original system are mutually coupled, making it impossible to directly establish an independent response model; this invention introduces a decoupling mechanism, such as... Figure 6(b) It is transformed into multiple independent RLC loops, so that the current at each measuring point can be expressed in a standard form, which facilitates trajectory construction and spectrum extraction.

[0059] for Figure 6 The equivalent network in (a), R niΣ L niΣ C niΣ (i=1~6) represent the negative line capacitance, the line impedance, and the equivalent resistance, inductance, and capacitance of each converter, respectively. Before simplifying the fault network, it is necessary to first eliminate the electrical coupling caused by the transition resistance in the circuits on both sides of the fault point, and decompose it into two independent networks, such as... Figure 6 As shown in (b). After decoupling, the transition resistance in the circuits on both sides of the fault point can be directly expressed as: (4) Where R f The transition resistance at the fault point, measured in ohms (Ω), is used to characterize the equivalent resistance between the fault point and ground in a unipolar ground fault; R f1 R represents the equivalent transition resistance distributed to the branch on the fault side after introducing the virtual break point K, in ohms (Ω); f2 This represents the equivalent transition resistance that is equivalently distributed to the branch on the other side of the fault point after the introduction of the virtual break point K, and the unit is ohms (Ω). This indicates the change in fault transient current at measuring point P12 at one end of the protected line after a fault occurs, in amperes (A). This represents the change in fault transient current in the equivalent branch on the other side of the virtual break point K, in amperes (A).

[0060] The above relationship, by introducing a current distribution ratio, reduces the single fault transition resistance R. f The equivalent decomposition is represented by the equivalent transition resistance R located on both sides of the virtual breakpoint. f1 and R f2 This enables decoupled modeling of transient responses on both sides of a fault point in a complex ring network structure, providing a foundation for establishing an independent RLC loop model in the future.

[0061] However, the feed paths are still interconnected through a common coupling branch, which makes it impossible to directly calculate the equivalent impedance between the distributed capacitance and the fault point. It is necessary to further decouple the common branch and construct a single-power supply feed loop from each branch to the fault point to directly obtain its transfer impedance.

[0062] Taking the common branch C1 as an example, the complex frequency domain expression of its voltage before decoupling is shown in equation (5): (5) (6) In the formula, , These are the current fault components of the decoupled branches B1 and B2, respectively. , These are the decoupling impedances for the common branch. Define k. Z The common branch impedance coupling coefficient, For branches B1 and B2: (7) Based on the fact that the voltage remains unchanged before and after decoupling, equation (8) can be easily obtained: (8) Based on the above analysis, the calculation proceeds backwards until all branches are merged to the fault point, simplifying the network to a low-order equivalent circuit containing only the fault point and each converter station. This allows the determination of any branch B. i Equivalent transfer impedance Z Bi (s), as shown in equation (9): (9) In summary, this invention, by introducing virtual breakpoints and transfer impedance modeling methods, realizes dynamic location, direction determination, and structural decoupling of single-pole grounding faults in complex flexible DC networks, laying a solid theoretical and engineering foundation for subsequent frequency domain response analysis and trajectory feature extraction.

[0063] II. Time-Domain / Frequency-Domain Current Response Calculation Model To quantify the impact of virtual breakpoint location changes on the current response at the measuring point and to establish a mathematical basis for distinguishing between faults within and outside the zone, this invention is based on Figures 5 to 9 For typical fault scenarios shown, current response models in the frequency domain and time domain are constructed respectively. Detailed explanations are as follows: (1) Fault modeling within the area when K is located on the faulty line ( Figure 5 & Figure 6 ) like Figure 5 As shown, if the fault point is located at the end of Line 1 and the line is relatively long, the virtual break point K may be located in the middle of the faulty line. In this case, the line is divided into two segments: the near fault end P12 side (between point K and the fault point); and the far fault end P11 side (between point K and the converter end).

[0064] To establish a current response model under this condition, this invention treats the fault network as an equivalent system of multiple superimposed RLC branches and uses the transfer impedance method to decouple the model, such as... Figure 6 As shown in (a). Furthermore, the coupling path on both sides of the fault point is eliminated by a transition resistor, resulting in two independent circuits, the structure of which is shown in [reference needed]. Figure 6 (b)

[0065] Under this model, the current response characteristics on both sides of P11 and P12 are as follows: P11 side: longer path, concentrated capacitance, the response is mainly determined by a single dominant RLC loop; P12 side: shorter path, more branches, the response is the superposition of multiple RLC branches.

[0066] The two differ significantly in waveform shape and oscillation mode, and the current directions are opposite. The frequency domain and time domain expressions are shown in formula (10) and formula (11) respectively, which constitute the physical basis of the "dual feature extraction" logic of this invention.

[0067] For the protection on both sides of the faulty line, P 11 The actual measured current is the short-circuit current supplied by branch B1 to the fault point, while P 12 The measured current is B1~B 12 The sum of the branch feeders.

[0068] (10) in: : Represents the fault transient current increment at measuring point P11 in the Laplace domain, in amperes (A). U represents the increment of the fault transient current at measuring point P12 in the Laplace domain, in amperes (A); dc Rated voltage of the DC system (or the amplitude of the DC bus voltage at the initial stage of a fault), in volts (V); S: complex frequency domain variable in the Plas transform, in the reciprocal of a second (s). -1 Z B1 (s): Equivalent transient impedance from measuring point P11 to the fault point, expressed in Laplace domain, in ohms (Ω); Z Bi (s): represents the equivalent transient impedance of P12 terminal to other branch converters (the iiith converter), in ohms (Ω). : Represents the path impedance of the common ground point (e.g., converter common bus) as seen from the fault point towards the voltage source, in ohms (Ω); R f Fault point transition resistance, in ohms (Ω); Therefore, the transient response of a single-pole grounding fault in a complex multi-terminal flexible DC distribution network is essentially a superposition of step responses from multiple second-order RLC circuits. Considering that the flexible DC distribution network is a weakly damped system, the current time-domain expression is obtained by inverse transformation of the complex frequency domain calculation results, as shown in equation (11): (11) In the formula, Let i be the amplitude of the current oscillation in loop i. The attenuation coefficient is... The oscillation angular frequency, This is the initial phase angle of the oscillation.

[0069] (2) Fault modeling within the zone when K is located on a non-faulty line like Figure 7 As shown, when the fault occurs in Line 1, and point K is offset to Line 4 (the non-faulted line) due to parameter coupling, the current response at P11 and P12 at both ends of the protected line exhibits the following characteristics: the current direction at both ends is consistent (both are positive); however, the number of RLC branches and equivalent parameters on both sides may still be different; the waveforms both show a mixed response of multiple RLC oscillations, but the waveform on one side is relatively "stable and neat", while the waveform on the other side is "divergent and distorted". This characteristic provides the basis for the subsequent construction of the "main axis offset difference criterion", and the frequency domain / time domain expressions are shown in formulas (12) and (13).

[0070] For the protection on both sides of the faulty line, P 11 With P 12 The measured currents are B1~B6 and B9~B 14 The sum of the branch feed currents, and the expressions for calculating the fault current components on both sides of the line are shown in equations (12) and (13): (12) (13) (3) Modeling of faults outside the protected line where K is located like Figure 8 As shown, if the fault point is located at the midpoint f2 of Line2, and point K falls into Line1 (the protected line), then the current response at both ends of P11 and P12 is as follows: the current direction is the same (both are negative); the response is mainly a single RLC loop oscillation; the waveform has good convergence and the trajectory is stable.

[0071] In this situation, traditional direction criteria may misjudge it as an in-zone fault, but because the trajectory shape is highly consistent and the difference in the main axis offset is very small, it can still be accurately identified as an out-of-zone fault by the trajectory characteristics.

[0072] The frequency domain and time domain expressions are given in formulas (14) and (15): (14)

[0073] (15) (4) Modeling of faults outside the zone where K is located on other lines like Figure 9 As shown, if point K falls into a non-faulty line (such as Line 2), the responses of measuring points P11 and P12 at both ends of Line 1 are as follows: the current directions are opposite; both are mixed responses of multiple RLC loops; the trajectory shape is complex and the disturbance is large, but the change trends on both sides are similar. In this case, the simple current direction criterion is prone to misjudgment, while the difference in spindle offset is small, which can help to correctly prevent operation.

[0074] The time-domain expressions are shown in formulas (16) and (17) respectively: (16)

[0075] (17) (5) Summary of Fault Characteristics (corresponding to Table 1) The influence of different K-point positions on the direction of the measuring current and the response characteristics in the above four typical scenarios is summarized in Table 1: Table 1 Summary of Fault Current Characteristics

[0076] The above frequency domain and time domain modeling results constitute the core data source for the next stage of this invention, "phase space mapping and trajectory feature extraction".

[0077] Phase space mapping and trajectory construction process To overcome the problems of unclear directionality and easy failure of correlation exhibited by traditional time-domain analysis in weak feature fault scenarios, this invention proposes to map the sampled transient current signal to a two-dimensional phase space and to perform direction and shape discrimination based on the geometric characteristics of the trajectory.

[0078] 3.1 Phase Space Mapping Principle and Embedding Construction (Combined) Figure 10 ) According to phase space reconstruction theory, any one-dimensional time series (such as transient current x(n)) can be reconstructed into a high-dimensional dynamic system trajectory through the delayed coordinate embedding method. This invention uses a two-dimensional embedding method, and the calculation method is shown in formula (18). The constructed coordinate points are: (18) in, To reconstruct the nth state vector in the phase space, This is the delay time.

[0079] like Figure 10 As shown in (a), when the system response is a single RLC loop damped oscillation, the delayed sampling point pairs approximately satisfy the Hilbert transform relation (i.e., orthogonality). In this case, the mapped trajectory in three-dimensional space presents a spiral convergent trajectory, and its two-dimensional projection is a standard elliptical trajectory (see...). Figure 10 (b) has the following characteristics: it is centrally stable and rotates around the origin; the main axis direction is clear and the trajectory is compact; the trajectory direction is determined by the polarity of the current. This highly regular and clearly directional trajectory structure provides a calculable basis for the subsequent extraction of direction criteria and main axis offset in this invention.

[0080] 3.2 Trajectory divergence characteristics under multiple RLC superposition responses In practical complex flexible DC networks, the current at the measurement point is usually the superposition of the responses of multiple RLC branches, the dominant frequency is no longer unique, and the frequency, phase and attenuation characteristics of each component are significantly different.

[0081] In this case, the orthogonality between delayed sampling pairs is broken, resulting in the mapped trajectory exhibiting the following characteristics (see...). Figure 11 The trajectory shape is irregular; the direction of the main axis is unclear; and the trajectory of each segment deviates from the center and diverges.

[0082] The present invention further provides a mathematical description in formulas (19) to (22), proving that multi-frequency mixed signals cannot form a single principal axis direction in two-dimensional phase space.

[0083] The key to phase space mapping lies in the selection of the delay time, which directly determines whether the reconstructed trajectory can effectively characterize the signal features. From the time domain perspective, the underdamped oscillation of a single RLC loop and the superposition response of multiple RLC loops mathematically correspond to the superposition of a single-frequency decaying sine and multiple decaying sines of different frequencies, respectively. The essential difference between the two lies in the difference in orthogonality.

[0084] (1) For a fault current dominated by a single RLC loop, its delayed T / 4 signal is approximately its Hilbert transform, that is, the two are orthogonal, as shown in equation (19): (19) In the formula, T is the oscillation period. Under ideal conditions without attenuation, the delayed signal and the original signal satisfy an orthogonal relationship at any time. For actual attenuated oscillation signals, this orthogonal relationship still holds approximately when the system damping is weak.

[0085] In two-dimensional phase space, let From equation (19), we can obtain: (20) At this point, x(t) and y(t) are geometrically orthogonal. Considering the decay term, the phase space trajectory becomes a contracting spiral, which projects onto the two-dimensional plane as a concentric elliptical trajectory that contracts with time, as shown below. Figure 10 As shown in (a) and (b).

[0086] At any time t, the instantaneous semi-major axis length of the ellipse is (Along the x-axis), the instantaneous semi-minor axis length is (Along the y-axis), both decay at an exponential rate, and the decay rate is determined by the damping coefficient of the loop. The larger the value, the faster the trajectory contracts, and it tends to return to the origin in a short time. The smaller the value, the slower the trajectory contraction, and the more likely it is to maintain a distinct elliptical shape over a longer period of time.

[0087] (2) When the fault transient response is composed of the superposition of multiple RLC loop components, its trajectory characteristics change essentially. For the response containing n components , usually take τ = T d / 4, T d as the dominant frequency corresponding period, and similarly construct the two-dimensional phase space equation as shown in Equation (21):

[0088] ; (21) Since there is no common delay time τ that can satisfy the orthogonality conditions of all components at the same time, Equation (21) holds only at the dominant frequency. For other frequency components . Suppose , , then the included angle between the principal axis direction on the two-dimensional plane of the k-th component and the coordinate axis is , and its coordinates can be expressed by Equation (22): ; (22) Thus, it can be seen that the principal axis directions of the ellipses of different frequency components are different, and the projections on the phase space are manifested as the superposition of ellipses with different directions, different axis lengths, and different attenuation rates. The ellipsoidal property of the overall trajectory weakens, the principal axis direction is blurred, the geometric orthogonality is destroyed, and it no longer presents a single shrinking spiral trajectory, as Figure 11 shown.

[0089] In addition, the direction discrimination can be further realized for the phase space trajectory. If the fault current is in the positive direction, within the initial stage (t ≤ τ) , the delayed signal is taken from the normal operating state before the fault, , that is, the phase space trajectory starts from the +x axis. As the fault develops (τ < t < T / 2) with decaying oscillation, the phase space trajectory is mainly located in the first quadrant. When enters the negative half cycle, the delayed signal is still in the positive half cycle, and the trajectory gradually moves from the first quadrant to the second quadrant; if the fault current is in the negative direction, within the initial stage (t ≤ τ) , the phase space trajectory starts from the -x axis. Within τ < t < T / 2, the phase space trajectory is mainly located in the third quadrant and gradually moves to the fourth quadrant, as Figure 12 shown.

[0090] In summary, the phase space trajectory converts the characteristics of the time-domain transient signal into intuitive geometric form differences. The corresponding protection criterion can be constructed through the trajectory form and the initial quadrant distribution to realize reliable identification of weak feature faults.

[0091] It can be seen from this that if the phase space trajectory exhibits the characteristics of a convergent ellipse, it usually corresponds to the measured point current being dominated by a single RLC response; if the trajectory shape diverges, the boundary is blurred, and the direction is chaotic, it usually corresponds to the superposition of multiple RLCs or a complex coupling response.

[0092] 3.3 Initial Quadrant Distribution and Direction Criterion Construction In addition to the trajectory shape, the distribution area of the phase space trajectory in the initial stage also reflects the current direction information and can be used to construct a direction criterion.

[0093] As Figure 12 shown: when the current is in the positive direction, the initial distribution of the trajectory is mainly concentrated in the first quadrant; when the current is in the negative direction, the initial stage of the trajectory is concentrated in the third quadrant; if the signal is zero-mean white noise or in a mixed state, the trajectory is disorderly distributed.

[0094] The present invention proposes to construct a "direction sign function" to perform positive and negative polarity statistics on the trajectory sampling points within the dominant period to form a direction criterion S, as shown in Formulas (26) to (28).

[0095] (1) Initial Quadrant Distribution Criterion First, define the sign function sgn, as shown in the formula.

[0096] ; (26) It can be seen from the analysis in Section 2.2 that the phase space trajectory starts from the x-axis, that is, when t ≤ τ, the trajectory direction is determined by x[n]; when τ < t < T / 2, the delayed signal already contains fault information, and at this time, the trajectory distribution is mainly characterized by y[n].

[0097] Therefore, the fault direction can be discriminated by comprehensively using the quadrant distributions of x[n] and y[n] at different times, and the direction criterion S is constructed as the average value of the sign functions of all sampling values within half a period.

[0098] ; (27) When a positive-direction fault occurs, S > 0 and approaches 1. When a reverse-direction fault occurs, S < 0 and approaches -1. Considering the actual transient signal fluctuations and noise interference, set the threshold S set = 0.2 (the present invention considers 20 dB noise interference), then the protection criterion can be expressed as: ; (28) In the formula, S1 and S2 are the current direction criteria on both sides of the line. It can be seen from Table 1 that if the currents on both sides of the line are in the positive direction, that is, both the S1 and S2 direction criteria are satisfied, it can be judged as an in-zone fault. If both the S1 and S2 direction criteria are not satisfied, it is judged as an out-of-zone fault. Otherwise, the trajectory shape needs to be further identified.

[0099] The direction criterion value ranges from [-1, 1], and a threshold S is set. set = 0.2 (set considering noise background), used for subsequent initial judgment within / outside the zone. In summary, by mapping the fault current from the time domain to a two-dimensional phase space and extracting features based on the two dimensions of trajectory directionality and morphological consistency, this invention effectively improves the robustness and discriminativeness of fault type identification in weak feature scenarios, providing theoretical and geometric support for the subsequent construction of dual protection criteria and systematic protection logic.

[0100] IV. Feature Extraction and Protection Criterion Construction This invention addresses the problem of weak, unstable, and easily confused transient signal characteristics of single-pole grounding faults in complex multi-terminal flexible DC power distribution systems. It proposes a dual-criteria identification mechanism based on phase space mapping trajectory, which achieves accurate differentiation between faults inside and outside the fault zone through directional discrimination and morphological consistency analysis.

[0101] The key processes in this section are as follows: 1. Use the Prony algorithm to extract the dominant frequency of the current signal; 2. Construct the phase space trajectory; 3. Extract directional features—initial quadrant distribution; 4. Extract morphological features—major axis offset; 5. Construct dual-criteria logic and form protection action judgment.

[0102] 4.1 Dominant Frequency Extraction (Prony Modeling, Equations 23-24) First, to ensure the effectiveness of phase space mapping and the stability of direction criteria, the dominant frequency of the input current signal needs to be extracted.

[0103] The present invention uses the Prony algorithm to perform complex exponential fitting on the sampled sequence, as shown in formula (23), to construct the p-order modeling expression and calculate the transient energy corresponding to each modal frequency, as shown in formula (24).

[0104] ;(twenty three) In the formula, Where N is the sampling interval, N is the number of sampling points, and p is the model order.

[0105] Define E k Let k be the transient energy of the signal within the protection window: ;(twenty four) Finally, the mode frequency with the highest energy was selected as the dominant frequency for that time period to determine the subsequent mapping delay time. = T / 4.

[0106] 4.2 Construction of Phase Space Coordinate Sequence Based on the period T and delay time τ determined by the dominant frequency, a two-dimensional phase space trajectory point sequence is constructed, as shown in formula (25): (25) In the formula, For delay points, .

[0107] 4.3 Initial Quadrant Directional Criterion (Formulas 26-28) As mentioned above Figure 12 As shown, the initial distribution region of the trajectory reflects the direction of the current. The present invention is constructed using the following steps: 1. Define the sign function sgn(x), see formula (26); 2. Select all sampling points within the dominant period (approximately T / 2) and calculate the mean of the sign function; 3. Obtain the direction criterion value S, as shown in formula (27).

[0108] The criterion value S ranges from [-1, 1]: S > S set : Determine the current to be in the positive direction; S < -S set : Determined as negative direction; |S| < S set The direction is unclear.

[0109] The direction criterion is applied to both ends of the protected line (denoted as S1, S2). Based on their combination relationship, a preliminary judgment logic is formed, as shown in formula (28).

[0110] If both S1 and S2 are positive, the fault is determined to be within the zone; if both S1 and S2 are negative, the fault is determined to be outside the zone; otherwise, the trajectory pattern needs to be further determined.

[0111] 4.4 Consistency between spindle offset and trajectory shape (Formulas 29~31) When the direction criterion cannot clearly determine the fault range, this invention introduces the spindle offset index to measure the consistency of the trajectory shape.

[0112] The analysis steps are as follows: 1. The trajectory is centered to eliminate center of gravity shift; 2. Construct the covariance matrix C, as shown in formula (29): (29) In the formula, , The phase space coordinates after centering. , For the variance of the corresponding variable, express and The covariance is used to measure the overall error between two variables.

[0113] 3. Perform PCA analysis to extract the direction of the first principal component and the corresponding direction angle. ; 4. During the fault period, extract multiple spindle orientation angles using a sliding window method, calculate their standard deviation, and form the "spindle offset" index. See formulas (30) and (31): (30) (31) Where M is the sequence length, .

[0114] Offset Explanation: The principal axis directions of a single RLC trajectory are consistent. Small; the principal axis of multiple RLC superimposed trajectories is prone to shift. big.

[0115] 4.5 Construction of Spindle Difference Criterion In cases where the orientation criteria at both ends conflict or the orientation is unclear, the present invention further compares the difference in spindle offset at both ends. Construct the difference criterion, as shown in formula (32): (32) like If the fault is classified as an internal fault, it is determined to be an external fault. The setting threshold is specified in the data. The typical value range is 12° to 15°, which can be dynamically set based on the on-site noise intensity and system response characteristics.

[0116] 4.6 Setting the Startup Criteria To avoid accidental activation, this invention sets a fault detection start criterion before entering the above identification process, which is based on the voltage difference between the positive and negative poles and ground.

[0117] As shown in formula (33): (33) These are the positive and negative voltages, respectively. The action threshold is set to avoid the maximum unbalanced voltage during normal system operation, and is typically taken as... .

[0118] 4.7 Summary of Judgment Criterion Logic (Dual Judgment Criterion Fusion) The criterion execution process of this invention can be summarized as follows: 1. Determine if the voltage start-up condition is met; if not, do not operate. 2. If start-up is met, execute direction criteria (S1, S2). 3. If the directions are consistent (both positive or negative), directly output the judgment. 4. If the directions are inconsistent, proceed to spindle offset judgment. 5. Compare the offset difference between the two ends. To make the final judgment.

[0119] This dual-fusion logic enhances the system's adaptability to weak features, complex network structures, high-impedance grounding, and strong noise backgrounds, and provides good anti-interference capabilities and engineering deployability.

[0120] V. Protection Process and Engineering Implementation Recommendations The single-pole grounding protection method of this invention is designed for complex multi-terminal flexible DC distribution network structures, featuring no boundary dependency, high noise immunity, and structural universality. To ensure the successful implementation of the protection strategy in practical engineering, this section outlines its complete protection process and provides system design and deployment suggestions.

[0121] 5.1 Overall Protection Process Description (in conjunction with...) Figure 13 ) like Figure 13 As shown, the protection process of this invention includes five functional modules: Step 1: Protection Startup Judgment Input: Voltage U between the positive and negative terminals of the line and ground p U n ; Execution start criteria | U p - U n | > U set If the conditions are met, the protection logic is activated, and the process proceeds to the next step.

[0122] Step 2: Current signal acquisition and Prony frequency extraction The transient current signal x(t) is collected from the measurement point, normalized, and windowed; the Prony algorithm is executed to extract the dominant frequency (see formulas 23 and 24); the delay time τ = T / 4 is calculated, and the phase space trajectory is constructed.

[0123] Step 3: Direction Criterion Determination Construct a sequence of phase space trajectory coordinate points (Formula 25); calculate the direction criteria values ​​S1 and S2 of the first T / 2 sampling segment of the trajectory (Formulas 26-28); if the directions are consistent (both positive or negative), directly output the in-zone / out-zone judgment.

[0124] Step 4: Trajectory Shape Judgment If the directions are inconsistent, perform PCA processing on the trajectory (Equations 29-31); extract the principal axis direction angle sequence and calculate the offset; calculate the difference in offset between the two ends. The fault is compared with the set threshold (Formula 32) and determined to be either an in-zone or out-of-zone fault.

[0125] Step 5: Output protection action Fault within the zone: Output trip command (polarity circuit breaker control); Fault outside the zone: Failure to operate, enters waiting state; Optional: Record waveform data for subsequent analysis.

[0126] 5.2 System Design and Module Division Recommendations To achieve the above process, it is recommended that the system design be divided into the following functional modules: Module Name Function Description Signal acquisition module Acquire current and voltage signals; the recommended sampling frequency is ≥20kHz, typically 50kHz. Startup Judgment Module Real-time detection of the voltage difference between the positive and negative terminals triggers the protection process. Data preprocessing module Filtering, normalization, window truncation Frequency extraction module (Prony) Calculate the dominant frequency, output period T, and delay τ. Phase Space Trajectory Construction Module Constructing a two-dimensional embedded coordinate sequence Feature extraction module Calculation of direction criterion and spindle offset Logical judgment module Implementing a protection decision-making process (integration of direction and morphological criteria) Motion control module Output trip command or alarm signal 5.3 Engineering Implementation Recommendations 1) Recommendations for Algorithm Deployment Platforms The method of this invention is applicable to deployment on the following two types of platforms: embedded hardware platforms, such as DSP, FPGA, and ARM processors; suitable for deployment in flexible DC protection terminals, station control units, and distributed relays; algorithms such as PCA and Prony can achieve high-speed parallel processing.

[0127] Simulation and debugging platforms, such as MATLAB / Simulink, are used for protection strategy simulation, verification, and online tuning. They can also be connected to PSCAD and other systems for full-network scenario simulation.

[0128] 2) Signal Input and Data Interface Recommendations The input interface should support multi-channel synchronous sampling; the input signals include: positive current, negative current, positive and negative voltage to ground; it can optionally be used with a GPS clock for high-precision synchronization (this invention does not rely on synchronization information); the output interface should support trip commands (dry contact), communication alarms (CAN / IEC61850), etc.

[0129] 3) Parameter tuning suggestions (default values): 5.4 Application Scenarios and Promotion Suggestions: The method of this invention is applicable to the following typical engineering scenarios: complex DC distribution networks with heterogeneous structures of multiple converters; systems without boundary elements (current limiting reactors) or with indistinct boundary characteristics; medium and low voltage flexible DC systems (±10kV, ±1.5kV) and other systems that do not have the ability to synchronize the clock across the entire network; and fault scenarios with weak characteristics such as high-resistance grounding and low signal-to-noise ratio.

[0130] Through the above process and design, the protection method of this invention has the following significant advantages: strong directionality: based on the initial quadrant of the trajectory, it achieves clear direction judgment with physical meaning; strong morphological recognition capability: the main axis offset adapts to the superimposed response of multiple RLCs, improving the tolerance for misjudgment; strong robustness: suitable for high-impedance fault (≥200Ω) and noise interference (≥20dB) environments; strong independence: it does not depend on communication or boundary elements, and has global self-consistency; flexible deployment: the algorithm is lightweight and adaptable to various control and protection platforms.

[0131] Example 3: I. System Modeling and Simulation Platform Description (see...) Figure 14 ) To verify the effectiveness of the protection method of this invention, a simulation platform based on PSCAD / EMTDC was constructed as follows. Figure 14 The model shown is a six-terminal ring-shaped flexible DC distribution network. The system includes various converter types (including MMC, VSC, and DCT), and the converters are interconnected via DC cables to form a complex multi-terminal interconnected topology, which is adaptable to real-world engineering applications.

[0132] The model uses a sampling frequency of 50kHz and a fault injection time of 0.5s to fully extract transient response information. The parameter configurations for each converter station are shown in Table 2, including the number of arm sub-modules, sub-module capacitance, arm inductance, smoothing reactor parameters, and IGBT on-resistance, among other key control components. Specifically, the MMC converter station arm contains 24 sub-modules with a 10000μF capacitor and a 0.01H arm inductance, providing strong transient control capabilities. The VSC and DCT converter stations are configured with different capacities of filter capacitors and smoothing reactors to simulate various converter access scenarios.

[0133] Table 2 Converter station parameters

[0134] The cable line parameters of the flexible DC distribution network are shown in Table 3. The DC voltage level of the system is ±10kV. All lines are equipped with current-limiting reactors. The inductance, resistance and mutual inductance per unit length of the line are 0.78mH / km, 0.083Ω / km and 0.1mH / km, respectively, to approximate the distributed parameter characteristics of the actual flexible DC line.

[0135] Table 3 DC System Parameters

[0136] This modeling platform is used to support the injection, feature extraction, and criterion response analysis of different fault conditions in subsequent implementation steps. It covers typical complex engineering scenarios such as multiple converter types, multiple fault locations, transition resistance, and strong noise disturbances, providing basic support for verifying the accuracy, robustness, and practicality of the method of this invention.

[0137] II. Fault Settings and Operating Condition Configuration (see...) Figure 15 (Tables 4 and 5) Based on the aforementioned multi-terminal flexible DC distribution network simulation model, to comprehensively evaluate the adaptability and criterion reliability of the protection method of this invention under different scenarios, various single-pole grounding fault conditions and signal interference conditions were set up, with specific configurations as follows: Figure 15 As shown, the parameters are detailed in Tables 4 and 5.

[0138] Table 4 Simulation results of different transition resistances in scenario C1

[0139] Table 5 Simulation results of different transition resistances in scenario C2

[0140] Fault settings include the following elements: 1. Diverse Fault Locations: Single-pole grounding faults are injected into multiple representative branch locations in the network, including different distance levels such as near the converter station, in the middle section, and far from the measurement point, to test the sensitivity of the trajectory pattern to changes in fault distance; 2. Wide Transition Resistance Coverage: Transition resistances Rf are set to 10Ω, 50Ω, 100Ω, and 200Ω to simulate a wide range of operating conditions from typical low-resistance faults to weakly characteristic high-resistance faults, which helps to verify the sensitivity and accuracy of the algorithm under extreme conditions; 3. Noise Disturbance Conditions: Random Gaussian noise is superimposed on the original current signal, and the signal-to-noise ratio (SNR) is set to ∞ (ideal), 40dB, 30dB, and 20dB to examine the robustness of the method to different background interference levels; 4. Dual-sided Measurement Point Configuration: Measurement points P11 and P12 are set at both ends of the fault branch, and the voltage and current response curves of the positive and negative poles to ground are recorded respectively to construct a dual-sided phase space trajectory, realizing the analysis of fault difference characteristics between inside and outside the fault area.

[0141] The operating condition numbers and combinational logic are shown in Table 4. Fault types include in-zone faults (IN), out-of-zone faults (OUT), and critical boundary faults (TRANS), with a total of 36 typical operating conditions designed. Furthermore, the signal disturbance settings are listed in Table 5, covering noise injection methods under different SNR values, used for simulation to examine the sensitivity and suppression capability of the present invention's criteria to noise interference. The operating condition parameters configured in this section will be used in subsequent chapters to construct phase space trajectories, extract spindle offset and direction criterion values, and further implement the protection strategy proposed in this invention to evaluate its protection performance under actual complex operating conditions.

[0142] III. Phase Space Trajectory Construction and Feature Extraction Analysis Figure 16 , Figure 17 ) To fully explore the differences in transient current signals after a unipolar ground fault, this invention employs a phase space reconstruction method to enhance the dimensionality of the single-point current signal, mapping the one-dimensional time-domain sequence into a two-dimensional trajectory structure, thereby revealing the differences in dynamic behavior corresponding to different fault types.

[0143] Under each set of simulation conditions, the fault transient current signal x(t) at both ends of the protected branch is extracted, and the dominant frequency fd is obtained using the Prony algorithm. Based on this, the phase space delay time τ=12fd is determined. Then, the two-dimensional phase space trajectory is constructed according to the following formula: The mapped two-dimensional trajectory reflects the evolution of the fault signal between adjacent sampling points, and its geometric shape is closely related to the transient response mechanism. A typical phase space trajectory is shown below. Figure 16 The figure shows the two-terminal current mapping results when there is a fault in the area; Figure 17 The comparison of trajectories under fault conditions outside the designated area is shown.

[0144] To achieve quantitative recognition based on trajectory morphology, this invention extracts the following two types of key features: 1. Direction Index: Based on the proportion of samples in the first quadrant (x>0, y>0) of the phase space coordinate sequence, the direction index S is constructed by combining the average value of the sign function. This value reflects the consistency of the initial direction of current change and is an indicator for initial screening of faults within and outside the fault zone. 2. Principal Axis Deviation (PAD): By centering the trajectory, principal component analysis (PCA) with a sliding time window is used to extract the principal axis orientation angle sequence. θi Then, its standard deviation is calculated as a trajectory consistency index. The smaller the spindle offset, the more regular the trajectory, which usually corresponds to an in-zone fault with a single RLC response; a large offset indicates a chaotic trajectory, which is mostly an out-of-zone response.

[0145] By comparing the trajectory shape, direction criteria, and spindle offset under different operating conditions, a multi-dimensional feature space can be constructed. This allows for accurate differentiation between faults inside and outside the zone under conditions without communication or boundary components, providing a data foundation and physical basis for the construction of subsequent protection criteria.

[0146] IV. Comparison of the enforcement of protection criteria and the effect of judgment ( Figure 18 Table 6) Based on the aforementioned simulation conditions and feature extraction, the protection strategy proposed in this invention is executed sequentially according to a dual-criteria identification process of "direction criterion + spindle offset difference criterion," and its logical framework is as follows: Figure 18 As shown.

[0147] The specific steps are as follows: 1. Direction Criterion Execution: Based on the direction criterion value S within the sampling window, determine the direction of change of the transient fault current at both ends of the line. If the directions at both ends are consistent (e.g., both are positive), it can be directly determined as an internal or external fault; if the directions are inconsistent, proceed to the next step. 2. Spindle offset difference criterion: Extract the spindle offset of the two ends of the trajectory, calculate the difference Δσ=|σθ1−σθ2|, and compare it with the tuning threshold. Tσ The comparison is performed. If the difference is greater than the threshold value, it is determined to be an in-zone fault; otherwise, it is an out-of-zone fault. 3. Fault type determination output: Based on the above criteria, the fault type is finally output and the corresponding protection action (such as tripping, alarm, etc.) is triggered.

[0148] Comparative tests were conducted using the method of this invention, the traditional directional protection method, and the correlation matching protection method under all 36 typical working conditions. The correct recognition rate, false judgment rate, and failure to operate rate of each method were statistically analyzed, and the results are shown in Table 6.

[0149] Table 6. Simulation results of noise interference

[0150] Simulation results show that: The method of this invention achieves an identification accuracy of over 98% under all fault conditions, and maintains a significant advantage, especially under high-resistance grounding (200Ω) and low SNR (20dB) conditions. Compared with traditional direction criteria which are susceptible to transient fluctuations and correlation methods which have poor adaptability to nonlinear responses, this method can still achieve accurate identification by relying on trajectory morphology characteristics even when directions are inconsistent. This method does not rely on boundary elements and communication networks, has distributed and local protection characteristics, and is suitable for various flexible DC topologies.

[0151] This section verifies the effectiveness, robustness, and engineering adaptability of the proposed dual-feature criterion logic of trajectory direction and main axis offset under typical complex working conditions, providing important basic support for subsequent engineering deployment.

[0152] V. Simulation Conclusions and Engineering Deployment Recommendations Figure 19 ) To further verify the engineering applicability and deployment value of the protection method of this invention under complex working conditions, the overall protection performance is summarized and evaluated based on the aforementioned feature extraction and criterion execution results. The results are as follows: Figure 19 As shown.

[0153] The figure shows a comparison of the method of the present invention with traditional protection schemes in terms of fault identification accuracy, false alarm rate, and failure to operate rate under different transition resistances (10Ω–200Ω), different signal-to-noise ratios (SNR from ∞ to 20dB), various topologies, and converter access types.

[0154] Simulation results show that: This invention provides a method with higher sensitivity for identifying high-resistance grounding and weak-feature faults, and maintains stability under strong noise interference. The phase space trajectory construction does not depend on boundary elements and electrical symmetry, and is applicable to various flexible DC power distribution topologies such as ring, chain, and star configurations. The criterion is based on the statistical construction of signal geometry, and has good robustness to signal waveform distortion and converter type changes. Core algorithms such as Prony analysis and principal component analysis (PCA) have mature digital implementation methods, suitable for deployment on embedded platforms such as DSP, FPGA, and ARM. The entire process does not rely on inter-station communication and synchronous sampling, supports distributed and localized protection deployment, and features fast action and structural decoupling.

[0155] In summary, the single-pole grounding fault protection method based on phase space transient mapping trajectory proposed in this invention can achieve accurate identification in complex flexible DC distribution systems without communication, boundary elements, or structural assumptions. It has good theoretical applicability, data availability, and engineering deployment feasibility, and can be widely applied in new flexible DC distribution networks, DC microgrids, multi-terminal DC systems, and other occasions.

[0156] It should be noted that the embodiments described in this specification are only for helping to understand the technical solution and core ideas of the present invention, and the technical features involved are not limited to the specific embodiments described above. For those skilled in the art, various equivalent substitutions, modifications, or combinations that can be made without departing from the essence of the present invention should be included within the protection scope of the present invention. The scope of protection should be determined by the appended claims.

Claims

1. A method for single-pole grounding protection of complex multi-terminal flexible DC distribution networks based on phase-space transient mapping trajectories, characterized in that, Includes the following steps: S1. Fault Initiation and Signal Acquisition: Detect the positive and negative pole voltages to ground of the DC line. When the voltage difference exceeds the set threshold, it is determined that a single-pole grounding fault has occurred, the protection is initiated, and the fault transient current signal at both ends of the DC line to be protected is acquired. S2. Phase space trajectory construction: Extract the dominant frequency of the fault transient current signal and determine the delay time based on the period corresponding to the dominant frequency; according to the delay time, map the one-dimensional current sequence into a two-dimensional phase space coordinate sequence to form a phase space trajectory; S3. Trajectory feature extraction: Extract geometric morphological features from the phase space trajectory, the features including trajectory direction features based on the initial quadrant distribution and trajectory morphological consistency features based on the principal axis offset; S4. Fault Identification and Judgment: Execute direction criteria based on the trajectory direction characteristics; when the current directions at both ends of the line are consistent, directly determine the fault type; when the directions are inconsistent, further execute the spindle offset difference criterion based on the trajectory shape consistency characteristics to distinguish between faults within and outside the zone.

2. The method according to claim 1, wherein, The extraction of trajectory direction features in step S3 specifically includes: In a two-dimensional phase space coordinate sequence, a preset time window is selected, and the mean value of the sign function of the sampled values ​​within the window is calculated to obtain the direction criterion value; The direction criteria values ​​at both ends of the line are compared with preset positive and negative thresholds respectively. When the criterion value is greater than the positive threshold, it is determined to be a positive direction, and when it is less than the negative threshold, it is determined to be a negative direction.

3. The method according to claim 2, wherein, The specific steps in step S4, which involve performing a direction determination based on trajectory direction features, include: If the direction criteria values ​​at both ends of the line are both positive, then it is determined to be a fault within the area; If the direction criteria values ​​at both ends of the line are negative, it is determined to be an external fault. If the direction criterion values ​​are one positive and one negative or have inconsistent signs, then the spindle offset difference criterion is activated.

4. The method according to claim 1, wherein, The extraction of trajectory morphology consistency features in step S3 specifically includes: Initial segment removal and centering are performed on the two-dimensional phase space coordinate sequence; Principal component analysis was performed on the centered data using a sliding time window to extract the principal axis orientation angles within each window. Calculate the standard deviation of the principal axis direction angle sequence as the principal axis offset representing the consistency of trajectory shape.

5. The method according to claim 4, wherein, The spindle offset difference criterion in step S4 specifically includes: Calculate the principal axis offset of the measuring points at both ends of the line; If the difference in spindle offset between the two ends is greater than the preset setting value, it is determined to be an in-zone fault; otherwise, it is determined to be an out-of-zone fault.

6. The method according to claim 1, characterized in that, The method further includes: When analyzing fault characteristics, an equivalent decoupling model of the network containing virtual breakpoints is constructed to characterize the transient response characteristics of the network on both sides of the fault point. The location of the virtual break point is determined by the line parameters, the fault location, and the equivalent impedance of different converters, and is used to guide the analysis and judgment criteria setting of trajectory characteristic differences.

7. A single-pole grounding protection device for complex multi-terminal flexible DC distribution networks used to implement the method of any one of claims 1 to 6, characterized in that, include: The signal acquisition and start-up module is used to acquire the current signal and the positive and negative voltage signals to ground at both ends of the line, and to issue a protection start-up signal when the voltage difference exceeds a set threshold. The data processing and trajectory construction module, connected to the signal acquisition and start-up module, is used to extract the dominant frequency of the fault current and construct a two-dimensional phase space trajectory based on the delay time. The feature extraction module, connected to the trajectory construction module, is used to extract trajectory direction features and trajectory shape consistency features; The protection judgment module, connected to the feature extraction module, is used to execute the direction criterion and the spindle offset difference criterion, and output the judgment result of faults inside or outside the zone.

8. A complex multi-terminal flexible DC distribution network system, characterized in that, It includes at least two interconnected DC lines, and a single-pole grounding protection device as described in claim 7, wherein the protection device is disposed on the DC line to be protected.

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