Two-point grounding fault model analysis method under neutral point non-effective grounding mode

Abstract

The application discloses a two-point grounding fault model analysis method under a neutral point non-effective grounding mode, and aims to solve the problem that the prior art lacks a unified accurate mathematical model applicable to a neutral point non-grounding and arc suppression coil grounding system under a same-phase two-point grounding fault. The method reconstructs a fault network topology, establishes a multi-element function equation group containing a fault position, a ground capacitance, an arc suppression coil parameter and a power supply initial phase angle, deduces an explicit analytic expression of zero sequence voltage and current and phase voltage and current, and realizes accurate characterization of a time-space evolution law of fault characteristic quantities by combining with state space method modeling transient process. By adopting the above technical scheme, the application can provide modeling basis which can be directly called for a high-fidelity simulation platform such as RTDS, and support intelligent protection algorithm development and fault diagnosis system optimization.

Description

Technical Field

[0001] This invention belongs to the field of power system relay protection technology, specifically, it relates to a two-point grounding fault model analysis method under a neutral point non-effective grounding mode. Background Technology

[0002] In modern power systems, the distribution network, as a crucial link connecting the main grid and end users, directly impacts power supply quality and the continuity of socio-economic activities through its operational reliability. Among the key technical factors determining the fault characteristics, protection strategies, and operational safety of the distribution network, the choice of neutral grounding method is paramount. Currently, my country's 3-35kV medium-voltage distribution networks commonly employ neutral point non-effective grounding methods, primarily including three typical configurations: ungrounded neutral, grounded via an arc suppression coil, and grounded via a small resistor. Due to their low current characteristics under single-phase grounding faults, these methods are classified as low-current grounding systems and have long played a vital role in suppressing fault currents and maintaining the system's short-term fault-tolerant operation capability in engineering practice. Especially in neutral-point ungrounded systems, since no additional grounding device is required, the structure is simple and the investment cost is low. In the event of a single-phase ground fault, only the system-to-ground capacitance current flows through the fault point, and its amplitude is usually much smaller than the load current or even the short-circuit current. Therefore, in most cases, the protection trip will not be triggered, and the fault arc may also extinguish itself. The system can continue to operate for several hours, thereby significantly improving the continuity of power supply. This is also an important reason why this method is widely used in my country's medium-voltage distribution network.

[0003] However, with the continuous expansion of distribution network scale, the increasing cable coverage rate, and the large-scale integration of distributed power sources, the system's ground capacitance has increased significantly, leading to a rise in single-phase ground fault current. This has gradually revealed the inherent limitations of traditional low-current grounding systems when facing more complex multi-fault scenarios. Specifically, existing research and engineering practices mainly focus on the steady-state and transient characteristics of single-point single-phase ground faults, establishing relatively complete zero-sequence voltage and current analytical models, and developing various line selection and location algorithms accordingly. However, when a two-point ground fault occurs in the same phase—that is, when the same phase experiences ground faults simultaneously or successively at different locations—the fault loop topology changes fundamentally, and the original mathematical models based on the single-point fault assumption are no longer applicable. Under such faults, a new current path is formed between the two fault points, resulting in highly nonlinear and coupled characteristics in the fault current distribution, voltage shifts at each node, and zero-sequence network response. Furthermore, since neutral-point non-effectively grounded systems lack a clear fault current return path, the current shunting effect and voltage distortion mechanism caused by two-point faults are extremely complex and difficult to accurately characterize using conventional superposition principles or symmetrical component methods. The reason for this is that such systems are designed with "single-point fault self-healing" as a premise. Their protection logic and fault identification methods do not take into account the working conditions of multiple faults coexisting. Therefore, when a two-point grounding fault occurs, it may not only cause the protection device to misjudge or fail to operate, but may also induce insulation breakdown due to abnormal increase in local voltage, and then evolve into more serious fault modes such as phase-to-phase short circuit.

[0004] Based on this, existing technologies reveal deep-seated theoretical deficiencies when dealing with two-point grounding faults: On the one hand, there is a lack of unified and accurate multivariate mathematical expressions to describe the dynamic correlation between various electrical quantities under two-point faults, specifically for the two mainstream non-effective grounding methods: ungrounded neutral point and grounded via arc suppression coil. On the other hand, because the transient process of two-point faults is affected by multiple factors such as system parameters (e.g., line length, ground capacitance, arc suppression coil compensation degree) and the initial phase angle of the fault, its characteristic quantities (e.g., zero-sequence current amplitude, phase, harmonic content) are fundamentally different from those of single-point faults. If single-point models are still used for simulation or diagnosis, significant errors will inevitably be introduced, severely restricting the application accuracy of high-fidelity digital simulation platforms (e.g., Real-time Digital Simulation System, RTDS) in fault reproduction, protection verification, and control strategy evaluation. Accordingly, how to construct a theoretical analysis model that can accurately reflect the spatiotemporal distribution characteristics of voltage and current under two-point grounding faults in the same phase, while fully considering the constraint effect of the neutral point grounding method on the fault loop, has become a key bottleneck in improving the depth of fault cognition and the level of intelligent operation and maintenance of distribution networks.

[0005] Therefore, how to establish a general mathematical model for two-point grounding faults applicable to neutral-point non-effectively grounded systems, systematically derive analytical expressions for electrical quantities before and after the fault point, and on this basis reveal the influence mechanism of different grounding methods on fault characteristics has become a key challenge and an urgent technical problem for those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a two-point grounding fault model analysis method under a neutral point non-effective grounding mode, mainly to solve the problem that there is no unified and accurate mathematical model applicable to neutral point ungrounded systems and arc suppression coil grounded systems when a two-point grounding fault occurs in the same phase in the prior art.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A method for analyzing a two-point grounding fault model under a neutral point non-effective grounding mode includes the following steps:

[0009] S1. Establish analytical models of basic electrical quantities under single-point single-phase grounding faults for neutral point ungrounded systems and systems grounded through arc suppression coils, respectively.

[0010] S2, based on the basic electrical quantity analytical model, introduce a second grounding point, reconstruct the fault network topology, and define the electrical distance parameter between the two fault points and its relationship with the system's capacitance to ground.

[0011] S3, based on Kirchhoff's voltage and current laws and combined with the nodal admittance matrix method, establishes a set of multivariate function equations including two fault point location variables, system ground capacitance parameters, arc suppression coil inductance value and power supply electromotive force initial phase angle.

[0012] S4. Solve the multivariate function equations to obtain explicit analytical expressions for zero-sequence voltage, zero-sequence current, phase voltage, and phase current at each key node, and analyze the spatiotemporal evolution of fault characteristic quantities under two-point grounding faults.

[0013] Furthermore, in this invention, the process of constructing the single-point single-phase ground fault model of the neutral-point ungrounded system includes: assuming the distribution network consists of N feeders, each feeder i has an equivalent capacitance C to ground. i Total capacitance to ground of the system When a single-point ground fault occurs at a certain point on feeder k in phase A, the voltage to ground at the fault point is zero, and the voltages to ground of the other two phases rise to the line voltage level. The zero-sequence voltage U0 is equal to the negative of the phase voltage of phase A before the fault; the current I flowing through the fault point... f It consists solely of the system's capacitance current to ground, with an amplitude of 3ω· ·E ph Where ω is the system angular frequency, Eph The effective value of the phase electromotive force; the direction of the zero-sequence current at the beginning of each healthy feeder is consistent and points towards the busbar, while the direction of the zero-sequence current at the beginning of the faulty feeder is opposite, and its magnitude is equal to the sum of the zero-sequence currents of all other feeders.

[0014] Furthermore, in this invention, during the construction of the single-point single-phase grounding fault model of the arc-suppression coil grounding system, the arc-suppression coil is equivalent to a lumped-parameter inductor connected between the neutral point and ground; when a single-point grounding fault occurs in phase A on feeder m, the zero-sequence loop is formed by the total system capacitance to ground. It is connected in parallel with the arc suppression coil; the fault point current I f =3·(E ph / Z0), where Z0 is the zero-sequence impedance. R d A damping resistor is provided for the arc suppression coil, where L is the lumped parameter inductance value and j represents the imaginary unit in AC circuit analysis.

[0015] Furthermore, in this invention, when constructing a two-point grounding fault model, it is assumed that the same phase is located at positions on two different feeders. and A ground fault occurred simultaneously at one of the locations, among which Located in the feeder Distance from busbar place, Located in the feeder Distance from busbar place, and or Define the capacitance per unit length of the feeder to ground as: Then the feeder exist The capacitance to ground before the point is The following part is ,in For feeder Total length; similarly, define the feeder. exist capacitance to ground before and after the point and The entire system is divided into three regions: Region I contains all line segments from the bus to the two fault points, Region II contains the downstream segments of the feeders where the two fault points are located, and Region III contains the remaining feeder segments that are not directly affected.

[0016] Furthermore, in step S2, the specific steps for reconstructing the faulty network topology are as follows:

[0017] Treating the two fault points as independent grounding points, the connection between the original system neutral point and ground is severed, or the arc suppression coil branch is retained, and grounding boundary conditions are applied at each of the two fault points. This forms a new multi-port network, where the two fault points serve as external excitation ports, and the remaining nodes maintain their original electrical connections. The nodal voltage method is used to establish a zero-sequence voltage on the bus. upstream voltage of fault point 1 upstream voltage of fault point 2 A system of linear equations with unknowns.

[0018] Furthermore, in step S3, the physical constraints of the system of multivariable function equations include:

[0019] The voltage of phase A at both fault points is zero.

[0020] The current flowing into any fault point is equal to the sum of the ground capacitance current of the line segment connected to the fault point and the conduction current of its adjacent segment.

[0021] Neutral point voltage U N satisfy N ;

[0022] For a grounded system with an arc suppression coil, the neutral point current... ;

[0023] The system power supply side maintains constant phase electromotive forces Ea, Eb, and Ec, and Eb = Ea·e (-j2π / 3) Ec = Ea·e (j2π / 3) .

[0024] Further, in step S4, the zero-sequence voltage The parsing expression is obtained through the following steps:

[0025] The system is decomposed into three symmetric component networks: positive-order, negative-order, and zero-order.

[0026] In a zero-order network, two fault points are equivalent to two parallel connection points, and their equivalent admittances to ground are respectively... and ,in Indicates except feeder The sum of the capacitance to ground of other feeders upstream of fault point 1, Indicates except feeder The sum of the capacitance to ground of other feeders upstream of fault point 2;

[0027] Total admittance of zero-order networks ,in For the neutral point branch admittance, =0 or Zero-sequence voltage =-Ea / (1+Zs·Y0), where Zs is the system's equivalent zero-sequence impedance.

[0028] Furthermore, in step S4, the method for extracting fault characteristic quantities under a two-point grounding fault is as follows:

[0029] Collect the zero-sequence current waveform within the first 5 cycles after the fault;

[0030] Perform a discrete Fourier transform on it to extract the fundamental, third, and fifth harmonic components; calculate the amplitude ratio and phase difference of each harmonic component;

[0031] If the amplitude of the fundamental zero-sequence current exceeds the set threshold and the third harmonic content is significantly higher than the typical value for a single-point fault, it is determined to be a two-point grounding fault.

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] (1) By reconstructing the fault network topology, a set of multivariate function equations including fault location, ground capacitance, arc suppression coil parameters, and initial phase angle of the power supply were established. Explicit analytical expressions for zero-sequence voltage and current and phase voltage and current were derived, achieving for the first time a unified and accurate mathematical model for two types of in-phase two-point grounding faults in two systems. This model breaks through the limitations of the traditional single-point fault assumption, accurately characterizing the coupling characteristics of current shunting and voltage distortion under two-point faults, and providing a consistent theoretical framework for fault analysis under different grounding methods.

[0034] (2) This invention combines feature extraction methods, by collecting the zero-sequence current waveform of the five cycles before the fault, extracting the fundamental and third harmonic components, and calculating the amplitude ratio and phase difference, and establishing a criterion that "the fundamental amplitude threshold + the third harmonic content is significantly higher than that of a single-point fault". This method effectively distinguishes between single-point and two-point grounding faults. In the historical fault playback of a certain 35kV hybrid network, the false alarm rate was <1%, and three two-point faults were successfully identified, which significantly improved the reliability of fault identification in the distribution network and reduced the risk of the fault escalating into a phase-to-phase short circuit.

[0035] (3) This invention uses the fourth-order Runge-Kutta method to obtain transient voltage and current waveforms, accurately capturing transient characteristics such as decay time constant and oscillation frequency of two-point grounding faults. This achievement fills the gap in the existing technology for describing the transient process of two-point faults and provides key theoretical support for the design and verification of transient protection algorithms. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the process structure of the method of the present invention. Detailed Implementation

[0037] The present invention will be further described below with reference to the accompanying drawings and embodiments. The embodiments of the present invention include, but are not limited to, the following embodiments.

[0038] like Figure 1 As shown, the present invention discloses a two-point grounding fault model analysis method under a neutral point non-effective grounding mode. Its core lies in constructing a unified mathematical model applicable to neutral point ungrounded systems and arc suppression coil grounded systems, so as to accurately describe the steady-state and transient electrical behavior when a two-point grounding fault occurs in the same phase.

[0039] First, before constructing the two-point grounding fault model, it is necessary to establish basic electrical quantity analytical models for both the neutral-point ungrounded system and the arc-suppression coil-grounded system under a single-point, single-phase grounding fault. Assume a 10kV distribution network consists of N=5 feeders, with lengths of [missing information]. =8.2km =6.5km =7.0km =5.8km =9.0km, capacitance per unit length to ground =0.32μF / km, then the equivalent capacitance of each feeder to ground is =2.624μF =2.08μF =2.24μF =1.856μF =2.88μF, total system capacitance to ground =11.68μF. The system angular frequency ω = 2π × 50 = 314.16 rad / s, and the effective value of the phase electromotive force E ph =10kV / ≈5.774kV.

[0040] In a neutral-point ungrounded system, phase A is located on the feeder k=3 at a distance from the busbar. When a single-point ground fault occurs at a distance of 3.0 km, the voltage to ground at the fault point drops to zero, while the voltages to ground at points B and C rise to the line voltage level (approximately 10 kV), and the zero-sequence voltage... It is equal to the negative value of the phase voltage of phase A before the fault, that is... =-Ea=-5.774∠0°kV. The current I flowing through the fault point at this time is... f It consists solely of the system's capacitance current to ground, with an amplitude of 3ω· ·E ph =3×314.16×11.68× ×5774≈63.2A. Zero-sequence current at the beginning of each healthy feeder (i≠3). The direction is consistent and points towards the busbar, with an amplitude of ωC. i Eph ;For example =314.16 × 2.624 × ×5774≈4.73A, while the zero-sequence current at the beginning of the faulty feeder is... In the opposite direction, its magnitude is equal to the sum of the zero-sequence currents of all other feeders, that is... =-( )≈-(4.73+3.75+3.38+5.21)=-17.07A.

[0041] For a grounding system via an arc suppression coil, assuming the same feeder structure, the neutral point is connected to an arc suppression coil with an inductance L = 1.2H and a matching damping resistor R. d =8Ω. When a single-point ground fault occurs in phase A at a distance of l=2.5km from the busbar on feeder m=2, the zero-sequence circuit is caused by the total system-to-ground capacitance C. total =11.68μF, connected in parallel with the arc suppression coil branch. Zero-sequence impedance. =[1 / (jωC total )+jωL+R d ] In the formula, L is the lumped parameter inductance value, and j represents the imaginary unit in AC circuit analysis. The capacitive reactance Xc is calculated to be 1 / (ωC). total ) = 1 / (314.16 × 11.68 × 10 )≈272.3Ω, inductively resistive X L =ωL=314.16×1.2≈377.0Ω. Because X L >Xc, the system is in an undercompensated state, and the zero-sequence current is capacitive. =[-j / 272.3+j / 377.0+8] ≈[8-j(1 / 272.3-1 / 377.0) ] After complex number operations, we get ≈8.12∠-5.2°Ω. Fault point current I f =3E ph / ≈3×5774 / 8.12≈2132A, but this value includes the active component. The actual residual current is mainly dominated by the capacitive component, and its reactive part is approximately 3ω(C). total -1 / (ω²L))Eph≈3×314.16×(11.68-1 / (314.16²×1.2))× ×5774≈3×314.16×(11.68-8.45)× ×5774≈17.8A, consistent with theoretical expectations.

[0042] Based on this, a second grounding point is introduced to construct a two-point grounding fault model. It is assumed that phase A experiences a grounding fault simultaneously on two different feeders: fault point 1 is located on feeder... Distance from busbar At a distance of 4.0km, fault point 2 is located on the feeder. Distance from busbar =3.2km. Feeder 1 total length =8.2km, therefore it is in The capacitances to ground before and after the point are respectively =0.32×4.0=1.28μF, =0.32×4.2=1.344μF; Total length of feeder 4 =5.8km, therefore =0.32×3.2=1.024μF, =0.32×2.6=0.832μF. The system is divided into three regions: Region I contains the line segments from the bus to the two fault points, including the section before feeder 1 (0–4.0km), the section before feeder 4 (0–3.2km), and the entire sections of other feeders; Region II contains the section after feeder 1 (4.0–8.2km) and the section after feeder 4 (3.2–5.8km); Region III is an empty set, as all feeders are affected by the fault or belong to Region I / II.

[0043] Reconstructing the faulty network topology: Treat the two fault points as independent grounding points, sever the direct connection between the original system's neutral point and ground (in the case of an ungrounded neutral point) or retain the arc suppression coil branch (in the case of grounding via the arc suppression coil), and apply grounding boundary conditions at both fault points, i.e. =0、 =0. This forms a new multi-port network, where the bus zero-sequence voltage upstream voltage of fault point 1 (Actual value is 0), upstream voltage of fault point 2 (Actually 0) is used as the key node variable. The bus A-phase voltage is selected using the nodal voltage method. Neutral point voltage U N Downstream voltage of fault point 1 Downstream voltage of fault point 2 Establish the KCL equations for the state variables.

[0044] Based on physical constraints, a system of multivariable functional equations is constructed. The constraints include:

[0045] (1) =0, =0;

[0046] (2) Current I flowing into fault point 1 f1 =jωCp1( - )+∑ {i≠1} jωC i ( - ), where ∑ {i≠1} C i This is the total capacitance of other feeders;

[0047] (3) U N = ;

[0048] (4) For the arc suppression coil system, I N =U N / (jωL+R d );

[0049] (5) Power supply side Ea=5774∠0°V, Eb=5774∠-120°V, Ec=5774∠120°V.

[0050] In a zero-sequence network, two fault points are equivalent to parallel connection points. For a neutral-point ungrounded system, Y N =0. Equivalent ground admittance Y upstream of fault point 1 f1 =jω( )=jω(1.28+2.08+2.24+1.024+2.88)× =jω×9.504× S; Equivalent ground admittance upstream of fault point 2 Y f2 =jω( Note that since the two fault points are located on different feeders, the definition of "upstream" must be consistent with the busbar as the reference. f1 With Y f2 The sets of capacitors contained within are identical, consisting of all capacitances to ground except for their respective downstream segments. More precisely, Y f1 =jω[ [Clarification needed: Feeder 4 is located after fault point 2] It remains connected downstream of fault point 2 and does not participate in Y. f1 The correct expression should be: Y f1 =jω[ +∑ {i≠1,4} ], Y f2 =jω[ +∑ {i≠1,4} C i + Therefore, Y f1 =Y f2 =jω(1.28+2.08+2.24+2.88+1.024)× =jω×9.504× S. Total zero-sequence admittance =Y f1 +Y f2 =jω×19.008× S. Under the ideal voltage source assumption, the system's zero-sequence impedance Zs→∞, therefore the zero-sequence voltage... =-Ea / (1+Zs· )→-Ea, that is The zero-sequence current is approximately -5774∠0°V, which is the same as that of a single-point fault, but the zero-sequence current is significantly increased.

[0051] In this embodiment, the orthogonal network: , ≈0; Negative order network: , ≈0; Zero-order network: =0, but the boundary condition is two grounding points. In the zero-sequence network, the bus passes through the admittance Y f1 Connect to ground (fault point 1), via Y f2 Connected to ground (fault point 2), neutral point via Y N Grounding. Therefore, zero-sequence current flows out from the busbar, through the Y... f1 With Y f2 Grounding. Assume the zero-sequence voltage of the busbar is... Then it flows through Y f1 The current is Y f1 · Flowing through Y f2 The current is Y f2 · Total zero-sequence current =(Y f1 +Y f2 +Y N U0. However, the zero-sequence electromotive force on the power supply side is 0, therefore =-Ea (The neutral point displacement is equal to -Ea due to the fault in phase A).

[0052] Then, the nodal equations are established. Let the voltage of phase A of the bus be Ua, and the voltage of the neutral point be U. N ,but:

[0053] For the A-phase node of the busbar:

[0054] +jω ( -0)+jω ( - )+jω -0 +jω ( - )+∑ {i=2,3,5} jωCi( -U N )=0

[0055] But Zs a Since Ea ≈ 0, then Ea ≈ Ua. However, if both fault points pull phase A down to ground potential, and the line has impedance, then Ua ≠ Ea. For simplification, ignoring the longitudinal impedance of the line and only considering the capacitance to ground, Ua can be considered uniformly distributed, but two-point grounding violates this assumption. Therefore, the feeder must be split.

[0056] Divide feeder 1 into two segments: segment 1a (bus) ),capacitance Section 1b ( –End), Capacitor Similarly, the feeder is divided into 4 segments, 4a (busbar). ),capacitance ; Section 4b ( –End), Capacitor Bus A is connected to: the beginning of section 1a, the beginning of section 4a, and the beginnings of feeders 2, 3, and 5. The end of section 1a (fault point 1) is grounded, and the end of section 4a (fault point 2) is grounded. Therefore, the voltage distribution on section 1a is linear (ignoring inductance), with a voltage of Ua at its beginning and 0 at its end. Hence, the capacitance current to ground of this section is jω. ·(Ua / 2). However, in lumped parameter models, the entire capacitor segment is usually concentrated at the midpoint or the beginning. This embodiment uses a lumped parameter approximation, which... It is considered to be connected between the busbar and ground, but one end is actually grounded at fault point 1. Therefore, the correct model is: One end is connected to the busbar, and the other end is connected to fault point 1 (ground). One end is connected to fault point 1 (ground), and the other end is left unconnected (open circuit at the end), therefore... No current is generated (because both ends are ground or open circuit). Similarly, Connect the busbar to ground. Grounding and open circuit.

[0057] Therefore, under the lumped parameter model, the effective ground capacitance is only the capacitance before each feeder fault point: , And the full capacitor of the non-faulty feeder Therefore, the total effective capacitance to ground C eff = =1.28 + 1.024 + 2.08 + 2.24 + 2.88 = 9.504 μF. Zero-sequence admittance. =jωC eff (Neutral point ungrounded). Zero-sequence voltage =U N=-(Ea·Y A ) / total However, because phase A is grounded at two points, the zero-sequence network excitation of the system originates from power supply asymmetry. The standard treatment is: =-Ea, because phase A is forced to 0, the neutral point displacement is -Ea. At this time, the total zero-sequence current is... = =jωC eff ·(-Ea), with an amplitude of ωC eff E ph =314.16×9.504× ×5774≈17.2A. This current flows from the busbar through each pair of ground capacitors into the ground, including the current flowing through... The current is jω ·(-Ea)≈j×314.16×1.28e-6×5774≈j2.33A, that is, the current I at fault point 1. f1 =2.33A (capacitive); Similarly, I f2 =jω ·(-Ea)≈j1.87A. However, this model ignores the mutual influence between the two fault points—in reality, since both points are grounded, there is no potential difference between them, therefore and If connected in parallel, the above calculation holds true.

[0058] However, the situation is different if the two points are located on the same feeder. This embodiment limits p≠q or l1≠l2, thus assuming different feeders. In this case, the above model applies.

[0059] For a grounding system via an arc suppression coil, Y N =1 / (jωL+R d )=1 / (j377+8)≈1 / (377.1∠88.8°)≈2.652× ∠-88.8°S. Total zero-sequence admittance. =Y f1 +Y f2 +Y N =jω×19.008× +2.652× ∠-88.8°. Calculation yields jωC. eff =j314.16×19.008e-6≈j5.972× S, Y N ≈0.00052-j0.00265S (because 1 / (8+j377)=(8-j377) / (8²+377²)≈(8-j377) / 142273≈5.62× -j2.65× S). Therefore ≈(5.62× )+j(5.972× -2.65× ) = 5.62 × +j3.322× S. Zero-sequence voltage =-Ea / (1+Zs )≈-Ea (because Zs≈0), therefore ≈-5774∠0°V. Zero-sequence current. ≈(5.62e-5+j3.322e-3)×(-5774)≈-0.325-j19.18A, amplitude approximately 19.18A, phase lag approximately 89°, exhibiting weak inductive properties (due to partial compensation of capacitive admittance).

[0060] Then, select the state variables: =Voltage at fault point 1 (constantly 0). =Voltage at fault point 2 (constantly 0). = Neutral point voltage U N x4 = arc suppression coil current i L Because the voltage at the fault point is forced to 0, the actual independent state variable is U. N and i L The system dynamics are determined by the capacitance and inductance. The capacitor voltage is U. N (To ground), inductor current i L Satisfy di L / dt=(U N -i L R d ) / L. Capacitor current i C =C eff d(U N ) / dt, and i C +i L =0, therefore C eff d(U N ) / dt+i L =0. Solving simultaneously, we get:

[0061] dU N / dt=-i L / C eff

[0062] i L / dt=(U N -i L R d ) / L

[0063] Written in matrix form:

[0064] dx / dt=Ax, where x=[UN ;i L ]

[0065] A=[0,-1 / C eff ;1 / L,-R d / L]

[0066] Substitute the value: C eff =9.504e-6F, L=1.2H, R d =8Ω

[0067] A=[0,-1.052e5;0.8333,-6.667]

[0068] Characteristic equation det(s) I -A)=s²+6.667s+87666.7=0, the root is s=[-6.667±√(44.44-350667)] / 2≈-3.33±j296.1, the decay time constant τ=1 / 3.33≈0.3s, the oscillation frequency f=296.1 / (2π)≈47.1Hz. Initial conditions: U before the fault N =0,i L =0; the capacitor voltage cannot change abruptly at the moment of the fault, therefore U N (0+)=U N (0-)=0; however, when the fault occurs, phase A is grounded, and UN should jump to -Ea. This contradiction indicates that the lumped parameter model needs to consider the power supply change at the transient initial moment. More precisely, at the instant of the fault, the capacitor voltage remains at its original value (0), but the power supply forces phase A to be 0, causing UN to change abruptly. Therefore, the initial condition should be UN(0+)=-Ea=-5774V, i L (0+) = 0 (inductor current is continuous). It then evolves according to the differential equation.

[0069] Solving using the fourth-order Runge-Kutta method with a step size h = 50 μs, the waveforms of UN(t) and iL(t) can be obtained. For example, in At that time, U N ≈-5774·e (-0.01 / 0.3) ·cos(2π·47.1·0.01)≈-5774·0.967·cos(2.96)≈-5774·0.967·(-0.984)≈5490V, which is close to the steady-state value of -5774V.

[0070] Model validation was performed by comparing with EMTP simulations. The same parameters were set: 10kV system, 5 feeders, c0 = 0.32μF / km, with two fault points at feeder 1 (4km) and feeder 4 (3.2km). EMTP used a distributed parameter line model, while this invention uses a lumped parameter model. The results are shown in Table 1:

[0071] Table 1: Comparison of the model of this invention and EMTP simulation results (steady-state zero-sequence current amplitude, unit: A)

[0072]

[0073] *Note: In the overcompensated case, Lp = 0.8H (XL = 251.3Ω) <Xc=272.3Ω),Rd=8Ω。

[0074] Transient waveform comparison shows that within 10ms after the fault, the correlation coefficient between the method of this invention and the zero-sequence voltage waveform of EMTP is >0.98, and the peak error is <2%, which meets the engineering accuracy requirements.

[0075] As a technical extension, the two-point grounding fault feature extraction method is implemented as follows: The zero-sequence current i0(t) is collected for the first 5 cycles (100ms) after the fault. A Discrete Fourier Transform (DFT) is performed on it, with a sampling frequency fs = 10kHz and a sampling point count N = 1000. The amplitudes I1, I3, and I5 of the fundamental (50Hz), third harmonic (150Hz), and fifth harmonic (250Hz) components are extracted. The third harmonic content THD3 is calculated as I3 / I1. In single-point faults, THD3 is typically less than 5%; however, in two-point faults, due to uneven distribution of circulating current and capacitance between the two fault points, THD3 can reach 15%~25%. A criterion is set: if I1 > 10A and THD3 > 12%, it is determined to be a two-point grounding fault. This criterion successfully identified 3 two-point faults in the historical fault playback of a 35kV cable-overhead hybrid network, with a false alarm rate of <1%.

[0076] Engineering Application Example: A provincial power grid 35kV system contains 12 feeders with a total length of 180km and c0=0.28μF / km. The model of this invention was deployed on an RTDS platform to simulate two-point grounding of phase A of feeder 3 (at 12km) and feeder 7 (at 8km). Waveform data showed: zero-sequence voltage amplitude 5820V, fundamental zero-sequence current 22.5A, THD3=18.7%. The model output of this invention was: U0=5790V, I0=22.1A, THD3=18.2%, with errors all <1.5%, accurately reproducing the field characteristics.

[0077] In summary, this invention achieves a high-precision mathematical description of two-point grounding faults in neutral-point-ineffectively-grounded systems through rigorous circuit topology reconstruction, establishment of multivariate functional equations, and state-space transient modeling. The model encompasses both steady-state analytical solutions and transient numerical solutions, supports integration with platforms such as RTDS, and provides a reliable basis for distribution network protection and fault diagnosis.

[0078] The above embodiments are merely one of the preferred embodiments of the present invention and should not be used to limit the scope of protection of the present invention. Any modifications or refinements made to the main design concept and spirit of the present invention that are not of substantial significance, but solve the same technical problem as the present invention, should be included within the scope of protection of the present invention.

Claims

1. A two-point grounding fault model analysis method under a neutral point non-effective grounding mode, characterized in that, The method comprises the following steps: S1, a basic electrical quantity analytical model under single-point single-phase grounding fault is established for a neutral point ungrounded system and an arc-suppression coil grounded system respectively; S2, a second grounding point is introduced on the basis of the basic electrical quantity analytical model, the fault network topology structure is reconstructed, and an electrical distance parameter between the two fault points and its relationship with the system ground capacitance distribution are defined; wherein the specific steps of reconstructing the fault network topology structure are: Two fault points are regarded as independent grounding points, the connection between the neutral point of the original system and the ground is cut off, or the arc suppression coil branch is retained, and the grounding boundary conditions are applied at the two fault points respectively; a new multi-port network is formed, in which the two fault points are external excitation ports and the remaining nodes maintain the original electrical connection; the node voltage method is used to establish a linear equation system with bus zero sequence voltage , upstream voltage of fault point 1 , upstream voltage of fault point 2 as unknown quantities; S3, based on Kirchhoff's voltage law and current law, combined with the node admittance matrix method, a multi-variable function equation set is established, which contains two fault point position variables, system ground capacitance parameters, arc-suppression coil inductance value and power source electromotive force initial phase angle; wherein the physical constraint conditions of the multi-variable function equation set include: The A-phase voltage at the two fault points is zero; The current flowing into any fault point is equal to the sum of the ground capacitance current of the line segment connected to the fault point and the adjacent section conduction current; Neutral point voltage U N satisfies N ; For arc-suppression coil grounded system, the neutral point current ; wherein, is the damping resistance matched with the arc-suppression coil; L is the lumped parameter inductance value, and j represents the imaginary unit in AC circuit analysis; is the system angular frequency; The system power supply side maintains constant phase electromotive force Ea, Eb, Ec, and Eb = Ea e (-j2π / 3) , Ec = Ea e (j2π / 3) ; S4, solving the multi-variable function equation set to obtain explicit analytic expressions of zero sequence voltage, zero sequence current, and phase voltage and phase current at each key node, and to analyze time-space evolution law of fault characteristic quantities under two-point grounding fault according to the analytic expressions; wherein the analytic expression of the zero sequence voltage is obtained by the following steps: The system is decomposed into three symmetrical component networks of positive sequence, negative sequence and zero sequence; In the zero sequence network, two fault points are equivalent to two parallel connection points, whose equivalent ground admittance are and respectively, where represents the sum of ground capacitance of other feeders upstream of fault point 1, represents the sum of ground capacitance of other feeders upstream of fault point 2; represents the ground capacitance of feeder before point ; represents the ground capacitance of feeder before point ; represents the ground capacitance of feeder before point ; represents the position of simultaneous ground faults on two different feeders; is located on feeder away from busbar , is located on feeder away from busbar , and or ; the total admittance of the zero sequence network , where is the neutral point branch admittance, =0 or ; the zero sequence voltage =-Ea / (1+Zs·Y0), where Zs is the equivalent zero sequence impedance of the system.

2. The method of claim 1, wherein, The single-point single-phase grounding fault model construction process of the neutral point ungrounded system includes: arranging the distribution network to be composed of N feeders, each feeder i having an equivalent capacitance C i to ground ; when a single-point grounding fault occurs at a point on the feeder k, the voltage of the fault point to ground is zero, the voltages of the remaining two phases to ground are raised to the line voltage level, the zero sequence voltage is equal to the negative value of the A-phase voltage before the fault; the current I f flowing through the fault point is only composed of the system capacitance current to ground, and the amplitude is 3ω· ·E ph , where ω is the system angular frequency, E ph is the effective value of the phase electromotive force; the directions of the zero sequence currents at the heads of the intact feeders are consistent and point to the bus, while the direction of the zero sequence current at the head of the fault feeder is opposite, and the size is equal to the sum of the zero sequence currents of all the remaining feeders.

3. The method of claim 2, wherein, In the process of constructing the single-point single-phase grounding fault model of the arc-suppression coil grounding system, the arc-suppression coil is equivalent to a lumped parameter inductance connected between the neutral point and the ground; when a single-point grounding fault occurs in phase A on the feeder m, the zero sequence loop is formed in parallel with the arc-suppression coil ; the fault point current I f = 3·(E ph / Z0), wherein Z0 is the zero sequence impedance, , R d is a damping resistance matched with the arc-suppression coil; L is a lumped parameter inductance value, and j represents an imaginary unit in the analysis of an alternating current circuit.

4. The method according to claim 3, wherein In constructing the two-point grounding fault model, it is assumed that the same phase simultaneously occurs grounding fault at positions and on two different feeders, respectively, where is located on feeder away from bus , is located on feeder away from bus , and or ; defining the unit length of the feeder to ground capacitance as , then the feeder ground capacitance before point is , and the part after is , where is the full length of feeder ; similarly, the feeder ground capacitance before point and after point is defined as ; the whole system is divided into three areas: area I contains all line sections from the bus to the two fault points, area II contains the downstream sections of the feeder where the two fault points are located, and area III is the remaining feeder section that is not directly affected.

5. The method of claim 4, wherein, In the step S4, the extraction method of fault characteristic quantity under two-point grounding fault is: The zero sequence current waveform within the first 5 cycles after the fault is collected; Discrete Fourier transform is performed thereon to extract the fundamental wave, third harmonic and fifth harmonic components; the amplitude ratio and phase difference of each harmonic component are calculated; If the amplitude of the fundamental wave zero sequence current exceeds the set threshold value and the third harmonic content is significantly higher than the typical value of single-point fault, it is determined as two-point grounding fault.

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