A method for staged modeling and superposition of early cable faults

Abstract

This invention discloses a method for phased modeling and superposition of early cable faults, belonging to the field of power system fault modeling technology. The method obtains system parameters and fault parameters of the high-voltage cable joint in an ungrounded system; based on these parameters, it establishes a fault current model for the interface flashover stage; based on these parameters, it establishes a fault current model for the sustained arcing stage; when the fault condition involves the coupling of the interface flashover stage and the sustained arcing stage, the fault current of the interface flashover stage is superimposed with the fault current of the sustained arcing stage to obtain a complete early fault current model. This invention significantly improves the accuracy of early cable fault modeling and the ability to simulate long-term faults.

Description

Technical Field

[0001] This invention relates to the field of power system fault modeling technology, and in particular to a method for phased modeling and superposition of early cable faults. Background Technology

[0002] In power distribution networks, medium-voltage cable joints are weak links in the cable insulation system. Environmental moisture can easily penetrate the composite insulation interface at the joint, leading to gradual discharge degradation. As moisture continues to penetrate, the insulation performance of the joint interface continues to decline. The discharge and carbonization processes repeat in cycles, and carbonized particles accumulate, eventually triggering intermittent, recoverable arc faults, i.e., early fault processes. Accurate modeling and analysis of early faults are of great significance for improving the reliability and safety of power distribution network operation.

[0003] Currently, various methods for modeling early cable faults and analyzing arc faults have been studied both domestically and internationally. Most existing studies treat the transition resistance at the fault point as a fixed resistance or model it based on a pure steady-state arc model, while giving little consideration to the carbonization accumulation effect caused by discharge, and failing to consider the differences in equivalent series impedance at different development stages of early faults.

[0004] Therefore, there is an urgent need in this field for a method for phased modeling and superposition of early cable faults. Summary of the Invention

[0005] In view of this, the present invention provides a method for staged modeling and superposition of early cable faults to solve the problem that the existing technology does not take into account the carbonization accumulation effect caused by discharge, and does not consider the difference in equivalent series impedance at different development stages of early faults.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: On one hand, the present invention provides a method for staged modeling and superposition of early cable faults, including: S1: Obtain the system parameters and fault parameters of the low-voltage cable joint in the ungrounded system. The system parameters include the three-phase ground equivalent parallel capacitance, the line equivalent resistance, and the line equivalent inductance. The fault parameters include the joint air gap equivalent capacitance, the arc resistance, and the additional series resistance considering the carbonization accumulation effect of the discharge channel. S2: Based on the system parameters and the fault parameters, establish a fault current model for the interface flashover stage. In the interface flashover stage, the fault part is equivalent to the equivalent capacitance of the joint air gap. The instantaneous breakdown process is simulated by a discharge switch. The focus is on the transient fluctuations caused by energy exchange between the three-phase ground equivalent parallel capacitance and the equivalent capacitance of the joint air gap. The forced response of the voltage source is ignored. A second-order homogeneous differential equation is established to solve the fault current for the interface flashover stage. S3: Based on the system parameters and the fault parameters, establish a fault current model for the continuous arc stage. In the continuous arc stage, the fault part is equivalent to the series combination of the arc resistance and the additional series resistance. The arc resistance adopts the Mayr arc model. The additional series resistance decreases exponentially with the development of the arc. Establish a first-order linear non-homogeneous differential equation to solve the fault current for the continuous arc stage. S4: When the fault condition involves the coupling of the interface flashover stage and the continuous arc stage, the fault current of the interface flashover stage is superimposed with the fault current of the continuous arc stage to obtain a complete early fault current model.

[0007] Preferably, the fault current model for the interface flashover stage in step S2 is established as follows: S21: Based on the short duration of the discharge during the interface flashover phase, the characteristic equation and characteristic roots of the second-order homogeneous differential equation are established, and their expressions are as follows:

[0008]

[0009] in, These are characteristic roots. The equivalent inductance of the line is... Let be the equivalent resistance of the circuit. The equivalent capacitance of the air gap of the connector is given. The attenuation coefficient is... It is the natural angular frequency; S22: The attenuation coefficient and the natural angular frequency satisfy the following relationship:

[0010]

[0011] in, The attenuation coefficient is... Let be the equivalent resistance of the circuit. The equivalent inductance of the line is... The natural angular frequency, The equivalent capacitance of the air gap of the connector; S23: Under underdamped conditions, the fault current during the interface flashover stage is:

[0012] in, This refers to the fault current during the interface flashover phase. Let be the voltage value of the three-phase ground equivalent parallel capacitor at the moment of breakdown. The equivalent inductance of the line is... The oscillation angular frequency under underdamped conditions. Let t be the attenuation coefficient, and t be time.

[0013] Preferably, the amplitude of the fault current during the interface flashover stage is determined by the voltage value at the time of breakdown, the attenuation rate is determined by the attenuation coefficient, and the oscillation frequency is jointly determined by the natural angular frequency and the joint air gap state reflected by the equivalent capacitance of the joint air gap.

[0014] Preferably, the fault current model for the continuous arcing stage in step S3 is established as follows: S31: The arc resistance adopts the Mayr arc model and satisfies the following relationship:

[0015] in, The arc resistance is given by t, where t is time. The Mayr arc time constant is... This refers to the fault current during the sustained arcing phase. Power dissipation; S32: The additional series resistance decreases exponentially with the development of the arc, and has two characteristic parameters: an initial value and a stable value, satisfying the following relationship:

[0016] in, For the additional series resistor, The initial value of the additional series resistor is... The stable value of the additional series resistance. Here, t is the decay time constant; S33: Based on Kirchhoff's voltage law, establish a first-order linear non-homogeneous differential equation containing the arc resistance and the additional series resistance, and solve it to obtain the fault current during the continuous arcing stage:

[0017] in, This refers to the fault current during the sustained arcing phase. The phase voltage amplitude of the system. The sum of the loop resistances. Let L be the angular frequency, and L be the equivalent inductance of the line. Let K be the initial phase angle of the fault, and K be the integration constant.

[0018] Preferably, the fault current during the continuous arc phase is composed of the superposition of the quasi-steady-state response generated by the first voltage source excitation and the transient component generated by the dynamic change of the second nonlinear resistance.

[0019] Preferably, the fault current in the interface flashover stage and the fault current in the continuous arc stage are independent current expressions, which are independently invoked or superimposed according to the fault stage during the early fault development process to simulate the fault conditions at different fault development stages.

[0020] On the other hand, the present invention provides a device for phased modeling and overlay of early cable faults, the device comprising: The acquisition module is used to acquire system parameters and fault parameters of the low-voltage cable joint in an ungrounded system. The system parameters include the three-phase ground equivalent parallel capacitance, the line equivalent resistance, and the line equivalent inductance. The fault parameters include the joint air gap equivalent capacitance, the arc resistance, and the additional series resistance considering the carbonization accumulation effect of the discharge channel. The first module is used to establish a fault current model for the interface flashover stage based on the system parameters and the fault parameters. In the interface flashover stage, the fault part is equivalent to the equivalent capacitance of the joint air gap. The instantaneous breakdown process is simulated by a discharge switch. The focus is on the transient fluctuations caused by the energy exchange between the three-phase ground equivalent parallel capacitance and the equivalent capacitance of the joint air gap. The forced response of the voltage source is ignored. A second-order homogeneous differential equation is established to solve the fault current for the interface flashover stage. The second module is used to establish a fault current model for the continuous arc stage based on the system parameters and the fault parameters. In the continuous arc stage, the fault part is equivalent to the series combination of the arc resistance and the additional series resistance. The arc resistance adopts the Mayr arc model. The additional series resistance decreases exponentially with the development of the arc. A first-order linear non-homogeneous differential equation is established to solve the fault current for the continuous arc stage. The superposition module is used to superimpose the fault current of the interface flashover stage and the fault current of the continuous arc stage when the fault condition involves the coupling of the interface flashover stage and the continuous arc stage, so as to obtain a complete early fault current model.

[0021] On the other hand, the present invention provides a computer device including a memory and a processor, the memory being used to store a computer program, and the processor being used to execute the computer program stored in the memory to implement the steps of any of the methods described in the specification.

[0022] On the other hand, the present invention provides a readable storage medium storing a computer program that, when executed by a processor, implements the steps of any of the methods described in the specification.

[0023] On the other hand, the present invention provides a computer program product, characterized in that it includes a computer program, which, when executed by a processor, implements the steps of any of the methods described in this specification.

[0024] This invention provides a method for phased modeling and superposition of early cable faults. The method first obtains the system parameters and fault parameters of the substation in an ungrounded medium-voltage cable system. The early faults at the joint are then modeled independently as an interface flashover stage and a sustained arc stage based on their physical characteristics. In the interface flashover stage, the fault portion is equivalent to the equivalent capacitance of the joint air gap. A second-order homogeneous differential equation is established, focusing on the transient fluctuations caused by energy exchange between the three-phase-to-ground equivalent parallel capacitance and the equivalent capacitance of the joint air gap. The forced response of the voltage source is ignored. The fault current in the interface flashover stage is then solved. The amplitude of the fault current is determined by the voltage value at the time of breakdown, the decay rate is determined by the line parameters, and the oscillation frequency is determined by the line parameters. The parameters and the air gap state of the joint jointly determine the fault. During the continuous arc stage, the fault part is equivalent to a series combination of arc resistance and additional series resistance. The arc resistance adopts the Mayr arc model. The additional series resistance decays exponentially with the development of the arc and has two characteristic parameters: initial value and stable value. A first-order linear non-homogeneous differential equation is established and solved to obtain the fault current during the continuous arc stage. The fault current is composed of the superposition of the quasi-steady-state response generated by the voltage source excitation and the transient component generated by the dynamic change of nonlinear resistance. Finally, when the fault condition involves the coupling of the interface flashover stage and the continuous arc stage, the fault currents of the two stages are superimposed to obtain a complete early fault current model. This invention constructs an early fault modeling mechanism that features "independent modeling of interface flashover-continuous arc in stages and controllable superposition of independent current expressions." This mechanism alleviates the shortcomings of existing technologies, such as the failure to divide development stages according to physical characteristics in single fault models, the failure to consider the key influence of air gap capacitance on transient current during interface flashover, and the failure to combine the Mayr arc model with a two-parameter additional series resistance to account for carbonization accumulation effects. This significantly improves the accuracy of early fault modeling and the ability to simulate long-term faults in ungrounded medium-voltage cables. Attached Figure Description

[0025] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0026] Figure 1 A flowchart of a method for phased modeling and superposition of early cable faults provided in an embodiment of the present invention; Figure 2This is a schematic diagram of an early fault equivalent model provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the fault current and connector capacitor voltage waveforms under a simulation model provided in an embodiment of the present invention. Figure 4 This is a schematic diagram of the fault current and connector resistance voltage waveforms under a simulation model provided in an embodiment of the present invention. Figure 5 This is a hardware architecture diagram of a computer device provided in an embodiment of the present invention; Figure 6 This is a structural diagram of a cable early fault staged modeling and superposition device provided in an embodiment of the present invention. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0028] The embodiments of the present invention are described below with reference to the figures.

[0029] like Figure 1 As shown, this invention provides a method for phased modeling and superposition of early cable faults, including: S1: Obtain the system parameters and fault parameters of the low-voltage cable joint in the ungrounded system. The system parameters include the three-phase ground equivalent parallel capacitance, the line equivalent resistance, and the line equivalent inductance. The fault parameters include the joint air gap equivalent capacitance, the arc resistance, and the additional series resistance considering the cumulative carbonization effect of the discharge channel.

[0030] In this invention, step S1 aims to determine the basic electrical parameters required for early fault modeling of cable joints, providing parameter input for the establishment of the fault current model in the interface flashover stage in step S2 and the fault current model in the continuous arc stage in step S3.

[0031] like Figure 2 As shown in (a), the discharge current loop during the early fault of the cable joint under water vapor intrusion is shown. In an ungrounded system, when the fault occurs, the three-phase ground capacitance discharges to the fault joint respectively. The breakdown channel can be regarded as the air gap and carbonization channel connected in series. To simplify the circuit analysis, the three-phase ground capacitance is equivalent to a parallel capacitor, which is denoted as the three-phase ground equivalent parallel capacitor.

[0032] During the interface flashover fault stage, the degree of carbide accumulation is relatively low. Therefore, the faulty part is mainly the air gap filled with water vapor, which can be equivalently represented as a capacitor, denoted as the equivalent capacitance of the joint air gap, such as... Figure 2 As shown in (b), the instantaneous discharge process is simulated by switch S, and the line equivalent resistance and line equivalent inductance are used to represent the resistive and inductive components of the cable line.

[0033] The equivalent circuit for the continuous arcing fault stage is as follows: Figure 2 As shown in (c), the fault portion is equivalent to a series combination of arc resistance and additional series resistance. The additional series resistance is an additional series resistance that takes into account the cumulative effect of carbonization in the discharge channel. Its resistance value is a dynamic parameter that changes with the stage of fault development and is affected by multiple factors such as the degree of carbonization channel development, interface temperature and humidity, and material thermal aging rate.

[0034] Figure 2 The fault model shown can characterize the dynamic development characteristics of early fault stages in cable joints. Its evolution law is determined by a combination of factors such as joint air gap state, arc combustion state, degree of carbonization accumulation at insulation interface, and system parameters. At the same time, since the models of the two stages are independent current expressions, they can be superimposed during the early fault development process to simulate a more complete and complex long-term fault condition.

[0035] The specific physical meanings and determination methods of each parameter are as follows: The three-phase ground equivalent parallel capacitance is the equivalent lumped parameter of the three-phase ground distributed capacitance of the low-voltage cable system in an ungrounded system. In an ungrounded system, when a single-phase ground fault occurs at a cable joint, the ground capacitance of the non-faulty phase forms a discharge circuit through the fault point. The three-phase ground capacitances are connected in parallel in the circuit, so they can be equivalent to a parallel capacitor connected to the fault circuit.

[0036] The equivalent resistance and equivalent inductance of the line are lumped equivalent parameters of the cable line's own resistance and inductance, used to reflect the resistance and inductance characteristics of the cable line when fault current flows. These two parameters can be calculated based on the cable type, length, and electrical parameters per unit length.

[0037] The equivalent capacitance of the joint air gap is the equivalent capacitance of the air gap in the faulty section during the interface flashover stage. In the early stage of water vapor intrusion, the accumulation of carbides is low, and the fault channel is mainly composed of water vapor medium. The electrical characteristics are mainly capacitive. Therefore, the fault section is equivalent to a capacitor, and its capacitance value is determined by the air gap geometry and the water vapor dielectric constant.

[0038] The arc resistance is the equivalent resistance during the continuous arc phase. For the arc resistance, the Mayr arc model is used for basic fitting. Due to the large range of actual arc duration (from several milliseconds to several cycles) and significant differences in combustion intensity in cable joints under water vapor intrusion environment, as well as the high amplitude transient impact that is prone to occur at the moment of arc ignition and arc extinction, it is necessary to comprehensively consider complex factors such as arc discharge energy and dielectric recovery process to achieve accurate modeling. The specific modeling of the arc resistance will be elaborated in step S3.

[0039] The additional series resistance is a dynamic parameter whose resistance varies with the stage of fault development. During the arc discharge fault stage, the additional series resistance drops significantly to several kΩ to several hundred kΩ, and continues to decrease with the discharge, possibly experiencing brief fluctuations of several kΩ due to the instantaneous energy release caused by high-amplitude discharge. When the fault develops into a permanent ground fault, the resistance of the fault junction becomes the additional series resistance, which can drop to several Ω to several hundred Ω. The carbonized channel penetrates both electrodes, and the fault exhibits metallic grounding characteristics. Based on these changing characteristics, the additional series resistance decays exponentially with the development of the arc. Its specific modeling will be detailed in step S3. S2: Based on the system parameters and the fault parameters, establish a fault current model for the interface flashover stage. In the interface flashover stage, the fault portion is equivalent to the equivalent capacitance of the joint air gap. The instantaneous breakdown process is simulated by a discharge switch. The focus is on the transient fluctuations caused by energy exchange between the three-phase ground equivalent parallel capacitance and the equivalent capacitance of the joint air gap. The forced response of the voltage source is ignored. A second-order homogeneous differential equation is established to solve for the fault current in the interface flashover stage.

[0040] In this invention, step S2 aims to establish a fault current model that matches the physical characteristics of the first stage of early cable joint faults after moisture intrusion—the interface flashover stage. During the interface flashover stage, carbide accumulation is low, the fault portion is mainly a moisture-filled air gap, and the electrical characteristics are primarily capacitive. The discharge duration is extremely short, therefore, it is crucial to focus on the transient fluctuations caused by energy exchange between capacitors. This stage model provides the initial fault state for establishing the sustained arc stage model in step S3, and together with the superposition of the two-stage models in step S4, constitutes a complete early fault current model.

[0041] In some implementations, the fault current model for the interface flashover stage described in step S2 is established as follows: S21: Based on the short duration of the discharge during the interface flashover phase, the characteristic equation and characteristic roots of the second-order homogeneous differential equation are established, and their expressions are as follows:

[0042]

[0043] in, These are characteristic roots. The equivalent inductance of the line is... Let be the equivalent resistance of the circuit. The equivalent capacitance of the air gap of the connector is given. The attenuation coefficient is... It is the natural angular frequency.

[0044] In this invention, when the insulation performance of the joint deteriorates to the critical breakdown voltage after moisture intrusion, switch S closes, and the early fault enters the interface flashover stage. Let the voltage of the three-phase-to-ground equivalent parallel capacitor at this time be , the voltage of the equivalent capacitance of the joint air gap be , the power supply voltage be , and the circuit fault current be . Due to the non-mutable nature of the inductor current and capacitor voltage, the initial fault conditions are:

[0045] in, The initial loop fault current. The voltage is the equivalent capacitance of the air gap at the initial moment. The initial power supply voltage. The voltage of the three-phase-to-ground equivalent parallel capacitor at the initial moment is given. Let be the voltage value of the three-phase ground equivalent parallel capacitor at the moment of breakdown. The phase voltage amplitude of the system. Angular frequency, This is the initial phase angle of the fault.

[0046] According to Kirchhoff's voltage law, the voltages between parallel nodes are equal, therefore:

[0047] in, The voltage of the three-phase-to-ground equivalent parallel capacitor is given. Let be the equivalent resistance of the circuit. This refers to the fault current during the interface flashover phase. The equivalent inductance of the line is... The equivalent capacitance of the air gap of the connector is given.

[0048] Taking the derivative of the above formula, the second-order differential equation of the fault model is obtained as follows:

[0049] in, Let be the equivalent resistance of the circuit. This refers to the fault current during the interface flashover phase. Let be the equivalent resistance of the circuit. The equivalent capacitance of the air gap of the connector is given. The phase voltage amplitude of the system. Angular frequency, The initial phase angle of the fault. For time.

[0050] According to prior research based on the present invention, the duration of interface flashover discharge is extremely short (typically on the order of milliseconds). Therefore, during the short conduction time, the forced response caused by the voltage source is negligible. The focus should be on the transient fluctuations caused by energy exchange between the three-phase ground equivalent parallel capacitance and the junction air gap equivalent capacitance. Therefore, by obtaining the solution to the homogeneous equation corresponding to the above second-order differential equation, the expression for the characteristic equation and characteristic roots as described in step S21 can be obtained.

[0051] S22: The attenuation coefficient and the natural angular frequency satisfy the following relationship:

[0052]

[0053] in, The attenuation coefficient is... Let be the equivalent resistance of the circuit. The equivalent inductance of the line is... The natural angular frequency, The equivalent capacitance of the air gap of the connector is given.

[0054] From the above relationships, it can be seen that the decay rate of the fault current during the interface flashover stage is jointly determined by the equivalent resistance and equivalent inductance of the line, while the inherent oscillation frequency is jointly determined by the equivalent inductance of the line and the equivalent capacitance of the joint air gap. When the state of the joint air gap changes (such as a decrease in air gap size or an increase in the water vapor dielectric constant), it leads to... When the value increases, the inherent oscillation frequency decreases accordingly.

[0055] S23: Under underdamped conditions, the fault current during the interface flashover stage is:

[0056] in, This refers to the fault current during the interface flashover phase. Let be the voltage value of the three-phase ground equivalent parallel capacitor at the moment of breakdown. The equivalent inductance of the line is... The oscillation angular frequency under underdamped conditions. Let t be the attenuation coefficient, and t be time.

[0057] In this invention, the oscillation angular frequency satisfies It is determined by the natural angular frequency and the attenuation coefficient.

[0058] As can be seen from the above formula, the amplitude of the fault current during the interface flashover stage is mainly affected by the voltage value at the time of breakdown, the attenuation rate is determined by the line parameters (i.e., the attenuation coefficient), and the oscillation frequency is affected by the line parameters and the joint air gap state (reflected by the equivalent capacitance of the joint air gap).

[0059] like Figure 3 As shown, it can be seen that the capacitor has a residual voltage after the discharge is completed. This means that when the capacitor undergoes another flashover breakdown, the corresponding initial conditions will change. If the capacitor carries a reverse residual voltage, it may cause a larger current surge, leading to further development of the fault.

[0060] Through the implementation of step S2 above, the present invention establishes a fault current model for the interface flashover stage, which fully considers the characteristics of the joint air gap capacitance and the transient fluctuations caused by energy exchange between capacitors. It provides the initial fault state for the establishment of the continuous arc stage model in step S3, and also provides an independent current expression for the interface flashover stage for the superposition of the two-stage models in step S4.

[0061] S3: Based on the system parameters and the fault parameters, establish a fault current model for the continuous arc stage. In the continuous arc stage, the fault part is equivalent to a series combination of the arc resistance and the additional series resistance. The arc resistance adopts the Mayr arc model. The additional series resistance decreases exponentially with the development of the arc. Establish a first-order linear non-homogeneous differential equation to solve the fault current for the continuous arc stage.

[0062] In this invention, step S3 aims to establish a fault current model that matches the physical characteristics of the second stage of early faults in cable joints after moisture intrusion—the continuous arcing stage. During the continuous arcing stage, with repeated interface flashovers, carbides gradually accumulate at the insulation interface, further deteriorating the insulation state at the joint, and the fault evolves from intermittent flashovers to continuous arcing. The fault model for this stage is a series combination of arc resistance and an additional series resistance, where the additional series resistance takes into account the carbonization accumulation effect of the discharge channel. This stage model, together with the interface flashover stage model established in step S2, constitutes a complete early fault current model, providing an independent current expression for the continuous arcing stage for the superposition of the two stage models in step S4.

[0063] In some implementations, the fault current model for the continuous arcing phase in step S3 is established as follows: S31: The arc resistance adopts the Mayr arc model and satisfies the following relationship:

[0064] in, The arc resistance is given by t, where t is time. The Mayr arc time constant is... This refers to the fault current during the sustained arcing phase. This represents power dissipation.

[0065] For the arc resistance, traditional methods such as the Mayr and Cassie models can achieve basic fitting. However, due to the large range of arc duration (from milliseconds to several cycles) and significant differences in combustion intensity in cable joints under moisture intrusion environments, as well as the susceptibility to high-amplitude transient impacts during arc ignition and extinguishing, accurate modeling requires comprehensive consideration of complex factors such as arc discharge energy and dielectric recovery processes. The Mayr arc model, based on the principle of thermal equilibrium, describes the dynamic change of arc resistance with arc current and dissipated power. When the heat generated by the arc current exceeds the dissipated power, the arc resistance decreases, and arc combustion intensifies; conversely, when the heat generated by the arc current is less than the dissipated power, the arc resistance increases, and the arc tends to extinguish. This model can effectively reflect the nonlinear time-varying characteristics of the arc during combustion and extinguishing processes.

[0066] S32: The additional series resistance decreases exponentially with the development of the arc, and has two characteristic parameters: an initial value and a stable value, satisfying the following relationship:

[0067] in, For the additional series resistor, The initial value of the additional series resistor is... The stable value of the additional series resistance. Let t be the decay time constant, and t be time.

[0068] In this invention, the additional series resistance is a dynamic parameter that varies with the stage of fault development. It is influenced by multiple factors, including the degree of carbonization channel development, interface temperature and humidity, and the rate of material thermal aging, making precise quantification difficult. Currently, only a rough range of resistance values ​​can be given through statistical analysis of experimental data. The resistance level of good insulation is in the MΩ range. During the arc discharge fault stage, the additional series resistance drops significantly to several kΩ to hundreds of kΩ, and continues to decrease with discharge, possibly experiencing brief fluctuations of several kΩ due to the instantaneous energy release caused by high-amplitude discharge. When the fault develops to permanent grounding, the resistance of the fault junction becomes the additional series resistance value, which can drop to several Ω to hundreds of Ω. The carbonization channel penetrates both electrodes, and the fault exhibits metallic grounding characteristics.

[0069] Based on the aforementioned characteristics and range of change, the additional series resistance is set to decay exponentially with the arc, possessing two characteristic parameters: an initial value and a stable value. This two-parameter exponential decay model can reflect the physical process of the carbonized channel gradually transitioning from an initial high-resistance state to a stable low-resistance state. The initial value reflects the insulation state before the fault, the stable value reflects the residual resistance after the carbonized channel is fully formed, and the decay time constant reflects the rate of carbonization accumulation. As the fault develops, the additional series resistance gradually decays from the initial value to the stable value, causing the fault current amplitude to increase under the decay effect, accurately reflecting the impact of carbonization accumulation on fault development.

[0070] S33: Based on Kirchhoff's voltage law, establish a first-order linear non-homogeneous differential equation containing the arc resistance and the additional series resistance, and solve it to obtain the fault current during the continuous arcing stage:

[0071] in, This refers to the fault current during the sustained arcing phase. The phase voltage amplitude of the system. The sum of the loop resistances. Let L be the angular frequency, and L be the equivalent inductance of the line. Let K be the initial phase angle of the fault, and K be the integration constant.

[0072] In a preferred embodiment, after the fault enters the arc discharge stage, the circuit fault current is: The initial conditions of its circuit are:

[0073] in, This is the power supply voltage. The phase voltage amplitude of the system. Angular frequency, The initial phase angle of the fault. The voltage of the three-phase-to-ground equivalent parallel capacitor at the initial moment is given. The fault current at the initial moment. The current flowing through the equivalent inductance of the line at the initial moment is denoted as .

[0074] According to Kirchhoff's voltage law, the loop voltage equation satisfies:

[0075] in, The equivalent inductance of the line is... This refers to the fault current during the sustained arcing phase. The arc resistance, For the additional series resistor, Let be the equivalent resistance of the circuit. The phase voltage amplitude of the system. Angular frequency, The initial phase angle of the fault. For time.

[0076] As can be seen from the above loop voltage equation, the equivalent circuit during the sustained arc stage is a first-order linear nonhomogeneous differential equation, where the time-varying coefficients are jointly determined by the nonlinear dynamic changes of the arc resistance and the additional series resistance. By solving this first-order linear nonhomogeneous differential equation, the expression for the fault current during the sustained arc stage in this step is obtained.

[0077] In a preferred embodiment, the fault current during the continuous arc phase is composed of the superposition of the quasi-steady-state response generated by the first voltage source excitation and the transient component generated by the dynamic change of the second nonlinear resistance. The quasi-steady-state response reflects the continuous sinusoidal component of the fault current driven by the power frequency power supply, and the transient component reflects the modulation effect of the arc resistance and the additional series resistance on the fault current over time.

[0078] The model was calculated using a numerical iterative method, and the system parameters were kept consistent with those during the interface flashover stage. The table below shows the relevant fitting parameters for the fault resistance.

[0079] To avoid an excessively high arc resistance decay rate and a mismatch between the decay rate of the additional resistor in the early stages of simulation, the power dissipation is set to a dynamic value that gradually increases between 0.3 and 1.5 kW.

[0080] like Figure 4 As shown, the fault current amplitude increases under the attenuation effect of the additional resistor. Meanwhile, the arc burns in two time periods, 0.34-0.51s and 0.65-0.8s, causing the fault current to be distorted. The voltage across the additional resistor drops significantly during the arcing period, which is consistent with the physical model of carbide accumulation and arc series voltage division.

[0081] Through the implementation of step S3 above, the present invention establishes a fault current model for the continuous arc stage, uses the Mayr arc model to describe the nonlinear time-varying characteristics of the arc resistance, and uses a two-parameter exponential decay model with initial and stable values ​​to describe the carbonization accumulation effect of the additional series resistance, thus providing an independent current expression for the continuous arc stage for the superposition of the two-stage models in step S4.

[0082] S4: When the fault condition involves the coupling of the interface flashover stage and the continuous arc stage, the fault current of the interface flashover stage is superimposed with the fault current of the continuous arc stage to obtain a complete early fault current model.

[0083] In this invention, step S4 aims to use the interface flashover stage fault current model established in step S2 and the continuous arc stage fault current model established in step S3 to simulate the complete development process of early faults in cable joints through the superposition mechanism of two independent current expressions.

[0084] In a preferred embodiment, the fault current during the interface flashover stage and the fault current during the continuous arc stage are independent current expressions. They are independently invoked or superimposed according to the fault stage during the early fault development process to simulate fault conditions at different fault development stages.

[0085] The superposition of the two-stage models in step S4 is based on the following physical characteristics and modeling mechanisms: First, in the early stages of fault development, when the joint insulation performance deteriorates to the critical breakdown voltage, it enters the interface flashover stage. At this time, the fault current is described by the fault current expression for the interface flashover stage established in step S2. With repeated interface flashovers, carbides gradually accumulate at the insulation interface, further deteriorating the insulation state at the joint. The fault develops from intermittent flashover to continuous arc discharge. At this time, the fault current is described by the fault current expression for the continuous arc discharge stage established in step S3.

[0086] Secondly, the fault current models for both stages are independent current expressions. The fault current in the interface flashover stage describes the transient oscillation process caused by energy exchange between capacitors, while the fault current in the sustained arcing stage describes the sustained arcing process, which includes quasi-steady-state response and transient components. Since the physical mechanisms and circuit topologies of the two stages are different, independent mathematical models have been established for each stage. Therefore, these models can be independently invoked or superimposed according to the actual fault development sequence.

[0087] Finally, in the actual early stages of fault development, interface flashover and persistent arcing may occur alternately or simultaneously. For example, when the carbonized channel is not yet fully formed, the fault may manifest as multiple interface flashovers followed by a brief persistent arcing; as the carbonized channel gradually stabilizes, the fault mainly manifests as persistent arcing, but interface flashover may occur again after the arc extinguishes. By superimposing the independent current expressions for the two stages, various complex long-term fault conditions described above can be flexibly simulated.

[0088] Specifically, the complete early fault current model can be expressed as follows: at any given time, the corresponding fault current expression is invoked according to the current stage of the fault; when the fault characteristics of two stages exist simultaneously, the fault currents of the two stages are superimposed. This superposition mechanism enables the model established by this invention to cover the complete fault evolution process from early interface flashover to continuous arc discharge and finally to permanent grounding.

[0089] In summary, the fault model proposed in this invention can characterize the dynamic development characteristics of early-stage faults in cable joints. Its evolution law is jointly determined by multiple factors such as the joint air gap state, arc combustion state, the degree of accumulation of carbides at the insulation interface, and system parameters. At the same time, since the models of the two stages are independent current expressions, they can be controlled and superimposed during the early-stage fault development process to simulate more complete and complex long-term fault conditions.

[0090] Through the implementation of step S4 above, the present invention utilizes the independent current expression established in steps S2 and S3 to simulate the complete development process of early faults in cable joints, providing accurate model support covering the entire life cycle of faults for distribution network fault detection, early warning and analysis.

[0091] like Figure 5 , Figure 6 As shown, this invention provides a device for phased modeling and overlaying of early cable faults. The device can be implemented in software, hardware, or a combination of both. From a hardware perspective, as... Figure 5 The diagram shown is a hardware architecture diagram of a computing device for a staged modeling and overlay device for early cable faults provided in an embodiment of the present invention. Figure 5 In addition to the processor, memory, network interface, and non-volatile memory shown, the computing device in the embodiment may also include other hardware, such as a forwarding chip responsible for processing packets. Taking software implementation as an example, such as... Figure 6 As shown, a device in a logical sense is formed by the CPU of the computing device in which it is located reading the corresponding computer program from the non-volatile memory into the memory for execution.

[0092] Reference Figure 6 This invention provides a device for phased modeling and overlaying of early cable faults, comprising: The acquisition module 100 is used to acquire system parameters and fault parameters of the low-voltage cable joint in an ungrounded system. The system parameters include the three-phase ground equivalent parallel capacitance, the line equivalent resistance, and the line equivalent inductance. The fault parameters include the joint air gap equivalent capacitance, the arc resistance, and the additional series resistance considering the carbonization accumulation effect of the discharge channel. The first establishment module 200 is used to establish a fault current model for the interface flashover stage based on the system parameters and the fault parameters. In the interface flashover stage, the fault part is equivalent to the equivalent capacitance of the joint air gap. The instantaneous breakdown process is simulated by a discharge switch. The focus is on the transient fluctuations caused by the energy exchange between the three-phase ground equivalent parallel capacitance and the equivalent capacitance of the joint air gap. The forced response of the voltage source is ignored. A second-order homogeneous differential equation is established to solve the fault current for the interface flashover stage. The second module 300 is used to establish a fault current model for the continuous arc stage based on the system parameters and the fault parameters. In the continuous arc stage, the fault part is equivalent to the series combination of the arc resistance and the additional series resistance. The arc resistance adopts the Mayr arc model. The additional series resistance decreases exponentially with the development of the arc. A first-order linear non-homogeneous differential equation is established to solve the fault current for the continuous arc stage. The superposition module 400 is used to superimpose the fault current of the interface flashover stage and the fault current of the continuous arc stage when the fault condition involves the coupling of the interface flashover stage and the continuous arc stage, so as to obtain a complete early fault current model.

[0093] It is understood that the structures illustrated in the embodiments of the present invention do not constitute a specific limitation on the integrated device for laser cleaning and microtexturing of metal alloy surfaces. In other embodiments of the present invention, the integrated device for laser cleaning and microtexturing of metal alloy surfaces may include more or fewer components than illustrated, or combine some components, or separate some components, or have different component arrangements. The illustrated components may be implemented in hardware, software, or a combination of software and hardware.

[0094] The information interaction and execution process between the modules in the above-mentioned device are based on the same concept as the method embodiment of the present invention, and the specific details can be found in the description of the method embodiment of the present invention, and will not be repeated here.

[0095] This invention also provides a computing device, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements the method in any embodiment of this invention.

[0096] This invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the method in any embodiment of this invention.

[0097] Embodiments of this application also provide a computer program product, which includes a computer program. A processor of a computer device reads the computer program from a computer-readable storage medium and executes the computer program, causing the computer device to perform any of the test methods described in the above embodiments.

[0098] Specifically, an apparatus equipped with a storage medium may be provided, on which software program code implementing the functions of any of the embodiments described above is stored, and the computer (or CPU or MPU) of the apparatus may read and execute the program code stored in the storage medium.

[0099] In this case, the program code read from the storage medium can itself implement the function of any of the above embodiments, and therefore the program code and the storage medium storing the program code constitute part of the present invention.

[0100] Storage media embodiments for providing program code include floppy disks, hard disks, magneto-optical disks, optical disks (such as CD-ROM, CD-R, CD-RW, DVD-ROM, DVD-RAM, DVD-RW, DVD+RW), magnetic tapes, non-volatile memory cards, and ROMs. Alternatively, program code can be downloaded from a server computer via a communication network.

[0101] Furthermore, it should be clear that not only can the program code read by the computer be executed, but also the operating system or other components operating on the computer can be instructed based on the program code to perform some or all of the actual operations, thereby realizing the function of any of the embodiments described above.

[0102] Furthermore, it is understood that the program code read from the storage medium is written to the memory set in the expansion board inserted into the computer or to the memory set in the expansion module connected to the computer. Then, based on the instructions of the program code, the CPU or other components installed on the expansion board or expansion module execute some and all of the actual operations, thereby realizing the function of any of the above embodiments.

[0103] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0104] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media that can store program code, such as ROM, RAM, magnetic disk, or optical disk.

[0105] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for phased modeling and superposition of early cable faults, characterized in that, include: S1: Obtain the system parameters and fault parameters of the low-voltage cable joint in the ungrounded system. The system parameters include the three-phase ground equivalent parallel capacitance, the line equivalent resistance, and the line equivalent inductance. The fault parameters include the joint air gap equivalent capacitance, the arc resistance, and the additional series resistance considering the carbonization accumulation effect of the discharge channel. S2: Based on the system parameters and the fault parameters, establish a fault current model for the interface flashover stage. In the interface flashover stage, the fault part is equivalent to the equivalent capacitance of the joint air gap. The instantaneous breakdown process is simulated by a discharge switch. The focus is on the transient fluctuations caused by energy exchange between the three-phase ground equivalent parallel capacitance and the equivalent capacitance of the joint air gap. The forced response of the voltage source is ignored. A second-order homogeneous differential equation is established to solve the fault current for the interface flashover stage. S3: Based on the system parameters and the fault parameters, establish a fault current model for the continuous arc stage. In the continuous arc stage, the fault part is equivalent to the series combination of the arc resistance and the additional series resistance. The arc resistance adopts the Mayr arc model. The additional series resistance decreases exponentially with the development of the arc. Establish a first-order linear non-homogeneous differential equation to solve the fault current for the continuous arc stage. S4: When the fault condition involves the coupling of the interface flashover stage and the continuous arc stage, the fault current of the interface flashover stage is superimposed with the fault current of the continuous arc stage to obtain a complete early fault current model.

2. The method according to claim 1, characterized in that, The fault current model for the interface flashover stage described in step S2 is established as follows: S21: Based on the short duration of the discharge during the interface flashover phase, the characteristic equation and characteristic roots of the second-order homogeneous differential equation are established, and their expressions are as follows: in, These are characteristic roots. The equivalent inductance of the line is... Let be the equivalent resistance of the circuit. The equivalent capacitance of the air gap of the connector is given. The attenuation coefficient is... It is the natural angular frequency; S22: The attenuation coefficient and the natural angular frequency satisfy the following relationship: in, The attenuation coefficient is... Let be the equivalent resistance of the circuit. The equivalent inductance of the line is... The natural angular frequency, The equivalent capacitance of the air gap of the connector; S23: Under underdamped conditions, the fault current during the interface flashover stage is: in, This refers to the fault current during the interface flashover phase. Let be the voltage value of the three-phase ground equivalent parallel capacitor at the moment of breakdown. The equivalent inductance of the line is... The oscillation angular frequency under underdamped conditions. Let t be the attenuation coefficient, and t be time.

3. The method according to claim 2, characterized in that, The amplitude of the fault current during the interface flashover stage is determined by the voltage value at the time of breakdown, the rate of decay is determined by the decay coefficient, and the oscillation frequency is jointly determined by the natural angular frequency and the joint air gap state reflected by the equivalent capacitance of the joint air gap.

4. The method according to claim 1, characterized in that, The fault current model for the continuous arcing stage described in step S3 is established as follows: S31: The arc resistance adopts the Mayr arc model and satisfies the following relationship: in, The arc resistance is given by t, where t is time. The Mayr arc time constant is... This refers to the fault current during the sustained arcing phase. Power dissipation; S32: The additional series resistance decreases exponentially with the development of the arc, and has two characteristic parameters: an initial value and a stable value, satisfying the following relationship: in, For the additional series resistor, The initial value of the additional series resistor is... The stable value of the additional series resistance. Here, t is the decay time constant; S33: Based on Kirchhoff's voltage law, establish a first-order linear non-homogeneous differential equation containing the arc resistance and the additional series resistance, and solve it to obtain the fault current during the continuous arcing stage: in, This refers to the fault current during the sustained arcing phase. The phase voltage amplitude of the system. The sum of the loop resistances. Let L be the angular frequency, and L be the equivalent inductance of the line. Let K be the initial phase angle of the fault, and K be the integration constant.

5. The method according to claim 4, characterized in that, The fault current during the continuous arc phase is composed of the superposition of the quasi-steady-state response generated by the first voltage source excitation and the transient component generated by the dynamic change of the second nonlinear resistance.

6. The method according to claim 1, characterized in that, The fault current during the interface flashover stage and the fault current during the continuous arc stage are independent current expressions. They are independently invoked or superimposed according to the fault stage during the early fault development process to simulate the fault conditions at different fault development stages.

7. A device for phased modeling and superposition of early cable faults, characterized in that, include: The acquisition module is used to acquire system parameters and fault parameters of the low-voltage cable joint in an ungrounded system. The system parameters include the three-phase ground equivalent parallel capacitance, the line equivalent resistance, and the line equivalent inductance. The fault parameters include the joint air gap equivalent capacitance, the arc resistance, and the additional series resistance considering the carbonization accumulation effect of the discharge channel. The first module is used to establish a fault current model for the interface flashover stage based on the system parameters and the fault parameters. In the interface flashover stage, the fault part is equivalent to the equivalent capacitance of the joint air gap. The instantaneous breakdown process is simulated by a discharge switch. The focus is on the transient fluctuations caused by the energy exchange between the three-phase ground equivalent parallel capacitance and the equivalent capacitance of the joint air gap. The forced response of the voltage source is ignored. A second-order homogeneous differential equation is established to solve the fault current for the interface flashover stage. The second module is used to establish a fault current model for the continuous arc stage based on the system parameters and the fault parameters. In the continuous arc stage, the fault part is equivalent to the series combination of the arc resistance and the additional series resistance. The arc resistance adopts the Mayr arc model. The additional series resistance decreases exponentially with the development of the arc. A first-order linear non-homogeneous differential equation is established to solve the fault current for the continuous arc stage. The superposition module is used to superimpose the fault current of the interface flashover stage and the fault current of the continuous arc stage when the fault condition involves the coupling of the interface flashover stage and the continuous arc stage, so as to obtain a complete early fault current model.

8. A computer device, characterized in that, The computer device includes a memory and a processor. The memory is used to store computer programs, and the processor is used to execute the computer programs stored in the memory to implement the steps of the method according to any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the steps of the method described in any one of claims 1-6.

10. A computer program product, characterized in that, Includes a computer program, which, when executed by a processor, implements the steps of the method according to any one of claims 1-6.

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