Dynamic deduction method for time-space distribution of partial discharge fault gas in high-voltage switch cabinet

Abstract

The application discloses a kind of high-voltage switchgear local discharge fault gas space-time distribution dynamic deduction method, comprising: obtaining the time series signal of multiple characteristic gas concentrations output by multiple gas sensors in high-voltage switchgear cavity;According to the three-dimensional geometric structure of cavity, the insulation medium attribute and the air flow boundary condition, a three-dimensional transient convection diffusion transmission state space model is constructed;Based on the state space model, the feature gas arrival time difference is extracted, and the fault source instantaneous gas release rate is inversely inversed;The instantaneous gas release rate is loaded into the state space model to forward deduce three-dimensional space-time concentration field, calculate cumulative transmission time lag error and carry out time lag compensation, obtain the real concentration transient change sequence of fault source;Combined with the concentration to discharge amount dynamic response calibration curve, the local discharge amount value is output by time sequence matching and amplitude mapping.The application realizes the accurate identification of early local discharge fault, reduces the occurrence probability of missed detection and misjudgment.

Description

Technical Field

[0001] This invention relates to the field of power distribution equipment technology, and in particular to a method for dynamic simulation of the spatiotemporal distribution of partial discharge fault gas in high-voltage switchgear. Background Technology

[0002] High-voltage switchgear is a critical piece of equipment in power distribution networks, and its insulation condition directly affects the safe and stable operation of the grid. Partial discharge is one of the main causes of insulation degradation and even breakdown faults in switchgear. Early detection and accurate assessment of the severity of partial discharge are crucial for ensuring the long-term reliable operation of the equipment. Gas detection methods determine the partial discharge status by monitoring the changes in the composition and concentration of characteristic gases produced by the decomposition of the insulating medium under partial discharge. Compared to traditional electrical detection methods such as pulse current methods and ultra-high frequency methods, gas detection is not affected by electromagnetic interference and is particularly suitable for detecting early partial discharges with low energy. However, the application of gas detection in high-voltage switchgear faces a key challenge: the characteristic gas must undergo a diffusion and propagation process within a sealed cavity from the point of generation at the discharge fault to detection by the sensor.

[0003] Existing research indicates that different characteristic gases exhibit significant differences in diffusion coefficients within the same medium, leading to varying arrival times at the sensor. Taking SF6 switchgear as an example, the concentration changes of characteristic decomposition gases generated by partial discharge show significant time delays during axial diffusion within the cavity. Studies show that achieving uniform diffusion in a closed system takes tens of minutes to several hours, with higher concentrations requiring longer times to reach uniformity. More importantly, during axial diffusion, the concentration of the characteristic gas decreases exponentially with increasing diffusion distance, implying a systematic deviation between the concentration measured by the sensor and the actual concentration at the fault source.

[0004] Currently, the mainstream method for retrieving partial discharge quantities based on gas detection is to establish a steady-state mapping relationship between gas volume fraction and discharge quantity. This assumes that the characteristic gas has diffused sufficiently and uniformly within the cavity, and the concentration measured by the sensor can directly reflect the magnitude of the discharge. However, this assumption ignores two key facts: first, there is a non-negligible diffusion time lag from the generation of the characteristic gas to its detection, and the time lag characteristics vary for different gases; second, the gas concentration is non-uniformly distributed during diffusion, and the concentration at the sensor location does not represent the true concentration level within the cavity.

[0005] Because existing methods fail to account for the impact of diffusion transient response delay on detection results, they often suffer from insufficient detection sensitivity in the early, weak discharge stages. When a discharge has just occurred, the characteristic gas has not yet diffused to the sensor location, and the sensor reading may be far lower than the actual discharge level or even zero, leading to missed or misjudged early faults. Therefore, there is an urgent need for a deduction method that can accurately describe the dynamic evolution of the spatiotemporal distribution of partial discharge fault gas within the switchgear cavity, in order to achieve accurate inversion of partial discharge quantity and effective identification of early faults. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a method for dynamically extrapolating the spatiotemporal distribution of partial discharge fault gas in high-voltage switchgear.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows: This invention discloses a method for dynamically extrapolating the spatiotemporal distribution of partial discharge fault gas in high-voltage switchgear, comprising the following steps: Step 1: Acquire the time-series signals of various characteristic gas concentrations output by multiple gas sensors pre-deployed inside the high-voltage switchgear cavity; Step 2: Based on the three-dimensional geometric structure of the high-voltage switchgear cavity, the properties of the insulating medium, and the airflow boundary conditions, construct a three-dimensional transient convection-diffusion transport state-space model to describe the diffusion evolution process after the fault gas is generated. Step 3: Based on the three-dimensional transient convection-diffusion transport state space model, background concentration interference is removed from the time series signals of the various characteristic gas concentrations, and the arrival time difference of each characteristic gas at different sensor deployment locations is extracted; Step 4: Based on the arrival time difference of each characteristic gas, and combined with the diffusion coefficient matrix in the three-dimensional transient convection-diffusion transport state space model, calculate the instantaneous gas release rate corresponding to the fault source location at each historical moment in reverse iteration. Step 5: Load the instantaneous gas release rate at each historical moment as a dynamic source term into the three-dimensional transient convection-diffusion transport state space model, and forward extrapolate to obtain the three-dimensional spatiotemporal concentration field distribution of the high-voltage switchgear cavity in the current moment. Step 6: Based on the three-dimensional spatiotemporal concentration field distribution, calculate the cumulative transmission time delay error introduced by the characteristic gas from the fault source location to each sensor deployment location, and compensate for the time delay error of the concentration reading at each sensor deployment location to obtain the true transient change sequence of concentration at the fault source location. Step 7: Input the actual concentration transient change sequence into the pre-stored concentration-discharge dynamic response calibration curve, and output the partial discharge value of the high-voltage switchgear under the current operating state through time matching and amplitude mapping.

[0008] Furthermore, step one includes: An array of electrochemical gas sensors is deployed along the surface of the insulating partition and the inner wall of the cavity in each compartment of the high-voltage switchgear. Each electrochemical gas sensor in the array is used to detect the concentration of one characteristic gas among the characteristic gases. The analog voltage signal output by each electrochemical gas sensor is continuously acquired at a preset sampling frequency, and the analog voltage signal is converted from analog to digital to generate the original concentration digital sequence corresponding to each electrochemical gas sensor. The original concentration digital sequence is subjected to median averaging filtering to remove impulse noise introduced by electromagnetic interference, and the filtered concentration digital sequence corresponding to each electrochemical gas sensor is obtained. Based on the physical deployment location of each electrochemical gas sensor within the high-voltage switchgear cavity, the filtered concentration digital sequences of all electrochemical gas sensors belonging to the same compartment are timestamped to generate time-series signals of various characteristic gas concentrations corresponding to each compartment.

[0009] Furthermore, step two includes: A computer-aided design three-dimensional geometric model of the high-voltage switchgear cavity is obtained. An unstructured tetrahedral mesh is performed on the computer-aided design three-dimensional geometric model to generate a set of computational mesh nodes including the internal busbars, insulating partitions, contact boxes and the inner wall of the cavity of each compartment. Each computational grid node in the computational grid node set is assigned insulation medium property parameters, including insulation medium density, insulation medium dynamic viscosity, and the diffusion coefficient tensor of the characteristic gas in the insulation medium. The airflow boundary conditions are set according to the actual operating conditions of the high-voltage switchgear cavity. The airflow boundary conditions include the inlet and outlet flow velocities of each compartment, the velocity no-slip boundary of the inner wall of the cavity, and the pressure difference boundary of the air passage between compartments.

[0010] Furthermore, step two includes: Based on the characteristic gas mass conservation equation and the Navier-Stokes momentum conservation equation, a three-dimensional transient convection-diffusion transport partial differential equation system is established on the computational grid node set, coupled with the diffusion coefficient tensor of the characteristic gas in the insulating medium. The system uses the characteristic gas concentration field and the gas flow velocity field as state variables. The source term of the three-dimensional transient convection-diffusion transport partial differential equation system is the time-varying release rate of the fault gas. The three-dimensional transient convection-diffusion transport partial differential equations are spatially discretized on the set of computational grid nodes using the finite volume method, and temporally discretized using the implicit Euler time-progression scheme, generating a three-dimensional transient convection-diffusion transport state-space model of the high-voltage switchgear cavity for iterative solution.

[0011] Furthermore, step three includes: For each characteristic gas, the three-dimensional transient convection-diffusion transport state space model is run under the condition of no partial discharge fault, and the time series prediction value of the background concentration of the characteristic gas at each sensor deployment location is calculated. The net concentration time series signal of a characteristic gas at each sensor deployment location is obtained by subtracting the predicted background concentration time series value from the concentration time series signal corresponding to the characteristic gas at each sampling point from the concentration time series signal of a variety of characteristic gas concentration time series signals. Using the pulse transfer function corresponding to the diffusion of the characteristic gas from any spatial point to each sensor deployment location in the three-dimensional transient convection-diffusion transport state-space model as the deconvolution kernel, the Richardson-Lucy iterative deconvolution algorithm is used to perform deconvolution operation on the net concentration time series signal to eliminate the signal broadening effect caused by sensor response hysteresis and local turbulence mixing, and obtain the deconvolution response sequence of the characteristic gas at each sensor deployment location. The moment when the concentration amplitude in the deconvolution response sequence first exceeds three standard deviations of the noise floor of the deconvolution response sequence is detected and marked as the arrival time of the characteristic gas at the sensor deployment location. The arrival times of the same characteristic gas at different sensor deployment locations are then compared pairwise to extract the arrival time difference of the characteristic gas at different sensor deployment locations.

[0012] Furthermore, step four includes: Using the arrival time difference of the same characteristic gas at any two sensor deployment locations as the observation input, and based on the theoretical value of the arrival time difference of the characteristic gas from different spatial points to any two sensor deployment locations as represented by the diffusion coefficient matrix in the three-dimensional transient convection-diffusion transport state space model, a set of nonlinear least squares localization equations with the fault source location as the unknown quantity is established. Solving the set of nonlinear least squares localization equations yields the spatial coordinates of the fault source location within the high-voltage switchgear cavity. Using the spatial coordinates of the fault source location as the spatial anchor point of the time-varying point source to be inverted, the historical time window is discretized into N equally spaced release moments. At each release moment, the instantaneous gas release rate variable to be solved is defined, forming an instantaneous gas release rate time series including N variables to be solved, where N is a positive integer greater than or equal to 10. Each instantaneous gas release rate variable in the instantaneous gas release rate time series is used as the source term excitation of the three-dimensional transient convection-diffusion transport state space model. The theoretical concentration response time series at each sensor deployment location is calculated under the single action of the unit pulse release rate corresponding to the instantaneous gas release rate variable. The theoretical concentration response time series at all release times are summed according to the principle of time superposition to obtain the theoretical composite concentration time series at each sensor deployment location. The objective function is to minimize the sum of squared residuals between the synthetic concentration time series and the net concentration time series signal at each sensor deployment location. The conjugate gradient iterative algorithm is used to update each instantaneous gas release rate variable in the instantaneous gas release rate time series one by one until the relative decrease rate of the objective function is less than the preset convergence threshold, at which point the iteration terminates. The instantaneous gas release rate time series corresponding to the termination of iteration is output as the instantaneous gas release rate corresponding to the fault source location at each historical moment.

[0013] Furthermore, step five includes: The instantaneous gas release rate is assigned one by one to the source term variable of the computational grid node where the fault source is located in the three-dimensional transient convection-diffusion transport state space model according to its corresponding release time. The background concentration steady-state field in the high-voltage switchgear cavity under the condition of no partial discharge fault is used as the initial concentration field of the three-dimensional transient convection-diffusion transport state space model. The measured airflow boundary conditions under the actual operating conditions of the high-voltage switchgear cavity are used as the dynamic boundary input of the three-dimensional transient convection-diffusion transport state space model in the entire historical time window before the current moment. Starting from the beginning of the historical time window, the three-dimensional transient convection-diffusion transport state space model is solved step by step in the forward direction using the temporal discrete step size of the three-dimensional transient convection-diffusion transport state space model. At each time step, the instantaneous gas release rate of the current time step is used to drive the three-dimensional transient convection-diffusion transport state space model to calculate the characteristic gas concentration value and airflow velocity value at each computational grid node at the current time step, until the forward direction is advanced to the current time, thus obtaining the full time history concentration field sequence from the beginning of the historical time window to the current time. The characteristic gas concentration values ​​at each computational grid node within the entire space of the high-voltage switchgear cavity at the current moment are extracted from the full-time history concentration field sequence. The characteristic gas concentration values ​​are used as the concentration field amplitude at each computational grid node. The three-dimensional spatiotemporal concentration field distribution within the entire space of the high-voltage switchgear cavity is constructed by combining the spatial coordinates of each computational grid node. The three-dimensional spatiotemporal concentration field distribution includes the concentration value change history of each characteristic gas at each spatial location within the entire space of the high-voltage switchgear cavity from the initial moment to the current moment.

[0014] Furthermore, step six includes: Extract the fault source concentration change curve of each characteristic gas at the fault source location over the entire time history from the three-dimensional spatiotemporal concentration field distribution, and extract the sensor location concentration change curve of the same characteristic gas at each sensor deployment location over the entire time history from the three-dimensional spatiotemporal concentration field distribution. The concentration change curve of the fault source and the concentration change curve of the sensor location are cross-correlated along the time axis to obtain the delay time corresponding to the maximum value of the cross-correlation function. The delay time is marked as the cumulative transmission time delay error of the characteristic gas from the fault source location to the sensor deployment location. Using the cumulative transmission time delay error as the time shift amount when the electrochemical gas sensor at the sensor deployment location detects the characteristic gas, the net concentration time sequence signal of the characteristic gas detected at the sensor deployment location is shifted forward along the time axis by the time shift amount, so that the shifted net concentration time sequence signal is aligned with the actual release time of the characteristic gas at the fault source location on the time axis, and the time delay compensated concentration sequence of the characteristic gas at the sensor deployment location is obtained. For each characteristic gas at each sensor deployment location, the above-mentioned cumulative transmission delay error calculation and net concentration time sequence signal time axis forward translation operation are performed to obtain the time delay compensated concentration sequence of all types of characteristic gases at all sensor deployment locations. The time delay compensated concentration sequences of the same characteristic gas at all sensor deployment locations are then inversely distance-weighted and fused according to the spatial distance between their respective sensor deployment locations and the fault source location to output the true concentration transient change sequence of each characteristic gas at the fault source location.

[0015] Furthermore, step seven includes: Electrochemical gas sensors of the same type and location as those in step one are pre-deployed within the high-voltage switchgear cavity. Under offline maintenance conditions, a sequence of simulated partial discharge pulses of known discharge levels is injected into the high-voltage switchgear cavity. The analog voltage signal output from each electrochemical gas sensor is collected, and analog-to-digital conversion and filtering are performed. Following the same processing flow as steps one through six, a transient change sequence of the actual concentration for calibration corresponding to each known discharge level is obtained. Each known discharge level and its corresponding transient change sequence of the actual concentration for calibration are used as a set of calibration samples. All calibration samples corresponding to all discharge levels are arranged in ascending order of discharge quantity and piecewise cubic spline interpolation is performed to generate a concentration-discharge dynamic response calibration curve covering the continuous discharge quantity range. The horizontal axis of the concentration-discharge dynamic response calibration curve represents the concentration value sequence, and the vertical axis represents the discharge quantity value.

[0016] Furthermore, step seven includes: Input the true concentration transient change sequence output in step six into the concentration-discharge dynamic response calibration curve. Use the rising edge start point, peak occurrence time, and decay time constant of the true concentration transient change sequence on the time axis as time series feature parameters. Search for the calibration sample with the smallest Euclidean distance to the time series feature parameters in each set of calibration samples of the concentration-discharge dynamic response calibration curve. Use the time index corresponding to the searched calibration sample as the time series matching anchor point of the true concentration transient change sequence on the concentration-discharge dynamic response calibration curve. Starting from the time-series matching anchor point, the normalized ratio of each concentration amplitude in the real concentration transient change sequence to the concentration value at the same time index position in the concentration-discharge dynamic response calibration curve is calculated to obtain the transient amplitude mapping coefficient at each time index position. The transient amplitude mapping coefficients at all time index positions are arranged in chronological order to form a transient amplitude mapping coefficient sequence. The median value of the transient amplitude mapping coefficient sequence is calculated as the optimal amplitude mapping coefficient. The product of the discharge value corresponding to the concentration-discharge dynamic response calibration curve at the time-matching anchor point and the optimal amplitude mapping coefficient is used as the instantaneous partial discharge component value of the high-voltage switchgear under the current operating state for that characteristic gas. The instantaneous partial discharge component value corresponding to each characteristic gas is weighted and averaged according to the number of sensors in the electrochemical gas sensor array for each characteristic gas in step one, and the partial discharge value of the high-voltage switchgear under the current operating state is output.

[0017] The technological advancements achieved by this invention compared to existing technologies are as follows: This invention constructs a three-dimensional transient convection-diffusion-transmission state-space model of fault gas within a high-voltage switchgear cavity, combines this model with the arrival time difference of multiple sensors to invert the instantaneous gas release rate of the fault source, and compensates for the cumulative transmission delay during propagation. This allows for accurate recovery of the true transient concentration change process of characteristic gas at the fault source location. It overcomes the problem of insufficient sensitivity in detecting early weak partial discharges caused by the failure to consider the diffusion transient response delay in existing technologies, improves the accuracy of partial discharge quantity inversion, achieves accurate identification of early partial discharge faults, and reduces the probability of missed detections and misjudgments. Attached Figure Description

[0018] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0019] In the attached diagram: Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0020] The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of the present invention will now be described with reference to the accompanying drawings.

[0021] like Figure 1 As shown, this invention discloses a method for dynamically extrapolating the spatiotemporal distribution of partial discharge fault gas in high-voltage switchgear, comprising: Step 1: Acquire the time-series signals of various characteristic gas concentrations output by multiple gas sensors pre-deployed inside the high-voltage switchgear cavity; Step 2: Based on the three-dimensional geometric structure of the high-voltage switchgear cavity, the properties of the insulating medium, and the airflow boundary conditions, construct a three-dimensional transient convection-diffusion transport state-space model to describe the diffusion evolution process after the fault gas is generated. Step 3: Based on the three-dimensional transient convection-diffusion transport state space model, background concentration interference is removed from the time series signals of the various characteristic gas concentrations, and the arrival time difference of each characteristic gas at different sensor deployment locations is extracted; Step 4: Based on the arrival time difference of each characteristic gas, and combined with the diffusion coefficient matrix in the three-dimensional transient convection-diffusion transport state space model, calculate the instantaneous gas release rate corresponding to the fault source location at each historical moment in reverse iteration. Step 5: Load the instantaneous gas release rate at each historical moment as a dynamic source term into the three-dimensional transient convection-diffusion transport state space model, and forward extrapolate to obtain the three-dimensional spatiotemporal concentration field distribution of the high-voltage switchgear cavity in the current moment. Step 6: Based on the three-dimensional spatiotemporal concentration field distribution, calculate the cumulative transmission time delay error introduced by the characteristic gas from the fault source location to each sensor deployment location, and compensate for the time delay error of the concentration reading at each sensor deployment location to obtain the true transient change sequence of concentration at the fault source location. Step 7: Input the actual concentration transient change sequence into the pre-stored concentration-discharge dynamic response calibration curve, and output the partial discharge value of the high-voltage switchgear under the current operating state through time matching and amplitude mapping.

[0022] Specifically, the purpose of step one is to construct a raw data foundation that can realistically reflect the dynamic changes of partial discharge fault gas within the high-voltage switchgear cavity. This provides continuous, synchronous input data with spatial distribution characteristics for subsequent establishment of a three-dimensional transient convection-diffusion-transmission state-space model, calculation of fault source release rate, and inversion of partial discharge quantity. This step does not acquire independent detection results from a single sensor, but rather time-series signals of various characteristic gas concentrations, including spatial location attributes, temporal attributes, and gas type attributes.

[0023] High-voltage switchgear enclosures typically consist of multiple interconnected or semi-interconnected compartments. Each compartment contains structural components such as busbars, contact boxes, and insulating partitions. These components alter the diffusion path of fault gases, causing significant differences in gas concentration at different locations. Therefore, an array of electrochemical gas sensors is pre-deployed along the surface of the insulating partitions and the inner wall of the enclosure within each compartment, forming a multi-point detection network with spatial coverage. The area near the insulating partitions is a common location for partial discharge, while the inner wall of the enclosure covers the main propagation path of the diffused gas. These two types of locations together form a relatively complete detection area, effectively acquiring diffusion information of fault gases at different spatial locations.

[0024] Each electrochemical gas sensor in the electrochemical gas sensor array is designed to detect only one characteristic gas. For example, in a high-voltage switchgear using SF6 insulation, separate electrochemical gas sensors can be installed to detect partial discharge decomposition products such as SO2, SOF2, and SO2F2. Independent detection channels are established for different characteristic gases, ensuring that changes in gas concentrations do not affect each other while maintaining a one-to-one correspondence in the detection results. Because different characteristic gases have different diffusion coefficients and diffusion rates, separately collecting the concentration changes of each gas provides a data basis for subsequent calculations of arrival time differences.

[0025] After sensor deployment is complete, the analog voltage signal output by each electrochemical gas sensor is continuously acquired at a preset sampling frequency. The output signal of the electrochemical gas sensor is essentially a current signal generated after the target gas participates in the electrochemical reaction, which is converted into an analog voltage signal by an internal conversion circuit. Its voltage amplitude changes continuously with the concentration of the target gas. Therefore, throughout the partial discharge monitoring process, each sensor maintains continuous sampling, rather than event-triggered sampling, thus ensuring a complete record of all concentration changes before, during, and after the partial discharge occurs.

[0026] The acquired analog voltage signal enters the analog-to-digital converter (ADC) module for digital processing. The ADC converts the continuous analog voltage into discrete digital quantities according to a fixed sampling period. Each sampling moment corresponds to a digital concentration value, thus forming the original digital concentration sequence.

[0027] Let the first The electrochemical gas sensor in the first The analog voltage output at each sampling time is Based on the concentration response relationship of this electrochemical gas sensor, the corresponding raw concentration digital value can be obtained: in, Indicates the first The original digital concentration values ​​corresponding to each electrochemical gas sensor; Indicates the first Concentration conversion coefficient of an electrochemical gas sensor; Indicates the first Zero-point compensation value of an electrochemical gas sensor.

[0028] Through the above conversion, the data output by different electrochemical gas sensors is uniformly represented as concentration values, providing a consistent data format for subsequent unified processing.

[0029] Because high-voltage switchgear operates in a high-voltage, high-electric-field environment for extended periods, circuit breaker operation, bus current changes, and electromagnetic coupling can easily introduce transient spike noise into the sampling lines. This type of noise typically manifests as abrupt changes in a single or a small number of sampling points, while real gas concentration changes are characterized by continuous and slow variations. Therefore, median averaging filtering is performed on the raw concentration digital sequence corresponding to each electrochemical gas sensor.

[0030] In the specific processing, a sliding data window is formed by multiple consecutive sampling points. First, the median value of all sampled values ​​within the window is calculated. Abnormal peak sampling points that are far from the median value are automatically removed. Then, the average value of the remaining sampled values ​​is calculated, and the resulting average value is used as the filtered concentration value at the current sampling time. Median value processing can effectively suppress isolated impulse noise, while averaging processing can further reduce random fluctuations, keeping the concentration curve smooth and continuous, while not changing the true concentration change trend during partial discharge.

[0031] After median averaging filtering, each electrochemical gas sensor yields a corresponding filtered concentration sequence. At this point, although the different sensors have the same sampling frequency, slight differences in acquisition channel buffering, communication delays, and analog-to-digital conversion start-up times can lead to millisecond-level time shifts between sensor data. Directly using this data for fault gas diffusion analysis will introduce additional errors in subsequent calculations of arrival time differences.

[0032] Therefore, based on the physical deployment location of each electrochemical gas sensor within the high-voltage switchgear chamber, the filtered concentration digital sequences of all electrochemical gas sensors within the same compartment are timestamped. Specifically, a unified system clock is used as the reference time axis, and each sampled data point is reassigned a unified time tag. When the sampling times of multiple sensors are not completely consistent, each sampled value is mapped to the unified time axis, ensuring that the same time tag corresponds to the concentration information of each sensor at the same moment.

[0033] After timestamp alignment, the data from all electrochemical gas sensors within the same compartment have a unified time reference, while retaining their respective spatial coordinates and gas type information. The data is then organized according to compartment number, and the filtered concentration sequences from all electrochemical gas sensors within the same compartment are combined to ultimately generate time-series signals for the concentrations of various characteristic gases corresponding to each compartment.

[0034] The time-series signals of various characteristic gas concentrations not only include the concentration changes of various characteristic gases over continuous time, but also the sensor deployment location and compartment information corresponding to each sampling point, thus forming a dataset with three attributes: time dimension, spatial dimension, and gas type dimension. This dataset completely preserves the dynamic response characteristics of partial discharge fault gases at different locations, times, and gas types during the diffusion and propagation process within the high-voltage switchgear cavity, providing a unified and continuous data input for subsequent establishment of a three-dimensional transient convection diffusion transport state-space model, extraction of fault gas arrival time difference, and inversion of fault source release rate.

[0035] Step one obtained time-series signals of various characteristic gas concentrations corresponding to multiple electrochemical gas sensors in each compartment. This data reflects the local concentration changes at the deployment locations of each sensor, but cannot directly reflect the propagation process of fault gas in the entire high-voltage switchgear cavity. Therefore, it is necessary to establish a three-dimensional transient convection-diffusion-transmission state-space model that can describe the propagation and evolution of fault gas in the entire cavity, taking into account the spatial structure of the high-voltage switchgear cavity itself, the flow characteristics of the insulating medium, and the actual operating conditions. This model will establish a unified connection between the discrete monitoring data obtained in Step one and the continuously changing concentration field in the entire cavity, providing a mathematical basis for subsequent fault source location inversion, instantaneous gas release rate calculation, and concentration field reconstruction.

[0036] High-voltage switchgear typically comprises multiple compartments, which are connected in a limited manner by air passages. It also contains numerous physical structures such as busbars, insulating partitions, and contact boxes. These structures not only alter airflow direction but also impede the diffusion of fault gases; therefore, it is essential to preserve their true spatial geometry intact.

[0037] In practice, a computer-aided three-dimensional geometric model of the high-voltage switchgear cavity is obtained. This three-dimensional geometric model fully includes all geometric information of the cabinet shell, each compartment space, busbar structure, insulating partitions, contact boxes, supporting components, and the inner wall of the cavity, while also retaining the relative positional relationships and spatial dimensional information between the various structures.

[0038] Since continuous geometric models cannot be directly used for subsequent numerical calculations, it is necessary to perform unstructured tetrahedral meshing on the entire three-dimensional geometric model.

[0039] Unstructured tetrahedral meshes can better fit complex curved surfaces and irregular spatial structures, enabling high spatial description accuracy in areas with large geometric changes, such as busbar corners, insulation partition edges, and near contact boxes. Meanwhile, relatively larger mesh cells are used in areas with smaller spatial changes, thus balancing computational efficiency and spatial representation capabilities.

[0040] After mesh generation, the entire high-voltage switchgear cavity is divided into a large number of interconnected tetrahedral elements. Each tetrahedral element corresponds to several computational mesh nodes, and all the computational mesh nodes together form a set of computational mesh nodes covering the entire high-voltage switchgear cavity.

[0041] The computational grid node set not only covers all spatial regions where gases can propagate, but also covers the actual deployment locations of each electrochemical gas sensor in step one. Therefore, the time series signals of various characteristic gas concentrations obtained in step one can be mapped to the corresponding computational grid nodes, realizing a one-to-one correspondence between monitoring data and model nodes.

[0042] After establishing the set of computational grid nodes, each computational grid node needs to be assigned corresponding insulating medium property parameters.

[0043] Since high-voltage switchgear is usually filled with SF6 gas or SF6 mixed insulation medium, different media determine the fault gas diffusion capacity and flow characteristics. Therefore, each computational grid node is configured with uniform or regionally differentiated insulation medium property parameters.

[0044] The properties of insulating media include the density of the insulating media, the dynamic viscosity of the insulating media, and the diffusion coefficient tensor of the characteristic gas in the insulating media.

[0045] Among them, the density of the insulating medium determines the airflow inertia and mass distribution; the dynamic viscosity of the insulating medium determines the fluid shear resistance inside the medium; and the diffusion coefficient tensor describes the diffusion ability of different characteristic gases along different spatial directions.

[0046] The diffusion coefficient tensor is described in three-dimensional matrix form and can be represented as: in, Represents the characteristic gas diffusion coefficient tensor; , , These represent the diffusion capacity in three spatial coordinate directions; the remaining elements represent the diffusion coupling effect between different directions.

[0047] When the medium inside the high-voltage switchgear is uniform and there is no obvious directionality, the above matrix can be degenerated into a diagonal matrix, retaining only the main diagonal elements for subsequent calculations. After assigning the medium properties, it is necessary to establish the airflow propagation environment under actual operating conditions.

[0048] Due to factors such as natural heat dissipation, equipment heating, and pressure difference of the sealing structure during long-term operation, there is always a slow airflow inside the cavity of the high-voltage switchgear. This airflow will change the propagation path of the fault gas. Therefore, it is necessary to establish corresponding airflow boundary conditions and set uniform airflow boundary conditions for the entire calculation area according to the actual operating conditions of the high-voltage switchgear.

[0049] The airflow boundary conditions include the flow velocity at the inlet and outlet of each compartment, the velocity no-slip boundary on the inner wall of the cavity, and the pressure difference boundary of the air passage between compartments. The flow velocity at the inlet and outlet of each compartment describes the magnitude and direction of the velocity of air or insulating medium entering and exiting the compartment. The velocity no-slip boundary on the inner wall of the cavity indicates that the velocity of the fluid at the contact point with the inner wall of the cabinet always remains zero, so that a real boundary layer is formed near the wall. The pressure difference boundary of the air passage between compartments describes the slow flow process formed between different compartments due to the pressure difference, so that a continuous flow field is formed between multiple compartments.

[0050] After establishing the geometric model, medium properties, and boundary conditions, a governing equation describing the propagation law of fault gas is established on the entire set of computational grid nodes. Since the propagation of fault gas is affected by both airflow transport and molecular diffusion, the characteristic gas mass conservation equation is used to describe the concentration change process, and the Navier-Stokes momentum conservation equation is used to describe the airflow motion process. The coupling relationship between the two is established through the diffusion coefficient tensor.

[0051] Finally, a set of three-dimensional transient convection-diffusion-transmission partial differential equations was established with the characteristic gas concentration field and the airflow velocity field as state variables. The characteristic gas concentration field represents the gas concentration distribution at any time at any spatial location in the entire high-voltage switchgear cavity; the airflow velocity field represents the flow velocity and flow direction of the insulating medium at each spatial location.

[0052] Since partial discharge continuously releases fault gas, the time-varying release rate of the fault gas is introduced as a source term in the concentration control equation, assuming the characteristic gas concentration is... The fault gas release rate The source term represents the mass of gas continuously released from the fault source into the surrounding space per unit time, which changes continuously with time, with different release intensities corresponding to different historical moments. The instantaneous gas release rate obtained in the subsequent step four is used as the input model for this source term.

[0053] After the above partial differential equations are established, they still belong to the continuous space control model and cannot be directly calculated at each time step. Therefore, further discretization processing is required.

[0054] Specifically, the finite volume method is used to perform spatial discretization on the entire computational grid node set. The finite volume method uses each tetrahedral grid cell as a control volume, transforming the continuous spatial integral equation into a mass exchange relationship between each control volume. This allows adjacent grid nodes to complete concentration transport and flow exchange through a common boundary, while ensuring mass conservation throughout the entire computational domain.

[0055] After spatial discretization, an implicit Eulerian time-progression scheme is used for time discretization. The implicit Eulerian time-progression scheme progressively advances the entire concentration field change process according to a fixed time step. After each time step calculation is completed, the result of the current time step calculation is used as the initial state for the next time step to continue the process, thereby continuously describing the entire process of the fault gas from release to diffusion.

[0056] Because the implicit Euler time-progression scheme has good numerical stability, even if the duration of fault gas diffusion is long or the time step is appropriately increased, the entire calculation process can be guaranteed to remain stable and converge without producing obvious numerical oscillations. Therefore, it is suitable for continuous calculation of long-term transient diffusion processes in the cavity of high-voltage switchgear.

[0057] After spatial and temporal discretization, a three-dimensional transient convection-diffusion-transmission state-space model of the high-voltage switchgear cavity is generated for iterative solution. This state-space model uses a set of computational grid nodes as its computational basis, characteristic gas concentration fields and airflow velocity fields as state variables, the time-varying release rate of fault gas as input, and the concentrations at each sensor deployment location corresponding to the various characteristic gas concentration time-series signals obtained in step one as observations, thus achieving a unified description of fault gas release, diffusion, transport, and sensor detection. The subsequent step three will further remove background concentration interference based on this state-space model and the various characteristic gas concentration time-series signals obtained in step one, and extract the characteristic gas arrival time difference between different sensor deployment locations, providing basic data for fault source location inversion and instantaneous gas release rate calculation.

[0058] Step one obtained time-series signals of various characteristic gas concentrations from multiple electrochemical gas sensors inside each compartment of the high-voltage switchgear. These signals accurately recorded the changes in characteristic gas concentrations over time at different locations. Step two further established a three-dimensional transient convection-diffusion-transmission state-space model that describes the propagation law of fault gases within the high-voltage switchgear cavity, enabling calculations of gas diffusion processes at any spatial location within the entire cavity. However, the concentration time-series signals acquired in Step one not only include the target gas components generated by partial discharge faults but also superimposed factors such as the background concentration formed by the long-term slow decomposition of the insulating medium, concentration drift caused by ambient temperature fluctuations, and sensor dynamic response lag. Directly using the raw concentration time-series signals to analyze the fault gas propagation process could easily lead to inaccurate judgment of the actual arrival time of the fault gas, further affecting subsequent fault source location inversion and instantaneous gas release rate calculations. Therefore, this step utilizes the three-dimensional transient convection-diffusion-transmission state-space model established in Step two to perform background concentration stripping, dynamic response recovery, and arrival time extraction on the various characteristic gas concentration time-series signals obtained in Step one, ensuring that subsequent calculations are based on the true diffusion response.

[0059] Each characteristic gas obtained in step one is processed independently, and different types of characteristic gases do not interfere with each other.

[0060] During the long-term operation of high-voltage switchgear, even without partial discharge faults, the insulating medium may still undergo extremely slow natural decomposition, or form a stable concentration due to historical operational residues. Therefore, it is necessary to first obtain the background concentration change process corresponding to this characteristic gas.

[0061] In the specific implementation process, the three-dimensional transient convection diffusion transport state space model established in step two is set as the operating state under no partial discharge fault conditions.

[0062] The so-called partial discharge fault-free condition refers to the time-varying release rate of the fault gas in the model always remaining zero. At this time, there is no new fault gas release inside the entire high-voltage switchgear cavity, and only the original concentration distribution of the insulating medium and the airflow state formed during normal operation are retained.

[0063] The model retains all the geometric structures, insulating medium property parameters, and airflow boundary conditions established in step two, but only disables the fault source term, so that the state space model can automatically calculate the concentration change process at each location in the entire high-voltage switchgear cavity under normal operating conditions.

[0064] Since the physical deployment location of each electrochemical gas sensor has been clearly recorded in step one, the model can directly read the concentration value at the corresponding computational grid node of each sensor.

[0065] After continuous time-progression calculations, the time-series predicted value of the background concentration corresponding to each sensor deployment location can be obtained.

[0066] The background concentration time series prediction value represents the theoretical concentration change sequence caused only by normal operation in the absence of partial discharge faults, and it serves as a reference benchmark for subsequent background concentration stripping.

[0067] Subsequently, the corresponding characteristic gas concentration time series signal obtained in step one is subtracted from the background concentration time series prediction value at each sampling point.

[0068] Let the first The electrochemical gas sensor in the first The filtered concentration value corresponding to each sampling time is The predicted background concentration at the corresponding time point is... The net concentration value can then be expressed as: in, Indicates the first The net concentration value corresponding to each electrochemical gas sensor.

[0069] After subtracting from each sampling point, the long-standing background concentration and slow drift portion in the concentration time series signal are effectively stripped away, leaving only the dynamic concentration change portion caused by partial discharge faults, thus forming the net concentration time series signal of this characteristic gas at each sensor deployment location.

[0070] After background concentration stripping is completed, the net concentration time series signal can reflect the fault gas propagation process, but it is still affected by two factors.

[0071] On the one hand, electrochemical gas sensors have a certain response time. When a faulty gas arrives at the sensor, its output concentration will not immediately reach the true concentration, but will gradually build up to form a slow upward curve.

[0072] On the other hand, during the diffusion and propagation of faulty gases, the originally sharp concentration changes gradually broaden due to local slow airflow and microscale mixing, resulting in a concentration response broadening phenomenon.

[0073] Both of these factors will delay the actual arrival time of the faulty gas, making it difficult to accurately calculate the propagation time difference between different sensors. Therefore, it is necessary to restore the actual diffusion response of the faulty gas.

[0074] The three-dimensional transient convection-diffusion-transport state-space model established in step two can calculate the theoretical concentration response formed at each sensor deployment location after a unit pulse of gas is released at any spatial location.

[0075] If we assume that any point in space releases a unit mass of fault gas instantaneously at a certain moment, then after forward propagation calculation, the state-space model can obtain the response curve of the concentration at the corresponding sensor location changing with time.

[0076] The response curve fully describes the propagation characteristics after the combined effects of diffusion propagation, local mixing, and the sensor's dynamic response. Therefore, it is defined as the pulse transfer function corresponding to this sensor.

[0077] Different sensor deployment locations correspond to different pulse transfer functions, and the same characteristic gas has an independent propagation response at different locations.

[0078] Subsequently, the pulse transfer function calculated in step two is used as the deconvolution kernel to perform deconvolution recovery on the net concentration time series signal obtained in step three. Specifically, the Richardson-Lucy iterative deconvolution algorithm is used for the solution. The Richardson-Lucy iterative deconvolution algorithm is a recovery method based on the idea of ​​successive approximation. Its core idea is to gradually recover the original concentration change process before propagation by continuously iterating under the condition of known propagation kernel function.

[0079] After each iteration, the recovered concentration sequence is re-convolved with the pulse transfer function and compared with the actual net concentration time series signal. The recovery result is continuously corrected based on the difference between the two.

[0080] As the iterations continue, the recovered concentration change curve gradually approaches the actual diffusion response after the fault gas is actually released.

[0081] After deconvolution processing, the time lag caused by the sensor response setup process is compensated, and the concentration response broadening caused by local turbulent mixing is significantly reduced, ultimately obtaining the deconvolution response sequence corresponding to each sensor deployment location.

[0082] Compared to the net concentration time-series signal, the deconvolution response sequence has a steeper rising edge, and its concentration change starts closer to the location where the fault gas actually reaches the sensor, thus enabling more accurate extraction of propagation time.

[0083] After obtaining the deconvolution response sequence, it is necessary to determine the time when the fault gas first arrives at each sensor deployment location.

[0084] Since the deconvolution response sequence may still have small random fluctuations, it is not appropriate to simply use the first time the concentration is greater than zero as the basis for arrival. Instead, statistical criteria should be used for judgment.

[0085] In the specific processing, all sampled values ​​of the deconvolution response sequence during the stable period before the fault occurred are statistically analyzed, and the standard deviation of its noise fluctuation is calculated.

[0086] Subsequently, using three standard deviations of the noise floor as the concentration detection threshold, when the concentration value of the deconvolution response sequence first exceeds this detection threshold, it indicates that the current concentration change has significantly exceeded the random noise level, and it can be considered that the fault gas has actually reached the sensor deployment location.

[0087] Therefore, the sampling time when the concentration amplitude first exceeds three standard deviations of the noise floor is defined as the arrival time of the characteristic gas at the corresponding sensor deployment location.

[0088] Using the above unified criteria can avoid the arrival time being advanced or delayed due to random noise fluctuations, and improve the consistency of arrival time extraction between different sensors.

[0089] After calculating the arrival times corresponding to all sensor deployment locations, the pairwise differences between the arrival times of all sensors for the same characteristic gas are calculated.

[0090] Let the first The arrival times corresponding to each sensor are: , No. The arrival times corresponding to each sensor are: The time difference between the two arrival times is expressed as: in, This represents the time difference in the propagation of the same characteristic gas from the fault source to two different sensor deployment locations.

[0091] Because different sensors have different distances from the fault source, different diffusion paths, and different airflow effects, different sensors form different sets of arrival time differences.

[0092] Finally, the arrival time differences between all sensors are stored according to the sensor number and the type of characteristic gas, forming an arrival time difference dataset for each type of characteristic gas.

[0093] This time-of-arrival (TOA) dataset fully reflects the propagation time sequence of fault gas within the high-voltage switchgear cavity, while eliminating the influence of background concentration, sensor dynamic response, and local mixing. The subsequent step four will use this TOA dataset as observation input, combined with the three-dimensional transient convection-diffusion-transmission state-space model established in step two, to inversely retrieve the spatial location of the fault source and further calculate the instantaneous gas release rate corresponding to each historical moment.

[0094] Step one obtained time-series signals of various characteristic gas concentrations from multiple electrochemical gas sensors, providing raw observation data for the entire fault analysis. Step two established a three-dimensional transient convection-diffusion-transmission state-space model of the high-voltage switchgear cavity, enabling numerical description of the propagation process of the fault gas within the cavity. Step three further removed background concentration interference and extracted the arrival time difference of each characteristic gas between different sensor deployment locations, ensuring that the propagation time information accurately reflects the diffusion pattern of the fault gas. This step utilizes the aforementioned propagation time information, combined with the state-space model established in Step two, to first invert the spatial location of the partial discharge fault source within the high-voltage switchgear cavity, and then further invert the instantaneous gas release rate corresponding to each moment of the fault source within the entire historical time window, thereby reconstructing the true release process of the fault gas during partial discharge.

[0095] Since step three yields the arrival time difference between different sensors, rather than the location of the fault source, it is first necessary to determine the spatial coordinates of the fault source based on the propagation time relationship.

[0096] In specific processing, for the same characteristic gas, two sensor deployment locations can be randomly selected to form a sensor pair, and the arrival time difference of the corresponding sensor pair can be used as the observation input.

[0097] Meanwhile, the three-dimensional transient convection diffusion transport state space model established in step two already includes the complete three-dimensional geometry of the high-voltage switchgear, the diffusion coefficient matrix, and the airflow boundary conditions. Therefore, it can simulate the propagation time required for fault gas to reach different sensor deployment locations after being released at any spatial location.

[0098] In the specific implementation process, all computational grid nodes of the high-voltage switchgear cavity are used as candidate fault source locations.

[0099] Assuming that each computational grid node may be a partial discharge fault source, unit fault gas release calculations are performed in the state-space model.

[0100] For each candidate computational grid node, the state-space model can calculate the propagation time of the fault gas to all the deployment locations of the electrochemical gas sensors, and further calculate the theoretical arrival time difference between any two sensors.

[0101] Since the state-space model established in step two has been coupled with the diffusion coefficient matrix, the theoretical arrival time difference corresponding to different spatial locations has taken into account factors such as the diffusion capacity of the insulating medium, local airflow, and complex geometric structures. Therefore, the propagation results are more consistent with the actual diffusion process of high-voltage switchgear.

[0102] Subsequently, the actual arrival time difference obtained in step three is compared with the theoretical arrival time difference calculated by the state-space model.

[0103] For any candidate fault location, the closer the theoretical arrival time difference is to the actual arrival time difference, the more likely that the spatial location is to be a real partial discharge fault source.

[0104] Therefore, a set of nonlinear least squares localization equations is established using the spatial coordinates of the fault source as unknown variables.

[0105] The goal of this set of equations is to find a spatial location within the entire high-voltage switchgear cavity that minimizes the overall error between the theoretical and actual arrival time differences of all sensors.

[0106] Let step three yield the first... The sensor and the first The actual arrival time difference between the sensors is The theoretical arrival time difference calculated by the state-space model is: The overall positioning target can then be represented as: in, This represents the total error due to the arrival time difference of all sensors.

[0107] By continuously adjusting the spatial coordinates of the fault source, the objective function is continuously reduced, and finally the spatial coordinates corresponding to the minimum objective function are obtained, which are the spatial coordinates of the partial discharge fault source in the high-voltage switchgear cavity.

[0108] Once the fault source is located, it can be assumed that the entire partial discharge process occurred at this fixed spatial location.

[0109] Therefore, the spatial coordinates of the fault source are used as the spatial anchor point of the time-varying point source to be inverted. The so-called spatial anchor point means that all subsequent fault gas releases are released from this fixed position, and the release intensity is allowed to change continuously with time.

[0110] Subsequently, the entire historical time window corresponding to the occurrence of partial discharge up to the current moment is discretized. In specific implementation, the entire historical time window is divided into multiple consecutive release moments according to a fixed time interval, and each release moment corresponds to an independent instantaneous gas release rate variable.

[0111] Assume the entire historical time window is divided into N release moments, where N is a positive integer greater than or equal to 10.

[0112] As the time window length increases, the number of release moments can be increased accordingly, thereby improving the accuracy of the release process recovery. The instantaneous gas release rates corresponding to all release moments together form the instantaneous gas release rate time series. This time series completely describes the change law of fault gas release intensity with time during the entire partial discharge process, where each variable is an unknown quantity to be inverted.

[0113] After establishing the release rate variables, it is necessary to analyze the impact of each release rate variable on the concentration changes of each sensor. In the specific process, each instantaneous gas release rate variable in the instantaneous gas release rate time series is used as the source term input of the state space model in turn. The remaining release times are kept in a zero release state. At this time, only one release time corresponds to a unit pulse release, and no fault gas is generated at all other release times. The state space model automatically calculates the propagation process corresponding to the unit release rate based on the three-dimensional transient convection diffusion transport state space model established in step two.

[0114] After the calculation is completed, the theoretical concentration response time series corresponding to each sensor deployment location under the action of unit release rate alone can be obtained. Since the entire propagation process satisfies the linear superposition relationship, the concentration response generated by the combined effect of each historical release moment can be obtained by linearly combining the theoretical concentration responses corresponding to all unit release rates according to the magnitude of the release rate.

[0115] In the specific processing, the theoretical concentration response time series corresponding to all release times are arranged sequentially according to the occurrence time of each release time, and then accumulated according to the principle of time superposition.

[0116] For any sensor deployment location, each release moment contributes a portion of the concentration response. The sum of the contributions from all release moments forms the theoretical synthetic concentration time series corresponding to that sensor. The theoretical synthetic concentration time series represents the concentration change process that each electrochemical gas sensor should theoretically detect if the current release rate time series is correct.

[0117] Subsequently, the theoretically synthesized concentration time series was compared with the net concentration time series signal obtained in step three. Since step three has completed background concentration stripping and dynamic response recovery, the net concentration time series signal can more realistically reflect the propagation results of the fault gas.

[0118] If there is still a difference between the theoretical synthesis concentration time series and the net concentration time series signal, it means that the current instantaneous gas release rate time series still needs to be adjusted. Therefore, the optimization objective is to minimize the sum of squared residuals between the theoretical synthesis concentration time series and the net concentration time series signal at all sensor deployment locations. The sum of squared residuals refers to the cumulative value of the squared difference between the theoretical concentration and the actual net concentration at each sampling time. The smaller the residual, the closer the current release rate time series is to the actual release process.

[0119] To continuously correct the instantaneous gas release rate variables corresponding to each release moment, this implementation method uses the conjugate gradient iteration algorithm for optimization. Each time the conjugate gradient iteration algorithm completes an iteration, it corrects the instantaneous gas release rate variables corresponding to all release moments based on the direction of the residual change between the current theoretically synthesized concentration time series and the net concentration time series signal, instead of adjusting each variable separately. Therefore, it can fully consider the mutual influence between different release moments and improve the overall convergence efficiency.

[0120] As the iterations continue, the instantaneous gas release rate corresponding to each release moment is continuously corrected, and the theoretical synthesis concentration time series gradually approaches the net concentration time series signal obtained in step three.

[0121] After each release rate update, the updated instantaneous gas release rate time series is reused to drive the three-dimensional transient convection-diffusion-transport state-space model established in step two, generating a new theoretical synthesis concentration time series, and recalculating the overall residual sum of squares.

[0122] Then, the relative decrease rate of the objective function between two consecutive iterations is calculated. When the relative decrease rate of the objective function is still greater than the preset convergence threshold, it means that the current release rate can still be optimized, and the next round of conjugate gradient iteration is continued. When the relative decrease rate of the objective function is less than the preset convergence threshold, it means that continuing to adjust the release rate can no longer significantly improve the consistency between the theoretical concentration and the actual concentration, and the entire iteration process is terminated at this time.

[0123] The final output is the instantaneous gas release rate time series corresponding to the termination of the iteration. This instantaneous gas release rate time series completely records the change process of fault gas release intensity at each release moment of the partial discharge fault source within the entire historical time window. It not only retains the dynamic characteristics of the partial discharge release intensity changing with time, but also fully integrates the time series signals of various characteristic gas concentrations obtained in step one, the three-dimensional transient convection diffusion transport state space model established in step two, and the arrival time difference information extracted in step three, realizing the reverse recovery from sensor observation data to the actual release process of the fault source.

[0124] The instantaneous gas release rate time series obtained in step four will be used as the dynamic source term input of the three-dimensional transient convection-diffusion-transmission state space model in step five, driving the fault gas concentration field in the entire high-voltage switchgear cavity to perform forward spatiotemporal extrapolation, thereby restoring the true three-dimensional spatiotemporal concentration field distribution in the entire cavity at the current moment.

[0125] Step 1 acquired time-series signals of various characteristic gas concentrations from multiple electrochemical gas sensors, providing raw observation data for partial discharge fault analysis. Step 2 established a three-dimensional transient convection-diffusion-transmission state-space model of the high-voltage switchgear cavity, providing a unified physical description framework for fault gas propagation. Step 3 used the state-space model to remove background concentration interference and extracted the arrival time difference between different sensor deployment locations. Step 4 further used the arrival time difference to invert and obtain the fault source location and the instantaneous gas release rate time series corresponding to each historical moment. At this point, the location of the partial discharge fault and the intensity changes of the released fault gas at each moment have been determined, but the gas concentration distribution at any spatial location within the entire high-voltage switchgear cavity at the current moment is still unknown. Therefore, this step uses the instantaneous gas release rate time series obtained in Step 4 as a dynamic source term to re-drive the three-dimensional transient convection-diffusion-transmission state-space model established in Step 2, performing a forward spatiotemporal extrapolation of the entire propagation process of the fault gas from the start of release to the current moment, thereby restoring the true three-dimensional spatiotemporal concentration field distribution within the entire high-voltage switchgear cavity at the current moment.

[0126] Step four has determined the computational grid node where the partial discharge fault source is located, and obtained the instantaneous gas release rate corresponding to each release moment within the entire historical time window. Therefore, the fault source release process needs to be reloaded into the state space model first.

[0127] In the specific implementation process, the instantaneous gas release rate time series output from step four is input into the three-dimensional transient convection-diffusion-transport state space model one by one according to the corresponding release time.

[0128] Each release moment corresponds to an instantaneous gas release rate variable. Each release rate variable only applies to the computational grid node where the fault source location is determined in step four, while the source terms of other computational grid nodes remain zero.

[0129] In other words, the fault gas is always released from the same fault source location, and the release intensity changes continuously over time. This allows the state-space model to recover the dynamic release behavior consistent with the actual partial discharge process, rather than using a fixed release rate or a one-time release method for approximate calculation.

[0130] After the dynamic source term loading is completed, it is also necessary to determine the initial state of the entire forward simulation calculation. Since a stable concentration distribution formed during normal operation already exists inside the high-voltage switchgear cavity before partial discharge occurs, zero concentration cannot be simply used as the initial condition.

[0131] In specific processing, the steady-state field of the background concentration obtained in the process of calculating the time-series prediction value of the background concentration in step three is used as the initial concentration field of the entire state space model. The steady-state field of the background concentration represents the stable concentration distribution that already exists in each computational grid node in the high-voltage switchgear cavity before partial discharge occurs.

[0132] By using the background concentration steady-state field as the initial concentration field, the entire fault gas propagation process is based on the real operating environment, rather than idealized initial conditions, thus ensuring that the subsequent concentration projection results are consistent with the actual monitoring results in step one.

[0133] Simultaneously, the measured airflow boundary conditions corresponding to the actual operating conditions of the high-voltage switchgear are loaded into the state space model. In step two, when establishing the state space model, the inlet and outlet velocities of each compartment, the velocity-free boundary of the inner wall of the cavity, and the pressure difference boundary of the air passage between compartments were already defined. This step directly uses the measured airflow boundary conditions corresponding to the entire historical time window as the dynamic boundary input.

[0134] As time progresses, the airflow boundary conditions corresponding to each historical moment are used in the calculation in sequence, so that the entire airflow propagation environment can continuously reflect the actual operating status of the high-voltage switchgear, and the diffusion path will not be deviated due to the use of fixed boundary conditions.

[0135] After setting the dynamic source term, initial concentration field, and dynamic boundary conditions, the forward simulation calculation of the entire fault gas propagation process can begin.

[0136] In the specific processing, the starting moment of the historical time window is used as the calculation starting point. The so-called starting moment of the historical time window refers to the first release moment corresponding to the establishment of the instantaneous gas release rate time series in step four, which is also the initial calculation moment before the partial discharge fault begins to release fault gas.

[0137] Subsequently, the calculation is performed step-by-step using the time-discrete step size adopted in step two when establishing the state-space model, with a complete state update performed at each time step. Specifically, at the beginning of the current time step, the instantaneous gas release rate corresponding to the current time step is first read and loaded into the computational grid node where the fault source is located as the input of the source term for the current time step.

[0138] Subsequently, based on the characteristic gas concentration value, airflow velocity value, and current dynamic boundary conditions of all computational grid nodes in the previous time step, the state of each computational grid node in the entire high-voltage switchgear cavity under the current time step is jointly solved.

[0139] Within each time step, the state-space model simultaneously calculates two state variables. One state variable is the characteristic gas concentration field, which represents the characteristic gas concentration value corresponding to each computational grid node within the entire high-voltage switchgear cavity at the current time step. Due to the continuous diffusion and propagation of the fault gas, the concentration field changes continuously over time, with different concentration distributions at different spatial locations. The other state variable is the airflow velocity field, which represents the flow velocity and direction of the insulating medium corresponding to each computational grid node at the current time step. Because the local airflow continuously propagates the fault gas, the airflow velocity field participates in the update of the concentration field at the completion of each time step, ensuring that airflow transport and molecular diffusion jointly influence the fault gas propagation process.

[0140] As time progresses, after each time step calculation is completed, the characteristic gas concentration field and gas velocity field obtained in the current time step are immediately used as the initial state for the next time step calculation to continue participating in the propagation calculation.

[0141] Therefore, the entire state-space model forms a continuous time recursion process, causing the fault gas to continuously diffuse, transport, and mix from the beginning of the historical time window until it propagates to the current moment.

[0142] Throughout the forward simulation, the concentration values ​​of all computational grid nodes at each time step are saved, thus ultimately forming a full-time history concentration field sequence covering the entire historical time window. This full-time history concentration field sequence not only saves the concentration field at the current moment, but also fully records the concentration change process corresponding to each time step since the partial discharge fault occurred.

[0143] In other words, for any given computational grid node, it is possible to query the entire concentration change history from the start of the historical time window to the current time; for any given time step, it is also possible to obtain the spatial concentration distribution corresponding to all computational grid nodes in the entire high-voltage switchgear cavity.

[0144] After completing the forward extrapolation of the entire historical time window, the time layer corresponding to the current moment is extracted from the concentration field sequence of the full time history. The so-called time layer corresponding to the current moment refers to the calculation result corresponding to the latest sampling time of the time series signal of multiple characteristic gas concentrations in step one. After reading this time layer, the characteristic gas concentration values ​​corresponding to all calculation grid nodes in the high-voltage switchgear cavity at the current moment can be obtained.

[0145] Subsequently, the characteristic gas concentration value corresponding to each computational grid node is used as the concentration field amplitude. Simultaneously, the concentration values ​​are mapped to their corresponding spatial locations using the three-dimensional spatial coordinates already saved when establishing the computational grid node set in step two. All computational grid nodes together form a three-dimensional space covering the entire high-voltage switchgear cavity. Therefore, after all concentration values ​​are mapped, the three-dimensional spatiotemporal concentration field distribution across the entire space of the high-voltage switchgear cavity at the current moment is formed.

[0146] The three-dimensional spatiotemporal concentration field distribution not only includes the concentration value corresponding to the current moment of each computational grid node, but also retains the concentration change information corresponding to each historical moment. Therefore, it can completely describe the concentration evolution process of each characteristic gas at any spatial location in the entire space of the high-voltage switchgear cavity from the start of the historical time window to the current moment.

[0147] Compared to Step 1, which only acquires discrete concentration time-series signals at the deployment locations of each electrochemical gas sensor, this step obtains a three-dimensional spatiotemporal concentration field distribution that extends the observation information from a limited number of sensors to the continuous space inside the entire high-voltage switchgear cavity, realizing the recovery from discrete monitoring data to a continuous spatial concentration distribution. Subsequent Step 6 will further calculate the cumulative transmission time delay error introduced by the propagation of fault gas from the fault source location to the deployment locations of each electrochemical gas sensor based on this three-dimensional spatiotemporal concentration field distribution, and perform time delay error compensation on the various characteristic gas concentration time-series signals obtained in Step 1, thereby recovering a more realistic transient concentration change sequence at the fault source location.

[0148] Step 1 acquired time-series signals of various characteristic gas concentrations from multiple electrochemical gas sensors within the high-voltage switchgear cavity. Step 2 established a three-dimensional transient convection-diffusion-transmission state-space model. Step 3 removed background concentration interference and extracted the arrival time difference between different sensor deployment locations. Step 4 inverted the fault source location and the instantaneous gas release rate corresponding to each historical moment. Step 5 further used the instantaneous gas release rate to complete the forward extrapolation of the three-dimensional spatiotemporal concentration field distribution within the entire high-voltage switchgear cavity. Although Step 5 restored the concentration distribution across the entire spatial range at the current moment, the concentration time-series signals actually acquired by each electrochemical gas sensor in Step 1 always have a propagation time lag, meaning that the concentration changes detected by the sensors are delayed relative to the actual release process of the fault source. Therefore, the concentration curves detected by different sensors cannot be directly used as the actual concentration change process at the fault source location. If the sensor detection results are directly used to establish a partial discharge quantity mapping relationship, the initial release process of the discharge will be delayed, affecting the accuracy of subsequent partial discharge quantity calculations. This step utilizes the three-dimensional spatiotemporal concentration field distribution recovered in step five to calculate the cumulative transmission time delay error introduced during the propagation of the fault gas. It then performs unified time compensation on the net concentration time series signal obtained in step three, restoring the detection results of each sensor to the actual release time of the fault source, and finally reconstructing the true concentration transient change sequence at the location of the fault source.

[0149] The three-dimensional spatiotemporal concentration field distribution obtained in step five not only preserves the concentration values ​​corresponding to each computational grid node in the entire high-voltage switchgear cavity at the current moment, but also completely preserves the concentration change process corresponding to all time steps within the entire historical time window. Therefore, it is necessary to extract the concentration change curves corresponding to the fault source location and the deployment location of each sensor separately.

[0150] In the specific processing, based on the spatial coordinates of the fault source determined in step four, the computational grid node where the fault source is located is located in the three-dimensional spatiotemporal concentration field distribution generated in step five.

[0151] Subsequently, the concentration values ​​of the computational grid node from the start of the historical time window to the current time are read and arranged in chronological order to form the fault source concentration change curve for each characteristic gas.

[0152] The concentration change curve of the fault source reflects the concentration change process of the fault gas after its actual release near the location of the partial discharge fault source, and serves as a reference benchmark for the entire time delay compensation process.

[0153] Meanwhile, based on the physical deployment locations of each electrochemical gas sensor recorded in step one, the corresponding computational grid nodes are located in the three-dimensional spatiotemporal concentration field distribution generated in step five.

[0154] Read the concentration values ​​of each computational grid node within the entire historical time window, and then assemble the sensor location concentration change curves for each electrochemical gas sensor deployment location in chronological order.

[0155] Because different sensors are located at different distances from the fault source, have different propagation paths, and different local airflow conditions, the concentration change curves at each sensor location all have different degrees of time delay. Their rise time, peak occurrence time, and decay process all lag behind the concentration change curve of the fault source to varying degrees.

[0156] After extracting the two types of concentration change curves, it is necessary to calculate the propagation time from the fault source location to the deployment location of each sensor.

[0157] This implementation uses cross-correlation analysis to calculate the propagation time delay. Cross-correlation analysis can evaluate the similarity of two concentration change curves under different time offset conditions. When the two curves reach the best correspondence, their corresponding time offset represents the cumulative time delay caused by propagation.

[0158] In the specific processing, for the same characteristic gas, the concentration change curve of the fault source is used as a reference sequence, and the concentration change curve of the corresponding sensor location is used as a comparison sequence.

[0159] Subsequently, the concentration change curve at the sensor position is continuously moved along the time axis to correspond to different time offsets, and the correlation between the two curves under each time offset condition is calculated.

[0160] As the time offset changes, the degree of correspondence between the two curves also changes. When the two curves are most consistent at a certain time offset, the corresponding cross-correlation function reaches its maximum value. At this time, the corresponding time offset represents the total propagation delay experienced by the fault gas from the fault source location to the sensor deployment location.

[0161] Therefore, the delay time corresponding to the maximum value of the cross-correlation function is defined as the cumulative transmission time delay error of the sensor deployment location corresponding to this characteristic gas.

[0162] Let the cumulative transmission time delay error corresponding to a certain sensor deployment location be . ,in, Indicates the first The cumulative transmission time delay error corresponding to each electrochemical gas sensor.

[0163] The cumulative transmission delay error comprehensively reflects the overall time delay formed by the diffusion and propagation of fault gas, local airflow transport, flow around complex spatial structures, and the dynamic response of the sensor. Therefore, it can truly reflect the total propagation time that fault gas takes to reach the sensor.

[0164] After completing the calculation of cumulative transmission delay error, the net concentration time sequence signal obtained in step three needs to be restored to the actual release time of the fault source.

[0165] Since the net concentration time-series signal obtained in step three has already been stripped of background concentration and dynamic response recovery has been completed, only the propagation time delay needs to be further eliminated to recover the true release time. In the specific processing, the cumulative transmission time delay error corresponding to each electrochemical gas sensor is used as the time shift amount.

[0166] Subsequently, the net concentration time sequence signal of the corresponding electrochemical gas sensor obtained in step three is shifted forward along the time axis by the corresponding time shift amount. The so-called forward shift of the time axis means keeping the concentration amplitude unchanged, only changing the time position corresponding to the concentration sequence, so that the originally delayed concentration change is restored to the actual release time of the fault source in advance.

[0167] After the time axis is shifted, the concentration change curves detected by each electrochemical gas sensor are re-corresponded to the actual release time of the fault source, so that the detection results of each sensor maintain a unified reference standard on the time axis.

[0168] After time shifting, a time-delay-compensated concentration sequence is obtained for each electrochemical gas sensor deployment location. This concentration sequence maintains the actual concentration amplitude detected by the sensor while eliminating the overall lag caused by propagation time, thus more accurately reflecting the release process of the partial discharge fault source.

[0169] Since multiple electrochemical gas sensors are usually arranged inside the cavity of a high-voltage switchgear, the same characteristic gas often corresponds to multiple detection results at different spatial locations. Therefore, it is still necessary to further integrate the information from multiple sensors to improve the accuracy of fault source concentration recovery.

[0170] In the specific processing, the above-mentioned cumulative transmission delay error calculation and time axis translation operation are repeatedly performed on all electrochemical gas sensors.

[0171] After all processing is completed, the time-delay compensated concentration sequence of all characteristic gases corresponding to all sensor deployment locations can be obtained.

[0172] Subsequently, for the same characteristic gas, all time-delay compensated concentration sequences are fused according to the spatial distance of their respective electrochemical gas sensors relative to the fault source. Considering that the detection results of electrochemical gas sensors closer to the fault source can more accurately reflect the real concentration changes near the fault source, while electrochemical gas sensors farther away are more affected by diffusion attenuation and local flow field, an inverse distance weighting method is adopted for fusion.

[0173] Specifically, the closer to the fault source, the greater the weight of the corresponding concentration sequence after time delay compensation; the farther away from the fault source, the smaller the corresponding weight. This can give full play to the advantage of the sensitive response of the near-range sensor, while using the long-range sensor to provide overall spatial constraints and improve the stability of the fusion result.

[0174] After all time delay compensation and concentration sequence fusion processing, the final output is the true transient change sequence of the concentration of each characteristic gas. The true transient change sequence of the concentration not only retains the amplitude of the true concentration change of the fault gas during the partial discharge process, but also eliminates the influence of background concentration interference, sensor response lag and fault gas propagation time delay. Its time axis directly corresponds to the actual release process of the partial discharge fault source, so it can truly reflect the dynamic evolution law of the concentration of each characteristic gas at the fault source location over time.

[0175] Compared with the time-series signals of various characteristic gas concentrations obtained in Step 1, the true concentration transient change sequence output in this step has been restored from the concentration observed at the sensor location to the true concentration at the fault source location, achieving reverse correction from the propagation result to the state of the release source. The subsequent Step 7 will perform time-series matching and amplitude mapping with the pre-established concentration-to-discharge dynamic response calibration curve based on this true concentration transient change sequence, thereby calculating the partial discharge value of the high-voltage switchgear under its current operating state.

[0176] Step 1 completed the acquisition of time-series signals of various characteristic gas concentrations; Step 2 established a three-dimensional transient convection-diffusion-transmission state-space model; Step 3 extracted the arrival time difference of the fault gas propagation to different sensor deployment locations; Step 4 obtained the fault source location and the instantaneous gas release rate corresponding to each historical moment through inversion; Step 5 restored the three-dimensional spatiotemporal concentration field distribution within the entire high-voltage switchgear cavity; Step 6 further eliminated the cumulative transmission time delay error during the fault gas propagation process, and finally restored the true concentration transient change sequence corresponding to each characteristic gas at the fault source location. At this point, the system has obtained concentration change information that can truly reflect the partial discharge fault gas release process. However, the true concentration transient change sequence still belongs to gas concentration information, and the insulation status evaluation of high-voltage switchgear usually uses partial discharge quantity as the evaluation index. Therefore, it is necessary to establish the correspondence between the true concentration change and the partial discharge quantity. This step pre-establishes a dynamic response calibration curve from concentration to discharge quantity, and combines it with the true concentration transient change sequence output in Step 6 for time-series matching and amplitude mapping, ultimately outputting the partial discharge quantity value of the high-voltage switchgear under the current operating state.

[0177] In order to ensure that the actual concentration changes can accurately correspond to different partial discharge amounts, it is necessary to establish a dynamic response calibration curve from concentration to discharge amount in advance.

[0178] In the specific implementation process, when the high-voltage switchgear is under offline maintenance, the internal structure of the high-voltage switchgear, the layout of each compartment, and the deployment method of the electrochemical gas sensors are kept completely consistent with step one. That is, the types, quantities, and physical deployment locations of the electrochemical gas sensors are kept consistent, so as to ensure that the calibration relationship established later can be directly applied to the actual operating state.

[0179] Subsequently, multiple simulated partial discharge pulse sequences corresponding to known discharge levels are sequentially injected into the high-voltage switchgear cavity. Different simulated partial discharge pulse sequences correspond to different partial discharge levels, so that the entire calibration process covers the continuous range of changes from weak partial discharge to higher partial discharge levels.

[0180] After each simulated partial discharge pulse injection corresponding to a discharge level is completed, all electrochemical gas sensors in step one simultaneously begin to collect the corresponding characteristic gas concentration change process. After each electrochemical gas sensor outputs an analog voltage signal, analog-to-digital conversion and median average filtering are performed sequentially to generate a digital concentration sequence corresponding to the discharge level.

[0181] Subsequently, instead of adopting a new processing flow, the data processing was carried out strictly in accordance with the data processing process that was completely consistent with steps one through six. Specifically, this included all the processing steps such as generating time-series signals of various characteristic gas concentrations, calculating the three-dimensional transient convection-diffusion-transmission state-space model, removing background concentrations, extracting propagation time delays, inverting the release rate of fault sources, restoring the three-dimensional spatiotemporal concentration field, and compensating for cumulative transmission time delays.

[0182] After unified processing, the true concentration transient change sequence corresponding to the current known discharge level can be obtained. Since the above process is repeated for each known discharge level, the true concentration transient change sequence corresponding to multiple discharge levels can be obtained respectively.

[0183] Subsequently, each known discharge level and its corresponding actual concentration transient change sequence are combined to form a set of calibration samples. All calibration samples are arranged in order of increasing partial discharge, so that the concentration change process changes continuously with the discharge level.

[0184] Since the actual partial discharge quantity is a continuously changing quantity, while the calibration sample only corresponds to a limited number of discharge quantity levels, it is necessary to further establish a continuous mapping relationship.

[0185] In the specific processing, piecewise cubic spline interpolation is performed on all calibration samples. Piecewise cubic spline interpolation can ensure a continuous transition of concentration change curves between adjacent calibration samples, while maintaining a smooth first-order change trend of the curve, so that a limited number of calibration samples can be expanded to form a dynamic response relationship covering the entire continuous discharge range.

[0186] Finally, a dynamic response calibration curve from concentration to discharge amount is generated. The horizontal axis of the dynamic response calibration curve from concentration to discharge amount represents the concentration value corresponding to the actual concentration change sequence, and the vertical axis represents the corresponding partial discharge amount. Therefore, any actual concentration change process can find the corresponding partial discharge amount on this dynamic response calibration curve.

[0187] After establishing the dynamic response calibration curve from concentration to discharge quantity, the discharge quantity can be calculated from the true concentration transient change sequence recovered in step six. Since different partial discharge processes not only exhibit different concentration amplitudes, but also differences in release rate, diffusion establishment rate, and concentration decay process, a simple mapping based solely on the concentration peak value is not feasible; the temporal characteristics of the entire concentration change process must be considered simultaneously.

[0188] In the specific processing, the real concentration transient change sequence output from step six is ​​input into the concentration to discharge dynamic response calibration curve.

[0189] Subsequently, three time-series characteristic parameters that can characterize the dynamic change law of concentration are extracted from the real concentration transient change sequence. The time-series characteristic parameters include the rising edge starting point corresponding to the rapid increase of concentration, the peak occurrence time corresponding to the maximum concentration, and the decay time constant corresponding to the concentration decrease phase.

[0190] The rising edge start point reflects the time position when the faulty gas begins to be released in large quantities; the peak occurrence time reflects the time position when the faulty gas diffusion reaches its maximum concentration; the decay time constant reflects the duration of the faulty gas concentration recovery process.

[0191] The three time-series characteristic parameters mentioned above together describe the entire process of real concentration change, and therefore can more accurately reflect the dynamic release characteristics of partial discharge.

[0192] Subsequently, three identical time-series feature parameters were extracted from all calibration samples corresponding to the dynamic response calibration curves from concentration to discharge amount. For each calibration sample, its corresponding time-series feature parameter was compared with the corresponding time-series feature parameter of the actual concentration transient change sequence. By calculating the overall difference between each calibration sample and the actual concentration change, the calibration sample whose temporal change pattern is closest to the actual concentration change was identified. Specifically, Euclidean distance was used to evaluate the overall similarity; the smaller the Euclidean distance, the closer the actual concentration change process is to the corresponding calibration sample. Therefore, the calibration sample with the smallest Euclidean distance was selected as the best matching sample.

[0193] Meanwhile, the time index corresponding to the calibration sample is defined as the time-series matching anchor point of the real concentration transient change sequence in the dynamic response calibration curve from concentration to discharge amount. After the time-series matching is completed, it is shown that the real concentration change process has been aligned with the calibration curve completion time. However, there may still be differences in the overall concentration amplitude between different partial discharge amounts, so amplitude mapping needs to be further completed.

[0194] In the specific processing, the time-series matching anchor point is used as the starting position, and the concentration value corresponding to each time index in the real concentration transient change sequence is normalized and the concentration value corresponding to the same time index in the concentration-to-discharge dynamic response calibration curve is calculated.

[0195] Suppose the true concentration transient change sequence is at the th... The concentration value corresponding to each time index is The concentration-to-discharge dynamic response calibration curve corresponds to the time index concentration value. The transient amplitude mapping coefficient corresponding to the time index position is expressed as: in, Indicates the first The transient amplitude mapping coefficients corresponding to each time index position.

[0196] After completing the calculation of the normalized ratio corresponding to all time index positions, the transient amplitude mapping coefficient sequence corresponding to the entire concentration change process can be obtained.

[0197] Since individual sampling points may be affected by local fluctuations, causing some mapping coefficients to deviate slightly, the average value is not used directly. Instead, all transient amplitude mapping coefficients are arranged in chronological order, and the median value is calculated as the final optimal amplitude mapping coefficient.

[0198] Using the median value can reduce the impact of local outlier sampling points on the overall mapping result, making the final mapping result more stable.

[0199] After the optimal amplitude mapping coefficient is calculated, the local discharge quantity corresponding to the current characteristic gas can be calculated. In the specific processing, the local discharge quantity on the dynamic response calibration curve from the concentration corresponding to the time-series matching anchor point to the discharge quantity is used as the reference discharge quantity.

[0200] Subsequently, the reference discharge quantity is multiplied by the optimal amplitude mapping coefficient to obtain the instantaneous partial discharge quantity component value corresponding to the current characteristic gas.

[0201] Since multiple electrochemical gas sensors are typically deployed for the same characteristic gas in step one, and each sensor can independently participate in the calculation of partial discharge quantity, multiple corresponding instantaneous partial discharge quantity component values ​​can be obtained for the same characteristic gas.

[0202] Considering that the number of electrochemical gas sensors corresponding to different types of characteristic gases may be different, in order to avoid the overall result being excessively affected by the large number of sensors for a certain type of characteristic gas, this embodiment performs a weighted average based on the number of various types of electrochemical gas sensors in step one.

[0203] Specifically, the more electrochemical gas sensors there are for a particular characteristic gas, the greater the proportion of its corresponding instantaneous partial discharge component in the overall calculation; when the number of sensors is small, its corresponding weight decreases accordingly.

[0204] After weighted fusion of the instantaneous partial discharge component values ​​corresponding to all characteristic gases, the final output is the partial discharge value of the high-voltage switchgear under the current operating state.

[0205] The partial discharge quantity value comprehensively utilizes the time-series signals of various characteristic gas concentrations obtained in step one, the three-dimensional transient convection-diffusion-transmission state-space model established in step two, the propagation time information extracted in step three, the recovered fault gas release process in step four, the reconstructed three-dimensional spatiotemporal concentration field in step five, and the recovered real concentration transient change sequence in step six, realizing the dynamic inversion of the entire process from fault gas diffusion information to partial discharge quantity. Compared with the traditional method of directly estimating discharge quantity based on sensor-detected concentration, this implementation method fully eliminates systematic errors caused by background concentration, spatial diffusion, propagation time lag, and concentration attenuation, making the output partial discharge quantity value closer to the real state of partial discharge inside the high-voltage switchgear, thereby improving the identification capability of early weak partial discharge and the accuracy of discharge quantity assessment.

[0206] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for dynamically extrapolating the spatiotemporal distribution of gas in a partial discharge fault in a high-voltage switchgear, characterized in that, Includes the following steps: Step 1: Acquire the time-series signals of various characteristic gas concentrations output by multiple gas sensors pre-deployed inside the high-voltage switchgear cavity; Step 2: Based on the three-dimensional geometric structure of the high-voltage switchgear cavity, the properties of the insulating medium, and the airflow boundary conditions, construct a three-dimensional transient convection-diffusion transport state-space model to describe the diffusion evolution process after the fault gas is generated. Step 3: Based on the three-dimensional transient convection-diffusion transport state space model, background concentration interference is removed from the time series signals of the various characteristic gas concentrations, and the arrival time difference of each characteristic gas at different sensor deployment locations is extracted; Step 4: Based on the arrival time difference of each characteristic gas, and combined with the diffusion coefficient matrix in the three-dimensional transient convection-diffusion transport state space model, calculate the instantaneous gas release rate corresponding to the fault source location at each historical moment in reverse iteration. Step 5: Load the instantaneous gas release rate at each historical moment as a dynamic source term into the three-dimensional transient convection-diffusion transport state space model, and forward extrapolate to obtain the three-dimensional spatiotemporal concentration field distribution of the high-voltage switchgear cavity in the current moment. Step 6: Based on the three-dimensional spatiotemporal concentration field distribution, calculate the cumulative transmission time delay error introduced by the characteristic gas from the fault source location to each sensor deployment location, and compensate for the time delay error of the concentration reading at each sensor deployment location to obtain the true transient change sequence of concentration at the fault source location. Step 7: Input the actual concentration transient change sequence into the pre-stored concentration-discharge dynamic response calibration curve, and output the partial discharge value of the high-voltage switchgear under the current operating state through time matching and amplitude mapping.

2. The method for dynamic extrapolation of the spatiotemporal distribution of partial discharge fault gas in high-voltage switchgear according to claim 1, characterized in that, Step one includes: An array of electrochemical gas sensors is deployed along the surface of the insulating partition and the inner wall of the cavity in each compartment of the high-voltage switchgear. Each electrochemical gas sensor in the array is used to detect the concentration of one characteristic gas among the characteristic gases. The analog voltage signal output by each electrochemical gas sensor is continuously acquired at a preset sampling frequency, and the analog voltage signal is converted from analog to digital to generate the original concentration digital sequence corresponding to each electrochemical gas sensor. The original concentration digital sequence is subjected to median averaging filtering to remove impulse noise introduced by electromagnetic interference, and the filtered concentration digital sequence corresponding to each electrochemical gas sensor is obtained. Based on the physical deployment location of each electrochemical gas sensor within the high-voltage switchgear cavity, the filtered concentration digital sequences of all electrochemical gas sensors belonging to the same compartment are timestamped to generate time-series signals of various characteristic gas concentrations corresponding to each compartment.

3. The method for dynamic extrapolation of the spatiotemporal distribution of partial discharge fault gas in high-voltage switchgear according to claim 1, characterized in that, Step two includes: A computer-aided design three-dimensional geometric model of the high-voltage switchgear cavity is obtained. An unstructured tetrahedral mesh is performed on the computer-aided design three-dimensional geometric model to generate a set of computational mesh nodes including the internal busbars, insulating partitions, contact boxes and the inner wall of the cavity of each compartment. Each computational grid node in the computational grid node set is assigned insulation medium property parameters, including insulation medium density, insulation medium dynamic viscosity, and the diffusion coefficient tensor of the characteristic gas in the insulation medium. The airflow boundary conditions are set according to the actual operating conditions of the high-voltage switchgear cavity. The airflow boundary conditions include the inlet and outlet flow velocities of each compartment, the velocity no-slip boundary of the inner wall of the cavity, and the pressure difference boundary of the air passage between compartments.

4. The method for dynamic extrapolation of the spatiotemporal distribution of partial discharge fault gas in high-voltage switchgear according to claim 3, characterized in that, Step two includes: Based on the characteristic gas mass conservation equation and the Navier-Stokes momentum conservation equation, a three-dimensional transient convection-diffusion transport partial differential equation system is established on the computational grid node set, coupled with the diffusion coefficient tensor of the characteristic gas in the insulating medium. The system uses the characteristic gas concentration field and the gas flow velocity field as state variables. The source term of the three-dimensional transient convection-diffusion transport partial differential equation system is the time-varying release rate of the fault gas. The three-dimensional transient convection-diffusion transport partial differential equations are spatially discretized on the set of computational grid nodes using the finite volume method, and temporally discretized using the implicit Euler time-progression scheme, generating a three-dimensional transient convection-diffusion transport state-space model of the high-voltage switchgear cavity for iterative solution.

5. The method for dynamic extrapolation of the spatiotemporal distribution of partial discharge fault gas in high-voltage switchgear according to claim 1, characterized in that, Step three includes: For each characteristic gas, the three-dimensional transient convection-diffusion transport state space model is run under the condition of no partial discharge fault, and the time series prediction value of the background concentration of the characteristic gas at each sensor deployment location is calculated. The net concentration time series signal of a characteristic gas at each sensor deployment location is obtained by subtracting the predicted background concentration time series value from the concentration time series signal corresponding to the characteristic gas at each sampling point from the concentration time series signal of a variety of characteristic gas concentration time series signals. Using the pulse transfer function corresponding to the diffusion of the characteristic gas from any spatial point to each sensor deployment location in the three-dimensional transient convection-diffusion transport state-space model as the deconvolution kernel, the Richardson-Lucy iterative deconvolution algorithm is used to perform deconvolution operation on the net concentration time series signal to eliminate the signal broadening effect caused by sensor response hysteresis and local turbulence mixing, and obtain the deconvolution response sequence of the characteristic gas at each sensor deployment location. The moment when the concentration amplitude in the deconvolution response sequence first exceeds three standard deviations of the noise floor of the deconvolution response sequence is detected and marked as the arrival time of the characteristic gas at the sensor deployment location. The arrival times of the same characteristic gas at different sensor deployment locations are then compared pairwise to extract the arrival time difference of the characteristic gas at different sensor deployment locations.

6. The method for dynamic extrapolation of the spatiotemporal distribution of partial discharge fault gas in high-voltage switchgear according to claim 1, characterized in that, Step four includes: Using the arrival time difference of the same characteristic gas at any two sensor deployment locations as the observation input, and based on the theoretical value of the arrival time difference of the characteristic gas from different spatial points to any two sensor deployment locations as represented by the diffusion coefficient matrix in the three-dimensional transient convection-diffusion transport state space model, a set of nonlinear least squares localization equations with the fault source location as the unknown quantity is established. Solving the set of nonlinear least squares localization equations yields the spatial coordinates of the fault source location within the high-voltage switchgear cavity. Using the spatial coordinates of the fault source location as the spatial anchor point of the time-varying point source to be inverted, the historical time window is discretized into N equally spaced release moments. At each release moment, the instantaneous gas release rate variable to be solved is defined, forming an instantaneous gas release rate time series including N variables to be solved, where N is a positive integer greater than or equal to 10. Each instantaneous gas release rate variable in the instantaneous gas release rate time series is used as the source term excitation of the three-dimensional transient convection-diffusion transport state space model. The theoretical concentration response time series at each sensor deployment location is calculated under the single action of the unit pulse release rate corresponding to the instantaneous gas release rate variable. The theoretical concentration response time series at all release times are summed according to the principle of time superposition to obtain the theoretical composite concentration time series at each sensor deployment location. The objective function is to minimize the sum of squared residuals between the synthetic concentration time series and the net concentration time series signal at each sensor deployment location. The conjugate gradient iterative algorithm is used to update each instantaneous gas release rate variable in the instantaneous gas release rate time series one by one until the relative decrease rate of the objective function is less than the preset convergence threshold, at which point the iteration terminates. The instantaneous gas release rate time series corresponding to the termination of iteration is output as the instantaneous gas release rate corresponding to the fault source location at each historical moment.

7. The method for dynamic extrapolation of the spatiotemporal distribution of partial discharge fault gas in high-voltage switchgear according to claim 1, characterized in that, Step five includes: The instantaneous gas release rate is assigned one by one to the source term variable of the computational grid node where the fault source is located in the three-dimensional transient convection-diffusion transport state space model according to its corresponding release time. The background concentration steady-state field in the high-voltage switchgear cavity under the condition of no partial discharge fault is used as the initial concentration field of the three-dimensional transient convection-diffusion transport state space model. The measured airflow boundary conditions under the actual operating conditions of the high-voltage switchgear cavity are used as the dynamic boundary input of the three-dimensional transient convection-diffusion transport state space model in the entire historical time window before the current moment. Starting from the beginning of the historical time window, the three-dimensional transient convection-diffusion transport state space model is solved step by step in the forward direction using the temporal discrete step size of the three-dimensional transient convection-diffusion transport state space model. At each time step, the instantaneous gas release rate of the current time step is used to drive the three-dimensional transient convection-diffusion transport state space model to calculate the characteristic gas concentration value and airflow velocity value at each computational grid node at the current time step, until the forward direction is advanced to the current time, thus obtaining the full time history concentration field sequence from the beginning of the historical time window to the current time. The characteristic gas concentration values ​​at each computational grid node within the entire space of the high-voltage switchgear cavity at the current moment are extracted from the full-time history concentration field sequence. The characteristic gas concentration values ​​are used as the concentration field amplitude at each computational grid node. The three-dimensional spatiotemporal concentration field distribution within the entire space of the high-voltage switchgear cavity is constructed by combining the spatial coordinates of each computational grid node. The three-dimensional spatiotemporal concentration field distribution includes the concentration value change history of each characteristic gas at each spatial location within the entire space of the high-voltage switchgear cavity from the initial moment to the current moment.

8. The method for dynamic extrapolation of the spatiotemporal distribution of partial discharge fault gas in high-voltage switchgear according to claim 1, characterized in that, Step six includes: Extract the fault source concentration change curve of each characteristic gas at the fault source location over the entire time history from the three-dimensional spatiotemporal concentration field distribution, and extract the sensor location concentration change curve of the same characteristic gas at each sensor deployment location over the entire time history from the three-dimensional spatiotemporal concentration field distribution. The concentration change curve of the fault source and the concentration change curve of the sensor location are cross-correlated along the time axis to obtain the delay time corresponding to the maximum value of the cross-correlation function. The delay time is marked as the cumulative transmission time delay error of the characteristic gas from the fault source location to the sensor deployment location. Using the cumulative transmission time delay error as the time shift amount when the electrochemical gas sensor at the sensor deployment location detects the characteristic gas, the net concentration time sequence signal of the characteristic gas detected at the sensor deployment location is shifted forward along the time axis by the time shift amount, so that the shifted net concentration time sequence signal is aligned with the actual release time of the characteristic gas at the fault source location on the time axis, and the time delay compensated concentration sequence of the characteristic gas at the sensor deployment location is obtained. For each characteristic gas at each sensor deployment location, the above-mentioned cumulative transmission delay error calculation and net concentration time sequence signal time axis forward translation operation are performed to obtain the time delay compensated concentration sequence of all types of characteristic gases at all sensor deployment locations. The time delay compensated concentration sequences of the same characteristic gas at all sensor deployment locations are then inversely distance-weighted and fused according to the spatial distance between their respective sensor deployment locations and the fault source location to output the true concentration transient change sequence of each characteristic gas at the fault source location.

9. The method for dynamic extrapolation of the spatiotemporal distribution of partial discharge fault gas in high-voltage switchgear according to claim 1, characterized in that, Step seven includes: Electrochemical gas sensors of the same type and location as those in step one are pre-deployed within the high-voltage switchgear cavity. Under offline maintenance conditions, a sequence of simulated partial discharge pulses of known discharge levels is injected into the high-voltage switchgear cavity. The analog voltage signal output from each electrochemical gas sensor is collected, and analog-to-digital conversion and filtering are performed. Following the same processing flow as steps one through six, a transient change sequence of the actual concentration for calibration corresponding to each known discharge level is obtained. Each known discharge level and its corresponding transient change sequence of the actual concentration for calibration are used as a set of calibration samples. All calibration samples corresponding to all discharge levels are arranged in ascending order of discharge quantity and piecewise cubic spline interpolation is performed to generate a concentration-discharge dynamic response calibration curve covering the continuous discharge quantity range. The horizontal axis of the concentration-discharge dynamic response calibration curve represents the concentration value sequence, and the vertical axis represents the discharge quantity value.

10. The method for dynamic extrapolation of the spatiotemporal distribution of partial discharge fault gas in high-voltage switchgear according to claim 9, characterized in that, Step seven includes: Input the true concentration transient change sequence output in step six into the concentration-discharge dynamic response calibration curve. Use the rising edge start point, peak occurrence time, and decay time constant of the true concentration transient change sequence on the time axis as time series feature parameters. Search for the calibration sample with the smallest Euclidean distance to the time series feature parameters in each set of calibration samples of the concentration-discharge dynamic response calibration curve. Use the time index corresponding to the searched calibration sample as the time series matching anchor point of the true concentration transient change sequence on the concentration-discharge dynamic response calibration curve. Starting from the time-series matching anchor point, the normalized ratio of each concentration amplitude in the real concentration transient change sequence to the concentration value at the same time index position in the concentration-discharge dynamic response calibration curve is calculated to obtain the transient amplitude mapping coefficient at each time index position. The transient amplitude mapping coefficients at all time index positions are arranged in chronological order to form a transient amplitude mapping coefficient sequence. The median value of the transient amplitude mapping coefficient sequence is calculated as the optimal amplitude mapping coefficient. The product of the discharge value corresponding to the concentration-discharge dynamic response calibration curve at the time-matching anchor point and the optimal amplitude mapping coefficient is used as the instantaneous partial discharge component value of the high-voltage switchgear under the current operating state for that characteristic gas. The instantaneous partial discharge component value corresponding to each characteristic gas is weighted and averaged according to the number of sensors in the electrochemical gas sensor array for each characteristic gas in step one, and the partial discharge value of the high-voltage switchgear under the current operating state is output.

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