A time reversal based method and device for partial discharge positioning in multi-chamber switchgear

Abstract

The application discloses a time reversal-based partial discharge positioning method and device for a multi-chamber switch cabinet, which comprises the following steps: obtaining an electromagnetic wave propagation response signal generated by partial discharge through a sensor arranged on the switch cabinet; intercepting the electromagnetic wave propagation response signal to obtain a discharge pulse segment; performing time reversal on the discharge pulse segment to obtain a reversed excitation signal; injecting the reversed excitation signal into a three-dimensional electromagnetic model of the multi-chamber switch cabinet, and obtaining the time-varying electric field intensity distribution of each position in the model by using the finite difference time domain method; identifying a spatial region where electric field energy is concentrated based on the time-varying electric field intensity distribution, and determining the spatial region as a partial discharge candidate region; arranging a plurality of candidate monitoring points in the candidate region, extracting an electric field time domain signal corresponding to each candidate monitoring point from the time-varying electric field intensity distribution; calculating a comprehensive evaluation value of each candidate monitoring point based on each electric field time domain signal; and determining a partial discharge position based on each comprehensive evaluation value.

Description

Technical Field

[0001] This application relates to the field of partial discharge detection technology for power equipment, and relates to, but is not limited to, a method and apparatus for locating partial discharge in multi-chamber switchgear based on time reversal. Background Technology

[0002] Partial discharge detection is a crucial method for assessing the insulation condition of power equipment. It enables the early detection of potential defects in the early stages of insulation development, thereby effectively preventing insulation breakdown accidents. With the increasing demands for equipment reliability in power systems, achieving accurate location of partial discharges has become a critical issue that urgently needs to be addressed in the field of power equipment operation and maintenance. Among various types of power equipment, switchgear, due to its complex internal structure and numerous chambers, exhibits diverse propagation paths and varying attenuation characteristics of partial discharge signals, making traditional location methods difficult to achieve ideal results.

[0003] Electromagnetic time-reversal (ETR) based localization methods are a representative partial discharge localization technique that has emerged in recent years. The basic idea of ​​this technique consists of two stages: forward and backward. In the forward stage, an electromagnetic pulse signal is generated by simulating a partial discharge event, and a sensor collects the response signal after propagation. In the backward stage, the collected signal undergoes time truncation and time-reversal processing, and the processed signal is reinjected into the model from the sensor location. According to the theory of ETR, the reinjected signal will produce a high electric field intensity focusing phenomenon within a specific time interval at the original partial discharge location. By observing this focusing phenomenon, the location of the partial discharge can be inferred. Currently, this method is mainly studied and verified in gas-insulated switchgear models. These devices are characterized by a cylindrical structure with no internal chambers, a relatively simple electromagnetic wave propagation path, and a pronounced focusing phenomenon.

[0004] However, directly applying the aforementioned electromagnetic time-reversal-based positioning method to switchgear with multiple chambers and complex internal structures presents significant problems. When the chamber where the sensor is located is not the same as the chamber where the partial discharge point is located, the signal reinjected during the backward stage will generate a high electric field response in the sensor's chamber, while the electric field strength in the chamber where the actual discharge point is located will be significantly reduced due to cross-cavity propagation attenuation. If the maximum electric field strength is still used as the positioning basis, the focusing signal of the actual discharge point will be masked by the high field strength region of the sensor's chamber, causing the positioning result to deviate from the true location. In addition, related technologies typically use the method of observing the electric field strength distribution on a pre-defined cross-section to determine the focusing position. However, there are many cross-sections in space, and the electric field distribution on cross-sections far from the actual discharge point cannot provide meaningful positioning information, nor can it reflect the actual distance relationship between the cross-section and the discharge point. This makes the selection of the cross-section highly random and subjective, reducing the accuracy of partial discharge detection. Summary of the Invention

[0005] In view of this, the embodiments of this application provide a method and apparatus for locating partial discharge in multiple chambers of switchgear based on time reversal, which at least solves the technical problem of inaccurate location of partial discharge in multiple chambers of switchgear.

[0006] The technical solution of this application embodiment is implemented as follows: In a first aspect, embodiments of this application provide a method for locating partial discharges in multiple chambers of a switchgear based on time reversal, the method comprising: Sensors deployed on the switch cabinet are used to acquire electromagnetic wave propagation response signals generated by partial discharge; the electromagnetic wave propagation response signals are truncated to obtain discharge pulse segments; the discharge pulse segments are then subjected to time inversion processing to obtain inversion excitation signals. The inversion excitation signal is injected back from the sensor at the corresponding position in the switch cabinet into the pre-constructed three-dimensional electromagnetic model of the switch cabinet multi-chamber. The time-varying electric field intensity distribution at each position in the three-dimensional electromagnetic model of the switch cabinet multi-chamber is obtained by the finite difference method in the time domain. Based on the electric field vector direction at each location in the time-varying electric field intensity distribution, multiple electric field streamlines are generated to identify spatial regions exhibiting electric field energy accumulation characteristics; the electric field streamlines extend along the electric field vector direction; the spatial range enclosed by the cluster of streamlines that converge to the same local spatial neighborhood is determined as a candidate region for partial discharge; the volume of the candidate region is smaller than the volume of the three-dimensional electromagnetic model of the multi-chamber switchgear; Multiple candidate monitoring points are deployed within the candidate area, and the electric field time-domain signal corresponding to each candidate monitoring point is extracted from the time-varying electric field intensity distribution; a comprehensive evaluation value for the corresponding candidate monitoring point is calculated based on each electric field time-domain signal. The location of partial discharge is determined based on the comprehensive evaluation value corresponding to each candidate monitoring point.

[0007] Secondly, embodiments of this application provide a time-reversal-based multi-chamber partial discharge localization device for switchgear, comprising: a sensor module, a storage module, and a processing module; wherein: The sensor module is used to acquire the electromagnetic wave propagation response signal generated by partial discharge through sensors deployed on the switch cabinet; The storage module is used to store a pre-built three-dimensional electromagnetic model of a multi-chamber switchgear. The processing module is connected to both the sensor module and the storage module, and is used to perform the following operations: The electromagnetic wave propagation response signal is truncated to obtain a discharge pulse segment; the discharge pulse segment is then subjected to time inversion processing to obtain an inverted excitation signal. The inversion excitation signal is injected back from the sensor at the corresponding position in the switch cabinet into the pre-constructed three-dimensional electromagnetic model of the switch cabinet multi-chamber. The time-varying electric field intensity distribution at each position in the three-dimensional electromagnetic model of the switch cabinet multi-chamber is obtained by the finite difference method in the time domain. Based on the electric field vector direction at each location in the time-varying electric field intensity distribution, multiple electric field streamlines are generated to identify spatial regions exhibiting electric field energy accumulation characteristics; the electric field streamlines extend along the electric field vector direction; the spatial range enclosed by the cluster of streamlines that converge to the same local spatial neighborhood is determined as a candidate region for partial discharge; the volume of the candidate region is smaller than the volume of the three-dimensional electromagnetic model of the multi-chamber switchgear; Multiple candidate monitoring points are deployed within the candidate area, and the electric field time-domain signal corresponding to each candidate monitoring point is extracted from the time-varying electric field intensity distribution; a comprehensive evaluation value for the corresponding candidate monitoring point is calculated based on each electric field time-domain signal. The location of partial discharge is determined based on the comprehensive evaluation value corresponding to each candidate monitoring point.

[0008] The beneficial effects of the technical solutions provided in this application include at least the following: This application acquires the electromagnetic wave propagation response signal generated by partial discharge using sensors deployed on the switchgear. The electromagnetic wave propagation response signal is truncated to obtain a discharge pulse segment. The discharge pulse segment is then subjected to time-reversal processing to obtain an inverted excitation signal. By truncating the electromagnetic wave propagation response signal, noise and interference components unrelated to partial discharge are removed, retaining only the discharge pulse segment containing partial discharge information. The time-reversal processing of the discharge pulse segment ensures that the inverted excitation signal has the characteristic of generating electric field focusing at the original discharge source location after reinjection. The inverted excitation signal is reinjected from the corresponding position of the sensor in the switchgear into a pre-constructed three-dimensional electromagnetic model of the switchgear's multi-chamber system. Using the finite-difference time-domain method, the time-varying electric field intensity distribution at each position in the three-dimensional electromagnetic model of the switchgear's multi-chamber system during reinjection is obtained. The inverted excitation signal is used to subsequently identify spatial regions where electric field energy accumulates, providing a basis for determining candidate regions where partial discharge occurs. Based on the time-varying electric field intensity distribution, spatial regions exhibiting electric field energy accumulation characteristics in the three-dimensional electromagnetic model of the multi-chamber switchgear are identified and designated as candidate regions for partial discharge. The volume of the candidate region is smaller than the volume of the three-dimensional electromagnetic model of the multi-chamber switchgear. Identifying spatial regions exhibiting electric field energy accumulation characteristics based on the time-varying electric field intensity distribution utilizes the characteristic of electric field focusing at the original discharge source location by the time-reversed back-injection signal. Designating spatial regions exhibiting electric field energy accumulation characteristics as candidate regions reduces the search range for subsequent localization operations from the entire three-dimensional electromagnetic model of the multi-chamber switchgear to a smaller spatial region, reducing computational load and improving partial discharge localization efficiency. Multiple candidate monitoring points are deployed within the candidate region, and the electric field time-domain signal corresponding to each candidate monitoring point is extracted from the time-varying electric field intensity distribution. A comprehensive evaluation value for the corresponding candidate monitoring point is calculated based on each electric field time-domain signal. This comprehensive evaluation value provides a basis for subsequent determination of the partial discharge location. By deploying multiple candidate monitoring points, detailed evaluation of each location within the candidate region can be performed, thereby improving the accuracy of locating the partial discharge location. The location of partial discharge is determined based on the comprehensive evaluation value corresponding to each candidate monitoring point. The comprehensive evaluation value integrates the signal characteristics of the candidate monitoring points in both the time and frequency domains. Since interference signals only exhibit abnormalities in specific dimensions, it is difficult to achieve high scores simultaneously across multiple evaluation dimensions. Determining the location based on the comprehensive evaluation value effectively filters out random interference, enhances the response weight of the true partial discharge location, and enables precise localization of partial discharge locations in complex electromagnetic environments. Therefore, this application improves the accuracy of locating partial discharges in multiple chambers of switchgear. Attached Figure Description

[0009] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort, wherein: Figure 1 A flowchart illustrating a time-reversal-based method for locating partial discharges in a multi-chamber switchgear, as provided in this application embodiment; Figure 2 A schematic diagram of the discharge pulse segment of the method provided in the embodiments of this application; Figure 3 A schematic diagram of the inversion excitation signal of the method provided in the embodiments of this application; Figure 4 A schematic diagram of the time-varying electric field intensity distribution of the method provided in the embodiments of this application; Figure 5 A waveform diagram illustrating the electric field energy accumulation characteristics of the method provided in the embodiments of this application; Figure 6 A schematic diagram illustrating the electric field energy accumulation characteristics in the method provided in the embodiments of this application; Figure 7 This is a schematic diagram illustrating the deployment of candidate monitoring points in the method provided in the embodiments of this application; Figure 8 This is a schematic diagram of a time-reversal-based multi-chamber partial discharge locating device for switchgear, provided in an embodiment of this application. Detailed Implementation

[0010] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. The following embodiments are used to illustrate this application, but are not intended to limit the scope of this application. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0011] In the following description, references are made to “some embodiments,” which describe a subset of all possible embodiments. However, it is understood that “some embodiments” may be the same subset or different subsets of all possible embodiments and may be combined with each other without conflict.

[0012] It should be noted that the terms "first, second, and third" used in the embodiments of this application are merely to distinguish similar objects and do not represent a specific ordering of objects. It is understood that "first, second, and third" can be interchanged in a specific order or sequence where permitted, so that the embodiments of this application described herein can be implemented in an order other than that illustrated or described herein.

[0013] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which the embodiments of this application pertain. It should also be understood that terms such as those defined in general dictionaries should be understood to have a meaning consistent with their meaning in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless specifically defined as herein.

[0014] This application provides a time-reversal-based method for locating partial discharges in multi-chamber switchgear. Figure 1 A flowchart illustrating a time-reversal-based method for locating partial discharges in multi-chamber switchgear, as provided in this application embodiment, is shown below. Figure 1 As shown, the method includes at least the following steps: Step S110: The electromagnetic wave propagation response signal generated by partial discharge is acquired by a sensor installed on the switch cabinet; the electromagnetic wave propagation response signal is intercepted to obtain a discharge pulse segment; the discharge pulse segment is processed by time inversion to obtain an inversion excitation signal.

[0015] The sensor has sufficient bandwidth to cover the main frequency components of the electromagnetic wave signal generated by partial discharge. The sensor can be one of the following: an ultra-high frequency sensor, a capacitively coupled sensor, or a high-frequency current transformer.

[0016] When the sensor is an ultra-high frequency sensor, the operating frequency band is between 300 MHz and 3000 MHz. The ultra-high frequency sensor is attached to the surface of the switch cabinet housing or embedded in the casting hole of the basin insulator in the form of a patch antenna.

[0017] When the sensor is a capacitively coupled sensor, electromagnetic wave signals are detected through capacitive coupling between the metal electrode and the internal conductor or outer shell of the switch cabinet. The capacitively coupled sensor can be fixed on the inner or outer wall of the switch cabinet shell.

[0018] When the sensor is a high-frequency current transformer, it is connected to the grounding wire or busbar of the switchgear to detect the pulse current signal generated by partial discharge.

[0019] Figure 2 This is a schematic diagram of the discharge pulse segment of the method provided in the embodiments of this application. Figure 2As shown, the horizontal axis represents the time axis, with the unit being nanoseconds (ns), and the vertical axis represents the signal amplitude of the discharge pulse segment.

[0020] The electromagnetic wave propagation response signal is the electrical signal output by the sensor. It contains the waveform information of the electromagnetic waves generated by partial discharge after propagating inside the switch cabinet.

[0021] A discharge pulse segment is a segment of signal extracted from the electromagnetic wave propagation response signal. The discharge pulse segment corresponds to the electromagnetic pulse generated during partial discharge. For example, a discharge pulse segment is obtained by extracting a signal from the electromagnetic wave propagation response signal between 0 and 80 ns.

[0022] Time-inversion processing is the operation of reversing the discharge pulse segments along the time axis. The inverted excitation signal is the signal obtained after time-inversion processing, and it is used for subsequent reinjection into the multi-chamber three-dimensional electromagnetic model of the switchgear. The inverted excitation signal is saved as an ASCII file.

[0023] Figure 3 This is a schematic diagram of the inversion excitation signal provided in the embodiments of this application. Figure 3 As shown, the horizontal axis represents time, and the vertical axis represents the amplitude of the inverted excitation signal. From the waveform characteristics of the inverted excitation signal, it exhibits transient high-frequency oscillations in the initial stage, with the signal amplitude rapidly reaching its peak. Subsequently, the waveform of the inverted excitation signal enters a relatively stable but slightly fluctuating middle and later stage, with the signal amplitude maintaining a high level and gradually decaying towards zero. This time-domain waveform characteristic indicates that the inverted excitation signal can effectively characterize the effective excitation component at the partial discharge location.

[0024] By truncating the electromagnetic wave propagation response signal, noise and interference components unrelated to partial discharge were removed, retaining only the discharge pulse segment containing partial discharge information. Time-reversal processing was then performed on the discharge pulse segment, enabling the reversed excitation signal to achieve electric field focusing at the original discharge source location after reinjection.

[0025] Step S120: The inversion excitation signal is injected back from the sensor at the corresponding position of the switchgear into the pre-constructed three-dimensional electromagnetic model of the multi-chamber switchgear. The time-varying electric field intensity distribution at each position in the three-dimensional electromagnetic model of the multi-chamber switchgear during the injection is obtained by using the finite-difference time-domain method.

[0026] The corresponding position of the sensor in the switch cabinet refers to the installation position of the sensor on the switch cabinet when collecting electromagnetic wave propagation response signals.

[0027] The multi-chamber 3D electromagnetic model of the switchgear is pre-built and corresponds to the actual switchgear structure. If the multi-chamber 3D electromagnetic model of the switchgear is a simulation model, a switchgear model of the corresponding scale is constructed, distinguishing each chamber and the openings of the busbars on the cabinet. If the multi-chamber 3D electromagnetic model of the switchgear is an experimental scenario, a simulation model with the same structure as the actual switchgear is built. This model includes equivalent models of the cabinet, busbars, insulating supports, and sensors to ensure that the electromagnetic wave propagation response signal collected in the forward stage is consistent with the electromagnetic environment in the model during the backward stage injection.

[0028] The Finite-Difference Time-Domain Method (FDTD) is a numerical method for solving electromagnetic field problems. It calculates the distribution of the electromagnetic field at various locations within the model by discretizing the space and time.

[0029] The time-varying electric field intensity distribution describes the electric field intensity value at each location in the three-dimensional electromagnetic model of the multi-chamber switchgear at every moment after the injection begins.

[0030] The inversion excitation signal is injected back from the sensor at the corresponding position in the switchgear into the pre-constructed three-dimensional electromagnetic model of the multi-chamber switchgear. The calculation time interval is set to 70ns to 80ns. Within this time interval, the time-varying electric field intensity distribution at each position in the three-dimensional electromagnetic model of the multi-chamber switchgear during the injection process is obtained by using the finite-difference time-domain method.

[0031] Figure 4 This is a schematic diagram of the time-varying electric field intensity distribution of the method provided in the embodiments of this application. Figure 4 As shown, the transparent cube represents the geometric structure of the switch cabinet. Within the transparent cube, the electric field intensity exhibits a non-uniform distribution. The electric field intensity in the region containing the irregular red dots is significantly higher than in other regions, representing the area of ​​strong disturbance to the surrounding electromagnetic environment caused by partial discharge.

[0032] Figure 5 A waveform diagram illustrating the electric field energy accumulation characteristics of the method provided in this application embodiment. (See attached image.) Figure 5 As shown, the horizontal axis represents time in nanoseconds, and the vertical axis represents electric field strength in volts per meter (V / m). The electric field time-domain signal at the candidate monitoring point maintains low amplitude fluctuations in the previous time period, with a significant electric field peak appearing near the focusing time window. This electric field peak is significantly higher than the aforementioned background electric field level, which can be used as a basis for judging whether the candidate monitoring point has electric field energy accumulation characteristics and is used in the subsequent calculation of the comprehensive evaluation value.

[0033] The inversion excitation signal is injected back from the sensor at the corresponding location in the switchgear into the three-dimensional electromagnetic model of the multi-chamber switchgear. This utilizes computer simulation to replace actual physical experiments, simulating the propagation process of the inversion excitation signal inside the switchgear. Calculations using the finite-difference time-domain method yield data on the time-varying electric field intensity generated by the inversion excitation signal at each location in the three-dimensional electromagnetic model of the multi-chamber switchgear. The inversion excitation signal is then used to identify spatial regions where electric field energy accumulates, providing a basis for determining candidate regions for partial discharge.

[0034] Step S130: Based on the electric field vector direction at each location in the time-varying electric field intensity distribution, multiple electric field streamlines are generated to identify spatial regions exhibiting electric field energy accumulation characteristics; the electric field streamlines extend along the electric field vector direction; the spatial range surrounded by the streamline clusters that converge to the same local spatial neighborhood among the multiple electric field streamlines is determined as a candidate region for partial discharge; the volume of the candidate region is smaller than the volume of the three-dimensional electromagnetic model of the multi-chamber switchgear.

[0035] The time-varying electric field intensity distribution describes the electric field intensity value at each location in the three-dimensional electromagnetic model of the multi-chamber switchgear at every moment after the injection begins.

[0036] The electric field energy concentration characteristic refers to the phenomenon in a time-varying electric field intensity distribution where the electric field intensity value in a certain spatial region is significantly higher than that in the surrounding region. This phenomenon is caused by the focusing effect of the inverted excitation signal at the original discharge source location.

[0037] Candidate regions are spatial areas initially identified as potentially containing partial discharge locations.

[0038] In the time-varying electric field intensity distribution obtained in the backward stage, the spatial distribution of electric field streamlines is influenced by the properties of the electric field streamlines themselves and the setting of their starting points. The electric field streamlines are distributed at various locations in the three-dimensional electromagnetic model of the multi-chamber switchgear. Due to the influence of the focusing electric field, streamlines naturally converge at the focusing point. The focusing time can be estimated based on the electromagnetic wave propagation response signal obtained in the forward stage; the focusing time is approximately 70 ns to 80 ns. The convergence of electric field streamlines is more easily observed near this focusing time.

[0039] Figure 6 This is a schematic diagram illustrating the electric field energy accumulation characteristics in the method provided in the embodiments of this application. Figure 6 The two boxes on the left represent locally amplified portions of the electric field energy accumulation characteristics. The locally amplified portion in the upper left region corresponds to the injection port at the sensor location, where the electric field streamlines exhibit a divergent pattern and do not form a convergent cluster. The locally amplified portion in the lower left region corresponds to the partial discharge location, where the electric field streamlines clearly converge to a local neighborhood, forming a convergent cluster, indicating that this location is a point of electric field energy accumulation.

[0040] In this application, the injection point of the reinjection signal is the location of the sensor, which exhibits a high electric field intensity response due to the influence of the reinjection signal. Numerous electric field streamlines also appear near the sensor location, but these streamlines at the injection point typically diverge from the injection point into the switchgear model or extend along the propagation path. At more distant locations, the electric field streamlines exhibit an irregular divergent or interlaced distribution, failing to form a streamline cluster structure that converges in an ordered manner to a single local neighborhood.

[0041] It should be noted that electric field streamlines are not solely determined by the magnitude of the electric field intensity, but rather are the result of continuously tracing the direction of the electric field vector in space. The shape of electric field streamlines primarily reflects the spatial distribution of the electric field direction, rather than just the intensity of the electric field at a specific point or region. Therefore, a region of high field strength does not necessarily correspond to a region of convergence of electric field streamlines.

[0042] Furthermore, this step passed the interference test, and the test results showed that the focusing effect of the electric field streamlines was caused by the focusing of the electric field intensity near the partial discharge location generated by the time reversal process, rather than by the concentration of the electric field intensity caused by the structural protrusion of the insulating support.

[0043] Based on the identification of spatial regions exhibiting electric field energy accumulation characteristics by time-varying electric field intensity distribution, the electric field focusing characteristic of time-reversed back-injection signals at the original discharge source location is utilized. Determining spatial regions exhibiting electric field energy accumulation characteristics as candidate regions reduces the search range for subsequent positioning operations from the entire multi-chamber three-dimensional electromagnetic model of the switchgear to a smaller spatial region, reducing computational load and improving partial discharge positioning efficiency.

[0044] Step S140: Deploy multiple candidate monitoring points within the candidate area, extract the electric field time-domain signal corresponding to each candidate monitoring point from the time-varying electric field intensity distribution, and calculate the comprehensive evaluation value corresponding to each candidate monitoring point based on the electric field time-domain signal.

[0045] Candidate monitoring points are multiple virtual locations deployed within a candidate region to monitor changes in the electric field at each candidate monitoring point. The electric field time-domain signal is the signal showing the change in the electric field intensity at the candidate monitoring point over time. The comprehensive evaluation value is used to measure the probability that a candidate monitoring point will become a partial discharge location.

[0046] Within the candidate area, multiple candidate monitoring points are set up by deploying a virtual sensor array. Figure 7 This is a schematic diagram illustrating the deployment of candidate monitoring points in the method provided in this embodiment of the application. Figure 7As shown, each crosshair serves as a candidate monitoring point. Multiple candidate monitoring points are sequentially arranged along the main extension direction of the candidate region at preset spatial intervals to discretely sample the electric field time-domain signal at different locations within the candidate region. This arrangement forms a set of candidate monitoring points covering multiple spatial locations within the candidate region, facilitating the subsequent extraction of the electric field time-domain signal corresponding to each candidate monitoring point and further calculation of the corresponding comprehensive evaluation value. The spatial location of the green crosshair is the final partial discharge location determined based on the comprehensive evaluation value.

[0047] The comprehensive evaluation value of the corresponding candidate monitoring point is calculated based on the time-domain signal of each electric field, providing a basis for subsequent determination of the partial discharge location. By deploying multiple candidate monitoring points, a detailed evaluation of each location within the candidate area can be performed, thereby improving the accuracy of locating the partial discharge location.

[0048] Step S150: Determine the location of partial discharge based on the comprehensive evaluation value corresponding to each candidate monitoring point.

[0049] Partial discharge location is the spatial location in which a partial discharge event occurs within the switchgear.

[0050] The comprehensive evaluation value integrates the signal characteristics of candidate monitoring points in both the time and frequency domains. Since interference signals only exhibit abnormalities in specific dimensions, it is difficult to achieve high scores across multiple evaluation dimensions simultaneously. Therefore, determining the location based on the comprehensive evaluation value can effectively filter out random interference, enhance the response weight of the true partial discharge location, and achieve accurate localization of partial discharge locations in complex electromagnetic environments.

[0051] This application acquires the electromagnetic wave propagation response signal generated by partial discharge using sensors deployed on the switchgear. The electromagnetic wave propagation response signal is truncated to obtain a discharge pulse segment. The discharge pulse segment is then subjected to time-reversal processing to obtain an inverted excitation signal. By truncating the electromagnetic wave propagation response signal, noise and interference components unrelated to partial discharge are removed, retaining only the discharge pulse segment containing partial discharge information. The time-reversal processing of the discharge pulse segment ensures that the inverted excitation signal has the characteristic of generating electric field focusing at the original discharge source location after reinjection. The inverted excitation signal is reinjected from the corresponding position of the sensor in the switchgear into a pre-constructed three-dimensional electromagnetic model of the switchgear's multi-chamber system. Using the finite-difference time-domain method, the time-varying electric field intensity distribution at each position in the three-dimensional electromagnetic model of the switchgear's multi-chamber system during reinjection is obtained. The inverted excitation signal is used to subsequently identify spatial regions where electric field energy accumulates, providing a basis for determining candidate regions where partial discharge occurs. Based on the time-varying electric field intensity distribution, spatial regions exhibiting electric field energy accumulation characteristics in the three-dimensional electromagnetic model of the multi-chamber switchgear are identified and designated as candidate regions for partial discharge. The volume of the candidate region is smaller than the volume of the three-dimensional electromagnetic model of the multi-chamber switchgear. Identifying spatial regions exhibiting electric field energy accumulation characteristics based on the time-varying electric field intensity distribution utilizes the characteristic of electric field focusing at the original discharge source location by the time-reversed back-injection signal. Designating spatial regions exhibiting electric field energy accumulation characteristics as candidate regions reduces the search range for subsequent localization operations from the entire three-dimensional electromagnetic model of the multi-chamber switchgear to a smaller spatial region, reducing computational load and improving partial discharge localization efficiency. Multiple candidate monitoring points are deployed within the candidate region, and the electric field time-domain signal corresponding to each candidate monitoring point is extracted from the time-varying electric field intensity distribution. A comprehensive evaluation value for the corresponding candidate monitoring point is calculated based on each electric field time-domain signal. This comprehensive evaluation value provides a basis for subsequent determination of the partial discharge location. By deploying multiple candidate monitoring points, detailed evaluation of each location within the candidate region can be performed, thereby improving the accuracy of locating the partial discharge location. The location of partial discharge is determined based on the comprehensive evaluation value corresponding to each candidate monitoring point. The comprehensive evaluation value integrates the signal characteristics of the candidate monitoring points in both the time and frequency domains. Since interference signals only exhibit abnormalities in specific dimensions, it is difficult to achieve high scores simultaneously across multiple evaluation dimensions. Determining the location based on the comprehensive evaluation value effectively filters out random interference, enhances the response weight of the true partial discharge location, and enables precise localization of partial discharge locations in complex electromagnetic environments. Therefore, this application improves the accuracy of locating partial discharges in multiple chambers of switchgear.

[0052] Based on the electric field vector direction at each location in the time-varying electric field intensity distribution, multiple electric field streamlines are generated to identify spatial regions exhibiting electric field energy accumulation characteristics; the electric field streamlines extend along the electric field vector direction; the spatial range surrounded by the streamline clusters that converge to the same local spatial neighborhood among the multiple electric field streamlines is determined as the candidate region for partial discharge.

[0053] Based on the electric field vector direction at each location in the time-varying electric field intensity distribution, multiple electric field streamlines are generated. These streamlines extend along the electric field vector direction, converging at locations where electric field energy is concentrated. The spatial region enclosed by the streamline clusters that converge to the same local spatial neighborhood is defined as the candidate region. This method narrows the search range for subsequent positioning operations from the entire 3D electromagnetic model of the multi-chamber switchgear to the candidate region where streamline clusters converge. The volume of the candidate region is smaller than the total volume of the 3D electromagnetic model of the multi-chamber switchgear, thereby reducing the amount of data required for subsequent calculations and improving positioning efficiency.

[0054] Optionally, the electromagnetic wave propagation response signal is truncated to obtain a discharge pulse segment, including: setting a voltage threshold and a time window threshold; determining the first zero-crossing point before the amplitude of the electromagnetic wave propagation response signal first exceeds the voltage threshold as the signal start point; determining the first zero-crossing point after the duration during which the amplitude of the electromagnetic wave propagation response signal does not exceed the voltage threshold reaches the time window threshold as the signal end point; and taking the signal segment between the signal start point and the signal end point as the discharge pulse segment.

[0055] This interception operation extracts the effective signal segment corresponding to partial discharge from the electromagnetic wave propagation response signal, removing the low-amplitude noise portion of the electromagnetic wave propagation response signal and providing a clean discharge pulse segment for subsequent time inversion processing.

[0056] Optionally, the step of performing time-reversal processing on the discharge pulse segment to obtain the inverted excitation signal includes: arranging the discharge pulse segment in reverse along the time axis to obtain the inverted excitation signal.

[0057] Optionally, the volume of the candidate region shall not exceed 25% of the total volume of the three-dimensional electromagnetic model of the multi-chamber switchgear.

[0058] Optionally, the comprehensive evaluation value is determined based on spatial factors, temporal factors, and energy factors; wherein: the spatial factor is used to characterize whether the candidate monitoring point is located within the candidate region; the temporal factor is used to characterize whether the time of occurrence of the electric field peak at the candidate monitoring point falls within a predetermined focusing time window; and the energy factor is used to characterize the strength of the electric field peak at the candidate monitoring point relative to the background electric field level.

[0059] The electric field time-domain signal of each candidate monitoring point is analyzed to extract the focused peak value and the electric field amplitude characteristics during non-focused periods, constructing a comprehensive evaluation value. A higher comprehensive evaluation value indicates that the candidate monitoring point is closer to the partial discharge location. The comprehensive evaluation value is determined based on spatial, temporal, and energy factors. The spatial factor refers to the spatial affiliation of the candidate monitoring point within the candidate region. The temporal factor is whether the electric field peak value at the candidate monitoring point falls within a predetermined focusing time window. The energy factor is the relative magnitude between the electric field peak value at the candidate monitoring point and the background electric field level.

[0060] The comprehensive evaluation value is calculated as shown in formula (1): Formula (1); in, For comprehensive evaluation, For spatial factors, Due to time factors, It is an energy factor.

[0061] The time factor uses the moment of peak focus as the criterion, which is derived from the time interval within which a valid signal first appears in the electromagnetic wave propagation response signal during the forward phase. Unlike positioning methods based on the arrival time of the first wave, this method uses a time interval as the criterion, thus being less affected by noise interference. The spatial factor uses the candidate region defined by the focusing of the electric field streamlines as the criterion. The energy factor compares the ratio of the electric field peak value to the background electric field level at each candidate monitoring point within the candidate region, and combines this with the magnitude of the electric field peak value to determine the location of the partial discharge. A higher comprehensive evaluation value indicates a closer proximity to the actual location of the partial discharge.

[0062] The energy factor is calculated as shown in formula (2): Formula (2); in, The focused peak value in the electric field time-domain signal. This represents the average value of the background electric field amplitude during the non-focusing period.

[0063] The spatial factors are calculated as shown in formula (3): Formula (3); in, Let be the coordinates of the candidate monitoring point, and i be the index of the candidate monitoring point. This is a candidate region.

[0064] The calculation of the time factor is shown in formula (4): Formula (4); in, To focus on the moment when the peak occurs, To focus on the time window.

[0065] The forward response occurs during the initial change phase of the electromagnetic wave propagation response signal, with the time window width set to 3 nanoseconds or 5 nanoseconds. Since the discharge pulse segment is truncated and time-reversed during the backward processing, the time interval of the peak occurrence in the backward response corresponds to the end of the inverted excitation signal, and must satisfy the time range constraint of the first response in the forward phase. Δt is the preset time buffer length, taken as 3 nanoseconds or 5 nanoseconds. [T-Δt,T] is the focusing time window, where T is the moment when the focused peak occurs in the electromagnetic wave propagation response signal, i.e., the moment corresponding to the total duration selected for the backward simulation.

[0066] Optionally, the focusing time window is determined based on the time segment in which the effective signal first appears in the electromagnetic wave propagation response signal, and the length of the focusing time window corresponds to the length of the discharge pulse segment.

[0067] Optionally, determining the partial discharge location based on the comprehensive evaluation value corresponding to each candidate monitoring point includes: determining the location corresponding to the candidate monitoring point with the largest comprehensive evaluation value as the partial discharge location.

[0068] The beneficial effects of this application include: First, this application introduces a process for determining candidate regions based on the focusing characteristics of electric field streamlines in the backward stage of time inversion. This process first identifies the candidate regions where partial discharges are located, and then performs subsequent localization analysis. Existing technologies, when the location of a partial discharge is known, perform cross-sectional observations of the field strength distribution, but lack a method to determine its approximate location. This application solves this problem and improves engineering feasibility.

[0069] Second, this application uses a comprehensive evaluation value to jointly constrain the time window, spatial range, and waveform peak characteristics of the focusing response, so that the partial discharge location no longer depends solely on the maximum value of the field strength in the cross section, but is based on a comprehensive evaluation value within the candidate region for comprehensive judgment, which is applicable to complex multi-chamber switchgear structures.

[0070] Third, this application addresses the problem that existing time-reversal positioning methods are susceptible to interference from high-field regions within the same chamber under different chamber propagation conditions. It proposes a two-level positioning strategy: determining candidate regions based on electric field streamlines and determining partial discharge locations based on comprehensive evaluation values. This reduces the inundation effect of non-target high-field regions on the actual partial discharge focusing area and improves positioning reliability.

[0071] Fourth, the positioning results of this application have been expanded from single-point extremum judgment to local high-response region judgment, which is more in line with the actual law that time inversion focuses on complex structures and manifests as local region enhancement rather than unique mathematical point extremum, and has better stability and interpretability.

[0072] Fifth, this application can be used in both pure simulation scenarios and application scenarios that combine actual sensor sampling with simulation back-injection, and has promotional value and engineering applicability.

[0073] Sixth, with available simulation or experimental data, this application can quantitatively evaluate the positioning effect using indicators such as the distance between the candidate region and the actual partial discharge region, the spatial scale of the candidate high-response region, and the final positioning error.

[0074] After determining the candidate region by focusing the electric field streamlines, the candidate region occupies less than 25% of the total volume of the three-dimensional electromagnetic model of the multi-chamber switchgear. After further determining the location of partial discharge based on the comprehensive evaluation value, the volume of the candidate region is reduced to 3.618%, and the positioning error is less than 2 cm.

[0075] The following describes a time-reversal-based method for locating partial discharges in multi-chamber switchgear, in conjunction with two specific embodiments. These specific embodiments are merely for illustrating the invention and do not constitute an undue limitation thereof.

[0076] Example 1: A three-dimensional electromagnetic model of a switchgear with multiple functional chambers is established. Sensors are installed in the first chamber, and a partial discharge power source is installed in the second chamber. Forward simulation is performed to acquire the electromagnetic wave propagation response signal generated by partial discharge through the sensors. The electromagnetic wave propagation response signal is intercepted to obtain the discharge pulse segment. The discharge pulse segment is then processed by time inversion to obtain the inverted excitation signal. The inverted excitation signal is reinjected from the corresponding position of the sensor in the switchgear into the three-dimensional electromagnetic model of the switchgear. The time-varying electric field intensity distribution is obtained by calculation using the finite-difference time-domain method. Multiple electric field streamlines are generated based on the electric field vector direction at each position in the time-varying electric field intensity distribution. The spatial range enclosed by the streamline clusters that converge to the same local spatial neighborhood is determined as the candidate region. Multiple candidate monitoring points are deployed within the candidate region. The electric field time-domain signal corresponding to each candidate monitoring point is extracted from the time-varying electric field intensity distribution. The comprehensive evaluation value of the corresponding candidate monitoring point is calculated based on each electric field time-domain signal. The position corresponding to the candidate monitoring point with the largest comprehensive evaluation value is determined as the partial discharge position. The results show that this method can determine the location of partial discharge.

[0077] Example 2: A single-chamber model of the switchgear was established, with partial discharge sources and sensors installed within the same chamber. The same forward sampling, time-reversal processing, back-injection, and backward simulation process as in Example 1 was employed. After determining candidate regions through electric field streamline analysis, multiple candidate monitoring points were deployed within these regions. The time-domain electric field signals of each candidate monitoring point were compared, and a comprehensive evaluation value was calculated. Results show that this method can also achieve partial discharge location identification and localization in a single-chamber scenario.

[0078] Figure 8 A schematic diagram of a time-reversal-based multi-chamber partial discharge locating device for switchgear, as provided in this application embodiment, is shown below. Figure 8 As shown, this application proposes a time-reversal-based multi-chamber partial discharge localization device for switchgear. The device 800 includes: a sensor module 810, a storage module 820, and a processing module 830; wherein: The sensor module 810 is used to acquire the electromagnetic wave propagation response signal generated by partial discharge through a sensor installed on the switch cabinet. The storage module 820 is used to store a pre-built three-dimensional electromagnetic model of a multi-chamber switchgear. The processing module 830 is connected to both the sensor module and the storage module, and is used to perform the following operations: The electromagnetic wave propagation response signal is truncated to obtain a discharge pulse segment; the discharge pulse segment is then subjected to time inversion processing to obtain an inverted excitation signal. The inversion excitation signal is injected back from the sensor at the corresponding position in the switch cabinet into the pre-constructed three-dimensional electromagnetic model of the switch cabinet multi-chamber. The time-varying electric field intensity distribution at each position in the three-dimensional electromagnetic model of the switch cabinet multi-chamber is obtained by the finite difference method in the time domain. Based on the electric field vector direction at each location in the time-varying electric field intensity distribution, multiple electric field streamlines are generated to identify spatial regions exhibiting electric field energy accumulation characteristics; the electric field streamlines extend along the electric field vector direction; the spatial range enclosed by the cluster of streamlines that converge to the same local spatial neighborhood is determined as a candidate region for partial discharge; the volume of the candidate region is smaller than the volume of the three-dimensional electromagnetic model of the multi-chamber switchgear; Multiple candidate monitoring points are deployed within the candidate area, and the electric field time-domain signal corresponding to each candidate monitoring point is extracted from the time-varying electric field intensity distribution; a comprehensive evaluation value for the corresponding candidate monitoring point is calculated based on each electric field time-domain signal. The location of partial discharge is determined based on the comprehensive evaluation value corresponding to each candidate monitoring point.

[0079] It should be noted that the descriptions of the above device embodiments are similar to those of the above method embodiments, and have similar beneficial effects. For technical details not disclosed in the device embodiments of this application, please refer to the descriptions of the method embodiments of this application for understanding.

[0080] It should be noted that, in the embodiments of this application, if the above-mentioned time-reversal-based multi-chamber partial discharge localization method for switchgear is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the embodiments of this application, or the part that contributes to the related technology, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause an electronic device to execute all or part of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, mobile hard drives, read-only memory (ROM), magnetic disks, or optical disks. Thus, the embodiments of this application are not limited to any specific hardware and software combination.

[0081] Correspondingly, embodiments of this application provide a computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program implements the steps in any of the time-reversal-based partial discharge localization methods for switchgear multi-chambers described in the above embodiments. Correspondingly, embodiments of this application also provide a computer program product, which, when executed by a processor of an electronic device, is used to implement the steps in any of the time-reversal-based partial discharge localization methods for switchgear multi-chambers described in the above embodiments.

[0082] It should be understood that the phrase "one embodiment" or "an embodiment" throughout the specification means that a specific feature, structure, or characteristic related to the embodiment is included in at least one embodiment of this application. Therefore, "in one embodiment" or "in an embodiment" appearing throughout the specification does not necessarily refer to the same embodiment. Furthermore, these specific features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. It should be understood that in the various embodiments of this application, the sequence numbers of the above-described processes do not imply a sequential order of execution; the execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application. The sequence numbers of the above-described embodiments are merely descriptive and do not represent the superiority or inferiority of the embodiments.

[0083] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0084] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or components can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the various components shown or discussed can be through some interfaces, and the indirect coupling or communication connection between devices or units can be electrical, mechanical, or other forms.

[0085] The units described above as separate components may or may not be physically separate, and the components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units; some or all of the units may be selected to achieve the purpose of the embodiments of this application according to actual needs. In addition, each functional unit in the embodiments of this application may be fully integrated into one processing unit, or each unit may be a separate unit, or two or more units may be integrated into one unit; the integrated unit may be implemented in hardware or in the form of hardware plus software functional units.

[0086] Alternatively, if the integrated units described above are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this application, or the parts that contribute to related technologies, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause the device automatic test line to execute all or part of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROMs, magnetic disks, or optical disks.

[0087] The methods disclosed in the several method embodiments provided in this application can be arbitrarily combined to obtain new method embodiments without conflict. The features disclosed in the several method or device embodiments provided in this application can be arbitrarily combined to obtain new method embodiments or device embodiments without conflict.

[0088] The above description is merely an embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for locating partial discharges in multi-chamber switchgear based on time reversal, characterized in that, The method includes: Sensors deployed on the switch cabinet are used to acquire electromagnetic wave propagation response signals generated by partial discharge; the electromagnetic wave propagation response signals are truncated to obtain discharge pulse segments; the discharge pulse segments are then subjected to time inversion processing to obtain inversion excitation signals. The inversion excitation signal is injected back from the sensor at the corresponding position in the switch cabinet into the pre-constructed three-dimensional electromagnetic model of the switch cabinet multi-chamber. The time-varying electric field intensity distribution at each position in the three-dimensional electromagnetic model of the switch cabinet multi-chamber is obtained by the finite difference method in the time domain. Based on the electric field vector direction at each location in the time-varying electric field intensity distribution, multiple electric field streamlines are generated to identify spatial regions exhibiting electric field energy accumulation characteristics; the electric field streamlines extend along the electric field vector direction; the spatial range enclosed by the cluster of streamlines that converge to the same local spatial neighborhood is determined as a candidate region for partial discharge; the volume of the candidate region is smaller than the volume of the three-dimensional electromagnetic model of the multi-chamber switchgear; Multiple candidate monitoring points are deployed within the candidate area, and the electric field time-domain signal corresponding to each candidate monitoring point is extracted from the time-varying electric field intensity distribution; a comprehensive evaluation value for the corresponding candidate monitoring point is calculated based on each electric field time-domain signal. The location of partial discharge is determined based on the comprehensive evaluation value corresponding to each candidate monitoring point.

2. The method according to claim 1, characterized in that, The comprehensive evaluation value is determined based on spatial factors, temporal factors, and energy factors; wherein: The spatial factor is used to characterize whether the candidate monitoring point is located within the candidate region; The time factor is used to characterize whether the peak electric field at the candidate monitoring point falls within a predetermined focusing time window; The energy factor is used to characterize the strength of the electric field peak at the candidate monitoring point relative to the background electric field level.

3. The method according to claim 2, characterized in that, The focusing time window is determined based on the time segment in which the effective signal first appears in the electromagnetic wave propagation response signal, and the length of the focusing time window corresponds to the length of the discharge pulse segment.

4. The method according to claim 1, characterized in that, The step of intercepting the electromagnetic wave propagation response signal to obtain a discharge pulse segment includes: Set the voltage threshold and time window threshold; The first zero-crossing point before the amplitude of the electromagnetic wave propagation response signal first exceeds the voltage threshold is determined as the signal start point; The first zero-crossing point after the duration during which the amplitude of the electromagnetic wave propagation response signal does not exceed the voltage threshold reaches the time window threshold is determined as the signal endpoint. The signal segment between the signal start point and the signal end point is defined as the discharge pulse segment.

5. The method according to claim 1, characterized in that, The step of performing time-reversal processing on the discharge pulse segment to obtain the inverted excitation signal includes: The discharge pulse segments are arranged in reverse order along the time axis to obtain the inverted excitation signal.

6. The method according to claim 1, characterized in that, The volume of the candidate region does not exceed 25% of the total volume of the three-dimensional electromagnetic model of the multi-chamber switchgear.

7. The method according to claim 1, characterized in that, Determining the partial discharge location based on the comprehensive evaluation value corresponding to each candidate monitoring point includes: The location corresponding to the candidate monitoring point with the largest comprehensive evaluation value is determined as the partial discharge location.

8. A time-reversal-based multi-chamber partial discharge positioning device for switchgear, characterized in that, include: The module consists of a sensor module, a storage module, and a processing module; among which: The sensor module is used to acquire the electromagnetic wave propagation response signal generated by partial discharge through sensors deployed on the switch cabinet; The storage module is used to store a pre-built three-dimensional electromagnetic model of a multi-chamber switchgear. The processing module is connected to both the sensor module and the storage module, and is used to perform the following operations: The electromagnetic wave propagation response signal is truncated to obtain a discharge pulse segment; the discharge pulse segment is then subjected to time inversion processing to obtain an inverted excitation signal. The inversion excitation signal is injected back from the sensor at the corresponding position in the switch cabinet into the pre-constructed three-dimensional electromagnetic model of the switch cabinet multi-chamber. The time-varying electric field intensity distribution at each position in the three-dimensional electromagnetic model of the switch cabinet multi-chamber is obtained by the finite difference method in the time domain. Based on the electric field vector direction at each location in the time-varying electric field intensity distribution, multiple electric field streamlines are generated to identify spatial regions exhibiting electric field energy accumulation characteristics; the electric field streamlines extend along the electric field vector direction; the spatial range enclosed by the cluster of streamlines that converge to the same local spatial neighborhood is determined as a candidate region for partial discharge; the volume of the candidate region is smaller than the volume of the three-dimensional electromagnetic model of the multi-chamber switchgear; Multiple candidate monitoring points are deployed within the candidate area, and the electric field time-domain signal corresponding to each candidate monitoring point is extracted from the time-varying electric field intensity distribution; a comprehensive evaluation value for the corresponding candidate monitoring point is calculated based on each electric field time-domain signal. The location of partial discharge is determined based on the comprehensive evaluation value corresponding to each candidate monitoring point.

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