KR101553005B1 - A partial discharge monitoring and diagnosis system for power devices - Google Patents

A partial discharge monitoring and diagnosis system for power devices Download PDF

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KR101553005B1
KR101553005B1 KR1020150055313A KR20150055313A KR101553005B1 KR 101553005 B1 KR101553005 B1 KR 101553005B1 KR 1020150055313 A KR1020150055313 A KR 1020150055313A KR 20150055313 A KR20150055313 A KR 20150055313A KR 101553005 B1 KR101553005 B1 KR 101553005B1
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partial discharge
signal
high frequency
discharge
sensor
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조선호
김영일
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지투파워 (주)
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/12Testing dielectric strength or breakdown voltage ; Testing or monitoring effectiveness or level of insulation, e.g. of a cable or of an apparatus, for example using partial discharge measurements; Electrostatic testing
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R23/00Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
    • G01R23/02Arrangements for measuring frequency, e.g. pulse repetition rate; Arrangements for measuring period of current or voltage
    • G01R23/06Arrangements for measuring frequency, e.g. pulse repetition rate; Arrangements for measuring period of current or voltage by converting frequency into an amplitude of current or voltage
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R23/00Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
    • G01R23/16Spectrum analysis; Fourier analysis
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/12Testing dielectric strength or breakdown voltage ; Testing or monitoring effectiveness or level of insulation, e.g. of a cable or of an apparatus, for example using partial discharge measurements; Electrostatic testing
    • G01R31/1227Testing dielectric strength or breakdown voltage ; Testing or monitoring effectiveness or level of insulation, e.g. of a cable or of an apparatus, for example using partial discharge measurements; Electrostatic testing of components, parts or materials
    • G01R31/1263Testing dielectric strength or breakdown voltage ; Testing or monitoring effectiveness or level of insulation, e.g. of a cable or of an apparatus, for example using partial discharge measurements; Electrostatic testing of components, parts or materials of solid or fluid materials, e.g. insulation films, bulk material; of semiconductors or LV electronic components or parts; of cable, line or wire insulation
    • G01R31/1272Testing dielectric strength or breakdown voltage ; Testing or monitoring effectiveness or level of insulation, e.g. of a cable or of an apparatus, for example using partial discharge measurements; Electrostatic testing of components, parts or materials of solid or fluid materials, e.g. insulation films, bulk material; of semiconductors or LV electronic components or parts; of cable, line or wire insulation of cable, line or wire insulation, e.g. using partial discharge measurements
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01RMEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R35/00Testing or calibrating of apparatus covered by the other groups of this subclass

Abstract

The present invention relates to a system for monitoring and diagnosing the partial discharge of a power facility. The system for monitoring and diagnosing the partial discharge of the power facility includes a sensor part which is installed in a housing and is composed of an ultra high frequency (UHF) sensor and a high frequency current transformer (HFCT) sensor, and a monitoring device which includes a fuzzy inference unit which determines the kind of the partial discharge or the partial discharge state. The system for monitoring and diagnosing the partial discharge of the power facility according to the embodiment of the present invention accurately and easily monitors and diagnoses the degradation of a power device system by using the UHF sensor, the HFCT sensor, and a radial basis function neutral network (RBFNN).

Description

[0001] The present invention relates to a partial discharge monitoring and diagnosis system for power equipment,

The present invention estimates partial discharge detection by insulation failure, connection failure, or disconnection in a power device housing such as a high voltage cable, a transformer, a gas insulated switchgear (GIS), a switchgear, an electric distribution panel, By detecting a partial discharge generated during partial discharge by using a UHF (Ultra High Frequency) sensor and a high frequency current transformer (HFCT), it is possible to detect a partial discharge by using RBFNN (Radial Basis Function Neural Network) To a partial discharge monitoring diagnostic system of a power plant.

Further, the present invention is characterized in that an electric signal is measured by a partial discharge in an electric power facility of an electric power equipment, a characteristic used for judging a partial discharge is extracted from an electric signal, and the type of the partial discharge The present invention relates to a partial discharge monitoring diagnostic system of a power plant.

In addition, the present invention is constructed by a hierarchical SCADA system (centralized remote monitoring and control system), and a plurality of transient ground voltage sensors or microwave sensors are installed in an electric facility or the like, and the sensors are controlled by a local monitoring device 30 And more particularly, to a partial discharge monitoring diagnostic system of a power facility in which a plurality of local monitoring devices are connected to a remote server and are all monitored and controlled at the center.

Generally, partial discharge refers to any of electric power equipment installed in various industries and power system substations, electric power equipment such as high voltage switchboard, high voltage cable, transformer, GIS (Gas Insulated Switchgear), switchgear, Discharge, a surface discharge occurring along the surface of an insulator, a void discharge occurring in a gap in an insulator, and the like.

It is very important to monitor the abnormality of the power equipment and to monitor the degree of deterioration of the insulator and to predict the repair time, and it is possible to predict and manage such by measuring and monitoring the partial discharge. For this purpose, a partial discharge of various power facilities such as high voltage cable, transformer, gas insulated switchgear (GIS), switchgear, power supply facility, high voltage panel, low voltage panel, motor control panel, Measuring devices are being used.

Electricity demand is continuously increasing due to the advancement of industry, and accidents caused by electric power facilities in high-voltage cables, transformers, GIS, power receiving facilities and power equipment systems are frequently occurring. Such accidents can cause technical losses as well as economic losses. Especially, high-voltage power equipment is regarded as a very important facility not only in the national infrastructure but also in civilian use, and the accident of power equipment is a nationally serious issue affecting the damage of human life, direct loss of electric power facilities, . Power equipment such as transformer, cable, breaker, switchgear, high voltage cable, transformer, GIS, PT, CT, arrester, etc. are installed in power system installed in power plants, substations and large factories. , Local discharge phenomena (partial discharge) caused by deterioration of the dielectric strength of the insulation, etc., are leading to accidents, which have a serious effect on the power supply system.

In addition, various kinds of insulators are used in such power devices in order to prevent a discharge phenomenon occurring in a high voltage situation. However, such insulation may cause gaps such as voids or delaminations during cooling and heating during operation for some reason or during operation. However, such a gap generates a partial electric discharge every time a high electric field is applied, and if such a partial discharge is repeated, the insulation is gradually eroded and the dielectric strength is reduced, resulting in serious dielectric breakdown. In order to solve this problem, it is desirable to remove the gap in the insulating material in advance to reduce the occurrence of partial discharge, but it is difficult to completely remove the gap in consideration of various reasons. In addition, the insulation characteristics of the insulator must be sufficiently inspected from the time of manufacture. Such inspections are effective for inspection of initial manufacturing defects, but insulative deterioration over time occurs during operation of the power equipment system, so that it is difficult to conduct substantial inspections. Therefore, in the past, the time interval between inspections increases, and it is impossible to accurately grasp the insulation characteristic at all times, resulting in an unexpected serious accident. In addition, the deterioration can be monitored by measuring the partial discharge.

Partial discharge in electric power equipment is a phenomenon that occurs when insulation deteriorates in electric power equipment, and most of them are generated in the last stage of insulation deterioration, and thus it is evaluated as the best method for deterioration diagnosis.

The partial discharge generated in the power equipment is not easy to detect due to the wide band of the electromagnetic wave signal and surrounding noise. As a detection method, a method using a UHF antenna has been proposed (Patent Documents 1, 2, 3, 4). When a local discharge due to insulation failure occurs in the insulator, an electromagnetic wave is generated, and the electromagnetic wave is generated through the power equipment system. In order to distinguish the electromagnetic wave signal from surrounding noise signals, the signal is filtered via a band pass filter, amplified, and then the partial discharge signal is detected using an analysis and judgment algorithm.

In addition, a technology for automatically analyzing a partial discharge using a neural network has been proposed [Patent Document 5].

On the other hand, among electric power facilities in electric power equipment, especially in the case of transformers, there is a very high probability that a partial electric discharge is likely to occur while being an important electric power facility of the water power distribution facility. In the case of an input transformer, effective measurement of the partial discharge signal generated by the transformer enables stable operation and cost reduction of the input transformer. However, the partial discharge detection method of the conventional inflow transformer includes a detection method using a coupling device, a partial discharge detection method using a gas analysis method, and an electromagnetic wave detection analysis method. Such a detection method according to the prior art has a disadvantage in that it is difficult to measure in real time and in the limit of the measurement, and in addition, the price is expensive and the competitiveness is remarkably deteriorated.

In addition, epoxy resin is the most used insulation material in the mold type transformer. Epoxy resins are widely used as insulating materials because they have high mechanical strength, excellent electrical insulation properties, and are relatively easy to mold. However, when the material is molded or a device is manufactured, foreign matter may enter, or micro voids or cracks may be generated. Deterioration diagnosis technique using partial discharge measurement has been actively studied, but research on partial discharge measurement and circuit technology suitable for electric power equipment system is still insufficient.

It is necessary to study the partial discharge measurement technology suitable for the electric power equipment such as the inflow transformer, the instrument transformer, the breaker, and the mold transformer used in the power equipment system, and it is necessary to develop an amplification circuit suitable for the measurement sensor. In other words, it is necessary to develop a technique for partial discharge detection method and amplification circuit generated in a power equipment system power facility so that it can be utilized for deterioration monitoring and diagnosis of a power equipment system.

Korean Registered Patent No. 10-1426792 (Announced 2014.08.05) Korean Patent Publication No. 10-2013-0028545 (published on Mar. 19, 2013) Korean Patent No. 10-1486994 (Announcement of Jan 29, 2015) Korean Registered Patent No. 10-1382418 (Announced 2014.04.08) Korean Patent Laid-Open No. 10-2012-0022126 (published on March 12, 2012)

SUMMARY OF THE INVENTION An object of the present invention is to solve the above-mentioned problems and to provide a power supply system in which a high-voltage cable, a transformer, a GIS (Gas Insulated Switchgear), a switchgear, Which detects a partial discharge occurring at the time of partial discharge by using a UHF sensor and a high frequency current sensor and determines the type of partial discharge using RBFNN (Radial Basis Function Neural Network) And to provide a partial discharge monitoring diagnostic system of the facility.

It is also an object of the present invention to provide a method and apparatus for measuring an electrical signal by partial discharge in a power plant of a power equipment system, extracting characteristics used for judging a partial discharge from an electrical signal, And to provide a partial discharge monitoring diagnostic system for a power plant.

Particularly, it is an object of the present invention to provide a high frequency current transformer (HFCT) for detecting an electromagnetic wave generated during a partial discharge by using a high frequency antenna sensor and a high frequency current transformer The present invention provides a partial discharge monitoring diagnostic system for a power plant that extracts characteristics from an electrical signal output from a sensor, and applies the extracted characteristics to RNFNN to determine types of void discharge, corona discharge, and surface discharge.

In order to accomplish the above object, the present invention provides a power supply system including a high-voltage cable, a transformer, a gas insulated switchgear (GIS), a switchgear, a power reception facility, A UHF detector for detecting an electrical signal of a very high frequency generated by a partial discharge in the power plant using microwave of 300 MHz to 3 GHz, And an HFCT (High Frequency Current Transformer) sensor for detecting an electrical signal of a high frequency current generated by a partial discharge, which is mounted on a ground line of a power facility provided inside the housing. And an electric signal of a high-frequency current detected by the sensor unit to obtain sampling data, extracting a characteristic quantity from the sampling data, and outputting the characteristic quantity to the RBFNN (Radial Basis Function Neural Network) And a fuzzy inference unit configured to determine whether a partial discharge is caused or a type of partial discharge according to an output value obtained by inputting a feature quantity, wherein the fuzzy inference unit comprises: a fuzzy inference unit for generating an electrical signal output from the UHF sensor or the HFCT sensor A signal detector for extracting and sampling a partial discharge signal and outputting sampling data of a partial discharge pulse signal by an electrical signal of a very high frequency or a high frequency current; A feature amount extracting unit for extracting a feature amount necessary for determining the type of partial discharge and partial discharge from the sampling data; The RBFNN neural network includes RBFNN inference (RBFNN), which is composed of a plurality of outputs so as to correspond to each of a plurality of partial discharge types, by applying an extracted characteristic quantity to an input to a RBFNN (Radial Basis Function Neural Network) part; And a partial discharge determination unit for determining the type of partial discharge or partial discharge according to output values of the plurality of outputs of the RBFNN neural network.

The signal detection unit extracts 5,000 data of each of the electrical signals of the very high frequency or the high frequency current at intervals of 0.5 seconds at a sampling rate of 10 kHz / s to generate sampling data .

The signal detection unit may comprise a coupling network and a low-noise high-frequency amplifier for amplifying a small signal to pass only partial discharge pulses of the very high frequency electrical signals to an amplifier, Wherein the low-noise high-frequency amplifier comprises a low-noise wide-band operational amplifier in two stages, configured to not limit the high-frequency cutoff frequency with high gain, and configured to amplify an electrical signal of the high- And the detection circuit is calibrated by using a discharge charge quantity of a known size in order to calculate the magnitude of an apparent charge of the partial discharge pulse in the electrical signal of the microwave or the high frequency current .

The present invention relates to a partial discharge monitoring diagnostic system for a power plant, wherein the feature quantity extracting unit is characterized by comprising: a feature quantity extracting unit for extracting, as the feature quantity, a kurtosis of the very high frequency sampling data obtained from the very high frequency electric signal, ) Converted into a frequency field and converted into a frequency field by FTT conversion to calculate an average value of frequency-based sizes calculated by converting the frequency field, a kurtosis of the high-frequency current sampling data obtained from the electrical signal of the high-frequency current, The asymmetry degree of the signal with respect to the waveform data of the high frequency current sampling data and the calculated total harmonic distortion factor after calculating the 1st to 15th harmonic with respect to the waveform data of the high frequency current sampling data, And extracts a feature quantity included in the feature quantity All.

The RBFNN inference unit comprises a neural network composed of an input layer, a hidden layer, and an output layer, wherein a radial basis function is used for the hidden layer, Wherein the input layer receives the feature quantity as a vector and outputs the sum of values obtained by multiplying output values of outputs output by the function of the hidden layer by connection weights in the output layer, do.

[Equation 1]

Figure 112015038215874-pat00001

Where x is the input vector of the feature quantity, y j is the jth output of the output layer, c is the number of clusters corresponding to the fuzz rule of the hidden layer, and a ij is the jth Output connection weights, and v i is the center of the i-th cluster.

The present invention relates to a partial discharge monitoring diagnostic system of a power plant, wherein the center v i of the cluster is a sample input vector set X = {x 1 , x 2 , ..., x N }, x k ∈ R n characterized in that the center while modifying the u ik represents the center and by the membership degree (n is the size of the input vector) obtained by converging the objective function of the following [equation 2] as a minimum.

[Equation 2]

Figure 112015038215874-pat00002
,

Figure 112015038215874-pat00003
,

Figure 112015038215874-pat00004

Where ∥ · ∥ denotes the weighted Euclidean distance, c is the number of clusters, m is the fuzzification coefficient, and X k is the k-th input vector.

In the partial discharge monitoring diagnosis system of the electric power facility, the partial discharge judgment unit calculates a maximum value among a plurality of output values calculated by the RBFNN speculation unit, judges normal if the maximum value is 0.5 or less, When the output having a maximum value of 0.5 and a maximum value is y 1 , a corona discharge is determined to be y 2 , and a surface discharge is determined to be y 3 .

As described above, according to the partial discharge monitoring diagnostic system of the electric power facility according to the present invention, the partial discharge occurring at the partial discharge is detected by using the UHF sensor and the high frequency current sensor, and the type of the partial discharge is judged using the RBFNN This makes it possible to more accurately and easily perform deterioration monitoring and diagnosis of the power equipment system.

1 is a block diagram of a configuration of a partial discharge monitoring diagnostic system of a power plant according to an embodiment of the present invention.
2 is a block diagram of a configuration of a monitoring apparatus according to an embodiment of the present invention;
3 is a block diagram of a configuration of a signal detection unit and a reasoning determination unit according to an embodiment of the present invention;
FIG. 4 is a graph illustrating frequency characteristics of a coupling network for allowing only partial discharge pulses of signals of a UHF sensor according to an embodiment of the present invention to pass through an amplifier. FIG.
5 is a circuit diagram (a) of an amplifier circuit for detecting breaker partial discharge according to an embodiment of the present invention, and FIG. 5 (b) is a circuit photograph.
6 is a configuration diagram of a calibration test system according to an embodiment of the present invention;
FIG. 7 is a graph showing an example of a detection calibration pulse waveform according to an embodiment of the present invention, and is a graph in which [50 mV / div, 500 ns / div] range.
8 illustrates a configuration of an experimental system according to an embodiment of the present invention.
Fig. 9 is a waveform graph of (a) power supply voltage-partial discharge pulse and (b) partial discharge pulse as an example of the detected waveform according to the experiment of the present invention, (50mV / div, 5ms / div), and Ch.2 is a partial discharge pulse (50mV / div, 5ms / div) .
10 is a circuit diagram (a) of the amplifying circuit for HFCT according to an embodiment of the present invention, and Fig. 10 (b) is a circuit photograph.
11 is a configuration diagram of a calibration experiment system according to an experiment of the present invention.
12 is a graph of a calibration pulse waveform (100 [pC]) according to an experiment of the present invention, with a graph in the range [100 mV / div, 2 μs / div].
13 is a diagram illustrating a partial discharge detection method using HFCT according to an experiment of the present invention.
FIG. 14 is a graph of a measured waveform according to an experiment of the present invention. The graph above is a graph for an applied voltage [5 kV / div, 5 ms / div] and the graph below shows a partial discharge pulse [50 mV / div, 5 ms / Graph for.
15 is a schematic diagram of a radiator low function neural network according to an embodiment of the present invention.
16 is an illustration of test data for a partial discharge test of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, the present invention will be described in detail with reference to the drawings.

In the description of the present invention, the same parts are denoted by the same reference numerals, and repetitive description thereof will be omitted.

First, a configuration of an overall system for implementing a partial discharge monitoring diagnostic system of a power plant according to an embodiment of the present invention will be described with reference to FIG.

1A, an overall system for implementing a system according to the present invention comprises a sensor unit 20, a monitoring device 30, and a remote server 40 installed in a power equipment system housing 10 . In addition, it may further comprise a load factor monitoring device 50 for monitoring the load factor of the monitoring device 30. [ The load factor is obtained as a percentage of the current load power versus the capacity of the transformer.

Also, as shown in FIG. 1B, the power equipment system according to the present invention can be constructed as a hierarchical SCADA system (centralized remote monitoring and control system). That is, a plurality of sensors 21 and 22 of the sensor unit 20 are installed in the electric equipment or the housing 10, and the sensors 21 and 22 are monitored by the local monitoring device 30 do. In addition, the local monitoring device 30 is all connected to the remote server 40 to transmit the monitoring and diagnostic data to the remote server 40. The remote server 40 may be provided at a central control center or the like to monitor the partial discharge status of all electric power facilities remotely and to confirm the diagnosis results.

Preferably, one local monitoring device 30 receives data by controlling six to seven sensors 21 and 22, and two or three local monitoring devices 30 are connected to the remote Is connected to the server (40) and is controlled by the remote server (40). Accordingly, each electric equipment is controlled by the local monitoring apparatus 30 and the remote server 40 according to a hierarchical structure, and transmits the detected data to the host apparatus or the server according to the hierarchical structure.

The sensor unit 20 includes a UHF (Ultra High Frequency) sensor or a microwave antenna sensor 21 and a high frequency current transformer (HFCT) sensor 22. The microwave antenna sensor 21 is installed inside the housing 10 and detects a microwave signal generated by partial discharge in the power facility 11 using microwave of 300 MHz to 3 GHz. Further, the high-frequency current sensor 22 is mounted on the ground line of the power facility 11 to detect an electrical signal.

When partial discharge occurs inside the power unit system housing 10, high frequency electromagnetic waves due to the discharge occur on the surface of the metal wall, causing a surface current.

The UHF sensor 21 is constituted by a microstrip patch type, has a frequency measurement range of 300 MHz to 3000 MHz, and detects an electromagnetic wave discharge signal inside the electric power system of the open structure. The UHF sensor 21 is mounted inside or outside the housing 10 and is used for detecting electromagnetic waves that accompany the partial discharge. The UHF sensor 22 may be a built-in type sensor installed inside the housing 10 or a sensor installed outside the housing 10.

The high frequency current sensor 22 may be a component within the power equipment system housing 10 that includes internal temperature of the power equipment system housing 10 or high voltage equipment such as busbars, breakers, MOF, CT, PT, Mounted on the ground line of the power equipment (11) to detect an electrical signal. If a partial discharge occurs inside the transformer, pulse-shaped discharge current flows to the external ground line. Therefore, the HFCT 22 can detect the partial discharge pulse current flowing through the ground line.

Power equipment systems are installed in buildings or factories that use a large amount of electric power. They are divided into high voltage cables, transformers, GIS (Gas Insulated Switchgear), switchgear, Various power equipment 11 for distributing and stably supplying electric power to the inside of the power unit 10 are installed. The power equipment systems may be a single power facility, and a plurality of power facilities may be configured in a complex manner. Hereinafter, the power equipment 11 in the power equipment system housing 10 will be described for convenience of explanation. The equipment or equipment 11 installed in the housing 10 of the power equipment system can be used in various applications such as a bus bar, a vacuum breaker VCB, a power transformer PT, a power meter, a load break switch, In addition, various mold-type insulation devices and component connecting parts, and components requiring insulation deterioration prediction. For example, the discharge diagnosis system of the electric power system of the present invention can be used as a device for monitoring equipment such as a molded case circuit breaker (MCCB), which is a low-voltage side constituent device inside a power system, and various distribution lines. Of course.

The discharge diagnosis system of the electric power system according to the present invention is provided with a sensing means for sensing the state of each device in the housing 10 to sense a discharge or a deterioration state through the electric power system.

Meanwhile, the sensor unit 20 and the monitoring device 30, the monitoring device 30, and the remote server 40 are connected by a network to perform data communication. Preferably, the sensor unit 20 and the monitoring device 30 are connected to the Internet by the UDP protocol, and the monitoring device 30 and the remote server 40 are connected to the Internet by the TCP protocol.

Next, the monitoring apparatus 30 receives the high-frequency antenna signal or the high-frequency current signal sensed from the sensor unit 20, analyzes the received high-frequency signal and the high-frequency current signal to detect the partial discharge, . Further, these partial discharge detection data are accumulated (calculated) to judge whether there is an abnormality in the electric power system. The monitoring device 30 monitors the discharge state in the area inside the electric power system system housing 10 or each electric power facility 11 and compares it with the reference signal pattern (UHF or HFCT signal pattern in the discharge phenomenon) Alternatively, a partial discharge is detected or an abnormality is determined according to the equipment configuration. In addition, the monitoring device 30 displays a measured discharge state of the inside or the equipment on the display as an image, detects a partial discharge, or detects an abnormality, and notifies the manager of the detection of the abnormality.

That is, the monitoring device 30 detects the discharge state, the partial discharge, or the like of the interior of the housing 10 based on the UHF signal, the HFCT signal, the signal of each electric power facility, Diagnoses that the deterioration state through the housing is inferred, and controls the internal state of the housing or generates an alarm signal according to the discharged or deteriorated state information in the diagnosed housing.

Preferably, the monitoring device 30 may be attached to the power system system housing 10. For example, the sensor unit 20 may be installed inside the power equipment system housing 10 or attached to each facility 11, and may install the monitoring device 30 outside the power equipment system housing 10 . At this time, the UHF signal and the high-frequency current signal are obtained from the UHF sensor 21 or the HFCT sensor 22 installed inside or outside the housing or the facility, and the monitoring device 30 analyzes the measured UHF signal and the HFCT signal, It is possible to judge whether a partial discharge or an abnormality exists in the inside of the apparatus system housing 10. [

The remote server 40 is a device having a computing processing function such as a personal computer (PC) or a server device and is connected to the monitoring device 30 via a network so as to measure the temperature, And judged data on the deteriorated state.

The remote server 40 can share the role with the monitoring device 30 and can process it. For example, the monitoring apparatus 30 monitors the UHF signal and the HFCT signal measured in real time to perform only a simple pattern comparison to monitor the type or abnormality of the partial discharge, and the remote server 40 monitors past signal pattern data and / By learning the above results, it can derive detection rule of partial discharge according to temperature, rule of abnormality, and set or manage discharge state pattern. In particular, the remote server 40 has excellent performance such as data storage capacity and computing ability, and the monitoring apparatus 30 may be inferior in performance to the remote server 40 as equipment installed in the field. In consideration of such a difference in performance, the functions between the remote server 40 and the monitoring apparatus 30 can be shared. Hereinafter, it will be described that the monitoring device 30 performs all the above functions.

Meanwhile, the remote server 40 is implemented as a computer system of a central station equipped with a power equipment system, but is not limited thereto, and may be a manager's portable communication device, for example, a smart phone, a PDA, or the like.

Further, the monitoring device 30 is connected to the load factor monitoring device 50 to monitor the load factor.

Next, the configuration of the monitoring apparatus 30 will be described in more detail with reference to Fig.

2, the monitoring apparatus 30 includes a signal detection unit 31, a display unit 32, a setting unit 33, a reasoning determination unit 34, and a storage unit 36. [ Preferably, an alarm unit 35 may be added.

The signal detecting unit 31 receives the data of the UHF signal and the HFCT signal measured from the sensor unit 20, performs partial discharge detection, and records each detected data. This will be described in detail below.

The setting unit 33 is an input device for presetting parameters, constants, conditions, integrity index threshold values, and the like for monitoring various monitoring apparatuses such as a reference pattern, an alarm reference, and an alarm type.

Next, the reasoning determiner 34 determines the type of the partial discharge using the RBFNN (Radial Basis Function Neural Network) from the detected data, and determines whether or not the power equipment system is abnormal.

RBFNN (Radial Basis Function Neural Network) is an intelligent algorithm that is widely used for pattern classification, pattern recognition, and system modeling. It uses partition function based on FCM clustering as an active function. It is also represented by the "If-then" fuzzy rule and driven by a fuzzy reasoning mechanism. The conditional, conclusion, and reasoning parts form a network structure. The conditional partitions the input space using FCM clustering, and the conclusion part expresses the partitioned local area as a constant term. Finally, the final output of the network depends on the fuzzy reasoning of the reasoning part.

The display unit 32 displays the data of the discharge state or the deteriorated state on the two-dimensional display. That is, the display unit 32 displays the position of the internal equipment of the housing 10 and the measured discharge state in the facility, or displays the deduced discharge state, deterioration state, or deterioration determination result on the screen. Particularly, the kind of the inferred partial discharge is displayed. In addition, it is possible to display the abnormality of each power equipment on the power equipment system layout map.

The storage unit 36 stores characteristics and patterns extracted from the respective power facilities 11 of the housing 10 or the positions of the installed UHF sensor 21 and the HFCT sensor 22, the discharge signal, the discharge signal, Features and patterns, feature matching, or pattern matching results. Also, a pattern of a signal collected in real time, a hysteresis signal pattern for comparing with the calculation result, a history calculation result, and the like are stored.

When the determination unit 34 determines that there is an error, the alarm unit 35 notifies the abnormal state. Particularly, information on the abnormal state and the electric power facilities of the electric power facilities or the abnormal state are informed together. If the characteristic pattern of the real-time measurement UHF signal or the HFCT signal coincides with (similar to) the reference characteristic pattern, the alarm is activated.

If the real-time measurement signal or the characteristic amount or the pattern matches or is similar to the characteristic amount or pattern of the boundary, the alarm is stored in the database and the signal sampling data, the characteristic amount, and the like collected through the UHF sensor 21 or the HFCT sensor 22 are stored in the database. It works. At this time, sudden partial discharge changes may occur due to the UHF sensor, HFCT sensor, peripheral device failure, or surrounding fire, so that quick action is required. Therefore, when an alarm occurs, the location of the alarm should be automatically displayed on the screen and the problem can be found.

Next, the detailed configuration of the signal detection unit 31 and the reasoning determination unit 34 according to an embodiment of the present invention will be described in detail with reference to FIG. 3 is a block diagram illustrating a detailed configuration of the signal detection unit 31 and the reasoning determination unit 34 according to the present invention.

3, the signal detecting unit 31 extracts and samples the partial discharge signal from the received high frequency (UHF) signal and the high frequency current signal HFCT of the sensor unit 20, Determines whether or not the partial discharge is generated, the kind of the partial discharge, and the like based on the detected sampling data.

The signal detecting unit 31 includes a UHF detecting unit 311 for extracting and sampling the partial discharge signal from the UHF signal and an HFCT detecting unit 312 for extracting and sampling the partial discharge signal from the high frequency current signal HFCT. The inference determining unit 34 includes a feature amount extracting unit 341 for extracting a feature amount from the sampling data, an RBFNN inference unit 342 for reasoning using the RBFNN algorithm, and a partial discharge And a determination unit 343.

First, the UHF detection unit 311 will be described.

The UHF detecting unit 311 receives the electrical signal output from the UHF sensor 21, extracts and samples the partial discharge signal, and outputs sampling data of the partial discharge signal by the UHF electrical signal. The UHF sensor 21 is a sensor using an electromagnetic wave responsive to a partial discharge, and is attached to a portion where a partial discharge is to be detected.

The UHF detecting unit 311 receives an electrical signal from the UHF sensor 21 and is composed of a signal processing unit and an A / D converting unit. The UHF detecting unit 311 receives waveform data of an electrical signal and extracts and samples the partial discharge signal. At this time, the sampling period and the number of data may be set differently as needed.

As an example, the UHF detecting unit 311 is configured to receive 5,000 pieces of electrical signals from the UHF sensor 21 at intervals of 0.5 seconds at a sampling cycle of 10 kHz / s. Here, the AD converter uses two channels.

Partial discharge pulses are weak signals in the range of several hundreds of kHz to several hundreds of MHz and are extremely small in the power supply frequency and can not be directly detected because they are exposed to ambient electrical noise. The UHF detector 311 designs a coupling network and a low-noise high-frequency amplifier for amplifying a small signal to pass only partial discharge pulses among the signals detected by the UHF antenna to the amplifier. The frequency characteristics of the coupling network are shown in Fig.

5 is a circuit diagram of a low noise amplifier for amplifying a small partial discharge pulse connected to an output of a coupling network. The low-noise broadband (1.6 nV / √Hz, 330 [MHz]) operational amplifier should be configured in two stages to avoid limiting high-frequency cutoff frequencies with high gain. The gain of the designed and fabricated amplifier is 40 [dB], and the frequency band of -3 [dB] can amplify the partial discharge pulse delivered from the coupling network without attenuation from 100 [kHz] to 300 [MHz].

In order to calculate the magnitude of the apparent charge of the detected partial discharge pulse, it is necessary to calibrate the detection circuit using a discharge charge amount of a known size. In the present invention, a calibrated pulse is input between the fixed conductor of the circuit breaker and the enclosure using a dedicated calibration pulse generator (CAL1A, 1 to 100 pC, positive / negative) ).

Fig. 7 shows an example of the waveform detected at the output of the amplifier when a negative pulse of 100 [pC] is applied. Since the output voltage of the amplifier is 98 [mV], it can be seen that the sensitivity of the partial discharge measuring apparatus is 9.8 [mV] / 10 [pC]. Considering the measurement range of the oscilloscope, the oscillator can be stably measured at 10 [pC] (about 20 [mV]) or more.

In the experiment of generating the partial discharge of the circuit breaker, as shown in FIG. 8, a needle electrode was provided to generate partial discharge in the internal fixed electrode conductor, and a high voltage transformer (AC 220 [V] / 20 kV) And the AC 13.2 [kV] corresponding to the voltage was applied. FIG. 9 shows an example of the detected waveform. In this experiment, a maximum of 97 [pC] (190 [mV]) is detected, and a waveform of FIG. 9B corresponds to 76 [pC].

The designed and fabricated partial discharge measurement device was calibrated with 1.96 [mV] / [pC] as a result of calibrating experiment on the circuit breaker. It is possible.

In the application experiment, the partial discharge pulse can be observed by generating the partial discharge arbitrarily by applying 13.2 [kV] between the phase and the ground like the high voltage distribution line.

Next, the HFCT detecting unit 312 will be described.

The HFCT detecting unit 312 receives the electrical signal output from the HFCT sensor 22, extracts and samples the partial discharge signal, and outputs sampling data of the partial discharge pulse signal based on the electrical signal of the high frequency current.

The HFCT detector 312 also receives the waveform data of the electrical signal and extracts and samples the partial discharge signal. At this time, the sampling period and the number of data may be set differently as needed. Preferably, the HFCT detecting section 312 samples the electrical signal of the partial discharge in the same manner as the UHF detecting section 311 in advance.

As an example, the HFCT detecting unit 312 is configured to receive 5,000 pieces of electrical signals from the HFCT sensor 22 at intervals of 0.5 seconds at a sampling cycle of 10 kHz / s.

Also, the HFCT detector 312 constantly amplifies and samples the electrical signal of the HFCT sensor 22. That is, when a partial discharge occurs in the transformer, a pulse-shaped discharge current flows to the external ground line. Therefore, the HFCT sensor 22 can be used to detect the partial discharge pulse current flowing through the ground line. Since the partial discharge signal is very small in size, an amplification circuit is required. Considering the characteristics of HFCT, a high-speed operational amplifier with a frequency band of 70 [MHz] is used and an HFCT amplifier circuit is constructed as shown in Fig.

The amplifier circuit performs a characteristic evaluation as a ratio of an output signal to a sinusoidal input signal and has a gain of 8 [dB] and a frequency band of 100 [kHz] to 10 [MHz]. In order to calculate the magnitude of the apparent charge of the detected partial discharge pulse, it is necessary to calibrate the detection circuit using a discharge charge amount of a known size.

Therefore, a calibration experiment is performed using the calibration pulse generator (CAL1A, 1 to 100 [pC]) as shown in FIG. 11 and the sensitivity is calculated from the magnitude of the detection signal for the calibration pulse. An example of the detected waveform when a positive pulse of 100 [pC] is applied is shown in Fig. The output voltage of the amplifying circuit is 120 [mV], and the conversion sensitivity of the partial discharge measuring apparatus is 12 [mV] / 10 [pC].

After performing the sensitivity calculation of the amplification circuit, an experimental system is constructed as shown in FIG. 13, and a partial discharge is generated using a high voltage transformer (AC 220 [V] / 15 [kV]).

The measurement results are shown in Fig. Partial discharge occurred near the maximum value of the applied voltage and partial discharge of maximum 116 [pC] (140 [mV]) when 7.5 [kV] was applied.

Next, the feature quantity extracting unit 341 will be described.

The feature quantity extracting unit 341 receives the sampling data output from the UHF detecting unit 311 and the HFCT detecting unit 312 and extracts feature quantities necessary for determining the type of partial discharge and partial discharge from the sampling data. Preferably, the feature amount extraction unit 341 calculates the following six feature amounts.

The first characteristic quantity is Kurtosis for the signal (or sampling data) of the UHF sensor 21, which calculates the kurtosis from the sampling data obtained from the UHF sensor 21.

The second feature quantity is an average of the spectral magnitudes for the signal (or sampling data) of the UHF sensor 21, which calculates an average value of the frequency-dependent magnitudes from the sampling data obtained from the UHF sensor 21. [ At this time, UHF detected sampling signal data is converted into a frequency field through Fourier transform such as FTT (Fast Fourier Transformation).

The third characteristic amount is a kurtosis with respect to the signal of the high frequency current sensor 22, and the kurtosis is calculated from the sampling data obtained from the high frequency current sensor 22.

The fourth characteristic quantity is the average of the spectrum magnitudes for the signals of the high frequency current sensor 22, which calculates an average value of the frequency-dependent magnitudes from the sampling data obtained from the high frequency current sensor 22 using the FFT calculation.

The fifth characteristic quantity is the total harmonic distortion factor for the signal of the high frequency current sensor 22. This is calculated from the waveform data measured from the high frequency current sensor 22 using the FFT calculation up to the 1st to 15th harmonic, Calculate the percentage.

The sixth feature is an asymmetry of the signal of the high-frequency current sensor 22, which calculates the asymmetry of the signal from the waveform data measured from the high-frequency current sensor 22.

Next, the RBFNN speculation unit 342 will be described.

The RBFNN inference unit 342 inputs six characteristic amounts obtained from the characteristic amount extraction unit 341 and determines the types of partial discharge such as void discharge, corona discharge, and surface discharge.

The basic neural network structure consists of an input layer, a hidden layer, and an output layer. Generally, neural network uses a sigmoid function in hidden layer, and output layer consists of one node. The Radial Basis Function Neural Network (RBFNN) network of the present invention uses a Radial Basis Function for the hidden layer.

In general, the RBFNN or NN is composed of one node in the output layer, but the RBFNN speculation unit 342 constitutes three output nodes. The output calculation method and the learning method according to this will be described. The RBFNN inference unit 342 constructs the RBFNN neural network as shown in FIG.

The input layer receives the input vector x = [x 1 , x 2 , x 3 , ..., x 6 ] T and transfers it to the hidden layer. Herein, the input vector means a vector composed of six characteristic quantities obtained by the characteristic quantity extracting unit 341. That is, x 1 is a first characteristic quantity, x 2 is a second characteristic quantity, ..., and x 6 is a value of a sixth characteristic quantity. The hidden layer uses a radial basis function. The output layer outputs the sum of values obtained by multiplying the values output by the function of the hidden layer by the connection weights a ij .

The structure of the RBFNN in FIG. 15 can be expressed by the following equation. The number of rules can be determined by experience.

[Equation 1]

The equation for the ith rule: If x is R i then y j = f ji (x)

Here, x denotes an input vector, R i is a membership function of an i (= 1, ..., c) group by FCM (Fuzzy C Means) clustering, f ji (x) Is the constant term of the i-th fuzzy rule for the (= 1, ..., s) th output. The conditional part before "then" performs the function of the active function in the network structure and the function of the belonging function in the linguistic aspect by using FCM clustering. After the "then" conclusion, the constant term is the connection weight of the network, which acts as a local model of the fuzzy rule, and the final output of the network in the inference unit is obtained as the inference result of the fuzzy rule.

In the present invention, the FCM clustering algorithm is applied to the FCM algorithm to calculate the output value to the hidden layer. The conditional function of RBFNN divides the input space by the number of c clusters (number of fuzzy rules) and outputs the degree of membership of each domain as a fuzzy set to reflect the characteristics of learning data. The FCM cluster method assigns membership degree to the distance between each data and the center of a specific cluster, and classifies data according to the membership degree.

FCM clustering obtains the membership value for each cluster of input data by minimizing Equation (2) which is an objective function.

&Quot; (2) "

Figure 112015038215874-pat00005

Here, c is the number of clusters (number of fuzzy rules), N is the number of input patterns, and m is a fuzzification coefficient. X k is the k-th input vector, and v i is the center of the i-th cluster. u ik is a real number between 0 and 1 indicating the degree of belonging to the kth data belonging to the i-th cluster and satisfies the conditions of Equations (3) and (4).

&Quot; (3) "

Figure 112015038215874-pat00006

&Quot; (4) "

Figure 112015038215874-pat00007

∥ · ∥ in Equation (2) uses a weighted Euclidean distance expressed by Equation (5).

&Quot; (5) "

Figure 112015038215874-pat00008

Where j is the standard deviation of the j-th input dimension of the input patterns. Weighted cladian distances are widely used because they provide reasonable distance information that is not significantly affected by the data size distribution. n-dimensional Euclidean space, the input vector set composed of N number of the pattern on the X = {x 1, x 2 , ..., x N}, x k ∈R n, 1≤k≤N and cluster center v = {v 1, v 2, ..., v c} , v i ∈R n, can be expressed as the membership degree of the 1≤i≤c membership matrix is expressed as u = [u ik] ik u and v i equation 6 is And 7, respectively.

&Quot; (6) "

Figure 112015038215874-pat00009

&Quot; (7) "

Figure 112015038215874-pat00010

The FCM clustering modifies the membership matrix U and the center v i (i = 1, ..., c) of each cluster while iterating Equations 6 and 7 and corrects the objective function Q (U, v 1 , v 2 , ..., v c ) to a specific value.

The conclusion of the RBFNN structure is to form the rule after "then" in equation (1) by expressing each local region separated from the conditional part as a local session model of the polynomial function. F i (x) is omitted, the subscript j (= 1, ..., s ) for output neurons in ji f (x) of equation (1) each have a constant term, a linear equation form as Equation 8, and 9.

&Quot; (8) "

Figure 112015038215874-pat00011

Finally, the final output of the proposed RBFNN structure is expressed by Equation (9) by fuzzy inference.

&Quot; (9) "

Figure 112015038215874-pat00012

Here, u i is equal to R i (x) in Equation (1), and the sum of all clusters is 1 as shown in Equation (3).

RBFNN should be applied after performing learning using test data. That is, the connection weights a ij between the hidden layer and the output layer.

First, the test data collects input / output value data of RBFNN through partial discharge test, and learns using the collected test data to determine connection weight.

The test data is composed of a vector having the structure shown in FIG.

In the case of the void discharge, the corona discharge, and the surface discharge, the characteristic quantities are extracted for each of the cases. In the case of the void discharge, the data obtained is y1 = 1, the corona discharge = y2 = 1, The test data is obtained by setting y3 to 1 and all values to 0 in the normal case. For the learning of RBFNN, 100 or more experimental data are obtained and applied for each case.

The learning method using test data is as follows.

The learning for the connection weight calculation proceeds to minimize the error expressed by Equation 10 for all patterns (test data). In the present invention, the number of outputs is three, and learning should be performed for each output. The following describes the first output.

&Quot; (10) "

Figure 112015038215874-pat00013

Here, q is the error E, N for the second pattern is a q number of input patterns. t q is the target value for the q-th pattern. y q is the final output of the network for the qth pattern and is shown in Equation (11).

&Quot; (11) "

Figure 112015038215874-pat00014

The connection weight a ij between the hidden layer and the output layer is calculated as many times as the number of test data as follows.

&Quot; (12) "

Figure 112015038215874-pat00015

&Quot; (13) "

Figure 112015038215874-pat00016

Where η is the learning rate, α is the momentum coefficient, p + 1 is the new value, p is the current value, and p-1 is the previous value.

a ij is the connection weight between the i th hidden layer and the j th output side, and the connection weights are learned in the same way for all connection weights.

The RBFNN speculation unit 342 is learned as described above, and the values of the output values y1, y2, and y3 are calculated.

Next, the partial discharge determination unit 343 will be described.

The partial discharge determination unit 343 determines the partial discharge from the output value calculated by the RBFNN inference unit 342. [ Judgment first calculates the maximum value among y1, y2, and y3. If the calculated maximum value is less than 0.5, it is judged to be normal. If the maximum value is greater than 0.5 and the output having the maximum value is y1, then it is determined that the discharge is void, y2 is corona discharge, and y3 is a surface discharge.

Although the present invention has been described in detail with reference to the above embodiments, it is needless to say that the present invention is not limited to the above-described embodiments, and various modifications may be made without departing from the spirit of the present invention.

10: Power equipment system housing 11: Power equipment
20: Sensor part 21: UHF sensor
22: HFCT sensor
30: Monitoring device 31: Signal detection part
32: display section 33: setting section
34: Reasoning judgment part 35: Alarm part
36: Storage unit 40: Remote server
311: UHF detecting unit 312: HFCT detecting unit
341: Feature extraction unit 342: RBFNN Reasoning unit
343: partial discharge judgment unit

Claims (7)

A partial discharge of a power facility for detecting a partial discharge occurring in a power facility inside a power equipment system housing of a high voltage cable, a transformer, a gas insulated switchgear (GIS), a switchgear, a power reception facility, A monitoring diagnostic system comprising:
A UHF (Ultra High Frequency) sensor installed inside the housing for detecting an electrical signal of a very high frequency generated by a partial discharge in the power facility using microwave of 300 MHz to 3 GHz, A sensor unit comprising a HFCT (High Frequency Current Transformer) sensor for detecting an electrical signal of a high frequency current generated by a partial discharge by being attached to a ground line of the equipment; And
A characteristic quantity is extracted from the sampling data by sampling an electrical signal of a microwave high frequency electric current and an electric signal of a high frequency current detected by the sensor unit, And a monitoring device that constitutes a fuzzy inference unit for determining whether the partial discharge is caused or not, according to an output value obtained by inputting the partial discharge,
Wherein the fuzzy inference unit comprises:
A signal detector for receiving an electrical signal output from the UHF sensor or the HFCT sensor to extract and sample a partial discharge signal and output sampling data of a partial discharge pulse signal by an electrical signal of a very high frequency or a high frequency current;
A feature amount extraction unit for extracting a feature amount necessary for determining the type of partial discharge and partial discharge from the sampling data;
The RBFNN neural network includes RBFNN inference (RBFNN), which is composed of a plurality of outputs so as to correspond to each of a plurality of partial discharge types, by applying an extracted feature quantity to an input to a RBFNN (Radial Basis Function Neural Network) part; And
And a partial discharge determination unit for determining a type of partial discharge or partial discharge according to an output value of a plurality of outputs of the RBFNN neural network.
The method according to claim 1,
Wherein the signal detecting unit extracts 5,000 pieces of data from the electrical signals of the very high frequency or the high frequency current at intervals of 0.5 seconds at a sampling period of 10 kHz / s to generate sampling data.
2. The apparatus according to claim 1,
And a low-noise high-frequency amplifier for amplifying a small signal, wherein the low-noise high-frequency amplifier comprises a low-noise broadband operational amplifier in two stages, and the high gain So that the high-frequency cut-off frequency is not limited,
And an amplifying circuit for amplifying an electric signal of the high-frequency current, wherein a high-speed operational amplifier is used,
Characterized in that the detection circuit is calibrated using an amount of discharge charge of a known size to calculate the magnitude of the apparent charge of the partial discharge pulse in the electrical signal of the microwave or the high frequency current Discharge monitoring diagnostic system.
The method according to claim 1,
Wherein the feature quantity extracting unit extracts, as the feature quantity, a kurtosis of the very high frequency sampling data obtained from the electrical signal of the very high frequency, a magnitude of the frequency by a frequency field calculated by converting the very high frequency sampling data into a frequency field by FTT (Fast Fourier Transformation) Frequency of the high-frequency current sampling data obtained from the electrical signal of the high-frequency current, an average value of the frequency-by-frequency magnitudes calculated by converting the high-frequency current sampling data into a frequency field by FTT conversion, Extracts a characteristic quantity including a total harmonic distortion factor calculated after the 1st to 15th harmonics with respect to the data and an asymmetry degree of the signal with respect to the waveform data of the high frequency current sampling data. Partial discharge monitoring diagnostic system.
The method according to claim 1,
Wherein the RBFNN reasoning unit forms a neural network composed of an input layer, a hidden layer, and an output layer, wherein the hidden layer uses a Radial Basis Function, and the output layer includes at least three outputs, And outputs the output value as a sum of values obtained by multiplying the output values of the output by the function of the hidden layer by the connection weight, wherein the output value is calculated by the following equation Partial discharge monitoring diagnostic system of power facilities.
[Equation 1]
Figure 112015065388718-pat00041

In addition, x is a feature quantity input vector, y j is a j-th output of the output layer, c is the number of clusters corresponding to the fuzz rule of the hidden layer, and a ij is a jth V i is the center of the i-th cluster, and m is the fuzzification coefficient.
6. The method of claim 5,
The center v i of the cluster is centered by a set of sample input vectors X = {x 1 , x 2 , ..., x N }, x k ∈ R n (where n is the size of the input vector) Is a center obtained by converging the objective function Q of Equation (2) to minimize while modifying u ik indicating the degree of affiliation.
[Equation 2]
Figure 112015065388718-pat00018
,
Figure 112015065388718-pat00019
,
Figure 112015065388718-pat00020

Where c is the number of clusters, m is the fuzzification coefficient, X k is the k-th input vector, N is the number of input vectors, v j is the center of the jth cluster.
6. The method of claim 5,
Wherein the partial discharge determination unit calculates a maximum value among a plurality of output values calculated by the RBFNN inference unit, and determines that the maximum value is less than or equal to 0.5, and determines that the output having a maximum value greater than 0.5 and a maximum value is y 1 Wherein the determination unit determines that the discharge is a void discharge, a corona discharge if y 2 , and a creeping discharge if y 3 .
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