CN113189456A - Transformer partial discharge positioning method and system based on density clustering - Google Patents
Transformer partial discharge positioning method and system based on density clustering Download PDFInfo
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- G01R31/12—Testing 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
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Abstract
A transformer partial discharge positioning method based on density clustering comprises the following steps: (1) 8 ultrasonic sensors are arranged on the outer shell of the transformer box body to detect partial discharge signals, and the output ends of the ultrasonic sensors are connected with an oscilloscope through a signal amplifier; (2) establishing 56 sets of positioning equations for solving the partial discharge position, and eliminating second-order terms to convert the 56 sets of positioning equations from nonlinearity to linearity; (3) solving 56 sets of positioning equations to obtain 56 initial sample values; (4) dividing 56 sample initial values into 6 classes, and averaging the sample initial values in each class to serve as a positioning result of the class; (5) and selecting the positioning result with the minimum positioning error as the optimal position of the partial discharge source according to the evaluation index. The invention further comprises a transformer partial discharge positioning system based on density clustering. The method can effectively solve the problem that the partial discharge positioning is sensitive to the arrival time difference error, and can realize the accurate positioning of the partial discharge in the transformer.
Description
Technical Field
The invention belongs to the technical field of high voltage, and particularly relates to a density clustering-based transformer partial discharge positioning method and system.
Background
Most faults of the power grid are caused by electrical insulation defects, and partial discharge is a phenomenon generated by the electrical insulation defects. The transformer is used as a main device, and the condition of the transformer directly influences the safe operation of a power grid. The partial discharge positioning detection is an important means for evaluating the insulation state of the transformer, and the accurate position of a partial discharge source is determined, so that the insulation state of equipment can be more accurately reflected, and a maintenance strategy is formulated, so that the service life of the equipment is prolonged, and the operation reliability of a power grid is ensured.
The key of the transformer partial discharge positioning is to establish a positioning equation set through arrival time difference data and coordinates of the ultrasonic sensor, so that the arrival time difference data is a key parameter in positioning, and solving the positioning equation set is a key link of partial discharge. In actual detection, under the influence of response speed of a detection system and noise interference factors, acquired arrival time difference data inevitably has errors; the system of positioning equations is non-linear, and solving the system of non-linear equations is complex and difficult. These all affect the accuracy of the transformer partial discharge location.
Disclosure of Invention
The invention aims to solve the technical problem of overcoming the defects of the prior art and provides a density clustering-based transformer partial discharge positioning method and system with strong universality, high positioning accuracy and high maintenance efficiency.
The invention solves the technical problem by adopting the technical scheme that a density clustering-based transformer partial discharge positioning method and system comprises the following steps:
the method comprises the following steps: 8 ultrasonic sensors are arranged on the shell of the transformer box body to detect partial discharge signals, and the output ends of the ultrasonic sensors are connected with an oscilloscope through a signal amplifier to obtain arrival time difference data 5;
step two: based on a time difference of arrival positioning method, any 5 ultrasonic sensors form a group and can establish a corresponding positioning equation set for solving the partial discharge position, namely 8 ultrasonic sensors can establish 56 positioning equation sets for solving the partial discharge position, and second-order terms are eliminated to convert the 56 positioning equation sets from nonlinearity to linearity;
step three: solving 56 sets of positioning equations by using a Gaussian elimination method to obtain 56 initial sample values;
step four: dividing 56 sample initial values into 6 classes by using a density clustering algorithm, and averaging the sample initial values in each class to serve as a positioning result of the class; step five: and selecting the positioning result with the minimum positioning error as the optimal local discharge source coordinate according to the evaluation index.
Further, in the first step, the frequency range of the ultrasonic sensor is 20-100 kHz, and the resonance frequency is 40 kHz; the output end of the ultrasonic sensor is connected with the oscilloscope through the signal amplifier by using a signal wire, the ultrasonic sensor is used for detecting a partial discharge signal, and the oscilloscope is used for collecting the partial discharge signal detected by the ultrasonic sensor.
Further, in the second step, the positioning equation set of the partial discharge position means that a corresponding positioning equation set for solving the partial discharge position is established for each 5 ultrasonic sensors;
assuming that the position coordinates of the partial discharge source are (x, y, z), the coordinates of the ultrasonic sensor are (x, y, z), respectivelyi,yi,zi) (i 1, 2.... n), the time required for the ultrasonic wave to reach the 1 st ultrasonic sensor from the local discharge source is T, and the time difference between the ultrasonic wave from the local discharge source and the i (i 2, 3.. n) th sensor and the 1 st sensor is Δ Ti1Then, the system of positioning equations for solving the partial discharge position is:
in the second step, eliminating the second order term means expanding each equation in the positioning equation set to make a difference, and when any 5 ultrasonic sensors are in one set, the equation (1) is converted into the following form:
in the formula, xi1＝xi-x1，yi1＝yi-y1，zi1＝zi-z1，
i＝1,2,...,5。
Further, in the fourth step, the density clustering algorithm includes the following steps:
s1, assuming 56 sample initial values to form a data set
Calculating two points S of a data set SiAnd sjThe Euclidean distance between the two elements is calculated according to the following formula:
dij＝||si-sj||2 (3)
s2, defining the maximum truncation distance dmaxThe following were used:
the truncated distance sequence Q is defined as follows:
Q＝{dci|dci＝i×K,K＝dmax/n,i＝1,2,...,56} (5)
then, calculate the point siLocal density of (p)iThe following were used:
in the formula, dcl∈Q
S3, calculating a point siDistance delta ofiThe following were used:
s4, calculating a point siGamma of (2)iValue and in gammaiArranging the points in the data set S in descending order of the values, and taking the first 6 points as clustering center points; point siGamma of (2)iThe value calculation formula is as follows:
s5, distributing the remaining 50 points to the points with higher local density rhoiAnd a minimum distance deltaiClustering.
Further, in the fifth step, the evaluation index is defined as follows:
when the number n of ultrasonic sensors is 8, equation (1) can be written as follows:
order to
Then equation (9) is converted to the following form:
let the average of 6 classes per class be Xk(x′k,y′k,z′k) (k is 1,2, …,6), and formula (10) can be substituted with:
then, the evaluation index EkThe calculation formula of (2) is as follows:
Ek＝||F(Xk)||1 (12)
evaluation index EkThe smaller the numerical value of (2) is, the closest the point to the actual local discharge source is shown, the positioning error is the smallest, and the point is taken as the optimal local discharge source coordinate.
A transformer partial discharge positioning system based on density clustering comprises the transformer partial discharge positioning method based on density clustering.
Compared with the prior art, the invention has the following beneficial effects: the transformer partial discharge positioning method and system based on density clustering are adopted, the system is strong in universality, the problem that the positioning result is poor due to the error of the arrival time difference in the existing transformer partial discharge positioning process is effectively solved, and the positioning accuracy is high.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention.
Detailed Description
The invention is further illustrated by the following figures and examples.
Referring to fig. 1, the present embodiment includes the following steps:
the method comprises the following steps: 8 ultrasonic sensors are arranged on the shell of the transformer box body to detect partial discharge signals, the frequency range of the ultrasonic sensors is 20-100 kHz, and the resonance frequency is 40 kHz. The output end of the ultrasonic sensor is connected with the oscilloscope through the signal amplifier, the ultrasonic sensor is used for detecting partial discharge signals, the oscilloscope is used for collecting the partial discharge signals detected by the ultrasonic sensor, and arrival time difference data can be obtained by reading waveforms on the oscilloscope.
Step two: and establishing a plurality of positioning equation sets for solving the partial discharge position based on the arrival time difference positioning method.
Referring to patent document 1, the position coordinates of the partial discharge source are set to (x, y, z), and the coordinates of the ultrasonic sensor are set to (x, y, z), respectivelyi,yi,zi)(i1,2, n), the time required for the ultrasonic wave to reach the 1 st ultrasonic sensor from the local discharge source is T, and the time difference between the ultrasonic wave from the local discharge source and the 1 st sensor from the i (i-2, 3i1Every 5 ultrasonic sensors form a group, and a corresponding positioning equation set for solving the partial discharge position is established as shown in formulas (1) to (5):
(x-x1)2+(y-y1)2+(z-z1)2＝v2T2 (1)
(x-x2)2+(y-y2)2+(z-z2)2＝v2(T+Δt21)2 (2)
(x-x3)2+(y-y3)2+(z-z3)2＝v2(T+Δt31)2 (3)
(x-x4)2+(y-y4)2+(z-z4)2＝v2(T+Δt41)2 (4)
(x-x5)2+(y-y5)2+(z-z5)2＝v2(T+Δt51)2 (5)
then, there are 56 combinations of the 8 ultrasonic sensors, that is, 56 positioning equations formed by equations (1) - (5) can be established.
The system of positioning equations formed by equations (1) - (5) is non-linear, and the system of positioning equations is converted from non-linear to linear by eliminating second order terms. Eliminating the second order terms means expanding each type of positioning equation set for difference, and the original positioning equation set can be converted from non-linearity to linearity.
The equation (2) and the equation (3) are expanded and subtracted to obtain the following equation
Let xi1＝xi-x1，yi1＝yi-y1，zi1＝zi-z1，i＝2,3,4,5。
Let's again li＝xi 2+yi 2+zi 2，i＝1,2,3,4,5。
Equation (6) can be rewritten as follows:
similarly, by expanding equations (3), (4), and (5) and subtracting equation (2), the following can be obtained:
referring to patent document 2, equations (7) to (10) can be written as follows
Wherein: reference patent document 1 is: yibaiqiang, how rigid, Zhang Hui, Li soldier, and how gill A partial discharge nonlinear model conversion solving and optimizing method based on multiple ultrasonic sensors [ P ]. Hubei: CN108536648A, 2018-09-14.
Reference patent document 2 is: a regularization-based substation partial discharge location method [ P ]. Anhui: CN109490728A, 2018-11-30.
Step three: the system of localization equations is solved using gaussian elimination.
56 sets of positioning equations are solved by using a Gaussian elimination method, and 56 initial values of samples are obtained.
Step four: and dividing 56 groups of sample initial values into 6 classes by using a density clustering algorithm, and averaging the sample initial values in each class to serve as a positioning result of the class. The steps of the density clustering algorithm are specifically as follows.
Assume 56 sample initial values to form a data set
i 1, 2.., 56, two points S of the data set S are calculatediAnd sjThe Euclidean distance between the two elements is calculated according to the following formula:
dij＝||si-sj||2 (12)
defining a maximum truncation distance dmaxThe following were used:
the truncated distance sequence Q is defined as follows:
Q＝{dci|dci＝i×K,K＝dmax/n,i＝1,2,...,56} (14)
then, calculate the point siLocal density of (p)iThe following were used:
in the formula, dcl∈Q。
Calculating a point siDistance delta ofiThe following were used:
calculating a point siGamma of (2)iValue and in gammaiThe points in the data set S are arranged in descending order of magnitude of the values, and the first 6 points are taken as cluster center points. Point siGamma of (2)iThe value calculation formula is as follows:
the remaining 50 points are assigned to the higher local density piAnd a minimum distance deltaiClustering.
Step five: and selecting the positioning result with the minimum positioning error as the optimal local discharge source coordinate according to the evaluation index.
The evaluation indexes are defined as follows:
when the number of the ultrasonic sensors is 8, the following equation system can be obtained:
order to
Then equation (18) is converted to the following form:
let the average of 6 classes per class be Xk(x′k,y′k,z′k) (k is 1,2, …,6), and formula (19) can be substituted with:
then, the evaluation index EkThe calculation formula of (2) is as follows:
Ek＝||F(Xk)||1 (21)
evaluation index EkThe smaller the numerical value of (2) is, the closest the point to the actual local discharge source is shown, the positioning error is the smallest, and the point is taken as the optimal local discharge source coordinate.
Applications ofExample (b): the size of the transformer box is 150cm multiplied by 100cm multiplied by 120cm, the coordinates of 1 PD source are (60,45,80) cm, and the coordinates of 8 ultrasonic sensors are S respectively1(10,0,10)cm,S2(10,100,10)cm,S3(140,100,10)cm,S4(140,0,10)cm,S5(20,0,110)cm,S6(20,100,110)cm,S7(130,100,110)cm,S8(130,0,110) cm, and the equivalent wave velocity of the ultrasonic wave in the transformer oil is 1500 m/s.
Let the theoretical time delay be tau, the simulated time delay after adding the error be tau', and define the time delay error as
Respectively adding 5 random time difference errors in a certain range, respectively e1∈(0,2％),e2∈(2％,4％),e3∈(4％,6％),e4E (6%, 8%) and e5E (8%, 10%). The simulated delay information is shown in table 1.
TABLE 1 theoretical arrival time difference and simulated arrival time difference error under different time difference errors
Suppose the actual coordinates of the PD source are (x)act,yact,zact) If the coordinates obtained by the positioning algorithm are (x, y, z), the PD positioning error is defined as the euclidean distance between the two points, i.e. the euclidean distance between the two points
The average value of the 56 sample initial values is defined as the positioning result before the present embodiment is used, and the specific positioning result is shown in table 2.
Table 2 positioning results and errors before and after using this example under different time difference errors
When the arrival time difference error is small (e.g. the arrival time difference error is e)1) The positioning results of the two methods are not very different. When the error of the arrival time difference reaches e2When the time difference of arrival error is increased, the positioning error after the use of the invention is obviously smaller than the positioning error before the use.
The simulation results and analysis are integrated to show that the density clustering-based transformer partial discharge positioning method and system are feasible.
Various modifications and variations of the present invention may be made by those skilled in the art, and they are also within the scope of the present invention provided they are within the scope of the claims of the present invention and their equivalents. What is not described in detail in the specification is prior art that is well known to those skilled in the art.
Claims (6)
1. A transformer partial discharge positioning method and system based on density clustering are characterized by comprising the following steps:
the method comprises the following steps: 8 ultrasonic sensors are arranged on the shell of the transformer box body to detect partial discharge signals, and the output ends of the ultrasonic sensors are connected with an oscilloscope through a signal amplifier to obtain arrival time difference data 5;
step two: based on a time difference of arrival positioning method, any 5 ultrasonic sensors form a group and can establish a corresponding positioning equation set for solving the partial discharge position, namely 8 ultrasonic sensors can establish 56 positioning equation sets for solving the partial discharge position, and second-order terms are eliminated to convert the 56 positioning equation sets from nonlinearity to linearity;
step three: solving 56 sets of positioning equations by using a Gaussian elimination method to obtain 56 initial sample values;
step four: dividing 56 sample initial values into 6 classes by using a density clustering algorithm, and averaging the sample initial values in each class to serve as a positioning result of the class; step five: and selecting the positioning result with the minimum positioning error as the optimal local discharge source coordinate according to the evaluation index.
2. The transformer partial discharge positioning method and system based on density clustering according to claim 1, characterized in that in the step one, the frequency range of the ultrasonic sensor is 20-100 kHz, and the resonance frequency is 40 kHz; the output end of the ultrasonic sensor is connected with the oscilloscope through the signal amplifier by using a signal wire, the ultrasonic sensor is used for detecting a partial discharge signal, and the oscilloscope is used for collecting the partial discharge signal detected by the ultrasonic sensor.
3. The transformer partial discharge positioning method and system based on density clustering according to claim 1, wherein in the second step, the positioning equation set of the partial discharge position means that a corresponding positioning equation set for solving the partial discharge position is established for each 5 ultrasonic sensors;
assuming that the position coordinates of the partial discharge source are (x, y, z), the coordinates of the ultrasonic sensor are (x, y, z), respectivelyi,yi,zi) (i 1, 2.... n), the time required for the ultrasonic wave to reach the 1 st ultrasonic sensor from the local discharge source is T, and the time difference between the ultrasonic wave from the local discharge source and the i (i 2, 3.. n) th sensor and the 1 st sensor is Δ Ti1Then, the system of positioning equations for solving the partial discharge position is:
in the second step, eliminating the second order term means expanding each equation in the positioning equation set to make a difference, and when any 5 ultrasonic sensors are in one set, the equation (1) is converted into the following form:
in the formula, xi1＝xi-x1，yi1＝yi-y1，zi1＝zi-z1，
4. The transformer partial discharge positioning method and system based on density clustering according to claim 1, wherein in the fourth step, the density clustering algorithm comprises the following steps:
s1, assuming 56 sample initial values to form a data set
Calculating two points S of a data set SiAnd sjThe Euclidean distance between the two elements is calculated according to the following formula:
dij＝||si-sj||2 (3)
s2, defining the maximum truncation distance dmaxThe following were used:
the truncated distance sequence Q is defined as follows:
Q＝{dci|dci＝i×K,K＝dmax/n,i＝1,2,...,56} (5)
then, calculate the point siLocal density of (p)iThe following were used:
in the formula, dcl∈Q
S3, calculating a point siDistance delta ofiThe following were used:
s4, calculating a point siGamma of (2)iValue and in gammaiArranging the points in the data set S in descending order of the values, and taking the first 6 points as clustering center points; point siGamma of (2)iThe value calculation formula is as follows:
s5, distributing the remaining 50 points to the points with higher local density rhoiAnd a minimum distance deltaiClustering.
5. The density clustering-based transformer partial discharge positioning method and system as claimed in claim 4, wherein in the fifth step, the evaluation index is defined as follows:
when the number n of ultrasonic sensors is 8, equation (1) can be written as follows:
order to
Then equation (9) is converted to the following form:
let the average of 6 classes per class be Xk(x′k,y′k,z′k) (k is 1,2, …,6), and formula (10) can be substituted with:
then, the evaluation index EkThe calculation formula of (2) is as follows:
Ek＝||F(Xk)||1 (12)
evaluation index EkThe smaller the numerical value of (2) is, the closest the point to the actual local discharge source is shown, the positioning error is the smallest, and the point is taken as the optimal local discharge source coordinate.
6. A transformer partial discharge positioning system based on density clustering, which is characterized by comprising the transformer partial discharge positioning method based on density clustering according to claims 1-5.
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Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108536648A (en) * | 2018-03-30 | 2018-09-14 | 武汉大学 | Shelf depreciation nonlinear model conversion based on multiple ultrasonic sensors solves and optimization method |
| CN109490728A (en) * | 2018-11-30 | 2019-03-19 | 合肥工业大学 | A kind of substation's partial discharge positioning method based on regularization |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108536648A (en) * | 2018-03-30 | 2018-09-14 | 武汉大学 | Shelf depreciation nonlinear model conversion based on multiple ultrasonic sensors solves and optimization method |
| CN109490728A (en) * | 2018-11-30 | 2019-03-19 | 合肥工业大学 | A kind of substation's partial discharge positioning method based on regularization |
Non-Patent Citations (1)
| Title |
|---|
| 王署东 等: "高压局部放电定位模型转换求解与改进K-means聚类优化方法", 《电子测量与仪器学报》, vol. 32, no. 11, pages 179 - 181 * |
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