TWI693415B - Transformer diagnosis method, system, computer program product and computer readable recording medium - Google Patents

Transformer diagnosis method, system, computer program product and computer readable recording medium Download PDF

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TWI693415B
TWI693415B TW108105144A TW108105144A TWI693415B TW I693415 B TWI693415 B TW I693415B TW 108105144 A TW108105144 A TW 108105144A TW 108105144 A TW108105144 A TW 108105144A TW I693415 B TWI693415 B TW I693415B
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transformer
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correlation coefficient
probability density
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TW202032148A (en
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林明鐘
余兆棠
吳秉育
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南臺學校財團法人南臺科技大學
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Abstract

A diagnosis method includes a correlation coefficient computation step, a probability density function estimation step, a threshold value determination step, a step for analyzing data of a gas sample, and a diagnosis step. A threshold value is determined according to the normal probability density function computed based on the correlation coefficient of a plurality of data sets representing normal amount of gas produced by dielectric oil of a normal transformer, and the abnormal probability density function computed based on another correlation coefficient of a data set representing abnormal amount of gas produced by dielectric oil of an abnormal transformer and the plurality of data sets representing normal amount of gas. The state of a testing transformer is determined by comparison between a correlation coefficient associated with the gas sample and the plurality of data sets representing normal amount of gas, and the threshold value obtained. The transformer diagnosis method may be implemented by the system or programmed for use with a computer.

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變壓器診斷方法及其系統、電腦程式產品及電腦可讀取記錄 媒體 Transformer diagnosis method and system, computer program product and computer readable record media

本發明係涉及變壓器，尤指變壓器診斷方法及其系統、電腦程式產品及電腦可讀取記錄媒體。 The invention relates to a transformer, especially a transformer diagnosis method and system, a computer program product and a computer-readable recording medium.

變壓器為變電設備的重要元件之一，其狀態直接影響供電穩定性及安全性，也因此變壓器狀態的診斷、檢修一直以來是各界重視的課題。 Transformer is one of the important components of substation equipment, and its state directly affects the stability and safety of power supply. Therefore, the diagnosis and maintenance of the state of the transformer has always been a topic that has been valued by all circles.

變壓器(例如油浸式變壓器)的診斷方式之一是利用其油中溶解的氣體含量做為判斷依據，相關技術例如有中國大陸發明專利編號第CN104820146A號之「基於變壓器油中溶解氣體監測數據的變壓器故障預測方法」、中國大陸發明專利編號第CN105550700A號之「一種基於關聯分析和主成分分析的時間序列數據清洗方法」等。 One of the diagnostic methods for transformers (such as oil-immersed transformers) is to use the dissolved gas content in the oil as a basis for judgment. Related technologies include, for example, the Chinese Mainland Invention Patent No. CN104820146A "based on monitoring data of dissolved gas in transformer oil. "Transformer fault prediction method", "Chinese Patent No. CN105550700A" "A time series data cleaning method based on correlation analysis and principal component analysis", etc.

但目前仍有待提出一種新的診斷方式，以便於檢測人員因應需求的不同來選擇。此外，目前的診斷方式並未將維護成本納入考量的依據。 However, there is still a new diagnostic method to be proposed so that the testing personnel can choose according to different needs. In addition, the current diagnostic methods do not take into account the maintenance cost.

爰此，為提出有別於過去的變壓器診斷方式，本發明人提出一種變壓器診斷方法，包含下列步驟：一相關係數運算步驟、一機率密度函數估算步驟、一門檻值演算步驟及一待診斷氣體樣品資料分析步驟與診斷步驟。 該相關係數運算步驟：以一相關係數運算模組運算正常變壓器絕緣油產生的多筆正常氣體含量資料間相關係數之一正常群相關係數分布資料，該相關係數運算模組並運算異常變壓器絕緣油產生之至少一筆異常氣體含量資料與前述多筆正常氣體含量資料間相關係數之一異常群相關係數分布資料，這些相關係數其數值介於-1與1之間。 該機率密度函數估算步驟：以一機率密度函數估算模組依據該正常群相關係數分布資料估算一正常群機率密度函數，該機率密度函數估算模組並估算該異常群相關係數分布資料之一異常群機率密度函數。 該門檻值演算步驟：以一門檻值演算模組依據該正常群機率密度函數、該異常群機率密度函數、歷史統計資料之設備故障統計機率及預設之檢修費用資訊，以最低費用為準則演算前述門檻值。 該待診斷氣體樣品資料分析步驟與診斷步驟：取得一待診斷變壓器絕緣油產生之一待診斷氣體樣品資料，以一樣品分析模組運算該待診斷氣體樣品資料與前述正常氣體含量資料之一待比對相關係數；接著以一比對模組比對該待比對相關係數與該門檻值，以在該待比對相關係數大於或等於該門檻值時，判斷該待診斷變壓器為正常。 Secondly, in order to propose a transformer diagnosis method different from the past, the inventor proposes a transformer diagnosis method including the following steps: a correlation coefficient calculation step, a probability density function estimation step, a threshold calculation step, and a gas to be diagnosed Sample data analysis steps and diagnostic steps. The correlation coefficient calculation step: a correlation coefficient calculation module is used to calculate one of the correlation coefficient distribution data among the correlation coefficients among the normal gas content data generated by the normal transformer insulating oil. The correlation coefficient calculation module also calculates the abnormal transformer insulating oil The generated at least one abnormal gas content data and one of the correlation coefficients between the aforementioned normal gas content data is an abnormal group correlation coefficient distribution data, and the value of these correlation coefficients is between -1 and 1. The probability density function estimation step: using a probability density function estimation module to estimate a normal group probability density function based on the normal group correlation coefficient distribution data, the probability density function estimation module and estimating one of the abnormal group correlation coefficient distribution data anomalies Group probability density function. The threshold calculation step: a threshold calculation module is used to calculate the minimum group cost based on the normal group probability density function, the abnormal group probability density function, historical statistical data of equipment failure statistics probability and preset maintenance cost information The aforementioned threshold. The gas sample data analysis step and the diagnosis step of the gas to be diagnosed: obtaining a gas sample data to be diagnosed produced by a transformer insulating oil to be diagnosed, and calculating the gas sample data to be diagnosed and the normal gas content data by a sample analysis module Compare the correlation coefficient; then compare the correlation coefficient to be compared with the threshold value with a comparison module to determine that the transformer to be diagnosed is normal when the correlation coefficient to be compared is greater than or equal to the threshold value.

進一步，前述正常氣體含量資料及前述異常氣體含量資料皆包含氫氣、乙烯、乙炔、甲烷、乙烷、一氧化碳之氣體種類的氣體含量資料。 Further, both the normal gas content data and the abnormal gas content data include gas content data of gas types of hydrogen, ethylene, acetylene, methane, ethane, and carbon monoxide.

進一步，該相關係數運算模組係依據一皮爾森積差相關係數(Pearson Product-Moment Correlation Coefficient)公式進行運算：

Figure 108105144-A0305-02-0005-1
其中r為任兩組氣體含量資料(xi及yi,i=1,2,…,n)間之相關係數；n代表前述氣體種類之編號。 Further, the correlation coefficient calculation module is calculated according to a Pearson Product-Moment Correlation Coefficient formula:
Figure 108105144-A0305-02-0005-1
 Where r is the correlation coefficient between any two sets of gas content data (xi and yi, i = 1, 2, ..., n); n represents the number of the aforementioned gas type.

進一步，該機率密度函數估算步驟：由該機率密度函數估算模組取得x筆正常變壓器之正常氣體含量資料，每筆正常氣體含量資料皆有6個變數：氫氣、乙烯、乙炔、甲烷、乙烷、一氧化碳，依上述皮爾森積差相關係數公式進行兩兩運算得到x(x-1)個相關係數值，再以機率密度函數估算法得到正常群機率密度函數

Figure 108105144-A0305-02-0005-12
。 Further, the probability density function estimation step: obtaining normal gas content data of x normal transformers from the probability density function estimation module, each normal gas content data has 6 variables: hydrogen, ethylene, acetylene, methane, ethane 1. Carbon monoxide, according to the above Pearson product difference correlation coefficient formula, perform pairwise calculation to obtain x(x-1) correlation coefficient values, and then use the probability density function estimation method to obtain the probability density function of the normal group
Figure 108105144-A0305-02-0005-12
.

進一步，該機率密度函數估算步驟：由該機率密度函數估算模組取得y筆異常變壓器之氣體含量資料，每筆異常氣體含量資料皆有6個變數：氫氣、乙烯、乙炔、甲烷、乙烷、一氧化碳，利用此y筆異常與前述x筆正常資料，依上述皮爾森積差相關係數公式進行兩兩交叉運算得到xy個相關係數值，再以前述機率密度函數估算法得到異常群機率密度函數

Figure 108105144-A0305-02-0005-13
。前述機率密度函數估算法為所屬領域通常知識者所慣用，可見於一般文獻中，故為求簡明，於此不再詳加敘述。 Further, the probability density function estimation step: obtain gas content data of y abnormal transformers from the probability density function estimation module, and each abnormal gas content data has 6 variables: hydrogen, ethylene, acetylene, methane, ethane, Carbon monoxide, using this y anomaly and the aforementioned x normal data, perform a pairwise crossover operation according to the above Pearson product difference correlation coefficient formula to obtain xy correlation coefficient values, and then use the aforementioned probability density function estimation method to obtain the abnormal group probability density function
Figure 108105144-A0305-02-0005-13
. The aforementioned probability density function estimation method is commonly used by those with ordinary knowledge in the field and can be found in the general literature, so for simplicity, it will not be described in detail here.

進一步，該門檻值依據維護與檢修成本最小化之一成本公式進行演算。詳細而言，該成本公式可包含：

Figure 108105144-A0305-02-0006-11
其中，cost為維護與檢修成本；η為待演算之門檻值；P(H1)與P(H0)分別為依據歷史資料統計得到之變壓器正常工作及異常之機率；C00為異常變壓器被判斷為異常時變壓器停機之檢修費用；C01為異常變壓器被判斷為變壓器正常，繼續運作發生故障而造成之損失與維修費；C10為正常變壓器被判斷為異常時變壓器停機之檢修費用；C11為正常變壓器被判斷為正常變壓器之費用(一般為0)；
Figure 108105144-A0305-02-0006-34
為前述估算得到之正常群機率密度函數；
Figure 108105144-A0305-02-0006-14
為前述估算得到之異常群機率密度函數。 Further, the threshold is calculated based on a cost formula that minimizes maintenance and repair costs. In detail, the cost formula can include:
Figure 108105144-A0305-02-0006-11
 Among them, cost is the maintenance and repair cost; η is the threshold value to be calculated; P(H1) and P(H0) are the probability of normal operation and abnormality of the transformer based on historical data statistics; C00 is the abnormal transformer is judged to be abnormal The maintenance cost of transformer shutdown at the time; C01 is the loss and maintenance cost of the abnormal transformer that is judged to be normal and the fault continues to operate; C10 is the maintenance cost of the transformer shutdown when the normal transformer is judged to be abnormal; C11 is the judgment of the normal transformer The cost of a normal transformer (generally 0);
Figure 108105144-A0305-02-0006-34
It is the normal group probability density function obtained from the aforementioned estimation;
Figure 108105144-A0305-02-0006-14
It is the probability density function of the anomaly group obtained from the aforementioned estimation.

本發明可為一種變壓器診斷方法，包含下列步驟：運算變壓器正常運作時絕緣油產生之多筆正常氣體含量資料間相關係數之一正常群相關係數分布資料，並運算異常變壓器絕緣油產生之至少一筆異常氣體含量資料與前述多筆正常氣體含量資料間相關係數之一異常群相關係數分布資料；估算該正常群相關係數分布資料之一正常群機率密度函數，並估算該異常群相關係數分布資料之一異常群機率密度函數；依據該正常群機率密度函數、該異常群機率密度函數、設備故障統計機率及檢修費用資訊，以最低費用為準則演算一門檻值，以該門檻值作為判斷一待診斷變壓器正常與否的依據。 The invention can be a transformer diagnosis method, including the following steps: calculating one of the correlation coefficient distribution data of one of the correlation coefficients among the normal gas content data generated by the insulating oil during normal operation of the transformer, and calculating at least one of the abnormal transformer insulating oil generated One of the correlation coefficient distribution data of the correlation coefficient between the abnormal gas content data and the aforementioned plurality of normal gas content data; estimating one of the normal group probability coefficient distribution data of the normal group correlation coefficient distribution data, and estimating the distribution of the abnormal group correlation coefficient distribution data An abnormal group probability density function; based on the normal group probability density function, the abnormal group probability density function, equipment failure statistical probability and maintenance cost information, a threshold value is calculated based on the minimum cost, and the threshold value is used as a judgment to be diagnosed The basis of whether the transformer is normal or not.

本發明亦可為一種電腦程式產品，內儲一程式，當電腦載入該程式並執行後，可完成如前所述之變壓器診斷方法。 The invention can also be a computer program product, which stores a program. After the computer loads the program and executes it, the transformer diagnosis method as described above can be completed.

本發明也可為一種電腦可讀取記錄媒體，內儲一程式，當電腦載入該程式並執行後，可完成如前所述之變壓器診斷方法。 The invention can also be a computer-readable recording medium that stores a program. After the computer loads the program and executes it, the transformer diagnosis method as described above can be completed.

本發明並可為一種變壓器診斷系統，包含：一處理單元、一儲存單元、一相關係數運算模組、一機率密度函數估算模組、一門檻值演算模組、一樣品分析模組及一比對模組。 該儲存單元連接該處理單元，儲存正常變壓器絕緣油產生之多筆正常氣體含量資料及異常變壓器絕緣油產生之多筆至少一筆異常氣體含量資料。 該相關係數運算模組連接該處理單元，用以運算前述多筆正常氣體含量資料間相關係數之一正常群相關係數分布資料，該相關係數運算模組並運算前述異常氣體含量資料與前述多筆正常氣體含量資料之一異常群相關係數分布資料。 該機率密度函數估算模組連接該處理單元，用以依據該正常群相關係數分布資料估算一正常群機率密度函數，並估算該異常群相關係數分布資料之一異常群機率密度函數。 該門檻值演算模組連接該處理單元，用以依據該正常群機率密度函數、該異常群機率密度函數、歷史統計資料之設備故障統計機率及預設之檢修費用資訊，以最低費用為準則演算一門檻值。 該樣品分析模組連接該處理單元，用以運算一待診斷變壓器絕緣油產生之一待診斷氣體樣品資料與前述正常氣體含量資料之一待比對相關係數。 該比對模組連接該處理單元，用以比對該待比對相關係數與該門檻值，以在該待比對相關係數大於或等於該門檻值時，判斷該待診斷變壓器為正常。 The invention can be a transformer diagnosis system, including: a processing unit, a storage unit, a correlation coefficient calculation module, a probability density function estimation module, a threshold calculation module, a sample analysis module and a ratio For modules. The storage unit is connected to the processing unit and stores a plurality of pieces of normal gas content data generated by normal transformer insulating oil and at least one piece of abnormal gas content data generated by abnormal transformer insulating oil. The correlation coefficient calculation module is connected to the processing unit for calculating one normal group correlation coefficient distribution data among correlation coefficients among the plurality of normal gas content data, and the correlation coefficient calculation module also calculates the abnormal gas content data and the plurality of data One of the normal gas content data is the abnormal group correlation coefficient distribution data. The probability density function estimation module is connected to the processing unit for estimating a normal group probability density function according to the normal group correlation coefficient distribution data, and estimating an abnormal group probability density function of the abnormal group correlation coefficient distribution data. The threshold calculation module is connected to the processing unit for calculating the probability of equipment failure statistics based on the normal group probability density function, the abnormal group probability density function, historical statistical data, and the preset maintenance cost information, based on the minimum cost as the criterion A threshold. The sample analysis module is connected to the processing unit, and is used to calculate a correlation coefficient of a gas sample data to be diagnosed produced by a transformer insulating oil to be diagnosed and a normal gas content data to be compared. The comparison module is connected to the processing unit for comparing the correlation coefficient to be compared with the threshold value, so as to determine that the transformer to be diagnosed is normal when the correlation coefficient to be compared is greater than or equal to the threshold value.

進一步，依據維護與檢修成本最小化之一成本公式進行演算前述門檻值。該成本公式包含：

Figure 108105144-A0305-02-0008-15
其中，cost為維護與檢修成本；η為待演算之門檻值；P(H1)與P(H0)分別為依據歷史資料統計得到之變壓器正常工作及異常之機率；C00為異常變壓器被判斷為異常時變壓器停機之檢修費用；C01為異常變壓器被判斷為變壓器正常，繼續運作發生故障而造成之損失與維修費；C10為正常變壓器被判斷為異常時變壓器停機之檢修費用；C11為正常變壓器被判斷為正常變壓器之費用(一般為0)；
Figure 108105144-A0305-02-0008-16
為前述估算得到之正常群機率密度函數
Figure 108105144-A0305-02-0008-17
為前述估算得到之異常群機率密度函數。 Further, the aforementioned threshold value is calculated according to a cost formula that minimizes maintenance and repair costs. The cost formula contains:
Figure 108105144-A0305-02-0008-15
 Among them, cost is the cost of maintenance and repair; η is the threshold value to be calculated; P(H 1 ) and P(H 0 ) are the probability of normal operation and abnormality of the transformer based on historical data statistics; C 00 is the abnormal transformer. The maintenance cost of transformer shutdown when judged to be abnormal; C 01 is the loss and maintenance cost caused by the abnormal transformer being judged to be normal and the operation continues to fail; C 10 is the maintenance cost of transformer shutdown when the normal transformer is judged to be abnormal; C 11 is the cost of a normal transformer judged as a normal transformer (generally 0);
Figure 108105144-A0305-02-0008-16
Is the probability density function of the normal group obtained from the aforementioned estimation
Figure 108105144-A0305-02-0008-17
It is the probability density function of the anomaly group obtained from the aforementioned estimation.

根據上述技術特徵可達成以下功效： According to the above technical features, the following effects can be achieved:

1.可依據該正常群機率密度函數、該異常群機率密度函數、設備故障統計機率及檢修費用資訊，以最低費用為準則演算一門檻值，以該門檻值作為判斷一待診斷變壓器正常與否的依據，讓門檻值的決定相較自訂方式更為客觀，使變壓器的診斷可符合成本效益。 1. According to the normal group probability density function, the abnormal group probability density function, equipment failure statistics probability and maintenance cost information, a threshold value can be calculated using the minimum cost as a criterion, and the threshold value is used as a criterion to determine whether the transformer to be diagnosed is normal or not The basis for making the threshold value more objective than the custom method makes the diagnosis of the transformer cost-effective.

2.依據成本公式調整門檻值，訂定機制相較於自訂方式較為客觀。 2. Adjust the threshold value according to the cost formula, and the setting mechanism is more objective than the custom method.

(100):變壓器診斷系統 (100): Transformer diagnostic system

(1):處理單元 (1): Processing unit

(2):儲存單元 (2): Storage unit

(21):正常氣體含量資料 (21): Normal gas content data

(22):異常氣體含量資料 (22): Abnormal gas content data

(23):待診斷氣體樣品資料 (23): gas sample data to be diagnosed

(3):相關係數運算模組 (3): Correlation coefficient calculation module

(4):機率密度函數估算模組 (4): Probability density function estimation module

(5):門檻值演算模組 (5): Threshold value calculation module

(6):樣品分析模組 (6): Sample analysis module

(7):比對模組 (7): Comparison module

(S01):相關係數運算步驟 (S01): Correlation coefficient calculation steps

(S02):機率密度函數估算步驟 (S02): Probability density function estimation step

(S03):門檻值演算步驟 (S03): Threshold value calculation steps

(S04):待診斷氣體樣品資料分析步驟與診斷步驟 (S04): Data analysis steps and diagnosis steps of the gas sample to be diagnosed

Figure 108105144-A0305-02-0013-25
:正常群機率密度函數
Figure 108105144-A0305-02-0013-25
: Normal group probability density function

Figure 108105144-A0305-02-0014-26
:異常群機率密度函數
Figure 108105144-A0305-02-0014-26
: Anomaly group probability density function

η:門檻值 η: threshold

[第一圖]係本發明實施例之系統方塊示意圖。 [Figure 1] is a schematic block diagram of a system according to an embodiment of the present invention.

[第二圖]係本發明實施例之主要步驟流程示意圖。 [Second figure] is a schematic flowchart of main steps of an embodiment of the present invention.

[第三圖]係本發明實施例之正常群機率密度函數及異常群機率密度函數之示意圖。 [Third figure] is a schematic diagram of a normal group probability density function and an abnormal group probability density function according to an embodiment of the present invention.

綜合上述技術特徵，本發明變壓器診斷方法及其系統、電腦程式產品及電腦可讀取記錄媒體的主要功效將可於下述實施例清楚呈現。 Based on the above technical features, the main functions of the transformer diagnosis method and system, computer program product and computer readable recording medium of the present invention will be clearly presented in the following embodiments.

請先參閱第一圖，係揭示本發明實施例變壓器診斷系統(100)，包含：一處理單元(1)、及連接該處理單元(1)之一儲存單元(2)、一相關係數運算模組(3)、一機率密度函數估算模組(4)、一門檻值演算模組(5)、一樣品分析模組(6)與一比對模組(7)。該儲存單元(2)用以儲存正常變壓器絕緣油產生之多筆正常氣體含量資料(21)、異常變壓器絕緣油產生之至少一筆異常氣體含量資料(22)及待診斷變壓器絕緣油產生之至少一筆待診斷氣體樣品資料(23)。於本實施例中，該變壓器診斷系統(100)是應用於診斷油浸式變壓器，故前述正常氣體含量資料(21)、前述異常氣體含量資料(22)及前述待診斷氣體樣品資料(23)皆包含氫氣、乙烯、乙炔、甲烷、乙烷、一氧化碳之氣體種類的氣體含量資料，以這些氣體種類作為診斷的指標，但並不以此為限。 Please refer to the first figure, which discloses a transformer diagnosis system (100) according to an embodiment of the present invention, including: a processing unit (1), a storage unit (2) connected to the processing unit (1), and a correlation coefficient calculation module Group (3), a probability density function estimation module (4), a threshold calculation module (5), a sample analysis module (6) and a comparison module (7). The storage unit (2) is used to store multiple pieces of normal gas content data (21) produced by normal transformer insulating oil, at least one piece of abnormal gas content data (22) produced by abnormal transformer insulating oil and at least one piece of transformer insulating oil to be diagnosed Information of gas samples to be diagnosed (23). In this embodiment, the transformer diagnosis system (100) is used to diagnose oil-immersed transformers, so the aforementioned normal gas content data (21), the aforementioned abnormal gas content data (22) and the aforementioned gas sample data to be diagnosed (23) All contain gas content data of gas types such as hydrogen, ethylene, acetylene, methane, ethane, and carbon monoxide. These gas types are used as diagnostic indicators, but not limited to this.

續請參閱第二圖搭配第一圖，本實施例之變壓器診斷方法係以上述變壓器診斷系統(100)來執行，或者可編程為一程式並儲存於電腦程式產品或電腦可讀取記錄媒體。當電腦載入該程式並執行後，可完成前述之變壓器診斷方法。本實施例之變壓器診斷方法，主要包括下列步驟：一相關係數運算步驟(S01)、一機率密度函數估算步驟(S02)、一門檻值演算步驟(S03)及一待診斷氣體樣品資料分析步驟與診斷步驟(S04)。要補充說明的是，該相關係數運算步驟 (S01)、該機率密度函數估算步驟(S02)及該門檻值演算步驟(S03)可預先執行取得比對所需的門檻值，以供後續不同待診斷氣體樣品資料反覆比對之用。 Please refer to the second figure and the first figure. The transformer diagnosis method of this embodiment is executed by the above-mentioned transformer diagnosis system (100), or can be programmed as a program and stored in a computer program product or a computer-readable recording medium. After the computer loads the program and executes it, the aforementioned transformer diagnosis method can be completed. The transformer diagnosis method of this embodiment mainly includes the following steps: a correlation coefficient calculation step (S01), a probability density function estimation step (S02), a threshold calculation step (S03), and a gas sample data analysis step to be diagnosed and Diagnostic step (S04). It should be added that this correlation coefficient calculation step (S01), the probability density function estimation step (S02) and the threshold value calculation step (S03) can be performed in advance to obtain the threshold value required for comparison, for subsequent repeated comparison of different gas sample data to be diagnosed.

續請參閱第二圖搭配第一圖，該相關係數運算步驟(S01)：以前述相關係數運算模組(3)運算正常變壓器絕緣油產生之多筆正常氣體含量資料(21)間之相關係數之一正常群相關係數分布資料，該相關係數運算模組(3)並運算異常變壓器絕緣油產生之至少一筆異常氣體含量資料(22)與前述多筆正常氣體含量資料(21)間之一異常群相關係數分布資料。這些相關係數其數值介於-1與1之間。 Continue to refer to the second figure and the first figure. The correlation coefficient calculation step (S01): use the aforementioned correlation coefficient calculation module (3) to calculate the correlation coefficient between the multiple normal gas content data (21) generated by the normal transformer insulating oil One normal group correlation coefficient distribution data, the correlation coefficient calculation module (3) also calculates an abnormality between at least one abnormal gas content data (22) generated by abnormal transformer insulating oil and the aforementioned multiple normal gas content data (21) Group correlation coefficient distribution data. These correlation coefficients have values between -1 and 1.

續請參閱第二圖搭配第一圖，詳細而言，該相關係數運算模組(3)係依據一皮爾森積差相關係數(Pearson Product-Moment Correlation Coefficient)公式進行運算：

Figure 108105144-A0305-02-0010-2
其中r為任兩組氣體含量資料(xi及yi,i=1,2,…,n)間之相關係數；n代表前述氣體種類之編號。 Please refer to the second figure and the first figure. In detail, the correlation coefficient calculation module (3) is calculated according to a Pearson Product-Moment Correlation Coefficient formula:
Figure 108105144-A0305-02-0010-2
 Where r is the correlation coefficient between any two sets of gas content data (xi and yi, i = 1, 2, ..., n); n represents the number of the aforementioned gas type.

續請參閱第二圖搭配第一圖，於本實施案例之機率密度函數估算步驟中，由該機率密度函數估算模組(4)取得x筆正常變壓器之正常氣體含量資料，每筆正常氣體含量資料皆有6個變數：氫氣、乙烯、乙炔、甲烷、乙烷、一氧化碳，依上述皮爾森積差相關係數公式進行兩兩運算得到x(x-1)個相關係數值，再以機率密度函數估算法得到正常群機率密度函數

Figure 108105144-A0305-02-0010-18
。 Please continue to refer to the second figure and the first figure. In the probability density function estimation step of this embodiment, the probability density function estimation module (4) obtains the normal gas content data of x normal transformers, each normal gas content There are 6 variables in the data: hydrogen, ethylene, acetylene, methane, ethane, carbon monoxide. According to the above Pearson product difference correlation coefficient formula, two (2) calculations are performed to obtain x(x-1) correlation coefficient values, and then the probability density function Estimation method to obtain probability density function of normal group
Figure 108105144-A0305-02-0010-18
.

續請參閱第二圖搭配第一圖，於本實施案例之機率密度函數估算步驟中，由該機率密度函數估算模組(4)取得y筆異常變壓器之氣體含量資料， 每筆異常氣體含量資料皆有6個變數：氫氣、乙烯、乙炔、甲烷、乙烷、一氧化碳，利用此y筆異常與前述x筆正常資料，依上述皮爾森積差相關係數公式進行兩兩交叉運算得到xy個相關係數值，再以機率密度函數估算法得到異常群機率密度函數

Figure 108105144-A0305-02-0011-19
。前述機率密度函數估算法為所屬領域通常知識者所慣用，可見於一般文獻中，故為求簡明，於此不再詳加敘述。 Please refer to the second figure and the first figure. In the probability density function estimation step of this embodiment, the probability density function estimation module (4) obtains the gas content data of y abnormal transformers, and each abnormal gas content data There are 6 variables: hydrogen, ethylene, acetylene, methane, ethane, carbon monoxide. Using this y-anomaly and the above-mentioned x normal data, carry out the pairwise crossover operation according to the above Pearson product difference correlation coefficient formula to obtain xy correlation coefficients Value, and then use the probability density function estimation method to obtain the probability density function of the abnormal group
Figure 108105144-A0305-02-0011-19
. The aforementioned probability density function estimation method is commonly used by those with ordinary knowledge in the field and can be found in the general literature, so for simplicity, it will not be described in detail here.

續請參閱第二圖搭配第一圖，該門檻值演算模組(5)可將該門檻值η進一步依據維護與檢修成本最小化進行演算。詳細而言，依據一成本公式調整，該成本公式包含：

Figure 108105144-A0305-02-0011-21
Please refer to the second figure and the first figure. The threshold value calculation module (5) can further calculate the threshold value η according to the minimum maintenance and repair cost. In detail, it is adjusted according to a cost formula, which includes:
Figure 108105144-A0305-02-0011-21

其中，cost為維護與檢修成本；η為待演算之門檻值；P(H1)與P(H0)分別為依據歷史資料統計得到之變壓器正常工作及異常之機率；C00為異常變壓器被判斷為異常時變壓器停機之檢修費用；C01為異常變壓器被判斷為變壓器正常，繼續運作發生故障而造成之損失與維修費；C10為正常變壓器被判斷為異常時變壓器停機之檢修費用；C11為正常變壓器被判斷為正常變壓器之費用(一般為0)；

Figure 108105144-A0305-02-0011-33
為前述估算得到之正常群機率密度函數；
Figure 108105144-A0305-02-0011-20
為前述估算得到之異常群機率密度函數。 Among them, cost is the cost of maintenance and repair; η is the threshold value to be calculated; P(H 1 ) and P(H 0 ) are the probability of normal operation and abnormality of the transformer based on historical data statistics; C 00 is the abnormal transformer. The maintenance cost of transformer shutdown when judged to be abnormal; C 01 is the loss and maintenance cost caused by the abnormal transformer being judged to be normal and the operation continues to fail; C 10 is the maintenance cost of transformer shutdown when the normal transformer is judged to be abnormal; C 11 is the cost of a normal transformer judged as a normal transformer (generally 0);
Figure 108105144-A0305-02-0011-33
It is the normal group probability density function obtained from the aforementioned estimation;
Figure 108105144-A0305-02-0011-20
It is the probability density function of the anomaly group obtained from the aforementioned estimation.

上述成本公式，使用成本最小化的最佳化分析可以得到一診斷準則：

Figure 108105144-A0305-02-0012-3
其中H0代表為異常，H1代表正常。先前估算之
Figure 108105144-A0305-02-0012-22
與
Figure 108105144-A0305-02-0012-24
為r的函數且P(H1)、P(H0)、C00、C01、C10、C11皆為對應設備之已知數值，據此公式可以推導得到：
Figure 108105144-A0305-02-0012-4
 至此完成診斷設計。(參考第三圖) The above cost formula, using the optimized analysis of cost minimization, can obtain a diagnostic criterion:
Figure 108105144-A0305-02-0012-3
 H 0 represents abnormality, and H 1 represents normal. Previously estimated
Figure 108105144-A0305-02-0012-22
versus
Figure 108105144-A0305-02-0012-24
It is a function of r and P(H 1 ), P(H 0 ), C 00 , C 01 , C 10 , and C 11 are all known values of the corresponding equipment. According to this formula, we can derive:
Figure 108105144-A0305-02-0012-4
 This completes the diagnostic design. (Refer to the third figure)

續請參閱第二圖搭配第一圖，該待診斷氣體樣品資料分析步驟與診斷步驟(S04)：以前述樣品分析模組(6)運算該待診斷氣體樣品資料(23)與前述正常氣體含量資料(21)之一待比對相關係數。具體來說，可計算該待診斷氣體樣品資料(23)與前述821筆正常變壓器之正常氣體含量資料(21)的至少一筆的相關係數或全部筆數的相關係數(例如取平均值)，即可取得該待比對相關係數。 Please refer to the second figure and the first figure, the analysis step and diagnosis step (S04) of the gas sample data to be diagnosed: the sample analysis module (6) is used to calculate the gas sample data to be diagnosed (23) and the normal gas content One of the data (21) to be compared with the correlation coefficient. Specifically, the correlation coefficient of at least one of the gas sample data to be diagnosed (23) and the normal gas content data (21) of the 821 normal transformers (21) or the total number of correlations (for example, the average value), that is, The correlation coefficient to be compared can be obtained.

續請參閱第二圖搭配第一圖，接著以前述比對模組(7)比對該待比對相關係數與該門檻值，以在該待比對相關係數大於或等於該門檻值時，判斷該待診斷變壓器為正常。反之，在該待比對相關係數大於或等於該門檻值時，可判斷該待診斷變壓器為異常。舉例來說，經過成本公式計算之門檻值為η，該門檻值η為0.7，因此當該待比對相關係數大於或等於0.7時，可判斷該待診斷變壓器為正常，若該待比對相關係數小於0.7時，可判斷該待診斷變壓器為異常(參考第三圖)。 Please refer to the second figure and the first figure, and then compare the correlation coefficient to be compared with the threshold using the aforementioned comparison module (7), so that when the correlation coefficient to be compared is greater than or equal to the threshold, Determine that the transformer to be diagnosed is normal. Conversely, when the correlation coefficient to be compared is greater than or equal to the threshold value, it can be determined that the transformer to be diagnosed is abnormal. For example, the threshold value calculated by the cost formula is η, and the threshold value η is 0.7, so when the correlation coefficient of the to-be-matched is greater than or equal to 0.7, it can be judged that the transformer to be diagnosed is normal. When the coefficient is less than 0.7, it can be judged that the transformer to be diagnosed is abnormal (refer to the third figure).

綜合上述實施例之說明，當可充分瞭解本發明之操作、使用及本發明產生之功效，惟以上所述實施例僅係為本發明之較佳實施例，當不能以此限定本發明實施之範圍，即依本發明申請專利範圍及發明說明內容所作簡單的等效變化與修飾，皆屬本發明涵蓋之範圍內。 Based on the description of the above embodiments, the operation, use and effects of the present invention can be fully understood. However, the above-mentioned embodiments are only preferred embodiments of the present invention, and cannot be used to limit the implementation of the present invention. The scope, that is, simple equivalent changes and modifications made in accordance with the scope of the present invention's patent application and the description of the invention, is within the scope of the present invention.

(S01):相關係數運算步驟 (S01): Correlation coefficient calculation steps

(S02):機率密度函數估算步驟 (S02): Probability density function estimation step

(S03):門檻值演算步驟 (S03): Threshold value calculation steps

(S04):待診斷氣體樣品資料分析步驟與診斷步驟 (S04): Data analysis steps and diagnosis steps of the gas sample to be diagnosed

Claims (6)

一種變壓器診斷方法，包含下列步驟：一相關係數運算步驟：以一相關係數運算模組運算正常變壓器絕緣油產生的多筆正常氣體含量資料間相關係數之一正常群相關係數分布資料，該相關係數運算模組並運算異常變壓器絕緣油產生之至少一筆異常氣體含量資料與前述正常氣體含量資料間相關係數之一異常群相關係數分布資料；一機率密度函數估算步驟：以一機率密度函數估算模組依據該正常群相關係數分布資料估算一正常群機率密度函數，該機率密度函數估算模組並估算該異常群相關係數分布資料之一異常群機率密度函數；一門檻值演算步驟：以一門檻值演算模組依據該正常群機率密度函數、該異常群機率密度函數、歷史統計資料之一設備故障統計機率及預設之一檢修費用資訊，以最低費用為準則演算一門檻值，其中，該門檻值依據一成本公式調整，該成本公式包含：
Figure 108105144-A0305-02-0015-5
 其中，cost為維護與檢修成本；η為待演算之門檻值；P(H 1)與P(H 0)分別為依據歷史資料統計得到之變壓器正常工作及異常之機率；C00為異常變壓器被判斷為異常時變壓器停機之檢修費用；C01為異常變壓器被判斷為變壓器正常，繼續運作發生故障而造成之損失與維修費；C10為正常變壓器被判斷為異常時變壓器停機之檢修費用；C11為正常變壓器被判斷為正常變壓器之費用；
Figure 108105144-A0305-02-0015-28
為前述估算得到之正常群機率密度函數；
Figure 108105144-A0305-02-0015-27
為前述估算得到之異常群機率密度函數； 一待診斷氣體樣品資料分析步驟與診斷步驟：取得一待診斷變壓器絕緣油產生之一待診斷氣體樣品資料，以一樣品分析模組運算該待診斷氣體樣品資料與前述正常氣體含量資料之一待比對相關係數；接著以一比對模組比對該待比對相關係數與該門檻值，以在該待比對相關係數大於或等於該門檻值時，判斷該待診斷變壓器為正常。 A transformer diagnosis method includes the following steps: a correlation coefficient calculation step: a correlation coefficient calculation module is used to calculate one of the correlation coefficient distribution data among a plurality of pieces of normal gas content data generated by normal transformer insulating oil, the correlation coefficient The calculation module calculates at least one abnormal gas content data generated by the abnormal transformer insulating oil and one of the abnormal group correlation coefficient distribution data between the correlation coefficients of the normal gas content data; a probability density function estimation step: a probability density function estimation module Estimating a normal group probability density function based on the normal group correlation coefficient distribution data, the probability density function estimation module estimates one of the abnormal group probability density functions of the abnormal group correlation coefficient distribution data; a threshold calculation step: using a threshold The calculation module calculates a threshold based on the minimum cost as the criterion based on the normal group probability density function, the abnormal group probability density function, one of the equipment failure statistics probability and the default one of the maintenance cost information The value is adjusted according to a cost formula, which includes:
Figure 108105144-A0305-02-0015-5
 Among them, cost is the cost of maintenance and repair; η is the threshold value to be calculated; P ( H 1 ) and P ( H 0 ) are the probability of normal operation and abnormality of the transformer based on historical data statistics; C 00 is the abnormal transformer. The maintenance cost of transformer shutdown when judged to be abnormal; C 01 is the loss and maintenance cost caused by the abnormal transformer being judged to be normal and the operation continues to fail; C 10 is the maintenance cost of transformer shutdown when the normal transformer is judged to be abnormal; C 11 is the cost of a normal transformer judged as a normal transformer;
Figure 108105144-A0305-02-0015-28
It is the normal group probability density function obtained from the aforementioned estimation;
Figure 108105144-A0305-02-0015-27
It is the probability density function of the abnormal group obtained by the foregoing estimation; a gas sample data analysis step and a diagnosis step to be diagnosed: obtaining a gas sample data to be diagnosed produced by a transformer insulating oil to be diagnosed, and calculating the gas to be diagnosed by a sample analysis module The sample data and one of the aforementioned normal gas content data are to be compared with the correlation coefficient; then the comparison module is to be compared with the threshold value by a comparison module, so that the correlation coefficient to be compared is greater than or equal to the threshold value When it is judged that the transformer to be diagnosed is normal. 如申請專利範圍第1項所述之變壓器診斷方法，其中，前述正常氣體含量資料及前述異常氣體含量資料皆包含氫氣、乙烯、乙炔、甲烷、乙烷、一氧化碳之氣體種類的氣體含量資料。 The transformer diagnosis method as described in item 1 of the patent application scope, wherein the normal gas content data and the abnormal gas content data include gas content data of gas types of hydrogen, ethylene, acetylene, methane, ethane, and carbon monoxide. 如申請專利範圍第2項所述之變壓器診斷方法，其中，該相關係數運算模組係依據一皮爾森積差相關係數(Pearson Product-Moment Correlation Coefficient)公式進行運算：
Figure 108105144-A0305-02-0016-6
 其中r為任兩組氣體含量資料(xi及yi,i=1,2,…,n)間之相關係數；n代表前述氣體種類之編號。 The transformer diagnosis method as described in item 2 of the patent application scope, wherein the correlation coefficient calculation module is operated according to a Pearson Product-Moment Correlation Coefficient formula:
Figure 108105144-A0305-02-0016-6
 Where r is the correlation coefficient between any two sets of gas content data (x i and y i , i=1,2,...,n); n represents the number of the aforementioned gas type. 一種電腦程式產品，內儲一程式，當電腦載入該程式並執行後，可完成如請求項第1項至第3項中任一項所述之變壓器診斷方法。 A computer program product that stores a program. When the computer loads the program and executes it, it can complete the transformer diagnosis method as described in any one of items 1 to 3 of the request item. 一種電腦可讀取記錄媒體，內儲一程式，當電腦載入該程式並執行後，可完成如請求項第1項至第3項中任一項所述之變壓器診斷方法。 A computer can read the recording medium and store a program. When the computer loads the program and executes it, it can complete the transformer diagnosis method described in any one of the items 1 to 3 of the request item. 一種變壓器診斷系統，包含：一處理單元； 一儲存單元，連接該處理單元，儲存正常變壓器絕緣油產生之多筆正常氣體含量資料及異常變壓器絕緣油產生之至少一筆異常氣體含量資料；一相關係數運算模組，連接該處理單元，用以運算前述多筆正常氣體含量資料間相關係數之一正常群相關係數分布資料，並用以運算前述至少一筆異常氣體含量資料與前述多筆正常氣體含量資料間相關係數之一異常群相關係數分布資料；一機率密度函數估算模組，連接該處理單元，用以依據該正常群相關係數分布資料估算一正常群機率密度函數，並估算該異常群相關係數分布資料之一異常群機率密度函數；一門檻值演算模組，連接該處理單元，用以依據該正常群機率密度函數、該異常群機率密度函數、歷史統計資料之一設備故障統計機率及預設之一檢修費用資訊，以最低費用為準則演算一門檻值，其中，該門檻值演算模組依據維護與檢修成本最小化之成本公式演算前述門檻值，該成本公式包含：
Figure 108105144-A0305-02-0017-30
 其中，cost為維護與檢修成本；η為待演算之門檻值；P(H 1)與P(H 0)分別為依據歷史資料統計得到之變壓器正常工作及異常之機率；C00為異常變壓器被判斷為異常時變壓器停機之檢修費用；C01為異常變壓器被判斷為變壓器正常，繼續運作發生故障而造成之損失與維修費；C10為正常變壓器被判斷為異常時變壓器停機之檢修費用；C11為正常變壓器被判斷為正常變壓器之費用；
Figure 108105144-A0305-02-0017-32
為前述估算得到之正常群機率密度函數；
Figure 108105144-A0305-02-0017-31
為前述估算得到之異常群機率密度函數； 一樣品分析模組，連接該處理單元，用以運算一待診斷變壓器絕緣油產生之一待診斷氣體樣品資料與前述正常氣體含量資料之一待比對相關係數；及一比對模組，連接該處理單元，用以比對該待比對相關係數與該門檻值，以在該待比對相關係數大於或等於該門檻值時，判斷該待診斷變壓器為正常。 A transformer diagnosis system includes: a processing unit; a storage unit connected to the processing unit, storing a plurality of pieces of normal gas content data generated by normal transformer insulating oil and at least one piece of abnormal gas content data generated by abnormal transformer insulating oil; a correlation coefficient The computing module is connected to the processing unit for computing one of the normal group correlation coefficient distribution data among the correlation coefficients among the plurality of normal gas content data, and for computing between the at least one abnormal gas content data and the multiple normal gas content data One of the correlation coefficients is the abnormal group correlation coefficient distribution data; a probability density function estimation module is connected to the processing unit to estimate a normal group probability density function based on the normal group correlation coefficient distribution data and estimate the abnormal group correlation coefficient distribution One of the data is the abnormal group probability density function; a threshold value calculation module is connected to the processing unit to be based on the normal group probability density function, the abnormal group probability density function, and historical statistics data One of the maintenance cost information, a threshold value is calculated based on the minimum cost, wherein the threshold value calculation module calculates the aforementioned threshold value according to a cost formula that minimizes maintenance and repair costs. The cost formula includes:
Figure 108105144-A0305-02-0017-30
 Among them, cost is the cost of maintenance and repair; η is the threshold value to be calculated; P ( H 1 ) and P ( H 0 ) are the probability of normal operation and abnormality of the transformer based on historical data statistics; C 00 is the abnormal transformer. The maintenance cost of transformer shutdown when judged to be abnormal; C 01 is the loss and maintenance cost caused by the abnormal transformer being judged to be normal and the operation continues to fail; C 10 is the maintenance cost of transformer shutdown when the normal transformer is judged to be abnormal; C 11 is the cost of a normal transformer judged as a normal transformer;
Figure 108105144-A0305-02-0017-32
It is the normal group probability density function obtained from the aforementioned estimation;
Figure 108105144-A0305-02-0017-31
It is the probability density function of the abnormal group obtained by the foregoing estimation; a sample analysis module, connected to the processing unit, for calculating the data of the gas sample to be diagnosed produced by the insulating oil of the transformer to be diagnosed and the data of the normal gas content to be compared Correlation coefficient; and a comparison module, connected to the processing unit, for comparing the correlation coefficient to be compared with the threshold value, so as to determine the diagnosis to be diagnosed when the correlation coefficient to be compared is greater than or equal to the threshold value The transformer is normal.
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