J. Cent. South Univ. Technol. (2007)01-0088-06

DOI: 10.1007/s11771-007-0018-z               

Application of extension method to fault diagnosis of transformer

DENG Hong-gui(邓宏贵)¹, CAO Jian(曹 建)¹, LUO An(罗 安)², XIA Xiang-yang(夏向阳)³

(1. School of Physics Science and Technology, Central South University, Changsha 410083, China;

2. School of Electrical and Information Engineering, Hunan University, Changsha 410082, China;

3. School of Electrical and Information Engineering, University of Theory and Technology, Changsha 410077, China)

Abstract: A novel extension diagnosis method was proposed for enhancing the diagnosis ability of the conventional dissolved gas analysis. Based on the extension theory a matter-element model was established for qualitatively and quantitatively describing the fault diagnosis problem of power transformers. The degree of relation based on the dependent functions was employed to determine the nature and the grade of the faults in a transformer system. And the proposed method was verified with the experimental data. The results show that accuracy rate of the diagnosis method exceeds 90% and two kinds of faults can be detected at the same time.

Key words: power transformer; fault diagnosis; extension theory; matter-element model; dependent function

1 Introduction

Power transformers are key components in transmission and distribution systems, because their reliabilities relate directly to the dependability of power system operation. Therefore, transformers must be routinely examined to find incipient faults and to catch any potentially extended deterioration as early as possible^[1-3].

A fuzzy expert system was applied to diagnosing incipient transformer faults^[4]. The diagnosis results of this approach are promising, however, the fuzzy expert system cannot learn from previous diagnosis results because the membership functions and the diagnostic rules are determined by practical experience or trial-and-error tests.

Adaptive self-learning fuzzy diagnosis systems which acquire knowledge directly from training data and thus overcome the disadvantages of the fuzzy expert system were developed for transformer fault diagnosis^[5-6]. However, the numbers of classification attributes and fuzzy partitions are limited to reduce the number of decision variables to be determined, due to the simultaneous determination of the membership functions and the inference rules in the diagnostic systems.

Artificial neural networks (ANNs) were proposed to deal with the transformer fault diagnosis^[7-8]. The ANNs can acquire new experiences by incrementally training from newly obtained samples. Moreover, they can interpolate and extrapolate from their experiences, yielding at least a best guess of the fault. However, certain issues, such as local convergence and determination of the network configuration and control parameters must be resolved before the ANNs can become a practical tool. Therefore, the above methods are ineffective to diagnose the faults of transformers. There is a dire need to search for a new method to solve the problem. Extension diagnosis method both describes precisely the complicated relationships among diverse dissolved gases and determines where and why faults occur in an operating transformer system through analysis faults of imaginative/real part, latent/apparent parts and negative/positive parts^[9-15]. So in this study, a new extension method to diagnose the transformer faults was investigated.

2 Principle of extension diagnosing methods

In the extensive method the extensive theory is combined with practical technology and the causes of faults is found by means of definitive rules. Figs.1 and 2 show the principle chart of diagnosing faults with extension methodology.

3 Procedures of employing extension diagno-sing methods

3.1 Total fault analysis

Let N be the matter that breaks down.

1) Build the set of characteristic-element for faults of N.

Fig.1 Flow chart of diagnosing of transformer with extension methodology

Fig.2 Sub-flow chart of steps 1, 2 and 3 in Fig.1

Let I={I₁, I₂, …, I_N}be the set of all possible faults of N. An existing fault I_i in N, denoted by I_i(N), (i=1, 2, …, n), has the set of characteristic-element as follows:

{M}={M_ij, i=1, 2, …, n,  j=1, 2, …, k_i}

where M_ij=(c_ij  V_ij) (i=1, 2, …, n  j=1, 2, …, k_i), V_ij=[a_ij, b_ij] is the defined range for measurement of I_i(N) with respect to the matter element variables(c_ij) when I_i(N) occurs. This range of measure is referred to as the classical field. V′_ij=[a′_ij, b′_ij] is the allowed range for measurement of I_i(N) with respect to c_ij when I_i(N) occurs. This range of measure is referred to as the allowable field.

2) Form the matter-elements R_ij for N’s all possible breakdowns.

   3) Form the matter-element R depicting the current situations of N.

where stands for the measured range on the current situations.

4) Compute the value of the dependent function.

      (1)

where .

5) Determine weight coefficients. Distribute differ- ent weights α_i1, α_i2, …, a_ij to all judging conditions in terms of magnitude.

6) Compute the grade of dependence for each fault.

      (2)

7) Determine the nature of the fault.

1≤i≤n

  If , a specific fault I₀ in N

will occur.

3.2 Locating fault

System faults may occur in either hard parts or soft parts. Fox example, the faults of a transformer may occur either by its mechanic parts, or the deterioration of its insulating oil, or the changes in the temperature of the external environment (i.e. too high temperature), and some man-made causes (i.e. improper operations) can make the transformer break down. Therefore, by analyzing the characteristics and corresponding measures of soft and hard parts of a transformer, and computing the grades of dependence of hard parts of a transformer, a specific fault can be precisely located.

3.2.1  Analyzing faults of hard parts

1) Build the set {M_pq} of characteristic-element for all possible faults of hard parts of N. Let 

hrN={N₁, N₂, …, N_l}={N_p, p=1, 2, …, l}.

Then the set of fault for element N_p can be denoted by

I_p={I_p1, I_p2, …, I_pm}={I_pq,  q=1, 2, …, m}.

An occurred fault I_pq in N_p, denoted by I_pq(N_p)(p=1, 2, …, l, q=1, 2,…, m) has the set {M_pq} of characteristic- element as follows:

{M_pq}={M_pq1, M_pq2, …, }

where M_pqs=(c_pqs, V_pqs) (s=1, 2, …, r_q), V_pqs=(a_pqs,  b_pqs) is the classical field,  is the allowable field.

2) Form the matter-element R_pq for N_p’s all possible faults.

(p=1, 2, …, l; q=1, 2, …, m)

3) Form the matter-element R_p depicting the current situations of N_p.

(p=1, 2, …, l; q=1, 2, …, m)

4) Compute the value of the dependent function.

      (3)       

5) Determine weight coefficients. Distribute different weights β_pq1, β_pq2, …, to all judging conditions in terms of magnitude.

6) Compute the grade of impendence for each fault.

                     (4)

7) Locate the fault. If max{λ(I_pq(N_p))}= , a specific fault will occur in .

3.2.2 Analyzing fault of soft parts

Follow the steps of analyzing the faults of hard parts, a specific fault caused by the soft parts of N can be located.

3.2.3 Total conjugation analysis

In addition to analyzing the fault caused by the soft/hard parts of N, it is necessary to analyze the fault caused by other conjugate parts of N, namely imaginative/real parts, latent/apparent parts and negative/positive parts in order to more precisely diagnose the faults and discover the potential faults.

1) Analyze faults of imaginative/real parts. The faults in a system may occur in either its real parts or its imaginative parts. For example, the faults of a transformer may be probably caused either by the damage of its spare (real parts), or by the foreign matters (i.e. greasy stain) existing in its internal space. So, based on the imaginative/real nature of matter-element, a specific fault can be located by analyzing the characteristic and corresponding measures of the imaginative/real parts, and comparing the measures with the formal ones.

In addition, because of the convertibility between the imaginative and the real parts, if the faults caused by the imaginative parts can be found in time, these faults can be effectively prevented from triggering those of the real parts. All the efforts can reduce the severity of the faults.

2) Analyze faults of latent/apparent parts. Analyzing the potential faults in a system has great significance. Analyzing the latent characteristics can help discover the potential faults when they occur. The analyses can effectively prevent the potential faults from occurring or substantially lessen the damage caused by those existing faults. For example, the greasy stain in transformer will not affect the transformer operations until it accumulates to a certain extent. The best solution to this problem is not to clear the greasy stain after its formation, but to add something else into the transformer to prevent its formation.

Because of the convertibility between the latent and the apparent parts, minor apparent faults sometimes may probably be a prelude to major latent faults. Early prevention against latent faults as well as timely fixing of apparent faults will effectively avoid more damage.

3) Analyze faults of negative/positive parts. The faults in a system with regard to a characteristic may be triggered either by the positive parts of this characteristic, or by its parts. Take a transformer for example, its faults with respect to the characteristic “operating state” may be caused by its positive parts, i.e. a deficient supply of insulating oil, or by its negative parts, i.e. waste gases or waste materials. So, through computing the measures of all the negative parts and examining them against the related criteria, a specific fault can be located.

3.3 Comprehensive diagnosis

By integrating the above analysis with related specialized knowledge the fault can be comprehensively diagnosed and located and its grade of dependence can be determined. As a result, the corresponding measures can be taken to prevent the fault and lessen the damage.

4 Application of extension diagnosing

methods for transformer fault

In general, fault diagnosis aims at a system internal breakdown. Transformer fault is not the proximate reflection of a single cause but of many factors, so lots of examinations, checks and measures must be carried out to collect more information, implement comprehensive judgment, find out the precise causes of faults and bring forward a sovereign remedy. A current technique to diagnose a transformer internal fault is the dissolved gas analysis (DGA).

4.1    Principle of extension diagnosis method based on DGA

In the process of operation, insulating oil and materials will deteriorate and decompose under the action of heat and electricity, as a result, many kinds of gas occur, such as H₂, CH₄, C₂H₆, C₂H₄, C₂H₂, etc. The decomposition will be enforced when the fault of local superheating or discharging occur in interior of a power transformer. As a rule, a specific kind fault corresponds to a kind of specific gas. As for the same kind of fault, there is different quantity of gas to some extent. So the nature and degree of a fault can be ascertained in term of constituent and content of dissolved gas in insulating oil of a transformer.

Practical experience shows that the proportion of each kind of gas in the general hydrocarbon varies when a malfunction occurs. With the increase of temperature,  the proportion of methane gradually falls off, on the contrary, the proportions of ethylene and ethane increase. A certain amount of acetylene will be produced if the temperature is too high. When the temperature increases to a point in which arc discharge occurs, dissolved gas will be chiefly made of acetylene. A series of remarkable innovations are made to diagnose fault of transformer in term of analysis of characteristic gas. An extension diagnosis method based on analysis of characteristic gas is proposed in this study.

4.2    Case analysis of extension diagnosis of transformer faults

1) Let I={I₁, I₂, …, I_N} be the set of all possible faults of transformer N. Table 1 lists the cataloguing nature of faults^[7].

Table 1 Cataloguing nature of faults

2) Form the matter-elements of the classic field R_ij and the allowable field  for N’s all possible breakdowns of transformer as follows:

where  c₁, c₂, c₃ and c₄ stand for the total content of hydrocarbon, content of H₂, content of C₂H₂ and ratio of C₂H₂ content to total content of hydrocarbon, respectively.

3) Calculate the degree of a fault according to Eqns.(1) and (2). Weight coefficients are determined by the following formula:

(i=1, 2, …, n; j=1, 2, …, k_i)

The content of C₂H₂ is major indicator to discriminate between superheating and discharge in the characteristic gas method. The superheating caused by discharge will also produce C₂H₂, so there is uncertainty with no strict determinacy between the two. But the extension diagnosis method can relieve the indeterminacy for its value of dependent function may be positive or negative. On the other hand, characteristic gas is generated by other causes when a transformer is in normal state, such as doing by halves of gas freeing to transformer oil or faults of devices for cooling. The faults raised by the above causes can be only solved through total conjugation analysis.

4.3    Analysis of actual example

1) Table 2 lists actual faults data detected by sampling and testing of the transformer insulating oil.

2) Form the matter-elements of the classic field and the allowable field according to Table 2, and compute the grade of dependence for each fault in steps of extension diagnosis(see Table 3).

The results of Table 3 show the accuracy rate of extension fault diagnosis exceeds 90%, so the extension

Table 2 Actual data of transformer faults

3) Build further sets of the matter-elements of the soft/hard parts imaginative/real parts, latent/apparent parts, and negative/positive parts to compute the grade of impendence for each fault and to locate faults, as a result, faults can be removed in time and loss can be reduced to a minimum.

1) The progress and principle of extension diagnosis method for transformer faults are investigated. The results of analysis and application show that the extension diagnostic method has uncommon excellences and features.  

2) Extension diagnosing method offers a means to combine qualitative analysis with quantitative analysis. With the aid of the conjugation analysis technique, the existing faults can be precisely located, the potential ones can be found and the damage be lessened. The grade of dependence of a fault can be definitely computed through the dependent function. As a result, there are more and more applications of extensive diagnosis method.

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(Edited by CHEN Wei-ping)

Received date: 2006-05-06; Accepted date: 2006-07-05

Corresponding author: DENG Hong-gui, PhD; Tel: +86-731-8836331; E-mail: denghonggui@163.com