J. Cent. South Univ. (2012) 19: 982-987

DOI: 10.1007/s11771-012-1100-8

Application of fuzzy analytic hierarchy process and neural network in

power transformer risk assessment

LI Wei-guo(李卫国)¹, YU Qian(俞乾)^{1, 2}, LUO Ri-cheng(罗日成)³

1. Beijing Key Laboratory of High Voltage & Electro Magnetic Compatibility,North China Electric Power University, Beijing 102206, China;

2. Yongzhou Electric Power Bureau, Hunan Electric Company, Yongzhou 425000, China;

3. College of Electrical and Information Engineering, Changsha University of Science and Technology,Changsha 410014, China

? Central South University Press and Springer-Verlag Berlin Heidelberg 2012

Abstract: In operation, risk arising from power transformer faults is of much uncertainty and complicacy. To timely and objectively control the risks, a transformer risk assessment method based on fuzzy analytic hierarchy process (FAHP) and artificial neural network (ANN) from the perspective of accuracy and quickness is proposed. An analytic hierarchy process model for the transformer risk assessment is built by analysis of the risk factors affecting the transformer risk level and the weight relation of each risk factor in transformer risk calculation is analyzed by application of fuzzy consistency judgment matrix; with utilization of adaptive ability and nonlinear mapping ability of the ANN, the risk factors with large weights are used as input of neutral network, and thus intelligent quantitative assessment of transformer risk is realized. The simulation result shows that the proposed method increases the speed and accuracy of the risk assessment and can provide feasible decision basis for the transformer risk management and maintenance decisions.

Key words: fuzzy analytic hierarchy process; risk assessment; power transformer; artificial neutral network

1 Introduction

To realize equipment and personnel safety, risk assessment applies theories and methods to identify and analyze the risk factors in equipment and judge the probability for the equipment to have accidents and hazards and their severity, so as to provide scientific decision basis for preventive measures [1-3]. As the core of energy transformation and transmission in an electric network, a large power transformer is one of the key equipments in power system, whose operation safety and reliability are directly related to the continuous and steady operation of the entire power system. With the continuous increase of power system scale and unit capacity of transformers, there will be more losses to national economy in the case of equipment faults [4-5]. Therefore, performing the risk assessment on large power transformer faults to identify possible risks and their impacts has important theoretical and practical value for making scientific and reasonable maintenance strategies and guaranteeing the operation safety of the electric network.

At present, the risk assessment-related research in the field of electrical engineering is mainly focused on power market, power system and power grid planning [6-8], while the research on electrical equipment, especially on power transformer risk assessment methods, is less. In the meantime, there is no perfect solution among current assessment methods. With power transformers as the subject, an assessment method based on the combination of fuzzy analytic hierarchy process (FAHP) and artificial neural network (ANN) is proposed, making use of such advantages of FAHP as short deciding time and little reference information required and such advantages of ANN as distributed information storage, parallel processing and self-learning. The method picks up the key information of power transformer operation risks and removes the interference of redundant information through FAHP, thus the speed and accuracy of transformer risk assessment is increased.

2 Theory

A large power transformer is a complicated system consisting of a body, winding, an iron core, bushings, tap switches (loaded), non-electricity protective switches and a cooling system etc. A structure model is shown in   Fig. 1. These components can be further divided into several subsystems. Each subsystem has respective fixed structure and functions, and the subsystems cooperate with each other closely. An abnormality or fault of any component or subsystem will cause dysfunction or failure of other components. Due to the complexity of its own structure, the faults of a power transformer are characterized by correlation, fuzziness and delay [9-11]. Thus, the risks arising from equipment faults are mostly described using natural language, whose most distinguishing characteristic is its fuzziness. And FAHP is an assessment method involving fuzzy factors or fuzzy concept during the overall assessment of a thing or phenomenon affected by several factors and can satisfy the multi-factor and multi-level assessment requirement of risks [12-13]. While ANN can simulate any nonlinear input/output relationship and is capable of approaching any continuous function and nonlinear mapping due to its simple structure and strong operability, and it is especially suitable for risk analysis and assessment of a complicated system [14-15]. Figure 2 shows the process of the method.

Fig. 1 Power transformer structure model

Fig. 2 Process of risk assessment based on FAHP and ANN

With the application of FAHP, the fuzzy consistency processing is carried out on each factor of transformer risks to obtain its absolute weight. And then, as the absolute weight of per risk factor, the risk factors can be further divided into two categories, i.e. key factors and ignorable factors. The key factors are taken as the input of the neutral network, and then the samples are trained according to the characteristics and structure of the BP neutral network to obtain the risk value within certain limit of error.

3 Fuzzy analysis of factor weight

On the basis of the analytical hierarchy process (AHP), FAHP improves the structural pattern, adjustment method of comparison judgment matrix and consistency check standard, which makes the consistency check and adjustment, a difficult point of AHP, scientific, accurate and simple.

3.1 AHP structure of transformer fault risk

There are many factors affecting the transformer risks. With reference to the test code and guidelines set forth in DL/T 596—1996 Preventive Test Code for Electric Power Equipment, as well as the experience of some transformer manufacturing, operation and maintenance experts, the fault risks of a transformer are decomposed into the AHP structure, as shown in Fig. 3.

3.2 Building fuzzy complementary judgment matrix of risk factors

In FAHP, factors are mutually compared and judged and are generally quantitatively expressed with the importance of a factor related to another. In such a way, the fuzzy judgment matrix A=(a_ij)_n×n is obtained. If a fuzzy judgment matrix has the following nature:

a_ii=0.5 (i=1, 2, ?, n)

a_ij+a_ji=1 (i, j=1, 2, ?, n)

It is a fuzzy complementary judgment matrix.

According to the AHP structure model of power transformers, we judge the membership of several factors affecting the power transformer risks using expert comprehensive evaluation method, collect the judgment information of experts in the field (assuming expert set D={d₁, d₂, ?, d_T}, where T refers to total number of experts), and then build the fuzzy complementary judgment matrix for risk factors at each layer of the AHP structure model. Under the consideration of fuzziness of expert judgment information, the expert judgment information is represented with triangular fuzzy  numbers. Meanwhile, to quantify the judgment, 0.1-0.9 scaling method shown in Table 1 is applied to providing numerical scale [16-17].

Fig. 3 AHP structure model of power transformer risk assessment

Table 1 0.1-0.9 numerical scales

Assuming that y₁, y₂, …, y_n are common members of some upper index Y_m, then the mutually compared fuzzy complementary judgment matrix  of indexes y₁, y₂, …, y_n built according to the judgment information provided by the expert k and the fuzzy judgment matrix scaling method shown in Table 1 is

In Eq. (1), all the elements  are triangular fuzzy numbers, where  indicate the most pessimistic estimate, the most possible estimate and the most optimistic estimate of the risk index y_i given by the expert k compared with y_j when comparison is made with the upper risk index Y_m, respectively.

3.3 Determination of weight coefficient

To pinpoint the relative importance of each set of risk factors relative to some upper index, the obtained triangular fuzzy complementary judgment matrix shall be ordered. With the assumption that there are n risk factors of the upper index Y_m and that the triangular fuzzy complementary judgment matrix assembly provided by T experts is  (k=1, 2, …, T), the weight calculation steps of each risk factor are described below [18]:

Step 1: Apply the weighting principle to summarize the triangular fuzzy complementary judgment matrix information provided by T experts and obtain the comprehensive fuzzy complementary judgment matrix of each set of risk factors at each layer  where:

           (2)

In Eq. (2), μ^(k) refers to the weight of the expert k in comprehensive judgment.

Step 2: Calculate and normalize the fuzzy evaluation value of the risk factors and obtain the fuzzy relative weight coefficient vector of each factor expressed using the triangular fuzzy numbers Q=  where:

     (3)

Step 3: Mutually compare triangular fuzzy number q_i according to Eq. (4) and build a possibility degree matrix [19-20]

With assumption that q_i=(l_i, m_i, u_i) and q_j=(l_j, m_j, u_j) are any two triangular fuzzy numbers, the possibility degree p_ij of q_i≥q_j is

    (4)

In Eq.(4),  Selection of the λ value depends on the decider’s risk attitude: when the decider is risk preferred, λ≥0.5; when the decider is risk neutral, λ=0.5; and when the decider is risk averse, λ≤0.5.

Step 4: Obtain the fuzzy consistency matrix  after consistency adjustment made on the possibility matrix P=(p_ij)_n×n according to Eq. (5), and then use Eq. (6) to obtain the relative weight coefficient   of n risk factors y₁, y₂, …, y_n under the index Y_m.

                            (5)

where (i=1, 2, …, n).

Step 5: Calculate the fuzzy weight of each risk factor at the index layer relative to the target layer. With the assumption that there are m indexes C₁, C₂, …, C_m at the criterion layer and their weights relative to the target layer are c₁, c₂, …, c_m, respectively, and there are n indexes D₁, D₂, …, D_n at the index layer and their weight relative to the criterion layer indexes C_j (j=1, 2, …, m) are d_1j, d_2j, …, d_nj, respectively (If D_k is irrelative with C_j, then b_kj=0), the absolute weights d₁, d₂, …, d_n of the index layer risk factors relative to the target layer can be given by

                                (6)

Through the above calculation, the weight coefficient of each index at the criterion layer, the relative weight coefficient (relative to the criterion layer) and absolute weight coefficient (relative to the target layer) of each risk factor at the index layer are finally obtained. The weight distribution is listed in Table 2.

With the absolute weight values of the risk factors in Table 2 taken as the selection criteria of key factors, the risk factors with relatively less weights removed, and more important factors selected as the input of ANN, the structure of neutral network is simplified.

4 ANN-applied transformer risk assessment case analysis

A tri-level BP neutral network is designed. Thirty- five risk factors with larger weights in Table 2 (i.e. factors marked with “*” in Table 2) are selected as the input of ANN. There is one node at the output layer corresponding to the output result of transformer risk assessment. According to the empirical formula in Ref. [21], the number of nodes at the hidden layer is assumed as  Logarithmic Sigmoid function is adopted as the transfer function from the input layer to the hidden layer and from the hidden layer to the output layer, i.e. the logarithm consistency processing is carried out on the input data before the action of the Sigmoid function.

To guarantee the precision of network training and network performance, 20 transformer risk assessment samples are divided into two groups, with the data of 15 samples taken as the training set and the data of the other 5 samples used for testing the generalization ability of the trained network. The neutral network toolkit in Matlab software is used to realize the training of the neutral network, and the function of Levenberg- Marquardt optimization strategy is used as the network training function. At the same time, the mean-squared error function MSE (mean-squared errors) is adopted as the network performance function. Assume that MSE is 10^-4 and network learning rate α=0.05.

The expert assessment results and the BP neutral network training results of the training set samples are listed in Table 3.

Table 2 Weight coefficient of each risk factor

Table 3 Expert assessment results and BP neutral network training results of training set samples

The output error and cycle index of the BP neutral network training set is shown in Fig. 4, in which, X-coordinate indicates the cycle iteration number and Y-coordinate, the deviation variance. It can be seen from Fig. 4 that upon 12 iteration adjustments, the error precision of network weighted value is lower than the pre-set value.

Fig. 4 Training deviation curve of BP neutral network

To test the generalization ability of the trained network, the rest five sets of data are simulated to obtain the output of five sets of input using the built nonlinear mapping relationship. Figure 5 shows the comparison between the BP neutral network simulation results and expert assessment results. It can be seen from Fig. 5 that the two results fit well with each other and have strong adaptive ability, which indicates the sound performance of the network. It is clear that the assessment method is feasible for the transformer risk assessment.

Fig. 5 Comparison between BP neutral network simulation result and expert assessment result

5 Conclusions

1) The input space of BP neutral network is analyzed with FAHP and optimization of ANN by selecting risk factors with larger weights. Thus, the structure of the BP ANN is simplified, the problem complexity reduces and the transformer risk assessment efficiency increases.

2) The simulation results show that the method provides a new idea for power transformer risk assessment with efficiency and fast speed, and is of certain practical values. However, as the research on the transformer risk assessment remains at its early stage and the selection of fault risk factors and weight calculation are still in lack of systematic theoretical means, which leads to deviation in derived conclusion, the assessment accuracy is to be further improved.

References

[1] HENLEY E J, KUMAMOTO H. Probabilistic risk assessment [M]. New York: IEEE, 1992: 467-480.

[2] HOANG P. Handbook of reliability engineering [M]. Berlin: Springer, 2002: 310-335.

[3] LIU N, ZHANG J H, XU W. Asset analysis of risk assessment for IEC 61850-based power control systems. Part II: Application in substation [J]. IEEE Transactions on Power Delivery, 2011, 26(2): 876-881.

[4] LAPWORTH J A, WILSON A. The asset health review for managing reliability risks associated with ongoing use of ageing system power transformers [C]// 2008 International Conference on Condition Monitoring and Diagnosis. Beijing, China: IEEE Computer Society, 2008: 605-608.

[5] WANG You-yuan, YUAN Yuan, Li Jian. Study on power transformer fuzzy risk assessment based on borda number theory [C]// 2008 International Conference on High Voltage Engineering and Application. Chongqing, China: IEEE Computer Society, 2008: 609- 612.

[6] KANG C Q, YANG G F, XIA Q. Development of multidimensional sequence operation theory with applications to risk evaluation in power system generation scheduling [J]. Science in China Series E: Technological Sciences, 2008, 51(6): 724-734.

[7] MIRANDA V, PROENCA L M. Why risk analysis outperforms probabilistic choice as the effective decision support paradigm for power system planning? [J]. IEEE Transactions on Power Systems, 1998, 13(2): 643-648.

[8] CHRIS J D, JANUSZ W B. Non-iterative method for modeling systematic data errors in power system risk assessment [J]. IEEE Transactions on Power Systems, 2011, 26(1): 120-127.

[9] XIAO F, JAMES D M. Power system risk assessment and control in a multiobjective framework [J]. IEEE Transactions on Power Systems, 2009, 24(1): 78-85.

[10] AHN Hyun-Mo, LEE Ji-Yeon, KIM Joong-Kyoung. Finite-element analysis of short-circuit electromagnetic force in power transformer [J]. IEEE Transactions on Industry Applications, 2011, 47(3): 1267-1272.

[11] BASTARD P, BERTRAND P P, MEUNIER M. A transformer model for winding fault studies [J]. IEEE Transactions on Power Delivery, 1994, 9(2): 690-699.

[12] XIONG Hao, SUN Cai-xin. Artificial immune network classification algorithm for fault diagnosis of power transformer [J]. IEEE Transactions on Power Delivery, 2007, 22(2): 930-935.

[13] SAATY T L. The analytic hierarchy process [M]. New York: McGraw-Hill, 1980: 372-397.

[14] LEE S K, MOGI G, KOIKE M. Fuzzy integrated analytic hierarchy process approach for selecting strategic big-sized R&D programs in the sector of energy technology development [C]// 2009 IEEE International Conference on Fuzzy Systems. Jeju: Korea Institute of Electrical and Electronics Engineering Inc, 2009: 1432-1438.

[15] ATIYA A F. Bankruptcy prediction for credit risk using neural networks: A survey and new results [J]. IEEE Transactions on Neural Networks, 2001, 12(4): 929-935.

[16] LI Z Y, PENG L H. An exploration of the uncertainty relation satisfied by BP network learning ability and generalization ability [J]. Sci China Ser F-Inf Sci, 2004, 47(2): 137-150.

[17] CHEN S J, HWANG C L. Fuzzy multiple attribute decision making [M]. Berlin: Springer, 1992: 412.

[18] LU Y J. Weight calculate method of fuzzy analytical hierarchy process [J]. Fuzzy Systems and Mathematics, 2002, 16(2): 79-85. (in Chinese)

[19] ZIMMERMANN H J. Fuzzy sets, decision making and expert systems [M]. Boston: Kluwer Academic Publishers, 1987: 295.

[20] LAN J W, XU Y, HUO L A. Research on the priorities of fuzzy analytical hierarchy process [J]. Systems Engineering-Theory & Practice, 2006, 26(9): 107-112. (in Chinese)

[21] XU Ze-shui. A method for priorities of triangular fuzzy number complementary judgment matrices [J]. Fuzzy Systems and Mathematics, 2002, 16(1): 47-50. (in Chinese)

(Edited by HE Yun-bin)

Foundation item: Project(50977003) supported by the National Natural Science Foundation of China

Received date: 2011-10-16; Accepted date: 2011-12-28

Corresponding author: LI Wei-guo, Professor, PhD; Tel: +86-10-51971434; E-mail: yuqian930@163.com