fusion. The proposed framework can integrate different kind of transformer condition monitoring data as well as failure statistics. By making use of these data and ...
12th IEEE International Conference on the Properties and Applications of Dielectric Materials - Xi'an - China
A Probabilistic Framework for Transformer Health Condition Assessment Shuaibing Li, Guangcai Hu, Bo Gao, Yan Yang*, Guangning Wu School of Electrical Engineering, Southwest Jiaotong University West Zone of Hi-tech District Chengdu, Sichuan 611756 P.R. China Abstract- A probabilistic framework for transformer health condition assessment is proposed based on Bayesian information fusion. The proposed framework can integrate different kind of transformer condition monitoring data as well as failure statistics. By making use of these data and information, an inference model is constructed using the Bayesian belief network and its parameters like the prior/condition probabilities are also determined with the availability of the obtained data, accordingly. In the model, the condition probability is taken as significance of the condition data on corresponding component and is decided by combing both the principal component analysis and expert’s experience, while the contribution of independent variables to dependent ones is quantified with a score-probability transform. The constructed model then derives a probabilistic health index to take into account the uncertainties in data acquisition, interpretation and modeling. Numeric experiments are carried out using several field collected datasets. The results demonstrate the applicability of the proposed model in transformer condition assessment.
I. INTRODUCTION Power transformer is one of the important components in power system. Any failures of the transformer can result in significant economic loss and great social impact. To ensure an accurate condition assessment of a transformer, kinds of condition monitoring techniques including oil characteristic tests, dissolved gas analysis, patial discharge measurement, polariation based measurement, and frequency response analysis have been introduced for assessing transformer’s health condition[1-3]. Each of the above techniques is normally focused on examing the health condition of a transformer from one aspect. As the transformer is constructed by many components with complicated structure, the data for interpreting the health condition may incooperate certain amount of inaccuracies, it is almost impossible for a single measurement to make a realible assessment of the transformer’s health condition. In reacent years, considerable attempts have been carried out to asess the health condition of transformers, including the health index methods and some data fusion based intelligent methods [4-17]. Both the health index method and the data fusion methods integrate the data of different types and from different sources for a trasnformer into a single score or index to reflect its overall condition. The health index or score may help rank transformers in a fleet. In the health index methods, the condition of a transformer is either decided as a weighted score summation or a certain
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condition value. With kinds of condition monitoring data, a score reflecting the overall condition of the transformer can be derived by scoring and weighting on the collected transformer data based on related standards (i.e. IEC, IEEE and CIGRE recommendations) and expertices from human experts. Then, each indiviudal score are integrated into a single index [6-17]. In comparison, methods like artificial neural networks (ANNs) or support vector machines (SVMs) or other algorithms use part of the data to construct a model to approximate the underlying relationship between the data and the transformer condition, then to estimate a value indicating the condition of the transformer [16-20]. In the information fusion methods, the fuzzy approach and evidence reasoning or Bayesian net are applied to handle the condition assessment of the transformer as a multi-attribute decision problem [21, 21]. By constructing an index system, original basic probability assignments are generated by the fuzzy model and are then utilized to combine all of the evidence and give an overall assessment with using evidential reasoning. For Bayesian methods, all available data are taken as prior knowledge to construct the Bayesian net. It will then be taken to decided the transformer’s health condition in a probabilistic form. Since the scoring and weighting methods are subjective in nature, the intelligent algorithm-based methods need certain amount of measurement data from transformers with known health conditions, and fuzzy approaches are more or less subjective, this paper proposes a dynamic information fusion approach within the framework of Bayesian belief network (BBN). It innovatively addresses a number of issues in developing an inference engine for traction transformer health condition assessment by constructing a hierarchical structure of BBN based on the construction and event tree of a transformer. The established BBN uses data statistics to determine the prior probability for each variable in BBN and decide the significance of each variable on the corresponding component using principal component analysis (PCA). The final form of indicating the health condition of a transformer is a probability, rather than a certain value. In the rest of this paper, a brief review on BBN is presented in Section II. Details of constructign the proposed probabilistic framework for transformer health index calculation are provided in Section III, case studies and analysis are carried out in Section IV. Finally, conclusions are drawn in Section V.
III. PROBABILISTIC HEALTH CONDITION MODELLING
II. THEOREM OF BAYESIAN BELIEF NETWORK AND BAYESIAN NETWORK BASED INFORMATION FUSION
A. Construction of The Bayesian Belief Network With reference to relevant standard [26-28], a four-layer hierarchical BBN is established in this paper and is shown in Fig. 1. Based on this network, the information fusion is performed and a probability health index is calculated. The construction of the BBN, the formulation of the dynamic information fusion, and the derivation of the probability health condition modelling are discussed as follows.
A. Bayesian Belief Network The Bayesian belief network is a graph-based technique for the inference of underlying relationships among a number of variables [23]. It has been applied to different fields for dealing with incomplete and even conflicting information from multi-source [24, 25]. A BBN uses a directed acyclic graph (DAG) to represent a set of random variables U = {Xi, i =1, …, n} with their individual states and the cause-effect relationships among them. In a DAG, the conditional probability of any child node with respect to its parent nodes needs defined on a conditional probability table (CPT). For those nodes only have child node or without any inputs, a probability distribution over all possible states needs to calculated and recorded on CPT. The joint probability distribution (JPD) over all variables in X is calculated as the product of condition probability distributions (CPDs) as
P U
P X 1 ,L , X n
n
P X
i
X i 1 , L , X 1
Transformer HI
Short circuit
Protection records
Lightning
Transformer data
External stress
Moisture
Winding
Paper quality
Load or temp. profile
Core
DGA factor
Online DGA
Oil
Oil quality factor
Oil sample analysis
Oil maintenance Bushing
Bushing maintenance
Tank and Aux.
Tank maintenance
Tap changer
TC maintenance
Maintenance records
(1)
i 1
where CPDs are obtained from the observations {X1, …, Xn}. B. Bayesian Network Based Information Fusion Once new evidence becomes available, the parameters of a BBN can be readily updated. Assuming a set of new evidence ej (j=1, …, m) regarding the variable Xi is given, the BBN can be updated by calculating the posterior probability P(Xi|e) [23].
P U , e
n
P X i | pa( X i )
i 1
m
e
j
(2)
j
where pa(Xi) denotes the parents of variable (node) Xi. The probability of variable Xi, given all evidence e, can be updated to include new evidence P ( X i , e) U \{ X i } (3) P Xi | e P(e) where the right-hand-side operator ∑U\{X}P(U) in (3) denotes the recursive marginalization of each variable excluding Xi. From the above it can be seen the BBN naturally satisfy well for information fusion. It provides a way for logical reasoning and data aggregation. Moreover, as it will be shown in the rest of this paper, it can also cope with uncertain, incomplete and even conflicting information arisen from the heterogeneous data sources and integrate them into one coherent structure for further analysis. Denoting F as the fusion function and Si is the i-th type of measurement, the process of multi-source information fusion within BBN can be expressed as [25]: (4) 4 F ( S1 , S2 ,L , Si )
Index Index Layer Layer
Component Component Layer Layer
Factor Factor Layer Layer
Data Data Layer Layer
Fig.1 Framework of proposed health index calculation.
In Fig.1, each kind of condition data is taken as a node of BBN, and each element of factor layer, component layer or index layer is a node of this BBN. In this BBN, the elements in data layer are called father nodes, while the remaining in other layers are taken as child nodes. The state of child node is determined by its father node(s). B. Determination of Prior Probability In Fig.1, the prior probabilities of each node in data layer are assigned according to statistics obtained from the datasets from utilities and literature. For those nodes without field measurement records from utilities, their prior probabilities are assigned only using statistics from the literature. For a certain measurement or test item of the transformer, its condition can be determined according to relevant standard and experts’ experience. In this paper, a four-level condition state is defined for all nodes in the established BBN in Fig.2, including “Good”, “Fair”, “Poor” and “Faulty”. A score ranking from one to four is given to the four states, e.g. if one test is classified as “Good”, its score is one. This condition score can be utilized for condition state decision for the child nodes in the upper layers and will be discussed in the coming section. The follows detail how health condition state of each node is determined. For dissolved gases, the condition states of each of them is determined according to IEEE and CIGRE recommendations, they are given in Table I. Regarding to oil sample test, the condition states of the dielectric strength, acid number, moisture in oil and dissipation factor are decided with
¦
where Θ is the fusion result. In this paper, the probability inference as in (2) and (3) is generalized to the fusion function F. The output Θ is the posterior probability of hypotheses that need to be inferred.
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reference to the IEC standard 60422 [29]. In terms of service age and moisture in paper, the former is decided same to that given in [30], while the latter is confirmed according to IEEE Std. 62 [31]. All of these state levels are provided in Table II. Since the content of moisture in paper cannot be measured directly, the moisture equilibrium curves are adopted to derive an equivalent value of moisture in paper from the water measured in oil.
transformer from one aspect. In this paper, the bushing DGA, power factor and maintenance records are considered. The condition state level of bushing DGA is based on [33-35], and given in Table IV. TABLE III CONDITION STATE LEVELS OF LWC AND SWC. Condition State Good Fair Poor Faulty LWC >1.75 1.5-1.75 1.25-1.75
