Power Distribution Systems Fault Cause Identification using Logistic ...

Power Distribution Systems Fault Cause Identification Using Logistic Regression and Artificial Neural Network Le Xu, Student Member, IEEE, and Mo-Yuen Chow, Senior Member, IEEE

Abstract-- Power distribution systems play an important role in modern society. When outages occur, fast and proper restorations are crucial to improve system reliability. Proper outage root cause identification is often essential for effective restorations. This paper reports on the investigation of two classification methods: logistic regression and neural network, applied in power distribution fault cause classifier (PDFCC) and comparison of their results. Logistic regression is seldom used in power distribution fault diagnosis, while neural network has been extensively used in power system reliability researches. Evaluation criteria of the goodness of PDFCC includes: correct classification rate, true positive rate, true negative rate, and geometric mean. This paper also discusses the practical application issues including data insufficiency, imbalanced data constitution, and threshold setting that are often faced in power distribution fault diagnosis. Two major distribution faults, tree and animal contact, are used to illustrate the characteristics and effectiveness of the investigated techniques. Index Terms-- classification, data insufficiency, fault cause identification, imbalanced data, logistic regression, neural network, power distribution systems, threshold setting

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I. INTRODUCTION

S the retail part of utilities, power distribution systems aim at providing reliable, economical, and safe supply of electricity to the users. Their proper operations keep industrial productions on track and people’s lives in order. However, power distribution systems are geographically dispersed and under various dynamic operating environments, they can be significantly affected by various faults, such as equipment failure, animal contacts, trees, lightning, etc. These faults often lead to power outages. In order to improve system reliability, power distribution management systems should have fast and proper response to power outages. Currently, when a power outage is reported to the control center, a typical response is that the operators estimate the probable outage location based on available information and call up the operation and maintenance (O&M) crews. These field workers need to find the exact location and identify the root cause of that outage in order to put power This work is supported by National Science Foundation Grant ECS0245383 L. Xu is with Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC 27695 USA (e-mail: [email protected]) M.-Y. Chow is with Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC 27695 USA (e-mail: [email protected])

1-59975-028-7/05/$20.00 © 2005 ISAP.

back on securely. This process sometimes can take a long time. Utilities have been making substantial effort to expedite the restoration procedure; for example, sectionalizing the feeders to quickly restore as many customers as possible on power by putting every subsection back once its proper working is assured instead of restoring the whole section together [1]. This paper focuses on the outage root cause identification. Reasonable fault cause estimation can provide workers with useful information for narrowing down the searching areas so as to expedite the restoration procedure, therefore increase system availability, improve customer satisfaction, and reduce economic loss. Power distribution fault cause identification can be viewed as a classification problem in that the outage is to be categorized into one of the existing fault cause classes carefully designed by domain experts. In this paper, a power distribution fault cause classifier (PDFCC) has been developed to address the fault cause identification problem. The investigation and results of two classification methods: logistic regression and neural network, applied to mine the historical outage data for power distribution fault cause identification are presented. A regular logistic regression is a parametric model used to analyze the problems with dichotomous dependent variables; it has been widely applied in medicine and biology areas, but it is seldom used in power system fault diagnosis. Neural network is a non-parametric method which has been extensively used in various research and application areas including power systems [2]-[4]. Evaluation criteria of the goodness of PDFCC includes: correct classification rate, true positive rate, true negative rate, and geometric mean. This paper also discusses the practical application issues like data insufficiency, imbalanced data constitution, and threshold setting that are often faced in power distribution fault cause identification problems. Tree and animal contact, which are two of the top customer interruption causes for most utilities, are used in this paper to illustrate the characteristics and effectiveness of the investigated techniques. II. POWER DISTRIBUTION FAULT DATA PREPROCESSING Duke Energy power distribution outage data are used to illustrate the proposed fault cause identification schemes. Every time a fault current is detected in the distribution system as a result of the activation of protective devices (e.g., a circuit breaker, a fuse); the fault related information is recorded into Duke Energy Power Distribution Fault Data Collection System as one record entry. Each fault record has thirty three

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information fields; based on domain experts’ suggestion, six of them are considered as containing most influential information for animal faults and tree faults [5], [6] and are selected to be used in this work. These factors are circuit ID number (CI), weather (WE), season (SE), time of day (TD), number of phases affected (NP), and protective devices activated (PD). Most of these six input factors are nonnumeric variables, and they are transformed into numeric nominal variables such that they can be easily represented. Take weather as an example, fair is represented by number 0; cold is denoted as 1; and so on. Besides these six influential factors, the attribute cause records the root cause of the outage, entered by the crew after finding the actual outage cause during the restoration process. Since this paper uses animal fault and tree fault as prototypes; the proposed PDFCC will categorize the root cause of an outage into one of three classes: tree fault (T), animal fault (A), or other causes (O). The outage database contains Duke Energy’s thirty two service regions in N. Carolina and S. Carolina ranging from 1994 to 2002. Considering different geographical features and system status, we select seven regions as reasonable representations of Duke Energy’s service areas: Chapel Hill (CHPL), Clemson (CLEM), Durham (DURH), Greenville (GREE), Hickory (HICK), Lancaster (LANC), and WinstonSalem (WINS). These seven regions cover metropolitan areas, cities, towns, rural areas, and wooded areas, and also embody both old systems and new systems. III. CLASSIFICATION METHODS There are many well-established classification methods. Empirical studies have shown that many algorithms have sufficiently similar accuracies such that the differences among those algorithms are statistically insignificant [7]. It is necessary to select a proper classification method considering practical issues like ease of implementation and computational requirements as well as accuracy. Logistic regression and neural network are two widely used classification methods. They can be easily and quickly implemented using existing software or toolboxes such as SAS and MATLAB. In this paper, we employ these two methods to mine the data and extract distribution fault cause classification models. A. Logistic Regression Logistic regression is a well known statistic method to analyze problems with dichotomous (binary) dependent variable. Dichotomous classification problems were commonly analyzed by ordinary least squares linear regression, however, a dichotomous dependent variable violates the normality assumption and homoscedasticity assumption of the linear regression model [8]. Consequently, researchers seek to develop appropriate alternative methods by trying to predict the probability of a case being classified into one category of the dependent variable as opposed to the other. Assuming the two possible values of the dependent variable are 1 and 0, the problem can be formulated as: P(Y = 1) = a + bX (1) where Y is the dependent variable, X is the independent variable vector, a and b are parameters to be identified based on the training data.

The probability value must be between 0 and 1, but the predicted value from the independent variables X in the right hand side of (1) may be less than 0 or greater than 1. In order to resolve this problem, the probability is transformed to odds, which refers to the ratio of the probability that the event will occur to the probability that the event will not occur: (2) odds(Y = 1) = P (Y = 1) / P (Y = 0) The odds does not have a maximum value; however, it has a minimum value bounded by zero: the odds is always nonnegative because it is the ratio of two probability values. A further transformation using the natural logarithm of the odds is performed. The natural logarithm of the odds is called logit, it can be any number between plus and minus infinity. logit(Y = 1) = ln[odds (Y = 1)] = α + βX (3) where α and β are parameters to be identified. The model specified in (3) is logistic regression model. Its unknown coefficients α and β are estimated with maximum likelihood method [8] using the training data. Equation (3) can be easily solved for the probability of the observed case being in the category of interest as shown in (4). P(Y = 1) = 1 / (1 + e − (α + βX ) ) (4) When logistic regression is applied as a classification method to separate patterns between two classes, the unknown parameters α and β are estimated from the training data first; then the probability P(Y = 1) of a test case is calculated using (4). In the end, the class label is assigned to that test case by comparing the calculated probability with the predefined threshold. B. Neural Network A neural network is a set of interconnected simple processing elements called neurons, where each connection has an associated weight. A neural network can achieve desired input-output mapping with a specified set of weights stored in the connections between neurons; therefore we can train the neural network to do a particular job by adjusting the weights on each connection [9]. The neurons are usually organized into a series of layers. A neural network typically consists of three or more layers. The input layer passes the data into the network. The data from the input layer arrive at the intermediate layer or the hidden layer with the associated connection weights. The hidden neurons take in the weighted inputs and calculate the outputs by their transfer functions. Their outputs are fed to the next hidden layer in turn (if there is more than one) or the output layer. The output layer then generates the results representing the mapping from the given input data. There is no clear rule to determine the number of neurons in each hidden layer, which is generally done by educated trial and error. Once the network structure has been determined, the network connection weights are learned from the training data. The most popular learning algorithm is back-propagation: the weights are initialized to small random numbers in the beginning, and then the inputs are propagated forward by activating the transfer functions in the neurons and calculating the outputs of each layer in turn. Afterwards, the error between the actual network output and desired response is propagated backwards to update the weights in order to

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minimize the network prediction error. Back-propagation iteratively processes the training samples through the input forward propagation and error backward propagation until specified accuracy or other terminating conditions are satisfied. When a neural network is used as a classification technique, its operation involves two steps: learning and recall. In the learning phase, all the network weights are adjusted to adapt to the patterns of the training data. In the recall phase, the trained network produces responses of the test data based on learned network parameters. IV. POWER DISTRIBUTION FAULT CAUSE CLASSIFIER A Power Distribution Fault Cause Classifier (PDFCC) (with flowchart shown in Fig.1) is developed for power distribution fault cause identification. Since we consider two fault causes, the PDFCC consists of two parallel branches. These two branches are the same in terms of structure and operating mechanism, but they work on different fault causes: branch A classifies an input fault as either an animal or non-animal fault, while branch T simultaneously works on tree faults. If we consider N fault causes, then we will have N parallel branches. When conflict happens, the outputs from two individual branches are mediated by the decision fusion module; it will be discussed in a later section.

methods for outage cause identification. Equation (5) indicates that the likelihood measure is related to both fault type and event. The likelihood measure for tree faults and that for animal faults are different even given the same event j . Thus, we need to utilize two branches to deal with two fault types in parallel. The data preprocessor modules take in the input X , calculate the likelihood measures Li , j corresponding to fault causes i and event j , and then pass it to classification modules. C. Classification Module (Animal/Tree) We use either logistic regression or neural network in this module for power distribution fault cause identification. Both methods implement a mapping from the likelihood measures Li , j as defined in (5) to a probability value Pi : f : Li , j → Pi

(6)

1) Logistic Regression: For the branch i , i ∈ { A, T } , six likelihood measures Li , j corresponding to influential factors are the independent variables, the probability Pi is the dependent variable. 2) Neural Network: The inputs and output are in correspondence with the independent variables and dependent variable of the logistic regression model. A three layer feed-forward network with one hidden layer of 40 nodes is used (which has been chosen through extensive simulation of different numbers of hidden nodes.) Five-fold cross-validation is used to prevent overfitting. D. Optimal Threshold Value Calculation (Animal/Tree)

Fig.1. The flow chart of Power Distribution Fault Cause Classifier.

A. System Inputs The input data to PDFCC consist of the six selected influential factors introduced in section II: X = {( x1 , x2 , x3 , x4 , x5 , x6 ) | x1 ∈ CI , x2 ∈ WE , x3 ∈ SE , x4 ∈ TD, x5 ∈ NP, x6 ∈ PD} B. Data Preprocessor (Animal/Tree) Four statistical measures have been proposed in [5] to examine the outage data from different perspectives. Likelihood measure, one of the developed measures, indicates the probability of an outage being caused by a specific fault under a specified condition. This measure can be expressed as: Li , j = N i , j / N j (5) where Li , j is the likelihood measure of fault i given event j , N i , j is the number of outages caused by fault i under event j , N j is the total number of outages under event j .

For example, if i indicates a tree fault and j indicates an icy weather condition, then the likelihood measure Li , j shows the conditional probability of the observed outage being caused by trees given the icy weather condition. Likelihood measure can provide useful information for fault cause identification when the exact cause of an outage is unknown, so it is logically used as the inputs to the classification

The output of the classification module, Pi , is the probability of the observed input data X being caused by fault i . In order to categorize the observed outage into one class or the other, a threshold is needed. With the selected threshold ζ i and calculated probability Pi , a class label can be generated: animal fault or non-animal fault for branch A, tree fault or non-tree fault for branch T. It can be mathematically represented as: 1, Pi ≥ ζ i , (7) Ci =  0, Pi < ζ i where Ci is the class label, “1” stands for the outage caused by fault i , “0” stands for the outage not caused by fault i . Usually the threshold ζ i is set as 0.5 (for 0 ≤ Pi ≤ 1 ) for an ideal case (e.g., plenty of data and they are all independent and identically distributed). However, the actual outage data used are imbalanced: the average proportion of tree faults is only 23.6% and animal faults is 13.2%, while other faults account for as much as 63.2%; therefore we adjust ζ i to an optimal value rather than use the fixed value of 0.5 to compensate for the asymmetry of the sample composition in the data in order to maximize the overall correct classification rate as shown in Fig. 2.

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V. RESULTS AND DISCUSSIONS

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For each selected region, 3/4 of its outage data are randomly selected as training data and the remaining 1/4 of the data are used as test data. As an example, Clemson has 8376 valid outage records, 6282 of them are training data and the remaining 2094 records are test data.

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Fig.2. Threshold selection for imbalanced data.

Fig. 2 shows an example of distributions of the calculated PT for tree and non-tree faults, represented by f t and f n − t , respectively. Both curves are asymmetric. The area under curve f n − t , denoted as Sn − t , shows the number of non-tree faults and the area under f t , denoted as St , indicates the number of tree faults. Threshold ζ 1 =a=0.50 and ζ 2 =b=0.55 are the decision lines: all the cases with PT ≥ ζ l , l ∈ {1, 2} are categorized as tree faults and all the cases with PT < ζ l are

A. Performance Measures A straightforward way to measure the overall accuracy of a classifier is to test the percentage of inputs that are correctly classified, denoted as correct classification rate (CCR). However, it is usually insufficient to simply observe CCR, especially when the data are imbalanced. For example, if a data set is composed of two classes, class M constitutes 95% of the data, while only 5% of the data are from class N. Then a classifier that predicts every case as the majority class M can still achieve a high overall accuracy (95%). As mentioned in section IV, the power distribution outage data used are imbalanced with respect to both tree faults and animal faults. Therefore, true positive rate Acc + , true negative rate Acc − , and geometric mean (g-mean) are further used to evaluate the performance of the techniques on the imbalanced data. These metrics are developed from confusion matrix as shown in Table II.

classified as non-tree faults. We want to maximize Sn −t , Pi | PA − ζ A |   A,| PA − ζ A |>| PT − ζ T |

True positive rate ( Acc + ) = TP /(TP + FN ) indicates how many of the animal/tree faults are correctly classified; true negative rate ( Acc − ) = TN /(TN + FP) shows how many of the non-animal/non-tree faults are correctly classified. Kubat et al. propose the geometric mean of accuracies ( Acc + × Acc − ) in [10] for imbalanced data sets. The idea behind g-mean is to maximize the accuracy on both classes. G-mean punishes big disparities between accuracies of classifying animal/tree faults and non-animal/non-tree faults: it is high when both Acc + and Acc − are large and the difference between Acc + and Acc − is small.

B. Results As discussed in section IV.E, the decision fusion module is to handle conflicting cases between two branches. In practice, only few conflicts occur (less than 0.1% of all the data encountered). So we compare the performance for two individual branches instead of the overall PDFCC performance in order to provide detailed interpretation of the results. Table III shows the average correct classification rate (CCR) that logistic regression and neural network get over seven selected service regions. From table III, two methods have similar performance on both animal faults and tree faults. Neural network has slightly higher accuracy though. However, the difference between these two techniques is so small, the largest difference is only 0.015, that they are statistically insignificant. Besides, the difference of CCR between training

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data and test data is also very small, which indicates neither of the methods overfits the training data.

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Table III. Average Correct Classification Rate for both faults with Logistic Regression (LR) and Artificial Neural Network (ANN) LR ANN Animal Training Data 0.899199 0.907709 Fault Test Data 0.897711 0.902081 Tree Training Data 0.81409 0.828804 Fault Test Data 0.8123 0.816733

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We further use animal faults to illustrate true positive rate, true negative rate, and geometric mean as shown in Fig.3-5, respectively.

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Fig.5. G-mean comparison.

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The imbalanced data typically cause the classifier to be biased towards the majority class (non-tree/non-animal fault), so as to have a low error rate for the majority class and get an unacceptable error rate for the minority class (tree/animal fault). Thus, we want to maximize the g-mean which indicates the performance of PDFCC on classifying both fault causes. Fig.5 indicates that neural network outperforms logistic regression in most of the regions. The advantage is as large as 0.114 on training data and 0.091 on test data; both occur in the region of DURH. With the comparisons, neural network and logistic regression have close overall classification accuracies. However, neural network achieves higher accuracy on classifying animal caused faults than logistic regression does and has similar performance on classifying non-animal caused faults to logistic regression’s. Considering that the animal fault is the minority class in our data and the non-animal fault is the majority, logistic regression is relatively biased towards the majority data due to the imbalanced data constitution and results in a relatively worse accuracy for the minority class, which increases the disparities between accuracies of classifying two classes and then affects the g-mean. Most real application data are not perfect; some of them are even extremely unbalanced. The effect of imbalanced data constitution has to be considered in order to have good classification accuracies on all the classes. Neural network has more balanced performance on both major and minor class than logistic regression.

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Fig.4. True negative rate comparison.

The true positive rate indicates the performance of two techniques on classifying the tree/animal faults. As shown in Fig.3, neural network has better performance on this task. Neural network outperforms the logistic regression in all of the regions for training data and in five out of seven regions on test data. The largest difference between two techniques is as large as 14.4% on training data and 11.8% on test data. Fig.4 shows the true negative rate achieved by logistic regression and neural network. Different from the case shown in Fig. 3 that neural network generally has higher true positive rate on both training data and test data, neither of these two methods shows obvious predominance. The largest difference between them is only 1.6% on training data and 2.1% on test data; both advantages are gained by logistic regression in the region of CLEM.

C. Discussions The probability Pi we are expecting from the classification module of PDFCC can be expressed as P( y = i | x1 ∩ x2 ∩ x3 ∩ x4 ∩ x5 ∩ x6 ) . A straightforward way is to calculate this conditional probability directly from the historical data and then apply the calculated results on the test data. This approach will work provided that enough data are available to calculate a statistically representative conditional probability P( y = i ) given different event combination ( x1 ∩ x2 ∩ x3 ∩ x4 ∩ x5 ∩ x6 ) . In our outage data, x1 (CI) includes at least 30 circuit ID numbers, this number differs from one region to another, x2 (WE) consists of 11 weather conditions, x3 (PD) has 10 categories, x4 (SE), x5 (TD) and

x6 (NP) all have 4 possible events, so we need at least 211,200

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data samples to cover every single possible combination of six different factors. However, the region with the most outage records from these seven selected regions only includes less than 40,000 outage data. So we will get a lot of zero probabilities and non-representative conditional probabilities because of data shortage using this approach. Alternatives such as approximate reasoning [11] have been investigated. In this work, we calculate the likelihood measures Li , j , which are the statistically representative conditional probabilities with respect to individual influential factor xk , k = 1, 2,..., 6 and then apply classification methods to implement the mapping from Li , j to Pi . This method successfully overcomes the difficulties due to data insufficiency and achieves satisfying results. As mentioned in the introduction section, a regular logistic regression is a parametric model that is seldom used in power system fault diagnosis while neural network is a nonparametric method which has been extensively used in power systems. Logistic regression, as a conventional statistical method, has formalized models to exhibit the nonlinear relationship between the independent and dependent variables while an artificial neural network can increase its flexibility by including hidden layers, which are often regarded as a substantial advantage of neural networks [12]. As seen from the results of PDFCC, neural network can adapt to the fault patterns for both classes in the imbalanced data better than logistic regression does and therefore gets higher g-mean values than logistic regression. Besides, neural network can achieve higher overall accuracy (CCR) than logistic regression does; however, the differences between these two techniques are so small as to be statistically insignificant. Both methods can be easily implemented by existing software, however, neural network requires a relatively long training time, and applying cross-validation requires even longer computational time. Logistic regression is a much quicker method.

VII. REFERENCES [1]

A. Pahwa. “Role of distribution automation in restoration of distribution systems after emergencies,” IEEE Power Engineering Society Summer Meeting, 2001.Vol.1, pp. 737 – 738. [2] K.Y. Lee, A. Sode-Yome, and Ho Park June, “Adaptive Hopfield neural networks for economic load dispatch,” IEEE Transactions on Power Systems, vol. 13, No. 2 pp. 519-526, 1998. [3] Y. Hayashi, S. Iwamoto, S. Furuya, and C.-C. Liu, “Efficient determination of optimal radial power system structure using Hopfield neural network with constrained noise,” IEEE Transactions on Power Delivery, vol. 11, No. 3 pp. 1529-1535, 1996. [4] D. Niebur and A.J. Germond, “Power flow classification for static security assessment,” in Proc. 1991 International Forum on Applications of Neural Networks to Power Systems, pp. 83 – 88. [5] L. Xu, M.-Y. Chow, L. S. Taylor, “Analysis of Tree-Caused Faults in Power Distribution Systems,” in Proc. 2003 North American Power Symposium, pp 122-127. [6] M.-Y. Chow and L. S. Taylor, “Analysis and prevention of animalcaused faults in power distribution systems,” IEEE Transaction on Power Delivery, vol. 10, no. 2, pp. 995-1001, 1995. [7] J. Han, M. Kamber “Data Mining: Concepts and Techniques,” Academic Press, Morgan Kaufmann Publishers, San Francisco, 2001 [8] P.D. Allison, “Logistic Regression using the SAS system,” SAS Institute Inc. 2000 [9] M.-Y. Chow, S.O. Yee, and L.S. Taylor, “Recognizing Animal-Caused Faults in Power Distribution Systems Using Artificial Neural Networks,” IEEE Transaction on Power Delivery, vol.8, No.3, pp. 12681274, 1993 [10] M. Kubat, R. Holte, and S. Matwin, “Machine Learning for the Detection of Oil Spills in Radar Images,” Machine Learning, vol.30, pp.195-215, 1998 [11] K. Tomsovic and B. Baer, “Methods of approximate reasoning for power system equipment condition and reliability analysis,” in Proc. 1996 Intelligent Systems Applications to Power Systems, pp.310 – 315. [12] M. Schumacher, R. Robner and W. Vach, “Neural networks and logistic regression,” Computational Statistics & Data Analysis, vol.21, pp.661701, 1996

VIII. BIOGRAPHIES Le Xu (S’01) received the B.Eng. degree in Automation from Tsinghua University, P.R. China, in 2001, and M.S. degree in Electrical Engineering from North Carolina State University, in 2003. He is currently working toward the Ph.D. degree in the Advanced Diagnosis Automation and Control (ADAC) Laboratory at North Carolina State University, Raleigh. His research interests include intelligent health monitoring of power distribution systems.

VI. CONCLUSIONS Power distribution faults significantly affect the reliability and availability of the services provided by utilities; fast and proper outage restorations are essential to improve the quality of services and customer satisfaction. In this paper, we have developed a power distribution fault cause classifier (PDFCC) to demonstrate the application of two classification methods, logistic regression and neural network, on the Duke Energy outage data for fault cause identification. Two major distribution fault types, tree and animal contact, are used as prototypes and four metrics, correct classification rate (CCR), true positive rate, true negative rate, and geometric mean, are employed to measure the performance with two techniques. This paper also investigated some practical issues often faced in power distribution fault cause identification such as insufficient data and imbalanced data constitution, and threshold setting. The advantages and disadvantages of these two techniques under these practical issues are also discussed.

Mo-Yuen Chow (S’81–M’82–SM’93) received the B.S. degree in electrical and computer engineering from the University of Wisconsin, Madison, in 1982, and the M.Eng. and Ph.D. degrees from Cornell University, Ithaca, NY, 1983 and 1987, respectively. Upon completion of the Ph.D. degree, he joined the Department of Electrical and Computer Engineering, North Carolina State University, Raleigh and holds the rank of Professor since 1999. His core technology is diagnosis and control, artificial neural network and fuzzy logic with applications to areas including motors, process control, power systems and communication systems. He has established the Advanced Diagnosis Automation and Control (ADAC) Laboratory at North Carolina State University.

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