The 19 th International Symposium on High Voltage Engineering, Pilsen, Czech Republic, August, 23 28, 215 GROUND RESISTANCE ESTIMATION USING INDUCTIVE MACHINE LEARNING V. P. Androvitsaneas *1, I. F. Gonos 1, G. D. Dounias 2 and I. A. Stathopulos 1 1 High Voltage Laboratory, School of Electrical and Computer Engineering, National Technical University of Athens, 9 Iroon Politechniou Street, Zografou Campus, Athens 1578, Greece 2 Department of Financial and Management Engineering, University of the Aegean, 41 Kountouriotou Street, 82 Chios, Greece *Email: <v.andro@mail.ntua.gr> Abstract: This work demonstrates the application of entropy information based inductive learning techniques for the estimation of the ground resistance of grounding systems, used for the safe operation of electrical installations, substations and power transmission lines. Ground resistance value must be kept in low levels, so that grounding systems are able to provide the lowest impede path for fault currents to be dispersed into the earth, in the shortest possible time. The key concern of the present work is the evaluation of grounding systems performance and the possible estimation of future formed values of ground resistance, since soil resistivity and rainfall data are available. For this purpose, measurements of soil resistivity in various depths of the ground and of rainfall height have been carried out over a period of four years or so, in a particular field inside the university campus. At the same time, the ground resistance values of few grounding rods, encased in ground enhancing compounds, are recorded as a function of time. The computational method generalizes over numerical data corresponding to these ground resistance measurements. For the modeling of the data, classes are represented by discrete intervals of measurements. Decision trees are constructed for approximating the discretevalued target function of ground resistance and then they are represented by production rules in order to improve the model comprehensibility. The error rates and the performance of the model on unseen cases are determined by a v-fold cross validation approach. Results seem promising for further development of the method. Inductive machine learning is used not primarily as a classifier aiming at obtaining high accuracy, but more as a knowledge discovery tool, finding interesting rules and decision patterns of high quality, to be checked further with statistical techniques. 1 INTRODUCTION Grounding systems constitute a quite essential part of the protection system of electrical installations, substations, and transmission or distribution lines against lightning and fault currents. These systems are designed primarily for power frequency earth fault conditions and they are used to divert high currents to the earth. Thus, a grounding system designed and constructed in a right way and complied with the robust requirements of the relevant international standards, is capable of dissipating high fault currents safely to the earth, providing protection and safety to humans and equipment from harm and damage respectively. In practice, all the parts of the grounding system are interconnected and may play a role in the dissipation of both power frequency faults and lightning impulse currents [1-2]. A grounding system, in order to be effective, has to keep its ground resistance in low levels during its lifecycle. International standards point out the influence of some factors like moisture, temperature and soil compaction on the soil resistivity and they recommend the periodic measurement of the ground resistance for the control of its values [1 2]. Nevertheless, most of the cases of electrical installations are characterized either by lack of space for the installation of the grounding systems, or the huge cost which often may be prohibitive for the construction. Furthermore, soil resistivity of the upper layer is subjected to seasonal variation due to weather conditions such as rainfall, ice and air temperature, which mainly effect on soil humidity, whereas the dissolved salts percentage and the soil consistency play a major role in soil resistivity value [3 5]. In the last decades the usage of ground enhancing compounds for soil alleviation, resulting in the diminishing of ground resistance, becomes more and more popular in engineering field. Ground enhancing compounds are usually used in high resistivity soil types and must be in full compliance with EN 62561-7:212 [6]. Therefore, great deals of research works have been occupied with the study and observation of the performance of these materials and their effect on ground resistance of several forms of grounding systems [7].
The periodic measurement of ground resistance is very often impeded by the residence and building infrastructure. In addition, many times it is essential for engineers to have an estimation of the behavior of constructed or in design phase grounding systems over time. For sidestepping this impediment, the present work aims to develop a novel tool for classifying, estimating and perhaps forecasting the ground resistance values of several grounding systems. Extending and amplifying the application of artificial intelligence techniques on grounding systems [8 9], this study is based on soil resistivity measurements at the location of interest and on local rainfall data, using inductive machine learning (IML) techniques and particularly decision trees with the respective production rules. Decision tree learning is one of the most widely used and practical methods for inductive inference. It is a method for approximating discrete-valued target functions that is robust to noisy data, in which the learned function is represented by a decision tree and capable of learning disjunctive expressions [1]. A decision tree is a simple representation for classifying examples, so it is one of the most successful techniques for supervised classification learning. It is also a method commonly used in data mining. The goal is to create a model that predicts the value of a target variable based on several input variables. A tree can be "learned" by splitting the training set into subsets based on an attribute value test. This process is repeated on each derived subset in a recursive manner called recursive partitioning [11]. The successive division of the set of training cases proceeds until all the subsets consist of cases belonging to a single class or when splitting no longer adds value to the predictions. This process of top-down induction of decision trees (TDIDT) is an example of a greedy algorithm and it is by far the most common strategy for learning decision trees from data [12]. A simple example of a decision tree for the concept e.g. Football training is illustrated in Figure 1 [1]. An example is classified by sorting it through the tree to the appropriate leaf node, then returning the classification associated with this leaf (in this case, Yes or No). This tree classifies Saturday mornings according to whether or not they are suitable for playing football. In data mining, decision trees can be described also as the combination of mathematical and computational techniques to aid the description, categorization and generalization of a given set of data. Data come in records of the form: (x,y) = (x 1, x 2, x 3,, x k, Y) (1) The dependent variable Y is the target variable that is to be understood, classified or generalized. The vector x is composed of the input variables x 1, x 2, x 3 etc., that are used for that task. No High Humidity Outlook Sunny Overcast Normal Yes Yes Rain Strong No Wind Weak Yes Figure 1: A decision tree for the concept Football training [1]. In general, decision trees represent a disjunction of conjunctions of constraints on the attribute values of instances. Each path from the tree root to a leaf corresponds to a conjunction of attribute tests, and the tree itself to a disjunction of these conjunctions. For example, the decision tree shown in Figure 1 corresponds to the expression [1]: (Outlook = Sunny Λ Humidity = Normal) V (Outlook = Overcast) V (Outlook = Rain Λ Wind = Weak) 2 DESCRIPTION OF THE EXPERIMENT AND DATA ACQUISITION This paper presents a part of an extended study on ground enhancing compounds performance, started in February 211 and is still carried on. The data acquired from the measurements in a period of four years are used for developing a model for the ground resistance estimation and forecasting. Thus, in this work three vertical grounding rods presently denoted as G 1, G 2 and G 3, St/e-Cu type A, dimensioned 17x15mm, with a minimum copper thickness of 254μm, have been evaluated in field conditions [7]. The rod G 1 has been driven into natural soil, while G 2 has been immersed in slurry bentonite and G 3 in a trade chemical enhancing compound. The experimental layout is illustrated in Figure 2. In this figure, P i are the probes used for the measurement of soil resistivity and ground resistance, where the subscript i denotes the distance (in meters) from the rod G 1 and the probe G 3,cp is the current probe for the ground resistance measurement of the rod G 3. The measurements performed at the experimental field, for a period of four years, concern soil resistivity (ρ) in some depths of the ground (1m, 2m, 4m, 6m, 8m), ground resistance of the grounding rods (R g1, R g2, R g3 ) and rainfall height (r) at the tested site. All the measurements have been performed according to the specifications indicated by the IEEE Std 81 [1], which provides complete
description of the methods for measuring ground resistance, instrumentation and safety precautions. Therefore, the well-known Wenner method and the fall of potential method have been used for the measurement of soil resistivity and ground resistance respectively. Soil resistivity presents a remarkable seasonal variance as a function of rainfall height. Ground enhancing compounds performance, in turn, is affected by the chemical composition of the material, the time and the soil conditions. As far as the ground resistance is concerned, it is affected both by the soil resistivity and by the used ground enhancing compounds. The graphs of Figures 3 and 4 give a depiction of the variance, the soil resistivity and the ground resistance present, as a function of time and rainfall. G 3 2m 1m 4m P 48 P 4 P 36 P 32 P 24 P 2 P 18 P 16 P 14 P 12 P 8 G 1 Figure 2: Experimental layout. Soil resistivity (Ωm) 5 4 3 2 2m G 3,cp Figure 3: Soil resistivity as a function of time and rainfall. G 2 1m 2m 4m 6m 8m Rainfall 9 8 7 6 5 4 3 2 1 Rainfall height (mm) Ground resistance (Ω) 7 6 5 4 3 2 Rg1 Rg2 Rg3 Rainfall Figure 4: Ground resistance as a function of time and rainfall. 3 PROPOSED IML METHODOLOGY FOR THE ESTIMATION OF GROUND RESISTANCE 3.1 Inductive machine learning concept Although a variety of decision tree learning methods have developed with somewhat differing capabilities and requirements, decision tree learning is generally best suited to problems with the following characteristics: Instances are represented by attribute-value pairs, The target function has discrete output values, Disjunctive descriptions may be required, The training data may contain errors, 9 8 7 6 5 4 3 2 1 The training data may contain missing attribute values. The particular problem of the ground resistance estimation has been found to fit the above characteristics. Most algorithms, developed for learning decision trees, are variations on a core algorithm that employs a top-down, greedy search through the space of possible decision trees. This approach is exemplified by the ID3 algorithm [11] and its successor C4.5 [12]. The algorithm C4.5 learns decision trees by constructing them top-down, beginning with the question which attribute should be tested at the root of the tree. To answer this question, each instance attribute is evaluated using a statistical test to determine how well it alone classifies the training cases. The best attribute is selected and used as the test at the root node of the tree. A descendant of the root node is then created for each possible value of this attribute and the training cases are sorted to the appropriate descendant node (i.e. down the branch corresponding to the case s value for this attribute). The entire process is then repeated using the training cases associated with each descendant node to select the best attribute to test at that point Rainfall height (mm)
in the tree. This forms a greedy search for an acceptable decision tree, in which the algorithm never backtracks to reconsider earlier choices. In order to define information gain precisely, a measure commonly used in information theory, called entropy, is defined. This characterizes the purity of an arbitrary collection of cases. Selecting one case at random from a set S of cases and announcing that it belongs to some class C j, this message has a probability [1, 12]: ( j, ) freq C S p = (2) j S where S is any set of cases, freq(c j, S) stands for the number of cases in S that belong to class C j and ISI denotes the number of cases in set S. So, the information it conveys is [1, 12]: log 2 ( j, ) freq C S S bits (3) To find the expected information from such a message pertaining to class membership, all the classes are summed over in proportion to their frequencies in S, giving [1-12]: ( ) Entropy S ( j, ) freq( C j, S ) k freq C S log S 2 S (4) j= 1 = One interpretation of entropy from information theory is that it specifies the minimum number of bits of information needed to encode the classification of an arbitrary member of S (i.e. a member of S drawn at random with uniform probability). Given entropy as a measure of the impurity in a set of training cases, a measure of the effectiveness of an attribute in classifying the training data can now be defined. This measure, called information gain, is simply the expected reduction in entropy caused by partitioning the cases according to this attribute. More precisely, the information gain, Gain(S, A) of an attribute A, relative to a set of training cases S, is defined as: Si Gain ( S, A) = Entropy ( S ) Entropy ( Si ) (5) S n i= 1 where n is the number of values of the attribute A and S i is the subset of S for which attribute A has value i. Note that the first term in (5) is just the entropy of the original training set S and the second term is the expected value of the entropy after S is partitioned using attribute A. The expected entropy described by this second term is simply the sum of the entropies of each subset S i, weighted by the fraction of cases that belong to S. 3.2 Application and results of inductive machine learning For the particular problem of ground resistance estimation a decision tree has been constructed, classifying the available ground resistance values of the training set, resulted from the field measurements, in predefined classes C j. The algorithm C5., a newer version of C4.5, was used for the decision trees construction and their produced rules. The thirteen attributes (parameters) that determine the classified values of ground resistance, used in the particular developed tree, are the daily value of soil resistivity at the depth of 1m, 2m, 4m, 6m and 8m on the day of measurement (ρ id ), the mean weekly value of soil resistivity at the same depths (ρ iw ), the mean monthly value of soil resistivity at depths of 1m and 2m (ρ im ) and the total rainfall height during the antecedent week (r w ) of the measurement day. It is noted that i = 1, 2, 4, 6, 8m in depth. For more convenience, the attributes are concisely presented in Table 1. The variable to be classified is the ground resistance of each tested grounding rod. The training set consists of 365 cases (covering a 4 years period) for the training and the validation of the decision tree. The categories (classes) to which cases are to be assigned have been established beforehand. More particularly, three different scenarios have been established for the class discrimination assigned to each rod, denoted with the letters a, b, c, as shown in tables 2, 4 and 6, considering both the uniformity of intervals and the uniform distribution of the cases among the classes. The column cases contains the cases assigned to the corresponding class during the evaluation of the model. Certainly, although the same letters are used to represent the various scenarios of each rod, the class discrimination (i.e. segmentation intervals) denoted by the same letter differs from one rod to another. Thus, a decision tree has been constructed for each individual hypothesis considering all the 13 attributes each time. Afterwards, a 1-fold cross validation (cv) run has been performed for each individual tree, as a more robust estimation of accuracy on unseen cases. The results of the developed IML model for each grounding rod are tabulated in the concentrating and concise Tables 3, 5 and 7 respectively. The extended cv error is the cv error considering each time an extended class, the default with the neighbouring classes. Table 1: Attributes Time interval Attribute Soil resistivity Rainfall height (total) Daily value ρ 1d, ρ 2d, ρ 4d, ρ 6d, ρ 8d Mean weekly value ρ 1w, ρ 2w, ρ 4w, ρ 6w, ρ 8w r w Mean monthly value ρ 1m, ρ 2m
Table 2: The three scenarios and the respective classes for the grounding rod G 1. Table 5: Results of the IML methodology for the grounding rod G 2. # R G1a R G1b R G1c [Ω] Cases [Ω] Cases [Ω] Cases 1-4 -9-98 4 2 4-9 9-12 37 98-116 24 3 9-15 88 12-14 36 116-137 38 4 15-21 78 14-17 29 137-162 32 5 21-26 54 17-19 39 162-191 44 6 26-31 27 19-22 37 191-227 49 7 31-36 36 22-26 41 227-268 36 8 36-41 32 26-33 38 268-317 2 9 41-46 22 33-38 37 317-375 44 1 46-51 21 38-45 35 375-445 37 11 51-56 3 45-71 36 445-525 31 12 56-61 1 - - 525-71 6 13 61-66 - - - - 14 66-71 3 - - - - Table 3: Results of the IML methodology for the grounding rod G 1. R G1a R G1b R G1c Nodes 94 15 94 Trees Error [%].3 1.1.8 Rules 77 92 9 Rules Error [%].5.5 1.1 CV Error [%] 35.4 38.3 37.8 Extended CV Error [%] 9. 1.4 1.7 Table 4: The three scenarios and the respective classes for the grounding rod G 2. # R G2a R G2b R G2c [Ω] Cases [Ω] Cases [Ω] Cases 1-25 -29-27 2 25-5 164 29-32 31 27-34 56 3 5-75 66 32-34 25 34-42 49 4 75-41 34-39 31 42-52 7 5-125 26 39-45 38 52-64 25 6 125-15 19 45-5 39 64-79 36 7 15-175 11 5-65 42 79-98 27 8 175-2 11 65-85 38 98-121 3 9 2-225 9 85-13 6 121-15 23 1 225-25 9 13-2 34 15-186 16 R G2a R G2b R G2c Nodes 51 67 69 Trees Error [%] 1.4.8.5 Rules 42 55 59 Rules Error [%] 2.2 1.4.8 CV Error [%] 19.5 26. 24.6 Extended CV Error [%] 3.6 5.2 5.8 Table 6: The three scenarios and the respective classes for the grounding rod G 3. # R G3a R G3b R G3c [Ω] Cases [Ω] Cases [Ω] Cases 1-25 -25-25 2 25-5 222 25-6 254 25-31 35 3 5-75 69 6-95 54 31-37 41 4 75-19 95-125 24 37-45 121 5-125 22 125-16 5 45-54 41 6 125-15 5 16-195 3 54-65 31 7 15-175 195-23 3 65-78 25 8 175-2 3 23-265 7 78-94 13 9 2-225 3 265-3 7 94-114 19 1 225-25 2 3-335 4 114-137 8 11 25-275 9 335-4 4 137-165 3 12 275-3 3 - - 165-198 3 13 3-325 1 - - 198-238 5 14 325-35 5 - - 238-287 11 15 35-375 1 - - 287-346 6 16 375-4 1 - - 346-4 3 Table 7: Results of the IML methodology for the grounding rod G 3. R G3a R G3b R G3c Nodes 45 39 8 Trees Error [%].3.3.8 Rules 43 29 68 Rules Error [%].3.5 1.1 CV Error [%] 15.1 14. 27.4 Extended CV Error [%] 5.5 3.8 9. 11 25-275 8 2-3 27 186-23 17 12 275-3 1 - - 23-3 16
3.3 Discussion The results for the rod G 1 show that despite the remarkably low misclassification errors of decision trees and production rules, the cross validation error on unseen cases is quite high in all the scenarios. In addition to this, the cross validation error increases as the range (in Ohms) of the class becomes smaller, e.g. in scenarios (b) and (c) with 38.3% and 37.8% respectively, against the scenario (a) with 35.4%. It is obvious that these errors are higher in the case of the rod G 1 than the respective errors for the rods G 2 and G 3. This could be attributed to the large variance of values that the ground resistance of G 1 presents, as the Figure 4 indeed points out. On the contrary, considering the default class and the class next to it as an extended class, the cv error significantly decreases to approximately 1/3 of the original. The rods G 2 and G 3, on the other hand, present some proposed scenarios, as R G2a, R G3a and R G3b, with satisfactory results. The error in the scenario (a) of G 2 reaches the value of 19.5%, while the corresponding values for scenarios (a) and (b) of G 3 are just 15.1% and 14%. It seems that the soil alleviation, the ground enhancing compounds achieve and the consequent consistence in the ground resistance values (Figure 4), result in a classification task with compensative results on unseen data. This means that the ground resistance forecast, given soil resistivity and rainfall data, is a most promising task. The main cause of the great difference in cross validation errors, among the various scenarios of each individual rod, is probably the nonuniform range of the classes in each scenario. This could be a field for further investigation on the best class establishment. 4 CONCLUSIONS A classification and forecast model based on inductive machine learning algorithms has developed for predicting the time variation of ground resistance. The present work is an attempt to apply another method of artificial intelligence in the service of grounding and particularly, in the field of ground resistance estimation, a field of great importance for the design of grounding systems and the unhindered protection they provide to people and to installations. The results are encouraging enough to keep on the work on constructing similar models for the estimation of grounding systems performance. The great difference in cross validation errors points out the need for better and more focused establishment of the necessary classes. Furthermore, a probable application of a suitable attribute selection algorithm could result in much lower errors on classified unseen cases. In conclusion, the results confirm the successful application of learning decision trees in the field of grounding and, after the necessary modifications of the algorithm, it is expected to be a powerful and reliable tool. REFERENCES [1] ANSI/IEEE Std 81-212: IEEE guide for measuring earth resistivity, ground impedance, and earth surface potentials of a grounding system, Dec. 28 th, 212. [2] ANSI/IEEE Std 8-213: IΕΕΕ Guide for safety in AC substation grounding, 213. [3] I. F. Gonos, A. X. Moronis, I. A. Stathopulos: Variation of soil resistivity and ground resistance during the year, Proc. 28 th Int. Conf. on Lightning Protection (ICLP 26), Kanazawa, Japan, September 18 th 22 nd, 26, pp.74-746. [4] O. Banton, M. A. Cimon, M. K. Seguin: Mapping field-scale physical properties of soil with electrical resistivity, Soil Science Society of America Journal, vol. 61, no. 4, pp. 11-117, 1997. [5] K. Shudha, M. Israil, S. Mittal, J. Rai: Soil characterization using electrical resistivity tomography and geotechnical investigations, Journal of Applied Geophysics, vol. 67, no. 1, pp. 74-79, 29. [6] EN 62561-7:212, Lightning Protection System Components (LPSC) Part 7: Requirements for earthing enhancing compounds, Jan. 212. [7] V. P. Androvitsaneas, I. F. Gonos, I. A. Stathopulos: Performance of ground enhancing compounds during the year, Proc. 31 st Int. Conf. on Lightning Protection (ICLP 212), Vienna, Austria, September 2 nd 7 th, 212, pp. 231-1 - 231-5. [8] V. P. Androvitsaneas, A. K. Alexandridis, I. F. Gonos, G. Dounias, I. A. Stathopulos: Wavelet neural network for ground resistance estimation, Proc. of 5 th Int. Conf. High Voltage Eng. & Appl. (ICHVE), Poznan, Poland, September 8 th 11 th, 214, paper A-7-5. [9] V. P. Androvitsaneas, I. F. Gonos, I. A. Stathopulos: Artificial neural network methodology for the estimation of ground enhancing compounds resistance, IET Sci. Meas. Technol., vol. 8, no. 6, pp. 552 57, Nov. 214. [1] T. M. Mitchell: Machine Learning, McGraw- Hill Science/Engineering/Math, 1997. [11] J. R. Quinlan: Induction of Decision Trees. Machine Learning 1, pp. 81 16, Kluwer Academic Publishers, 1986. [12] J. R. Quinlan: C4.5: programs for machine learning, San Mateo, California, USA, Morgan Kaufmann Publishers, 1993.