Earth resistance measurement
By Manuel Jaime Leibovich
Abstract:The main factors that should be considered in order to get an accurate earth resistance measurement in electrical systems are analyzed. The measurement system geometry, including minimum distances that should be taken into account, is particularly considered. 
Introduction:The grounding system is an essential element for the electrical system security and it is required to:
Due to the fact that it is a system designed to guarantee safety, its effectiveness should be verified. The diffusion resistance value is the parameter normally considered to be the most relevant one to test grounding system quality and its capacity to carry out its function properly. But the correct measurement of this parameter needs to fulfill several requirements, which will be analyzed in this issue. Physical nature of the earth resistance:The understanding of the earth resistance physical nature will help us evaluate the conditions to be fulfilled in order to get its correct measurement. According to its definition, resistors have two terminals and its resistance is defined as the quotient of the voltage applied on those terminals and the current circulating between them as a consequence of that voltage. The value of the resistance (eq. 1) depends on the type of material (resistivity) and its physical dimensions (area and length of the resistive element), as it is shown in figure 1. Only one of the terminals is evident in the earth resistance. In order to find the second terminal we should recourse to its definition: Earth Resistance is the resistance existing between the electrically accessible part of a buried electrode and another point of the earth, which is far away (Figure 2). The idea is that outside the earth volume next to a buried electrode, through which a current is injected, all the planet volume is equipotential related to that current. Any point of that equipotential volume (Figure 3) can be considered as the second electrode of the earth resistance. In order to justify the previous statement, we will closely analyze the resistance geometry in the area surrounding the buried electrode, which, in the following example, is supposed to be hemispherical (Figure 4). The current being injected in the earth through the buried electrode goes out from it in all directions, with a uniform density (supposing the ground is electrically homogeneous), and it must later go through the various layers illustrated in figure 4. Each layer offers a resistance to the passing current, which is proportional to the ground resistivity and to the layer thickness (resistance length in Figure 1), and inversely proportional to the layer's area, according to eq.1. Then, the total resistance is the sum of many small resistances in series. The thickness is arbitrarily defined as thin enough so as to consider both surfaces of the layer as of the same area (requirement necessary to apply eq. 1). Really, the thickness is infinitesimal and the sum of the resistances is an integral as shown in eq. 2, where r0 is the radius of the buried hemisphere. In order to allow an easier physical visualization of the phenomenon, we could imagine the structure of an onion, made up of a great number of very thin layers, each of which represents one of the resistances of the series. The important concept to be observed is that, since the ground resistivity was supposed to be homogeneous and the thickness of all the layers is the same, the only element that is modified (it increases) as we go away from the electrode is the surface of the layer. In figure 4, it can be observed that surface S3 is much bigger than the surface S1. When the surface increases, the resistance decreases in the same proportion and therefore the contribution made by the remote layers to the total resistance tends to be insignificant. Calculations for the case of an hemispherical electrode show that in the nearest region, up to a distance equivalent to 10 times the electrode radius, the 90% of the total resistance is concentrated. In other words, the contribution made to the resistance by the layers located outside this area, is not significant. And as there is no resistance, there is no fallofpotential either. Consequently, outside the region closest to the electrode (called resistance area), all the ground is at the same potential. Measurement method:In order to measure the resistance, we need to apply a voltage among its terminals that causes the circulation of a current through it. One of the terminals is the earth system accessible contact E. The second one, according to the definition, is any other point of the earth that is really far away from the first. In order to carry out the measurement, we should hammer an auxiliary electrode H at that point. The second electrode will inevitably have its own earth resistance and resistance area. If we look at figure 5, we will see that:
FallofPotential MethodA third electrode S is used in order to avoid the error introduced by the earth resistance of electrode H, The S rod is hammered at any point outside the E and H influence zones, giving as a result a geometry similar to the one shown in Figure 6. This arrangement is known as FallofPotential Method and it is the most commonly used for the earth resistance measurement in small or medium dimension systems, in which the separation of the resistance areas is obtained with reasonable distances between electrodes. The current circulates through the earth system E and the auxiliary electrode H, and the voltage is measured between E and the third electrode S. This voltage is the fall of potential that the test current produces in the earth system resistance, Rx, which in this way can be measured without being affected by the earth resistance of the H rod. The 62% ruleMany publications that make reference to the FallofPotential Method indicate that, in order to obtain a correct measurement, the three electrodes must be well aligned and the distance between E and S must be the 61.8% of the distance between E and H (figure 7). This concept comes from a careful mathematical development for the particular case of an hemispherical electrode, published by Dr. G. F. Tagg (Note. 1) in 1964. Nevertheless, this configuration is not easily applied in the real life. The first problem to be faced is that real earth systems have complex geometries and it is difficult to assimilate them with an hemisphere in order to precisely determine its center, from which distances can be measured accurately enough. Besides, in urban areas it is difficult to find places where the rods can be hammered, and it is rare for those available places to coincide in their position with the 62% rule requirements (alignment and distances relationship). Fortunately, by using the same calculations of the previously mentioned paper we can derive another geometry, which is easier to apply. Consider the segment joining E with H and the straight line that intersects that segment at its middle point and that is perpendicular to the mentioned segment. By placing the electrode at any point lying on the straight line the measured value of the resistance will fall between 0.85 and 0.95 of the true value of the earth resistance of the electrode. Then, multiplying the measured value by 1.11 the correct earth resistance value is obtained, with an error lower than ±5%. It is also observed that as the voltage electrode goes far away from the segment EH, the area where the measured value is within the indicated range of tolerance becomes wider, making the method to be more tolerant to changes in the position of the voltage electrode in both directions. In Figure 8, if the electrode S is hammered at any point outside the gray areas, the error will be lower than ±5% when applying this procedure that we will call "The 1.11 rule". Perhaps the expected error caused by the suggested method may appear to be too high. In order to evaluate this point, we will cite again the same Dr. Tagg´s paper: "...bearing in mind that a high degree of accuracy is not necessary. Errors of 510% [in the measurement of earth resistance] can be tolerated... This is because an earth resistance can vary with changes in climate or temperature, and, as such changes may be considerable, there is no point in striving after a high degree of accuracy." "Recipe" for the 1.11 rule
A more detailed analytical study of the development that leads to 1.11 factor rule does not fall within the scope of this paper, but it can be found in a paper written by the same author(Note. 2). Auxiliary electrodes earth resistanceCurrent and potential auxiliary electrodes are also earth electrodes, often of small dimensions, and due to this they can present a fairly high earth resistance (also depending on the soil resistivity). As it has already been seen, the 3 electrodes method is a configuration that makes it possible to eliminate the influence of these resistances on the measurement. However, earth testers constructive limitations impose restrictions to the earth resistances maximum value of the auxiliary ground rods. Related to current electrodes, the limitation is imposed by the features of the builtin generator of the earth tester. A very high resistance of this electrode would limit the current that the equipment can inject into the soil, with a subsequent decrease in the measurement sensibility. Concerning the potential electrode, the limitation is determined by the voltmeter circuit input impedance of the earth tester, which must be far greater than the earth resistance of this auxiliary electrode. The IEC 615575 standard, specific for earth testers, determines that the instrument must provide a correct measurement result with an error lower than ±30% for any resistance of the auxiliary electrodes of up to 100 x Ra with a maximum of 50kW, being Ra the measured resistance value. It also requires the instrument to be able to determine that this condition is fulfilled, in order to avoid an error of this kind to go unnoticed. Several instruments carry this out automatically, warning the operator and blocking measurement when the resistance of any auxiliary electrode is excessive. If this is not the case, then the measure procedure should include this checking before each test. InterferencesWhen a grounding system resistance of an energized installation is measured, a significant voltage of industrial frequency and possible harmonics between the earth electrode E and the potential electrode S appears due to the existence of an earth fault current. The same happens during measurements in soils in which there are spurious currents circulating, such as it happens in the vicinity of some substations. These interfering voltages can be much higher than the ones the equipment should measure. This is because the injected currents are always small, perhaps a few milliamps, in order to preserve operators' safety. The greatest challenge that a good Earth tester faces is to be able to distinguish the potential drop in earth resistance due to the test current from the interfering voltages (which may have a substantially greater magnitude). This distinction is easier to achieve if the frequency of the injected current coincides neither with the industrial frequency nor with any of its harmonics. This condition is mathematically expressed in equation 3. Where: Fg = Frequency of the current injected by the internal generator Fi = Industrial frequency (50 Hz or 60 Hz, depending on the country) N = Any integer greater than zero Each manufacturer chooses an N value that he considers to be adequate, from which the equipment operating frequency results. The 270Hz frequency has the peculiarity of complying with this condition for N = 4 in the 60 Hz regions, and at the same time, it is very close to comply with it for N = 5 in the 50Hz region. Other adequate frequencies following the same criterion are: 330Hz, 570Hz, 630Hz, 870Hz, 930Hz, 1170Hz, 1230Hz, 1470Hz, 1530Hz, etc. The separation is carried out using high selectivity filters. A very adequate configuration is the synchronous rectifier, in which the same system that generates the test current controls the switches that rectify the signals that should be measured. This model is equivalent to a highly selective and efficient filter, which allows for accurate measurements even with intense interferences. If the grounding system behaves as a simple resistance, its value is independent from the measurement frequency. However, some grounding systems present a reactive component. In such a case, their behavior depends on the frequency of the circulating current. For fault currents the frequency will be low, of about 50 or 60Hz. But, when it has to dissipate an atmospheric discharge current, an inductive component may compromise the grounding system efficiency.
