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Earthing is a continuous headache in power distribution systems, especially in small or medium grids with considerable power, several consumer groups and transformers to distribute electrical energy at different voltages. If there are no exact rules, which are strictly applied, such grids tend to detoriate. For instance electrical current starts to leak to the earth through defect insulations, fuses will not trip due to missing or inadequate earthing and three phase systems run out of balance. Not only can the power losses raise to uneconomic heights (one third have been reported in Nepal), but also people, animals and equipment are exposed to danger by this uncontrolled current flow.
The soil is a conductor, not a very good one, but good enough to be both a cheap substitute for wires (see part Distribution Systems, SWER) and a dangerous source for electrical shocks. To understand the connections and find remedies, we need a basic insight in the conduction of current in the ground.
Contrary to wires, current will spread out when injected in the ground, 'thinning out' quickly at a growing distance from the injection point. This 'thinning' of the current has the following effect: although the specific resistance of soil is generally rather high, the growing cross-section of the current flow reduces the resistance continuously.
It is important to understand the relation and differences between specific resistance p, the resistance R and the resistance distribution R(r). The first two are proportional, where R is the specific resistance multiplied by a geometry factor, e.g. in case of a cubic conductor the length I divided by the cross-section A. R is determined by Ohms law (R = U/I), which is well defined for lumped circuits. In our case, however, the current spreads out, the resistor(the ground) has only one contact (the earth contact) so the voltage U is not simple to determine, and we need a more subtlr way to define the earth resistance.
Fig 1 Current and Potential
Distribution in a homogeneous material and an approximation of the earth
resistance with lumped resistors.
The resistance distribution it(r) is adequate. It is defined like Ohms law: it(r) = U(r)II, but takes into consideration that the resistance varies with the distance r from the earth contact.
Suppose a ground consists of some homogeneous material and has a constant specific resistance. The earth contact, a metallic sphere, is deeply dug in. Note: A spherical earth contact of course is not a practical form, but due to its perfect symmetric it is easy to derive some understanding and basic formulas. The current will enter this soil radially. The resistance distribution can be seen as made of a series of concentric spherical shells with constant thickness Dr. The surface A of these shells grows quickly with increasing distance from the injection point. So the contribution of each following shell to the total resistance diminishes quickly. The resistance distribution will rise steeply and approaches a constant value at some distance away from the earth contact. This resistance to 'infinity' is defined as the earth resistance RE.
The previous considerations can be expressed in mathematical terms.
Fig 2 a) resistance of a cube; b)
resistance of a sphere, this value is only exact for very small shell
thicknesses Dr!
Formula 2 Calculations of the earth
resistance (see also Fig 1&2) for a hypothetical spherical earth contact.
Once calculated as an approximation (series resistance of thin shells) and the
exact calculation with an integral.
Fig 3 The development of the earth
resistance RE W with growing distance from the center of a metal
sphere of 0.5m diameter. ( d = 100 Wm). It shows a) the decreasing resistance of
20cm thick 'soil shells' (see fig1 and 2), b) the stabilizing earth resistance,
c) the exact calculation and d) the value at infinity.
Another simple earth contact is a steel rod or stick (normally a galvanized pipe). Its theoretical earth resistance is given in formula 3, Fig 5. The major advantage is the simple installation (no digging is needed) and the possibility to reach better conducting soil strata in some depth.
Fig 5 Earth resistance for a stick
earth contact. Here t is the length of the stick and d its diameter.
We find two important conclusions:
The earth resistance RE grows to infinity if the earth contact surface becomes very small -> always maximize the earth contact surface and the injected current produces a voltage drop proportional to the resistance it(r) around the earth contact, hence is a function of the distance from the earth contact -> the voltage changes (drops or rises) quickly close to the earth contact and stabilizes far away towards the neutral earth potential.
According to the shape of the relation "voltage versus distance' this effect is called the potential funnel (or potential well, potential trough).
To transmit electrical energy through the ground, we are only interested in a small voltage drop at the earth contact (apply the first conclusion). For protection, however, we have to consider the shape of the potential funnel too.
Is the potential varying strongly at short ranges, it is possible to have dangerous voltages (this is the same as potential differences) over let's say one meter distance. These voltages are called step and contact voltage. Simply making a step or touching two things a short distance apart might cause death. For instance animals and people dying through lightning during thunderstorms are normally not directly struck, but get lethal voltages in the potential funnel of a nearby hitting lightning!
Fig 6 Step and contact voltage in a
potential funnel
Besides reaching low earth resistances, it is needed to shape the potential funnel to avoid accidents!
The specific resistance d of the soil is one of the key parameters for the resistance of an earth contact. It is a function of the chemical composition, the humidity and the temperature and may vary widely. The specific resistance is given in Ohm meter [Wm]. Extensive research in Switzerland has revealed the following relations:
Fig 7 Specific resistance for
different types of soil.
Fig 8 Relative varintion of the
specific resistance d as a junction of season.
Soil has a negative temperature coefficient of about a = 0.023 - 0.037, so the resistance inversely follows the temperature, showing a marked maximum in winter and minimum in summer (European climate!).
Also the water content of soil changes the specific resistivity. Generally the higher the content the lower the resistance, so any measurements to determine the earth resistance should take place only days after heavy rains, not during monsoon or at high ground water level. Frost increases the resistance considerably, so dig-in-the-earth contact is recommended for such zones.
To measure the specific earth resistance, special measurement tools are available. Their basic principle is to inject through two probes a current into the ground and to sense with another one (or two) probe(s) the potential at the surface.
This is very much the same approach as is used to determine the resistance distribution of the earth contact, so we will briefly explain this first.
The normal tool for the measurement is a bridge (see Fig 9). An AC current, produced by a hand-driven generator, is injected through the earth contact (1) and the auxiliary probe (2) (the distance between these two should not be less than 20 to 40m to ensure the auxiliary probe to be outside of the potential funnel). An identical current, produced with a 1:1 current transformer, is passing through the internal resistor R.
FIGURE
TABLE
Fig 9 Bridge method to measure the
resistance distribution in the ground and to determine the potential at the
surface.
The sensing probe S is placed at the position where we need to know the voltage drop/resistance. The variable resistor r is adjusted until the bridge is balanced (V = 0). Now the variable resistor equals the resistance distribution at S and the Voltage U equals the voltage drop to the earth contact. One major advantage of this method is the currentless sensing probe. With no measuring current in (S) in the balanced bridge, no distortion of the results will happen.
To know the potential funnel around an earth contact, several measurements are made along straight lines at pre-fixed distances. It is convenient to indicate the relative resistance along the measuring direction (e.g. it(r) relative to R(¥), the resistance very far away or the earth resistance RE) The plot 'R(r) [%] versus distance' is proportional to the earth potential U [%] and the step and contact voltage (Us & Uc respectively) are easily extracted.
Fig 10 Measuring principle to
collect a potential distribution at the surface for a ribbon earth contact (Cu
30/3mm x 4m; depth 0.2m).
Uc is the voltage between the earth contact and the ground surface (contact voltage). Us is the step voltage between two neighboring points I m apart. The maximum of Us is at the place where the resistance curve is at the steepest.
The specific resistance d of the soil is proportional to the resistance measured above. The proportionality factor depends on the geometry of the earth contact and the probes and is given in tables.
The depth and earth contact is dug-in and influences the earth resistance. Norm ally the less it IS covered by soil the higher and steeper the potential funnel is.
Fig 11 Influence of the dig-in depth
on the earth resistance.
The closer the surface, the higher the resistance. For t =
¥ the value is the same as in the previous formula.
A rod or stick earth
contact is even more sensitive to the depth it is driven in.
Fig 12 Comparison of the earth
resistance of a sphere and stick earth contact as a function of the depth t.
The calculation is done according to the above formulas {3}and {4}. The sphere diameter r0 is 0.5m, the rod diameter is 0.05m and p is 100 Qm.
By varying the dig-in depth, we can also widely vary the shape of the resistance curve and so shape the step and contact voltages of any earth contact.
If the earth contact reaches the surface, the contact voltage is very low, but the distribution is steep and consequently the step voltage high. Digging in the earth contact deeply smooths the distribution, lowers the step voltage, but increases the contact voltage.
Fig 13 Resistance (voltage)
distribution at the surface in case of a vertically dug-in plate t5(500/500mm)
at two different depths.
To avoid distortions, the electrical connections are done with isolated cables.
It is useful to distinguish between two types of earth contacts, the artificial and the natural earth contacts: the first is especially designed and installed, the latter is already existing, conducting structures like water supplies, cables and foundations.
5.1. Artificial Earth Contacts
Formerly metal sheets were used, but nowadays metal ribbons are standard. They are readily available, easy to transport and very flexible in installation.
There are three prominent forms to dig them in: straight, as a ring or a cross. Other forms are of course possible. The first might be the simplest and during construction any adequate straight ditch could be used. With the second it is easily possible to adjust the shape of the potential funnel around the earth contact by digging in several different ribbon rings, varying their dimensions and dig-in depth and connect them in parallel. The last is adequate for high impulse voltages (lightning), as under this condition the earth resistance increases considerably due to high frequency components.
If there is a better conducting strata at some depth, stick earth contact can be used. They offer also under 'normal' conditions several advantages: no digging necessary stable resistance top pan is easy to insulate to decrease step voltage
Zinc coated steel tubes are simply driven in with a (motor driven) hammer. Several tubes can be connected in series to reach the necessary length.
Fig 14 Using the reinforcement steel
matt as earth contact.
5.2. Natural Earth Contacts
The most common natural earth contact is the water supply system, as soon as it reaches extensions of several hundred meters. The earth resistance might then be as low as 0.5 W. In modem water supply grids, however, the pipes or their connections might be made of PE or similar plastic materials. In this case the water supply grid cannot be used. If available, the armour of any dug-in cable could be used as a substitute. It is important not to exceed current densities of 10A/mm2 in lead armours for more than 0.5 seconds to avoid dangerous temperature increases. In modem earthing systems, the armour steel of reinforced concrete foundations is always used as earth contact. The steel needs a cross-section of at least 50 mm2 per bar. Longitudinal bars are electrically connected as well as junctions, corners and dilatation gaps. Contacts for potential equalization and lightning protection have to be provided. Even if no reinforced concrete is used, the foundation can be used as an earth contact. In this case a steel wire (100 mm2) or a steel ribbon is integrated into the foundation.
5.3. Contact Materials
The chemical disintegration of the earth contact is a complicated process. The dug in material is corroding by itself. Then it is electrically connected to other materials, which together with some electrolyte (the soil) form a battery and destroy the earth contact. This effect can be accentuated by stray DC currents in the soil or DC components in the earth current. Tests have shown that materials like stainless steel and lead are not reliable. Galvanized (zinc coated) iron ribbons are useful except in connection with for instance copper, but also ungalvanized steel constructions, cast iron and concrete Armour can quickly destroy the zinc layer. Avoiding thicknesses below 2.5 mm still ascertains alife-span of several decades. Copperis an excellent but expensive altemative, however, it is aggressively corroding less precious metals in the same earth circuit.
Any current injected into the soil will cause an increase of the temperature due to the earth resistance. Close to the earth contact this temperature might change considerably as the resistance peaks at the earth contact surface. As we have seen before, the temperature coefficient of the earth resistance is negative, and in the first moment the resistance will drop (about 10-15%). If the heat produced is not able to dissipate into the soil, the earth might reach temperatures of 100°C and all water starts to evaporate. Soon the soil will be completely dry and the earth resistance will rise abruptly ten to twenty fold. To avoid any such problems it is advisable to keep the power dissipation below 5 kW per square meter earth contact surface.
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