• Punctual Ground Connection (PGC):  A ground connection installation consisting of simple or mixed electrodes, usually concentrated symmetrics and reduced coverage area in the soil.  The purpose of a PGC is to supply the zero referential potential additionally to protecting persons.

• GCR Measurement Current:  It determines the measurement range and efficiency of the soil’s electric parameters.  Portable measurement instruments inject up to dozens of miliamperes (short range); and autonomous measurement systems, dozens of amperes (long range).

• GCR Measurement Potential: It appears in the soil when the measurement current flows.  Its magnitude is the difference between the potential obtained by the GC and the zero potential of the Remote Earth, located in an intermediate point of the soil surface accomplishing said electric condition.

• Ground Connection Resistance (GCR): It corresponds to the resistance opposed by a GCE and the surrounding soil to the passage of a measurement current that is collected in another point of the soil sufficiently far away and in the presence of a net d.d.p. with respect to the Remote Earth represented by an intermediate point.

• Maximum Dispersion Potential (MDP): It is the maximum voltage a GC may obtain with respect to the zero referential potential of the Remote Earth each time it disperses a fault current disperses into the soil of the system’s Earth.  Its magnitude is limited strictly to 5 Kw.

• Earth-return Circuit: It allows system or fault currents return to the own source.  It is formed by the GCE or the Earth Fault point, then the soil and subsoil or other conductor mean, and finally the GC from the source or the Parasite Capacitances Phases (sound)-Earth.

• Final User Grounding: It is the only connection for the low tension of a user.  It consists of an exclusive conductor, which departing from the output terminal of the Distribution Board, descends with the minimum run towards the GC to which it connects soundly.

• Inner System of the Grounding: It develops upstream of the steady loads or the socket from the final user’s installation.  It consists of the Earth Conductors (protection) converging on the Distribution Board’s equipotential bar together with the Phase Conductors.

• Down-to-Earth Circuit Charge: It consists of the Parasite Capacitances from the entire down-to-earth connection system shown when a GCR is measured capturing the electric charge supplied by the instrument’s source producing a lower d.d.p. which leads to low erroneous values.

The measurement from the GCR soil surface of a bare metal electrode buried in intimate electric contact with the soil is related to the capability of said installation to allow the circulation of the measurement current injected directly, so after its passage through the soil it is collected in another known and sufficiently far point while measuring the potential difference with respect to a third simple intermediate point located at a specified distance.

Fig 1.- Arrangement of Classic and Alternate GCR Measurements – Potential Drop Method

• Classic Measurement Scheme.  It is applied with the Potential electrode (b) located over the same Current electrode directrix (c) or instead making with it any angle of up to 90º.  The results of said display are very reliable when measuring PGCs with portable instruments which measurement current is of up to tenths of miliamperes.
• Alternate Measurement Scheme.  It is applied with the Potential electrode (b) making an angle from over 90º to 180º with the extension of the Current electrode directrix (c). The results of said display are very reliable when measuring wide-range GCs with currents of tenths of amperes which otherwise may cause coupling inaccuracies.

Impedance is the ohmic parameter characterizing GCs. However, they are usually interpreted as DRs given the practical difficulty of reducing the resistive component and due to the fact that currents at a Commercial Frequency are involved during faults to earth, especially in the case of PGCs.

a.- Electric Scheme of GCs

It is important to remember that the assemblies of GCEs to be run by currents evacuating through the soil have an electric configuration, where the Resistance (which depends on the Resistivities of the electrode, the filling and the soil itself), the Inductance (which depends on the length of the buried conductor) and the Capacitance (which depends on the form of the electrode’s assembly) are present (Fig 2).  These components form an intermediate Impedance between the connection point of the electric installation and the Remote Earth where the Potential and the Resistance or Impedance is zero by definition.

Fig 2.- Electric Representation and Performance of a GCE installed

b.- Current Dispersion in the Soil

Current dispersion in the soil occur through the Ground Connection Impedance (GCI), a parameter expressed in Ohms, as a pure Resistance, where the passage of the current injected causes three tension drops before reaching the Remote Earth: in the electrode itself (with an insignificant value), in the filling (with a low value) and in the natural soil (its value depends on the bedded soil Resistivity).  Thus, the GC disperser performance will be subject to the Current type and rate.

• Direct Current Dispersion.  A non-variable magnitude parameter according to the time and the steady rate in which dispersion only participates the resistive component, due to which it does not impose length restrictions or form of buried electrode. 

• Alternating Current Dispersion.  Periodic and steady-rate variable magnitude parameters in which dispersion prevails the resistive component and participating in lesser degree the inductive component and very few the capacitive component.  Length restrictions and the electrode’s form are minimal.

• Oscillating Current Dispersion.  Non-periodic and transitory rate variable magnitude parameters (Rays, Maneuvers) in which dispersion the inductive component prevails initially, restricting the passage of current with a quenching  rate that depends on the Circuit Time constant (L/R).  Therefore, they demand small lengths of buried conductor and the presence of the capacitive component if possible.

GCs disperser performance could be interpreted approximately from the conventional measurements of the low-frequency DR where every magnitude (R > 1 ohm) will indicate a resistive performance, while the inductive character of the Impedance will prevail when (R < 0.5 ohm).

c.- Equivalent Electric Radius of a GC

According to the parameters derived from the current in the soil explained in the First Part (ELECTROREDES 2002-I, Title 6), the injected current is dispersed in the entire volume of the uniform Resistivity (r) soil, rapidly shaping a series of hemispheres with decreasing current densities when increasing the separation distance.  Said concept allows considering that every GCE, especially those with regular geometry, may be represented in its bed as from a radius (r0) equivalent conductor hemisphere, which may be inferred considering the expressions of its Absolute Resistance (R0) and Dispersion Resistance (RT) determined analytically.

Fig 3.- Scheme of the Equivalent Electric Radius of a Vertical GC

Whether it would be the case of a vertical electrode with a length (I) and diameter (d), buried in a well of identical length and medium diameter (dp) in a Uniform Resistivity ® soil, the following expressions will be obtained:

Absolute Resistance : 

Dispersion Resistance: 

Making equal R0 = RT , and clearing (r0), resulting in 

Equivalent Electric Radius:

There are several methods based on the measurement of an injected current and the corresponding d.d.p. between the GC and a reference point.  These values are processed with the Ohm’s Law to obtain the DR.  It is worth mentioning that only the Classic Method is of unlimited application to any GC installation for any type of soil.

a.- Indirect Method or Three-Point Method

Applicable especially for PGCs in low-Resistivity soils (Fig 4).  It is necessary to form a triangle on the ground using two measurement electrodes which DRs are called (R2 and R3) and should be separated to each other, and the GC at greater distances (=50 r0).  The, the GCE shall have a DR (R1), which is looked for.

Fig 4.- GCR Measurement Connections Display – Three-Point Indirect Method

GCR Determination in the Electrode (R1)

The procedure consists of determining the Total Resistance of the pair combinations from the Original Resistances without considering the Mutual Resistances that would appear significantly in case of failing to comply the condition of having a big separation between the measurement points.  The solution in the form of simultaneous equations allow to obtain the DR (R1).

First measurement: R12 = R1 + R2

Second Measurement:        R13 = R1 + R3

Third Measurement: R23 = R2 + R3

Application of Three-Point Methods

Notwithstanding the simplicity of the Method, it should be mentioned that when the measurement electrodes show a much higher Resistance than that of the GC –which frequently occurs—the errors of the individual measurements will be reflected conclusively in the final result, making it not reliable.

b.- Classic Method of Potential Drop

This method needs to use two auxiliary measurement electrodes very distant from the GC (Fig 5).  One electrode will close the current circuit remaining effectively out of the GC’s influence, and therefore its contact interface with the soil should have low Resistance.  The other electrode dedicated to the Potential circuit measuring the tension drop until the zero Potential point which represents the Remote Earth.  In this case, the requirement of the electrode’s contact with the soil is minimal (< 3000 w), nevertheless the density of current lines in said place should be very low.

Fig 5.- Classic Arrangement of GCR Measurements

The measurement consists of making flow a Current (I) generated by a source between the GCE (a) and the farthest electrode with which the Current circuit (a, c) closes, recording the Tension drop (V) between the GC and the nearest electrode, which corresponds to the Potential circuit (a, b) so said Potential circuit would be placed in the point identified by its zero Potential.

Determination of the Electrode’s GCR (Raa)

The method is based on the measurement of the Resistance existing between every two electrodes driven into the ground in the points (a, b, c), each with a proper DR (Raa, Rbb and Rcc), considering that keeping the current (I) with the same value, mutual Resistances are produced in both electrodes (Fig 6).  For example, (Rab and Rba) result from measuring the Resistance between electrodes (a, b).

Fig 6.- Scheme of the Principle – Total Resistance Measurement between two points in the Soil

Following the same procedure between points (a-c) and (b-c) of (Fig 5), adding and then subtracting, it gives the following result: 

As electrode 8b) is connected to a high-Impedance voltmeter, it may be concluded there would not flow any current through said measurement point.  Therefore, replacing

resulting in

According to the above, the DR (Raa) will be obtained when the result of the equation in parenthesis is zero.

Determination of Measurement Circuit Distances

Considering an homogeneous soil with unique Resistivity (r), the condition established to determine (Raa) is analyzed considering that the potentials between every two points vary inversely proportional to their distances.  Then, if

R_aa + R_ac - R_bc = 0 may be interpreted as

Resulting in a second-degree equation, which positive root solution allows establishing the general relationship of the measurement distances of current circuits (d) and Potential (p)

p = 0,618 x d p.u.

Therefore, the Potential electrode (b) should have to be placed exactly at distance (p) to represent the zero value of the Remote Earth (Fig 7) given that in other point even inside of the same trajectory would represent a potential other than zero that would be subtracted or added to the measurement.

Fig 7.- Measurement Currents and Potentials for the Classic Method of Potential Drop

Subtracted Potential: It occurs when the electrode (b) is placed nearer to GC (a) resulting in measurements (optimistic) of lesser Resistance than the actual resistance.

Aggregate Potential: It occurs when the electrode (b) is placed nearer to Current electrode (c), resulting in measurements (pessimistic) of greater Resistance than the actual resistance.

Application of the Classic Method of Potential Drop - Approximate

The measurement method described for homogeneous soil imposes a display of measurement distances (d, p) proper for each GC which depends on its coverage.  In every case, the results will also depend on the correct relation of said distances and the location and good contact with the soil of the measurement electrodes placed at the end of the straight trajectories starting from the GC, whether it would be on the same direction or divergent making an angle lower than 90º.

Application of the Classic Method of Potential Drop - Accurate

The principle and basic implementation conditions of Measurements are identical to the approximate procedure.  The difference is established when considering the case where the soil bedding –which is actually for electric use—corresponds in most cases to a two-stratum scheme.  This means that the relation of distances (p and d) will be different every time depending on the Resistivities of said strata, and therefore, each accurate measurement shall need a new relation of distances (p/d) for the exact location of point (b) of zero Potential.  There are two procedure somewhat laborious.

a.- Point-by-Point Measurements (Fig 8)

In cases with soils with thick superficial strata and especially with much contrast of Resistivities, or when establishing analytically and exactly the DR’s value of a GC, considering the soil’s conformation, it is decided to first determine a characteristic of points with apparent value measured on the soil.

Fig 8.- Characteristics of Apparent GCR Measurement Points

Distance (d) is divided into 10 equal segments for the progression of the set of measurements of (r) with the corresponding distance (p), the points obtained are (R against p), drawing the curve with a mathematic regression and determining the Conic or Nonstop Function f(p).

DR’s exact value (RT) is determined in the projection of the Conic Inflection Point in the Axis of Ordinates after having been located with the abscissa value resulting when f’’(p) = 0, or when f’’(p) is not defined.  The difference with the approximate Measurement may be seen projecting also the abscissa (p=0.618 d) in the Axis of Ordinates; usually there is a minimum difference.

b.- One-Point Measurement

Considering that the soil Resistivities in the two-strata model have influence in the injected current (I) based on its Reflection Coefficient (K), the soil parameters in the two-strata model (r1, r2, h1) should be included.

Based on the conditions (d > 20 r0 y h1 > 5 r0), the equation of the Classic Measurement Method Potentials is solved considering the relations of the measurement distance (d) with the distance of the Potential electrode (p/d) and the thickness of the superficial stratum (h1/d) having the reflection coefficient (k) as a family-curve parameter.

For the accurate measurement, having determined 8d) from (r0), distance (p) should be determined reaching abscissas with the relation (h1/d) intercepting the curve with reflection factor (k) from where it projects to the ordinates in order to obtain the relation (p/d) with which the unique measurement is executed.

4. CONDITIONS FOR MEAUREMENT ACCURACY

The random form of the bedded soil composition as well as the characteristics and coverage of the GC installations to be measured under the same procedure indicate that the range of Resistances may be wide and as such could be inclined to errors or distortions prompted by several sources participating in the measurement process.

The Measurement Current

The need to use the supply source of a portable instrument or a power unit is related to the coverage of the GCE.  The classic comparator instruments (tellurometers, geometers) that usually have minimal ranges, are used to measure PGCs, free of any down-to-earth connection, while the autonomous power sources ranging KW are used for extended groundings. 

The measurement current must flow exclusively through the circuit including GCE (a) with the auxiliary current electrode (c), i.e. the GC must be totally free of any other connection representing an unsustainable consumption of energy due to the capacity of the source, As in the case of the “down-to-earth” connection (Fig 9) from the mass clamps or the panel’s equipotential bar, which circuits include parasite Capacitances to Earth creating additional tension drops recorded by the instrument in giving lower values to that of the currently existing Resistance.

Fig 9.- Scheme of a GCR Measurement including the down-to-earth circuit for connection

On the other side, considering the passage of erratic currents from the system through the soil at a commercial frequency, it is not advisable to use the same low service frequency for the measurements.  It would be better to use a higher or lower non-harmonic frequency from FI, or instead, a direct current with a switching device during the measurement process in order to prevent soil polarization.

Measurement Circuits

The accuracy of measurements depends on the distance (d) established for the Current circuit in relation to the GC coverage represented by its Equivalent Electric Radius (r0), according to which if the range of the portable instrument’s wiring according to Catalogue is lower than said required distance (d) then the measurements will increase even more the error giving always lesser Resistances than the actual ones.

For an Equivalent Electric Radius GC (r0) in Fig 10, each curve of points (r against p) correspond to a distance also fixed (d).  It is then noted that the results carry less errors each time greater distances (d) are taken.

Fig 10.- Measurement Characteristics based on the Distance Error Parameter (d)

After establishing the corresponding margins of error, the correlation of both fixed parameters (d/r0) allow identifying the ratio for the range considered admissible, which as a logarithmic variation magnitude where several random factors participate during the field measures may be:

Error = 3.3 %, when

Therefore, Standard IEEE-81 recommends for (d) a minimum of 50 m (d « 125 r0), and the IEC Rule a minimum of 40 m (d « 100 r0) to guarantee a greater accuracy.  However, it is difficult to comply with the conventional portable instruments with lower range.

In practice, when measuring in PGCs, the acceptable error could be of up to (5%), which takes to establish a minimum measurement distance applicable on the soil with portable instruments.

The potential difference between the GCE and the Remote Earth (V=0) representative point must be established correctly from the measurement circuit, i.e., the GC coverage should not have influence on the measurement electrode used as potential probe (the current lines should not be closed through said electrode).

a.  The application of the Principle of Potential Drop to the GCR measurement of punctual electrodes installed have been basically analyzed considering the representative location of the Remote Earth within the measurement scheme.

b.  The most common measurement methods for GCRs have been described emphasizing the interpretation guidelines and application of the Classic Method of Potential Drop due to the greater approximation or accuracy that may be obtained based on either parameter electrical and/or physical applied in the measurement.

c.  We have shown that for GCR reliable measurements in any type of bedded soil, the modality of the Classic Method of Potential Drop – Approximate, is the most advisable due to its simplicity, good resolution and minimal error.

Engineer Justo YANQUE M.