Soil Resistivity Measurement: Two-Layer Model, Proposed Revisions to IEEE Standard 80-2000 and IEEE Standard 81-1983 P Calixto Author Affiliation: Electrical Department of ABB Lummus Global B.V., The Netherlands Abstract: Some simplification to Sunde's procedure, shown in IEEE Standard 80-2000 13.4.2.2, two-layer soil model by graphical method is proposed, with the introduction of a modified Sunde's curve. Comments on Appendix B of IEEE Standard 81-1983 are offered to correct some formula and improve concepts. Keywords: Soil resistivity measurement, two-layer model. Introduction: IEEE Standard 80-2000 offers a graphical method for determining a two-layer model. Sunde's curves are used, for exam- ple, for soil type 1 (Table E2 in Annex E). The Sunde's curve can be re- placed by a table (or a graph, if a graphical solution is desired) where the apparent resistivity is represented by (pa / pl) = (p2 / pl/'m with m varying from 0.1 to 0.9. This will limit the representation to the range of useful values of(pa / pl), for the determination of the layer depth h. If a graphical method is to be used, the ordinate will then be m in uniform scale versus a/H in logarithmic scale, with parameters (p2 / pl). The ta- ble (see Table 1) has the advantage of facilitating interpolation and be- ing more accurate. The set of pl, p2 and H calculated in this manner can be used for more sophisticated calculations such as the steepest descent method, described in IEEE Standard 81-1983, Appendix B. For this, the formu- las of Equations B8 have to be corrected. Modified Sunde's Method: The parameters pl and p2 are obtained by inspection of resistivity measurements. Only h is obtained by Sunde's method as follows: a) Plot a graph of apparent resistivity pa on the y-axis versus pin spacing on the x-axis. b) Estimate pl and p2 from the graph plotted in a). The pa corre- sponding to a smaller spacing is pl and the larger spacing is p2. Extend the apparent resistivity graph at both ends to obtain these extreme resis- tivity values if the field data is insufficient. c) Determine p2 / pl from Table 1 and read the corresponding value for (a/h), or interpolate them if the ratio (p2 / pl)is not shown. The most - .., 5.89 5 3 5 34 5.10 - 494 4.79 4.50 4.37 4.24 4.17 4.12 4.18 4.32 4.48 4.68 4.87 5.06 0.81 0.9 m+>p2/pl= 0.001 0.002 0.003 0 005 0.007 0.01 0.02 0.03 0.05 0.07 0.1 0.2 0.3 0.4 0.5 0.6 07 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 06 1.7 1.8 1.9 2 3 -5 7 10 15 20 30 40 50 1.00 1.62 1248 1.65 60 70 [ 1.04 1.71 2.71 4.27 6.81 11.1 80 11.05 1.75 2.81 4.48 7.22 11.9 1.79 90 100 1.08 [1.83 2.99 .48 i 7.98 13.4 120 1.10 1.90 3.14 5.18 8.66 14.8 170 [1.14 2.04 13.46 Js 5.90 110.2 117.9 132.7 64.6 150 200 300 [1.21 2.28 14.07 J 7.30 113.2 j24.5 47.1 97.1 400 56 306~~~~~~~~~~~~~~~ 2.52-i-1- -- I-. . -- 500 IEEE Power Engineering Review, April 2002 0.98 1.02 1.06 1.12 1.16 1.25 1.28 1.04 1.05 1.07 1.12 1.17 1.23 1.31 1.7 1.86 1.38 1.98 1.48 1.56 2.11 2.41 2.18 2.34 2.60 2.90 3.63 4.42 4.72 4.04 4.67 5.63 6.27 8.15 8.88 6.36 7.61 9.59 11.0 15.2 16.9 12.7 16.7 19.6 28.8 32.7 36.3 59.1 72.5 120 141 Table 1. Modified Sunde curve 600 1.30 2.61 4.97 9.53 18.4 36.3 73.8 161 426 700 1.33 2.69 5.20 10.1 19.8 39.6 81.6 181 483 800 1.34 2.76 5.41 10.7 21.2 42.7 89.1 200 540 900 1.36 2.82 5.60 11.6 22.4 45.7 096.4 219 594 1000 11.38 2.88 15.78 . _111.6 23.6 148.6 103 237 649 l-- --T i, -.-- -.-, - -- . .. 1.99 3.34 730.3 400 F56.7 7306 2.52 675.5 368 66 0272-17241021$17.00(02002 IEEE
Transcript
Soil Resistivity Measurement:Two-Layer Model, Proposed Revisions to IEEEStandard 80-2000 and IEEE Standard 81-1983
P Calixto
Author Affiliation: Electrical Department of ABB LummusGlobal B.V., The Netherlands
Abstract: Some simplification to Sunde's procedure, shown inIEEE Standard 80-2000 13.4.2.2, two-layer soil model by graphicalmethod is proposed, with the introduction of a modified Sunde's curve.
Comments on Appendix B of IEEE Standard 81-1983 are offered tocorrect some formula and improve concepts.
Keywords: Soil resistivity measurement, two-layer model.Introduction: IEEE Standard 80-2000 offers a graphical method
for determining a two-layer model. Sunde's curves are used, for exam-ple, for soil type 1 (Table E2 in Annex E). The Sunde's curve can be re-
placed by a table (or a graph, if a graphical solution is desired) wherethe apparent resistivity is represented by (pa / pl) = (p2 / pl/'m with mvarying from 0.1 to 0.9. This will limit the representation to the range of
useful values of(pa / pl), for the determination of the layer depth h. If agraphical method is to be used, the ordinate will then be m in uniformscale versus a/H in logarithmic scale, with parameters (p2 / pl). The ta-ble (see Table 1) has the advantage of facilitating interpolation and be-ing more accurate.
The set of pl, p2 and H calculated in this manner can be used formore sophisticated calculations such as the steepest descent method,described in IEEE Standard 81-1983, Appendix B. For this, the formu-las of Equations B8 have to be corrected.
Modified Sunde's Method: The parameters pl and p2 are obtainedby inspection of resistivity measurements. Only h is obtained bySunde's method as follows:
a) Plot a graph of apparent resistivity pa on the y-axis versus pinspacing on the x-axis.
b) Estimate pl and p2 from the graph plotted in a). The pa corre-
sponding to a smaller spacing is pl and the larger spacing is p2. Extendthe apparent resistivity graph at both ends to obtain these extreme resis-tivity values if the field data is insufficient.
c) Determine p2 / pl from Table 1 and read the corresponding valuefor (a/h), or interpolate them if the ratio (p2 / pl)is not shown. The most
important values of a/h is m = 0.5, which corresponds to the inflexion ofSunde's curve, i.e., values most sensitive to h.
d) From the graph in a) read the probe spacing a corresponding to pa= (pl * p2), i.e., the geometric mean of pl and p2.
e) Divide the probe spacing a by a/h found in c; this will be depth ofthe upper layer h.
Using the soil data from soil type 1 in Table E.2 of Appendix E, aplot of resistivity versus spacing can be drawn. See Figure 22 of theStandard. Both p 1 and p2 can be determined by visual inspection. As-suming pl = 1002.m and p2 = 300Q.m, the following example illus-trates the modified Sunde's graphical method:
a) Plot Figure 22.b) Choose pl = 100l.m and p2 = 300Q2.m.c) p2/pl=300/100 = 3. Read in Table 1 the corresponding value for
m = 0.5, a/h = 2.25.d) Read the probe spacing corresponding to (100+*300) = 173
Q.m, h = 13.8 m.e) The depth of upper layer is 13.8/2.25 = 6.13 m or 20.1 ft.
This compares favorably with the 6.1 m (20 ft.) using EPRI TR-100622[B63].
Extended Calculation with Modified Sunde's Method: Insteadof using only m = 0.5 in Table 1, it is possible to use all values from 0.1up to 0.9. The result will give a more thorough examination of the mea-sured resistivity to locate possible irregularities. Table 2 exemplifies theapplication of this method via spreadsheet, the graphic was replaced bylogarithmic interpolation, i.e., y = yl *(y2/yl)A(ln(x/xl)/ln(x2/xl)). Thesoil 2 is shown as well.
Steepest Descent Method: This method is described by IEEE Stan-dard 81-1983, Appendix B. All three parameters pl, p2, and h can becalculated, starting with assumed initial values that can be obtained asdescribed above. Table 3 shows the results of this method for soils type1 and 2.
The following comments apply:Equations (1) and (2) should be used for only one average value of
apparent resistivity (N = 1). The equations imply harmonic mean of themeasured values. It is more common practice to use arithmetic or geo-metric mean (harmonic mean is the smallest of all three). The decisionon what average to be used is left then to the engineer.
The convergence factors (t, y, and y ) should be more clearly de-fined; presently they are implied to be 0.005/(68/6p).
We need to obtain the (6P/6p) value for the next iteration, based onits value on the previous iteration. The expression for the derivatives(Eq. B8) should be corrected as follows:
For 6p / 5p2 the term (1I-KA2) should read (1-K)A2.For 5p / h the term in the summation (KAn) should read (nA2*KAn).The signs of(t, ¢r, and y) should be reversed sometimes to reach con-
vergence, minus to decrease the initial value and plus to increase it.References:[ 1 ] IEEE Guidefor Safety in AC Substation Grounding, IEEE Stan-
Copyright Statement: ISSN 0282-1724/02/$17.00 ( 2002 IEEE.Manuscript received 12 August 2001. This paper is published herein inits entirety.
A New Method for Determining ReferenceCompensating Currents of Three-PhaseShunt Active Power Filters
Gary W ChangAuthor Affiliation: Department of Electrical Engineering, Na-
tional Chung Cheng University, Taiwan.Abstract: Using a shunt active power filter (SAPF) has been proved
as an effective method to compensate reactive power and to mitigateharmonic currents of nonlinear loads. When designing a SAPF, it iscrucial to generate reference currents for determining actual compen-sating current injections to the point ofcommon coupling. In contrast tothe conventional instantaneous reactive power theory, which needs co-ordinate transformations, the new method proposed in this letter is todetermine reference compensating currents based on the balance of theinstantaneous reactive and active power generated in the SAPF. It isshown that the proposed method is suitable for reactive and harmonicpower compensation by using a SAPF. In addition, to maintain the sinu-soidal source currents this method also eliminates the need for install-ing energy storage devices for reactive power compensation as well asthe dc source for the harmonic compensation in the active power filter.Therefore, a simpler design of the SAPF with minimal line losses canbe expected.
Keywords: Active power filter, reference compensating current, in-stantaneous reactive power theory, coordinate transformation, instanta-neous power balance.
Introduction: The concept of using the SAPF for reactive and har-monic power compensation was introduced more than two decadesago. By measuring load currents and voltages, the SAPF can injectcompensating currents as well as absorb or generate reactive power atthe point of common coupling for controlling harmonics and compen-sating reactive power of the connected load.
In 1983, Akagi et al. proposed an innovative approach based on in-stantaneous reactive power theory (i.e., p - q theory) to compute SAPFreference compensating currents. This approach inspired the develop-ment of many other p - q theory-based methods for realizing the SAPF[I],[2]. Willems indicated that the p - q theory is complete only inthree-phase systems without zero-sequence component, however [3].Also, the instantaneous reactive power theory-based method requirescoordinate transformations between the a - b - c coordinates and thep - q coordinates, which increases the complexity of designing theSAPF controller. More recently, Peng et al. proposed a theory that gavea generalized definition of the instantaneous reactive power in thea - b - c coordinate [4]. Although Peng's approach does not need thecoordinate transformation, it requires an additional function for instan-taneous reactive power vector calculation in the SAPF controller.Based on the instantaneous reactive power space vector defined in [4]
Figure 1. Schematic diagram of the three-phase SAPF compensation
IEEE Power Engineering Review, April 2002
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