1999 IEEElASME JOINT RAILROAD CONFERENCEDallas, Texas DESIGN OF GROUNDING SYSTEMS FOR TRI-MET PORTLAND WESTSIDE LIGHT RAIL TRACTION POWER SUBSTATIONS Ralph S. Thomas, P.E. LTK Engineering Services Portland, Oregon Abstract : 9 Kinh D. Pham, P.E. Elcon Associates, Inc. Portland, Oregon Power rectifiers Dc switchgear and negative cubicle Auxiliary ac and dc power system The Westside and Hillsboro Light Rail extensions in Portland, Oregon were open for revenue service in September, 1998. The 18mile extensions extend the existing Eastside line rail service from downtown Portland to downtown Hillsboro. The alignment includes atgrade street crossings, street-running operation, several fully grade separated sections and a 3mile tunnel. Primary power is provided by the utilities at 12.5 kV and rectified by 18 mainline traction power substations to deliver 750 dc power to the light rail vehicles. Each substation has three separate grounding systems: a) an ac ground mat designed per IEEE Std 80-1986 for safe step and touch potentials, b) a dc ground mat for dc surge arrestor ground; the dc switchgear enclosure is connected to the dc ground mat through a low-resistance grounding scheme, c) an isolated ground rod for the utility incoming shields. This paper provides a detailed technical description including grounding calculations for each grounding system. Test and measurement data obtained for the installed grounding systems are presented and discussed. 1.O Introduction Each traction power substation consists of the following major components: 15 KV medium voltage switchgear Rectifier transformers The 15 kV medium voltage switchgear interfaces between the utility power company (Portland General Electric) and the transformerrectifier unit. Instantaneous and time delay overcurrent protection together with negative sequence and undervoltage relays and instrumentation meters are provided inside the switchgear. The three winding traction power transformer with two secondary windings is coupled with the power rectifier to provide a nominal dc output voltage of 750 Vdc. Primary windings are connected in delta. The two secondary windings are connected in delta and wye with 30 degree phase shift to obtain twelvepulse rectification (ANSI ckt no. 31). Transformer winding temperature devices are furnished with the traction power transformer; rectifier diode temperature and monitoring devices are furnished with the power rectifiers. Dc output of the power rectifiers delivers power to the light rail vehicles through the 1000 Vdc rated switchgear assemblies and via the overhead contact system and negative return rails. Protective relays associated with the dc switchgear include reverse current trip device, over-current trip and rate-of-rise relays, reclosing and load measuring devices, transfer trip and dc switchgear enclosure fault detection. The traction power substation single-line diagram is shown in Figure One. Page 1 0-7803-5533-4/99/S10.00 0 1999 IEEE 55 Authorized licensed use limited to: Walt Disney World Co - (IBM Journal Only). Downloaded on June 03,2010 at 21:27:09 UTC from IEEE Xplore. Restrictions apply. it is necessary to install a grounding system for effectively connecting the 15 kV ac switchgear. The grounding system provides a means to safely discharge lightning strokes to earth. Potential gradient: The change in voltage per unit distance.2010 at 21:27:09 UTC from IEEE Xplore. switching or in-rush currents caused by normal system operations. including the earth.2 General Description Ground: A conducting connection. below the surface of the earth. Ground grid: A grounding electrode consisting of interconnected bare horizontal conductors and vertical rods buried in the earth to provide a common electrical bond between equipment. the grounding system assists in minimizing voltages between different points along. Downloaded on June 03. ground currents caused by fault conditions. equipment. For the ac equipment. approximately equipotential surface consisting of conducting material. The passage of these currents through the soil and metallic conductors causes high voltages which can be dangerous to human life. Remote earth: A point where the cross-sectional area of the earth is sufficiently large that the potential gradient caused by a ground fault current is infinitesimally small. Ground mat: A small. the low voltage cables used for controls.(IBM Journal Only).0 Grounding of Ac equipment and the Ac Ground Mat Definitions 2. provides low impedance paths through the earth for load currents. and provides a common ground reference which assists in the coordination of insulation throughout the system. The potential differences can be the result of lightning discharges. and malfunction of. Grounding system: The electrically interconnected components used for grounding. connected to a ground grid to provide protection from dangerous step and touch voltages. where an electric circuit. and auxiliary power. structures. the ground grid. or structure is connected to earth or to some conductor that.1 Step voltage: The voltage difference between two points on the surface of the earth separated by a distance. Ground fault current A current resulting from an unintentional electrical connection between an energized power conductor and the earth or the grounding system. and can cause damage to. Ground potential rise: The voltage difference between the grid and remote earth as developed by the ground fault current flow between the soil and the grid. and the earth. 2.2. is connected to earth. Restrictions apply. substation equipment. Ground grid resistance: The resistance (in ohms) between the grid and a remote grounding electrode of negligible resistance. intentional or accidental. reduce step and touch potentials to safe levels and confines dangerous soil currents to inaccessible areas. Touch voltage: The voltage difference between a grounded metallic object and a point on the surface of the earth at a distance equal to the normal maximum horizontal reach assumed to be one meter. It also allows the detection of ground fault currents by protective relaying systems. communications. the traction power transformer and other auxiliary ac equipment enclosures together and to earth in order to limit to safe values any potential difference between them and from them to earth. The ground grid is designed to maintain ground grid voltage rise and soil surface potential gradients within safe limits. The grounding system is also utilized to shield control cables and other low voltage wiring from the effects of electromagnetic interference (EMI) and capacitive coupling. . and between. By tending to reduce the voltages across the ac ground grid. and all electrically grounded objects in a substation. in the direction of maximum potential gradient. assumed to be one meter. in turn. Page 2 56 Authorized licensed use limited to: Walt Disney World Co . the second is more valid because magnitude of tolerable current flowing through the human body is taken into consideration [I]. transmission towers. Furthermore all this equipment is housed inside a grounded building. 2.942. b) In other E - touch tolerable dt * Page 3 57 Authorized licensed use limited to: Walt Disney World Co . 2. The design calculations do allow some factor of safety. it is a very conservative design to follow the IEEE Standard 80 to design ac ground mats for traction power substation ac equipment. breakers. 15 kV station service transformer. The finished surface covering the site. Hence. and installed vertically beneath the site usually reaching lower resistivity soil. The calculations of step and touch potentials are based on the IEEE Standard 801986. and that an excessive fault clearing time occurs.5 Design Calculations Two basic approaches to designing grounding systems are used worldwide: a) In some countries. With proper caution. etc. These include distribution. due to the improbability that a person will simultaneously be in a vulnerable location while walking. by errors in testing.5% of adults to withstand contacted voltages without suffering ventricular fibrillation.3 Human Factors The design calculations for grounding systems for ac . at the instant of fault occurrence.4 Ac Grounding System The ac grounding system consists of four major components. Downloaded on June 03.ps E step tolerable dt Tolerable touch voltage for a human body of 70 kg: 157 + 0.equipment are based on test statistics which will allow 99. faulty construction.(IBM Journal Only). but are considered tolerable. etc. are all exposed.2010 at 21:27:09 UTC from IEEE Xplore. The following is quoted from the IEEE standard 80-1986. transmission. It should be mentioned that the intent of the IEEE Standard 80 is to provide guidance and information pertinent to safe grounding practices in high voltage ac outdoor substation. Personal discomfort and inability to "let go" are uncommon. Restrictions apply. page 17. countries. A properly designed grounding system will reduce the probability essentially to zero. The probability of lethal shock due to ground fault current is relatively small. Tolerable step voltage for a human body of 70 kg: 157 + 0. The soil beneath and around the substation." In contrast to high voltage outdoor substations where most of the equipment such as buses. Ground rods connected to the ground grid. and dangerous conditions introduced.1 Maximum Tolerable Step and Touch Potentials The following equations are obtained from IEEE guide for safety in substation grounding Standard 80-1986 [l]. ac panelboards. either conventional or gas insulated. . are all enclosed and grounded. all equipment inside the traction power substations such as 15 KV switchgear.pS 2. a grounding system is considered adequate when the grounding resistance is lower than the recommended value."This guide is primarily concerned with outdoor substations. a grounding system is considered safe when step and touch potentials are lower than the permissible values. The ground grid cables embedded or buried beneath the substation site surface. but this could be lost. generating plant substations. the methods described herein also applicable to indoor portions of such substations.5. such as the USA. or lack of proper maintenance. or to substations that are wholly indoors.2. Of these two approaches. or standing and touching a grounded metallic object.236. and that the fault has caused a sufficiently large current flow. the ground fault current could be relatively low and the time it takes for the dc feeder breakers to clear the fault would be unduly long. The main reason is to minimize stray currents and corrosion effects on underground utilities such as gas. E mesh - Km . Hence. : Total length of ground grid conductors in meters. The following equations are obtained from IEEE Guide for safety in substation grounding Standard 80-1986 [5]. The negative bus is connected to the dc ground mat through a diode. A positive fault to the enclosure will cause the current to flow from the enclosure to ground through the low resistance relay (device no. 64) and energizes this relay which trips the ac and dc feeder breakers. The dc switchgear cubicles and power rectifiers are connected to the dc ground mat through a low resistance instantaneous over current relay as shown in the single-line diagram. Ki. p.2010 at 21:27:09 UTC from IEEE Xplore.2 Calculated Step and Touch Potentials After E-mesh and E-stepyof the grid are calculated. Restrictions apply. water pipes.0 Grounding o f Dc Switchgear Equipment and the Dc Ground Mat. High surface resistivity and fast fault clearing time will give high tolerable step and touch potentials. Tri-Met has adopted the low-resistance dc equipment enclosure grounding method. Downloaded on June 03. L Km : Mesh coefficient which takes into account spacing.5. The worst possible touch potential (called the mesh potential) occurs at or near the center of a grid mesh. This voltage relay is set to trip in the range of 60 volts to 90 volts. Ki' : Irregularity factor Modern rail transit systems within the United States are designed to keep the running rails insulated from ground. a voltage relay (device 164N)is connected between the negative bus and ground.(IBM Journal Only). Ks : Step coefficient which also takes into account the grid geometry. The return circuit back to the traction power substation would be closed via the earth to track if the substation negative bus is isolated. The diode grounding device will provide a return path from the ground to the substation Page 4 58 Authorized licensed use limited to: Walt Disney World Co . When there is a ground fault between the OCS and ground. 2. 3. Ki . I L Ks . Industrial practice has made the mesh potentials the standard criteria for determining safe ground grid design. This requires the power rectifier assemblies and dc switchgear enclosures be mounted on an insulating floor mat inside the substation and connected to ground through the low resistance grounding scheme. . they are compared to the values of the tolerable touch voltage (E touch tolerable) and tolerable step voltage (E-step tolerable) respectively to determine whether or not the designed grounding grid can be judged to be safe. I L E step Where: I - : Maximum ground fault current in amperes. This relay will trip the dc feeder breakers when the negative rail-to-earth potential becomes high to avoid a dangerous situation. diameter and depth of burial of the ground grid conductors.Where: ps : the surface resistivity in ohm-meters p : Soil resistivity in ohm-meters t : the duration of fault in seconds The surface resistivity and duration of fault are used to establish maximum tolerable step and touch potentials. p. the area in the vicinity of the fault could subject to a high voltage of 750 Vdc. In addition. etc. Tri-Met has retained LTK Engineering and Tice Electric Company to perform stray current testing and ground resistance tests at each substation. The grounding tests were based on the IEEE standard 81. . Stray current test data include average and peak values . As clearly illustrated in the field test measurements.O ohm x 3500 A = 3500 V). The Tri-Met test procedures required that the current reference ground rod must be driven at least 100 feet from the ground mats and the measurements were made at 10-foot intervals beginning 25 feet from the test electrode The test was performed on the ac and dc ground mats at the Elmonica Yard traction power substation.5 feet below grade. 4. the stray leakage currents are excessive at Tektronix and Washington Park substations where the ac and dc ground mats were inadvertently tied together. A digital ammeter was included in the circuit to read the test current. Three bare 410 pigtails for the ac mat and a single 4/0 insulated pigtail for the dc ground mat are available. The lug is then grounded to a single. the dc mat is 5 feet wide and 27 feet long. Tri-Met has implemented a stray current monitoring program and if excessive leakage currents are detected. A plot of ground resistance readings for each ground mat was provided to Tri-Met engineers for review.0 The grounded concentric shield which is integral with the 12. tests were required for the ac and dc ground mats at each traction power substation to determine the ground resistances. The ground mats are considered inadequately grounded if the flat portion of the plotted data shows greater than 5ohm resistance. After start revenue operation. and separation between ac and dc ground mats.(IBM Journal Only). Both ac and dc ground mats are buried about 2. Measures to mitigate excessive stray leakage currents are now under investigation and this problem will be corrected.5 kV. The reference point for the voltage measurements was a second driven rod approximately 500 feet to the east. 6. This isolation is required to minimize stray current corrosion to underground utilities and minimize the effects of faults on the utility system on Tri-Met system. an ac ground fault of 3500 A will raise the ground mat (1. The dc equipment and the surge arresters are rated 1000 Vdc maximum while the medium voltage equipment has a maximum design voltage of 15 kV (RMS) with a BIL of 95 kV. 5. 3 phase. For example.negative bus and thus enable faster fault clearing. Test results were tabulated and are included in the Appendices to this paper. The test current was generated by applying 120 Vac between one of the ac mat pigtails and a driven rod about 450 feet to the north.2010 at 21:27:09 UTC from IEEE Xplore. The ac ground mat and dc ground mat are physically separated about 20 feet apart to limit the voltage on the dc ground mat due to transfer of potential from the ac ground mat. dc ground mat to earth. The conductor for the voltmeter circuit Page 5 59 Authorized licensed use limited to: Walt Disney World Co .0 Incoming Utility Shield and ending 75 feet from it. The dc mat is about 25 feet east of the ac mat. Restrictions apply. The dc surge arrestor ground is also connected to the dc ground mat.0 ohm) potential to 3500 V ( 1. Connecting the dc surge arrester grounds to the ac ground mat could result in equipment failure. Additional field test to evaluate the transferred potential experienced at a dc ground mat. The grounding diodes will also allow leakage current to retum to the substations but also create a lower resistance path for stray current leaving the rails. The ground resistance tests included ac ground mat to earth. Additional rods and/or deeper driven rods are required until the ground resistance requirement is met. The ac mat is about 45 feet wide and 50 feet long. Downloaded on June 03. in direct line between the center of each mat and the current reference electrode. The conductor used for the current circuit consisted of several lengths of welding cable to minimize conductor resistance. the grounding diode will be disconnected between the negative bus and the dc ground mat. 3 wire utility service conductors provided by Portland General Electric is terminated in the utility metering cubicle on an electrically isolated lug.0 Field Tests During construction. isolated ground rod located about 50 feet distant from the ac and dc ground mats. Pham. The digital voltmeter. Walt Stinger.E. Mr. The incoming utility shield is terminated on an electrically isolated lug and grounded to a single. for their help with preparation of this paper. The calculations are included in the Appendix B. .0 A separate dc ground mat was designed for the dc switchgear equipment to confine dc leakage stray current to the dc ground mat. References [l] IEEE Guide for Safety in AC Substation Grounding. was Principal Electrical Engineer responsible for the detailed traction power and electrical design of the Westside Light Rail. . Restrictions apply. Page 6 60 Authorized licensed use limited to: Walt Disney World Co . Senior Engineer with LTK Engineering Services.2010 at 21:27:09 UTC from IEEE Xplore. Thomas. ANSIAEEE Standard 80-1 986 Kinh D. and other ac equipment enclosures was based on the IEEE standard 80 with considerations of step and touch potentials.- consisted of about 2500 feet of #I4 AWG insulated copper conductor. "Grounding of Traction Power Substations". As shown in these plots. The measured values agree reasonably well with the calculated values. Pittsburgh. and Mr.E. IEEE standard 3991996. 7. traction power transformer.8 f 2 x 0. The test was performed by connecting the current circuit and then taking a series of voltage and measurements to the east and the north at 5 foot intervals from the southeast corner of the ac ground mat. isolated ground rod to minimize stray current corrosion to underground utilities. Dennis Porter. was Traction Electrification Design Manager for the Westside Light Rail. Thanks also go to Mike McDonald for conducting the transferred potential tests on the dc ground mat at Elmonica Yard substation. About the Authors . while the measured values show approximately 15%. The ac and dc ground mats were isolated to prevent damage to dc equipment such as dc surge arrester due to high ground potential rise on the ac ground mat under ac ground fault condition. Ralph S. Downloaded on June 03. P. PA. The ac ground mat designed for grounding of the ac switchgear equipment. Test results and plots are documented in Appendix A. past Director of Systems Engineering for Tri-Met. [2] [3] Acknowledgement Conclusions The grounding systems for Tri-Met traction power substations were designed with the following features: The authors would like to thank Mr. Pham. with very high input impedance (11 MQ). The calculated values indicated that the potential at a dc mat will be approximately 37% of the ac mat ground potential rise. Supporting calculations using advanced computer grid modeling were also performed to verify the test results. the transferred potential on the dc ground mat is sufficiently well below the 1000 Vdc rated dc surge arrester. A more probable value is 245 V using the same ground fault current and ac ground mat resistance and the measured percentage (15%) of the ground potential rise of the ac ground mat.8 ohms. In either case. IEEE Recommended Practice for Power System Analysis.(IBM Journal Only). and the calculated percentage of 37% of the ground potential rise of the ac ground mat (2038 A x 0. this translated to a maximum potential of 603 V on the dc ground mat assuming the utility ground fault current of 2038 amperes and a ac ground mat resistance of 0. makes the resistance of the test conductor negligible. P. Mr. The test set-up is shown in Figure 2. For the ground mats tested. Kinh D.37 = 603 Vac rms). the potentials measured are decreasing approximately logarithmically with distance from the ac mat. . proceeding of the 1989 APTA Rapid Transit Conference. Downloaded on June 03.2010 at 21:27:09 UTC from IEEE Xplore. i Traction Power Substation Sinale Line Diagram Fiaure 1 0 B Page 7 F . . . 61 Authorized licensed use limited to: Walt Disney World Co .U -:.cl* c" I I I I I I I 8 r------1 . Restrictions apply.(IBM Journal Only). (IBM Journal Only). Restrictions apply. . Downloaded on June 03. .2010 at 21:27:09 UTC from IEEE Xplore.* CURRENT REFERENCE . AC GROUND MAT TEST POINTS (NPICAL) DC GROUND MAT VOLTAGE REFERENCE Test SetuD for Measurina Transferred Potential from AC Mat to DC Mal Fiaure 2 Page 8 62 Authorized licensed use limited to: Walt Disney World Co . 4 0 .572 6. .048 4.. A voltmeter was connectedto a second driven rod approximately 500 feet to the east and voltage measurements were then taken of the mat voltage and at 5 foot intervals both east and north.716 15.248 raw-voltage-easti = 9. .. Vm is the measured voltage on the AC mat._ -.67 vei = raw-voltage-easti - Vm = 1.. 0. The . .668 12. ten measurements were taken to the east and five to the north. Downloaded on June 03.2010 at 21:27:09 UTC from IEEE Xplore._ --. Restrictions apply.144 10.24 Voltage East of AC Mat vs Distance 0.(IBM Journal Only). 2 . --. An AC source (120 VAC) was connected to the AC mat and to a 2 foot driven rod approximately 450 feet to the north of the mat. I 14 16 ( 1 I 2 I 4 I 6 I 8 I 10 I 12 distancei 912 1195 Page A-I 63 Authorized licensed use limited to: Walt Disney World Co .6 ve.524 3. -0.Appendix A Observed Ground Potential Rise The data presented on this page was obtained by field measurement. = 1.096 .10 idit 1. The AC and DC mats tested are located at the Elmonica Maintenance Facility.8 distance. .. The distances are expressed in meters for easy comparison to the calculated values.192 13.248 volts subtracted from the measured voltage is the voltage measured with current source open circuited.i current = 2. i = 1...524.33 . Since the DC mat is located 20 feet east of the AC mat. 6 Observed Ground Potential Rise distancei raw-voltage-northi mi = raw-voltage-northi - .Appendix A i = 1. . given the mat to earth resistance.572 n i ".2010 at 21:27:09 UTC from IEEE Xplore. I 6 I I 8 I 7 9 10 The final graph below is the voltage to the east of the mat expressed as a percentage of the mat voltage versus the distance. Downloaded on June 03.. This normalized graph should be the most useful in determining the voltage at a specific distance from the AC mat with varying fault currents. i =].248 4.lo 9/21195 Page A-2 64 Authorized licensed use limited to: Walt Disney World Co . Restrictions apply.* 1 I 2 I 3 I 4 I 5 distance..(IBM Journal Only). (IBM Journal Only). - Vm 0. Downloaded on June 03. Restrictions apply.2 ( 2 4 6 8 10 12 14 16 distancei 9/21/95 Page A-3 65 Authorized licensed use limited to: Walt Disney World Co .6 Observed Ground Potential Rise 0. .Appendix A 0.4 ve.2010 at 21:27:09 UTC from IEEE Xplore. 33 vert-elem-7 .40 13. All coordinates are referenced to the southwest corner of the AC ground mat.05) (15.10) L stack(stack(ew-grid.72 -3.11 13.24 = stack( stack( stack(stack( ew-elem-l .24 0 0 ) = (0 5.1 = stack( stack( stack( stack( vert-elem.72 0 5.ns-elem-2) .97 13.72 0 9.05) = (15.ns-elem-5) ns-grid = stack( stack( stack(ns-grid-1.vert-elem-2) .72 0 ) = (4.27 13.vert-elem-4) .05) = (5.74 0 ) (0 8.40 0 0 6.24 0 = (9.91 0 -3.72 0 ) = (6.vert-elem-5) ~ert~~d2 stack( stack( stack( vert-grid.72 0 15.ns-length + 1O. vert-elem-9) stack( vert-grid = stack( stack( vert-grid.23 0 15.86 0 0 6.05) = (9. ew-elem-2).91 13.84 0 0 8. Also defined are the total length of ground conductor in the grid and the east-west and north-south overall dimensionsfor use in the calculations that follow.97 ew-elem-2 ew-elem-4 ew-elem-6 ns-elem-2 ns-elem-4 ns-elem-6 ns-elem-8 vert-elem-2 vert-elem-4 vert-elem-6 vert-elem-8 = (0 2.05) vert-elem-10 = (15.1 .86 0 15.49 0 15.ew-length + 8.27 0 0 4.ew-elem-6) = stack(stack( stack( stack(ns-elm-1 . ew-elem-5) stack( ew_grid.1 .72 0 ) = (0 0 0 15.72 0 ) (0 0 0 0 13.ns-elem-7) .33 0 0 5.91 0 15.49 0 ) = (0 10.33 0 -3.vert-elem-S).vert-length 9/21I95 Page B-1 66 Authorized licensed use limited to: Walt Disney World Co . Downloaded on June 03.74 0 15.72 -3.97 0 ) (0 13.vert-elem.72 0 ) (8.72 -3.72 -3.24 8.33 13.vert-elem-3) .05) 13. north-south. Restrictions apply.86 -3.05 ) 0 0 9. .= (0 13.72 0 ) = (15.86 -3.72 0 0 13.ns-elem-4) . ew-elem-3).05) = (5.72 0 15.24 6.05) (0 6.(IBM Journal Only).11 0 0 13.vert-elem-6).24 6. vert-elem-7) .13 0 0 2.72 0 ) 0 0 0 0 -3.05 ew-length = 15.ns-elem-8) vert-grid. ew-elem-4).24 2.24 13.24 0 -3.vert-grid-2) .91 13.ns-grid) .2010 at 21:27:09 UTC from IEEE Xplore. ns-elem-6) .24 5.24 = (13.1 .24 13.84 13.72 0 ) = = (2. and vertical orientations.72 0 ) (10.= 6.1 .24 10.vert-grid) ns-length = 13.24 13.24 total-length .23 0 ) = 0 15.97 0 0 10.13 13.Calculated Ground Potential Rise Appendix B The three matrices below define the coordinates of the endpoints of the grid elements in east-west.ns-elem-3) . ew-elem-l ew-elem-3 ew-elem-5 ns-elem-1 ns-elem-3 ns-elem-5 ns-elem-7 vert-elem-1 vert-elem-3 vert-elem-5 (0 0 0 15.05) vert-elem-9 ew-grid-l ew-grid ns-grid-1 = 13.72 vert-length = 3. J.i)2 Vxj = E.i)2 + (Zlj.I 3.1 [i=O (In(Xlj.i = /(Xlj i)2 + (Ylj.1 ~ .1 J-0 1..1 5. . -L.144 + ns-length 0 0 0 The Ground Potential Rise calculations that follow are based on the actual current measured in the field test and the previously measured soil resistivity.1 1. = A .096 + ew-length tp-ew = 7.62 + ns-length 12.3 J.i = . -L. + Vy.o 1. . J. = J(Xlj.048 + ns-length 0 0 4. -L. 2 1. current ( 5 = = 2. J J J Page 8-2 67 Authorized licensed use limited to: Walt Disney World Co . = A .32 + (Ylj. Downloaded on June 03. The current density is assumed to be uniform as well. The formulas used are based on Eq 224 on page 354 of IEEE 399-1990 and assume that superposition is valid.2010 at 21:27:09 UTC from IEEE Xplore.572 + ns-length 0 0 6.192 + ew-length 0 0 13.33 current total-length p = 29. = A . j. J. -L.096 + ns-length 0 0 0 7.2 22.J + (z2j.s 12j.l(X1.I J.144 + ew-length 10.048 + ew-length 4. -L. is included for reference and for the final graph which shows the measuredvoltage as a percentage of the mat voltage versus the distance.62 + ew-length 9.67 Vm = 1.J r + (Zlj.J RXj.52 j =0.9 Y l .(IBM Journal Only). J.i)) Ve.’ ’ = J(Xlj. = A . .Appendix B Calculated Ground Potential Rise The two arrays immediately below are the coordinates of the test locations. while the DC ground mat is located to the east of the AC ground mat receivingthe applied voltage. + VX. = A .512 + ew-length 6.524 + ns-length 0 0 3. Note that the test points extended 50 feet to the east and only 30 feet to the north.ij2 + (Y2j..1 174 Z l . . J = Vx. Vm. The applied voltage was oriented north-south.i)2 r Ky. -L.i) - + Rxj.O X 2 .. Restrictions apply.668+ew-length 0 0 0 0 0 0 0 0 0 0 0 0 0 0 tp-ns = 0 1.i)2 + (zlj. J.716 + ew-length 0 0 15.23 A = tp-ew X l .1 Y 2 .J2 RZj. J.J + (Ylj.524 + ew-length 3.i + Rj.1 i = 0. The voltage measured on the mat.2 1.24 + ew-length 0 9. = A . . 1.. . i ) 2 + (Y2j. 5 A = tp-ns (Xlj.5 0.i) . 8 0.ln(Y2j 1=6 + Ryj . ~ ) ) J 4.J + (z2j. Downloaded on June 03.i)2 + (Zlj.7 Ve.i)) vz.Appendix B 0.6 0. iJ 13 ("(XIj.9 I 1 i i Calculated Ground Potential Rise Voltage East of AC Mat vs Distance i i i 0 .a h(Z2j.i)2 vxj = qc 23 P. f vx.524 10 12 14 16 j = 0.i)) v.4 0 . ~ . 3 0 2 4 6 8 j-1.i) i=O Vy. Restrictions apply. = (x2ji)2 + (Ylj. . + v y .a -' ( h ~ ( Y l+ ~ Rj. J -0..J2 + ( Y l j .J2 j ( X l j i)2 + (Ylj.J = q i= RZj. J =- 4.J2 + (Zlj.i i= 14 + kj. + Rj. iJ h1(X2~ + R x ~ . = P.(IBM Journal Only). J + (2lj.. = v x .524+ 1.2010 at 21:27:09 UTC from IEEE Xplore.J2 j ( x l j . J J J J 912 1I95 Page 8-3 68 Authorized licensed use limited to: Walt Disney World Co . Appendix B Calculated Ground Potential Rise 0.524 10 12 14 16 912 1195 Page B-4 69 Authorized licensed use limited to: Walt Disney World Co .8 - 0..7 - V.1.524+ 1.9 I I I I I I I I 0.2 2 4 6 8 j. J 0.5 0.524+ 1. Downloaded on June 03.9 Percentage of Mat Voltage vs Distance I I I 0.4 0.3 0.7 I I I I 0 .2010 at 21:27:09 UTC from IEEE Xplore. .4 2 3 4 5 6 j.524 7 8 9 10 j := 0.6 - 0. 6 0. Restrictions apply.(IBM Journal Only).1. 2010 at 21:27:09 UTC from IEEE Xplore.70 Authorized licensed use limited to: Walt Disney World Co .(IBM Journal Only). Downloaded on June 03. . Restrictions apply.