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According to my knowledge GPR provides information about the maximum potential that can happen under a faulty condition. But how can we find the potential distribution within the grid (i.e.in the soil enclosed by the grid) analytically?

Hi Pryianga,

Thank you for your question regarding Ground Potential Rise distributions within a grounding grid; it is our pleasure to help.

When you see a Ground Potential Rise (GPR) study, they generally fall into one of two categories: 1) they provide a maximum GPR only, or 2) they provide a GPR distribution across the system.  The difference in the amount of calculations and work involved between these two types of studies couldn’t be more striking. 

The first report basically calculates the resistance (sometimes they use impedance, but not often) of the ground system, generally using a single or a predetermined two layer soil model (fixed or limited depths, resistivities, etc.).  It then uses Ohm’s Law to apply the fault current to get a maximum GPR.  This type of analysis often cannot take into account material characteristics (steel vs copper vs aluminum, etc.) and must assume that the ground grid is made of an imaginary super-conductor with zero impedance.  This means that they cannot take into account for voltage drops across the length of the conductor, nor can they calculate the leakage-current into the soil as the fault currents propagate through the ground system and out into the surrounding earth.  This results in a simple maximum GPR. This maximum GPR is often then applied as the basis for Step & Touch Voltage hazards across the entire grid.  This is of course simply inaccurate.  Touch Voltages in particular only occur at arm-length from touchable objects.  Applying touch voltage criteria to open areas of a facility results in vast over protection in areas that don’t need it, and often under-protection in area’s that do.

The second style report takes into account the impedance of the system (at frequency) in complex multi-layered soil models with no limitations regarding depths, resistivities, or number of layers.  To do this the characteristics of the conductors within the ground system must be considered.  Steel rebar in footings and foundations, steel ground rods with copper coatings buried vertically, bare copper conductor buried horizontally in the ground, and insulted conductors bonding items above-grade, all must be taken into account.  Each of these items will have different factors regarding relative resistivity (both real and imaginary parts), permeability, inductance, capacitance, etc., that will change given the length of the item, radius, depth buried, etc.  Once the fault current is applied (must include the zero-sequence impedance, clearing time, and amperage) to the model, each individual piece of the grounding system must be individually calculated taking into account all of the above factors.  Long conductors must be broken into smaller segments (typically 1-ft) so that the leakage current into the soil, voltage drops, etc. can be properly calculated, which of course will change with the soil model as the ground system conductors pass through the varying soil layers.  Even for a small 20-ft x 20-ft grid, this requires thousands, if not hundreds of thousands, of individual calculations.

Once this is completed, you will be able to see the GPR distribution across the grid.  There are in fact many “hot spots” that will typically occur in a grid (typically near the fault location and then at the corners of a grid).  This also allows you to determine quite possibly the single most important factor of a grounding system, the Ground Potential Difference (GPD).  Lowering the GPD is generally more important than lowering the GPR when it comes to human safety.

Once you have a GPR distribution, then you can finally start accurately calculating Step & Touch Voltage hazards.  This is another massive task, as individual Touch voltages must be calculated at any place within the grid that can be ‘touched” by personnel.  A faulting transformer bank will have a higher touch voltage than the wall of the control building.  Only a category #2 report can demonstrate this.  And that takes an additional level of calculations for each and every variation within the system, for both touch and step voltage hazards; again this is many thousands if not hundreds of thousands of additional calculations.  This is the only way to get an accurate GPR analysis completed.

It should be obvious by now, that you need some computer assistance to do a proper GPR analysis.  Given today’s computer environment, it is borderline unethical to conduct GPR analysis by using hand calculations; at a minimum hand-calculated GPR studies are simply bad engineering.  Now that said, there are many computer programs out in the market place today that conduct nothing more than fancy Category #1 type analysis.  In particular, most of the Electrical Engineering Software programs that are used for load flow, arc-flash, short-circuit analysis, relay coordination studies, etc. (etap, SKM, etc.) have grounding analysis modules that do NOT conduct a Category #2 analysis.

To our knowledge the only Computer software program that accurately conducts a GPR study is the CDEGS program from Safe Engineering Services (www.sestech.com).  Of note, is that the MALT module is their version of the Category #1 style software that is produced to compete with etap, SKM, etc.  To conduct a Category #2 study, you would need the MALZ and/or HIFREQ modules.  The CDEGS program is also one of the most validated Electrical Engineering software programs in production.  It is used to write code by the NFPA (National Electrical Code), the IEEE, UL, TIA, EIA, the US Government, and many more.

We hope this helps answer your questions.  If you have need for a Category #2 GPR analysis, please do not hesitate to contact us at 310-318-7151 California time, and someone will be happy to discuss your project with you free of charge.

Best regards,

The Engineering Team at E&S Grounding Solutions

 

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