Substation Grounding Grid: Touch, Step, GPR and Conductor Size

Geometry and earth current

The grid has equally spaced square meshes inside a rectangle, with perimeter conductors included: $L_x=N_xD$, $L_y=N_yD$ and $L_C=(N_x+1)L_y+(N_y+1)L_x$. Optional rods are bonded at corners and distributed around the perimeter. The earth current is $I_G=I_fS_fD_f$; the conductor heating current is a separate fault-study input.

Resistance and GPR

Sverak is used for the headline resistance and GPR:

Laurent–Niemann adds the finite-length term $\rho/L_T$ to the equivalent surface-plate term $\rho\sqrt{\pi}/(4\sqrt A)$. Open background: Balakrishnan (1990), printed pp. 7–10; published resistance checks: Silva et al. (2017), PDF p. 3.

The Schwarz comparison combines grid, rod-bed and mutual resistances using IEEE 80-2013, §14.3. Its shallow-grid coefficients are the explicit approximation in Perng et al. (2018), PDF p. 5: $k_1=1.41-0.04r$ and $k_2=5.5+0.15r$, where $r$ is the longer-to-shorter side ratio. They do not replace the edition’s depth-dependent coefficient assessment. The rod logarithm follows IEEE Eq. (60), with rod radius defined explicitly; it differs from Perng Eq. (9). No rods returns the horizontal-grid resistance without evaluating a singular coupled expression.

Touch and step criteria

The geometry factors follow IEEE 80-2013, §16.5, checked against the licensed edition; the open development of the revised irregularity factor and geometry count is in Balakrishnan, printed pp. 29–32. For a rectangle, $n=(2L_C/L_p)\sqrt{L_p/(4\sqrt A)}$. The displayed steps expose $K_m$, $K_s$, $K_i$, $K_{ii}$ and the effective lengths. $K_{ii}=1$ with perimeter rods, otherwise $(2n)^{-2/n}$.

The surface factor uses a 0.09 m empirical length and reduces to one for bare soil. With $I_B=k/\sqrt{t_s}$, the body circuit uses 1000 Ω and contact coefficients 1.5/m for touch and 6/m for step. The body coefficients are 0.116 and 0.157 A·√s for the two weight criteria (Perng, PDF p. 3). Retain full precision; published IEEE examples round intermediate factors.

Copper thermal area

An adiabatic energy balance integrates temperature-dependent resistivity:

The result is converted explicitly from SI area to mm². Annealed-copper constants follow the IEEE 80-2013 thermal model; the displayed steps state each constant and its reference temperature. The independent KME manual, PDF p. 37, provides a rounded copper short-circuit-factor check.

Coverage of the spacing study

The selected layout and every sweep point are screened against the model envelope before a voltage comparison is accepted. The screen uses the benchmark coverage discussed in IEEE 80-2013, §16.7, together with this tool's narrower spacing range: area 6.25–10,000 m², one to forty meshes per side for the continuous trend, valid burial/diameter geometry, perimeter-rod node capacity and a strictly positive mesh factor. Invalid voltage samples are gaps, never zero or negative voltage estimates. Gray spans and the omitted-sample count explain these gaps. Passing this coverage screen is not a numerical accuracy guarantee.

The foot-contact-only covering model is restricted here to 0.08–0.15 m thickness, consistent with the usual surfacing band discussed in IEEE 80-2013, §§7.4 and 12.5. This tool also requires the covering to be no thicker than one quarter of burial depth. That additional ratio is a conservative scope screen adopted here, not an IEEE acceptance criterion or a quantified error bound. Outside either screen, use layered-soil analysis rather than crediting the covering only in the foot-contact circuit.

• Uniform, linear-resistivity soil at 50/60 Hz; negligible voltage drop along the bonded grid. Only the screened thin covering modifies foot contact; its effect on bulk grid resistance and surface potentials is neglected.
• Equal square meshes; a closed rectangular perimeter; rods of equal length bonded to perimeter nodes, including corners. Rod symbols in the plan are illustrative and are not an installation layout.
• The same wet covering exists at every assessed foot location, including at least the one-metre step outside the corner. Choose bare soil if that covering is not assured.
• Body weight is a choice of published criteria, not a continuous person-specific safety prediction. Footwear resistance is not credited.
• Fault currents include the assessed system growth. The user supplies the division/decrement factors and the equivalent rms conductor duty; this tool does not solve the network fault or protection study.
• Annealed copper with constant volumetric heat capacity and linear resistivity versus temperature. No heat loss, current-sharing credit, corrosion allowance or joint derating is included.

The method basis is IEEE Std 80-2013, published in 2015 with Cor 1-2015; check against the standard in force. The licensed edition was consulted for equation and worked-example verification; its text, tables and drawings are not reproduced.

Tool limits: 2.5–15 m spacing; 2–40 whole meshes per side for the selected layout; grid area no greater than 10,000 m²; 0.26–2.49 m burial; conductor diameter below one quarter of burial depth; rectangular aspect ratio at most 8:1; shock and thermal durations 0.03–3 s. Every spacing sample must separately satisfy the coverage screen, including a positive mesh factor and enough perimeter nodes for the fixed rods. The trend can include fractional mesh counts between one and forty, following the geometric envelope of IEEE 80-2013 §16.7. Its benchmark coverage is a boundary for this tool, not proof that every combination inside the envelope has the same accuracy.

Credited surface covering must be 0.08–0.15 m thick, at least as resistive as the underlying soil, and no thicker than one quarter of grid burial depth. The thickness band follows the usual surfacing discussed in §§7.4 and 12.5; the depth-ratio limit is an additional conservative screen adopted by this tool, not a universal IEEE thin-layer criterion. Merely putting the conductor below the covering is insufficient. Use layered-soil analysis outside these bounds; selecting bare soil is appropriate only if no covering is being credited.

For the approximate Schwarz coefficients this tool additionally requires $h/\sqrt A\le0.05$ and physically consistent self/mutual resistances. These extra restrictions are scope limits of this implementation, not general acceptance limits in IEEE 80.

Layered soil, irregular or unequal grids, complex rod locations, large interconnected stations and appreciable conductor inductance need detailed modelling. Check fences, accessible metal, metal-to-metal touch, transferred potentials, cable screens, remote bonds, protection and reclosing separately. Verify wet/seasonal soil and covering properties by site data.

The chart is a continuous analytical spacing study at fixed footprint and fixed rods, not an optimization or a buildable layout. Intermediate line counts can be fractional. Invalid samples are omitted; gray spans and the omission count identify portions outside the model. Green/red regions assess only supported mesh and step voltage samples. The dotted line marks the selected spacing. The native chart converts its metre/volt axis labels with the displayed units; schematic labels remain explicitly SI.

The PASS card requires the geometry and covering screens as well as voltage and copper thermal comparisons. It makes no claim about omitted design duties. Copper final temperature must respect the weakest conductor, connection and surrounding material.

A PASS here does not approve a substation design.