Grounding grids are essential for ensuring safety and operational reliability in electrical substations. Calculating the grounding grid parameters accurately prevents hazardous step and touch voltages.
This article explores the IEEE standards for grounding grid calculations, providing formulas, tables, and real-world examples. Learn how to design effective grounding grids for substations.
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- Calculate grounding grid resistance for a 50m x 50m substation with 10 ground rods.
- Determine step voltage for a grid with 5m spacing and soil resistivity of 100 Ω·m.
- Estimate grid conductor size for a 100m x 100m grounding grid with 20 conductors.
- Compute touch voltage for a substation grounding grid with 0.5 Ω resistance and 2000 A fault current.
Common Values for Grounding Grid Design According to IEEE Standards
| Parameter | Typical Range | Units | Notes |
|---|---|---|---|
| Soil Resistivity (ρ) | 10 – 1000 | Ω·m | Varies with soil type, moisture, and temperature |
| Grid Conductor Diameter (d) | 10 – 25 | mm | Commonly copper or galvanized steel |
| Grid Spacing (s) | 3 – 10 | m | Distance between conductors in the grid |
| Ground Rod Length (L) | 1.5 – 3 | m | Driven vertically into the soil |
| Fault Current (If) | 1000 – 40000 | A | Maximum expected short-circuit current |
| Allowable Touch Voltage (Vt) | 50 – 100 | V | Based on IEEE Std 80 safety criteria |
| Grid Resistance (Rg) | 0.1 – 5 | Ω | Depends on grid size and soil resistivity |
Key Formulas for Grounding Grid Calculations per IEEE Standards
1. Grounding Grid Resistance (Rg)
The grounding grid resistance is a critical parameter that determines the effectiveness of the grounding system in dissipating fault currents safely into the earth.
Rg = (ρ / L) × F
- Rg: Grounding grid resistance (Ω)
- ρ: Soil resistivity (Ω·m)
- L: Total length of grounding conductors (m)
- F: Grid geometry factor (dimensionless), depends on grid layout and spacing
The factor F accounts for the grid shape, conductor spacing, and mutual coupling effects. For a square grid:
F ≈ (ln(2L / d) – 1)
- d: Conductor diameter (m)
2. Step Voltage (Vstep)
Step voltage is the potential difference between two points on the ground surface approximately 1 meter apart, which a person might experience during a fault.
Vstep = If × Rstep
- Vstep: Step voltage (V)
- If: Fault current flowing into the ground (A)
- Rstep: Step voltage resistance (Ω), depends on soil resistivity and grid design
IEEE Std 80 provides detailed methods to calculate Rstep based on soil layers and grid configuration.
3. Touch Voltage (Vtouch)
Touch voltage is the voltage difference between a grounded object and the feet of a person touching it during a fault.
Vtouch = If × Rtouch
- Vtouch: Touch voltage (V)
- Rtouch: Touch voltage resistance (Ω), influenced by grid design and soil resistivity
4. Ground Potential Rise (GPR)
GPR is the maximum voltage rise of the grounding system relative to remote earth during a fault.
GPR = If × Rg
- GPR: Ground potential rise (V)
- Rg: Grounding grid resistance (Ω)
- If: Fault current (A)
5. Conductor Cross-Sectional Area (A)
Determining the conductor size is essential to ensure thermal and mechanical stability during fault conditions.
A = (If × √t) / (k × √ΔT)
- A: Cross-sectional area of conductor (mm²)
- If: Fault current (A)
- t: Duration of fault current (s)
- k: Material constant (for copper, k ≈ 226)
- ΔT: Allowable temperature rise (°C)
This formula is derived from the adiabatic heating equation, ensuring the conductor withstands thermal stress.
Extensive Tables of Grounding Grid Parameters
| Grid Size (m x m) | Grid Spacing (m) | Total Conductor Length (m) | Estimated Grid Resistance (Ω) | Soil Resistivity (Ω·m) |
|---|---|---|---|---|
| 25 x 25 | 5 | 200 | 1.2 | 100 |
| 50 x 50 | 5 | 400 | 0.7 | 100 |
| 100 x 100 | 5 | 800 | 0.4 | 100 |
| 50 x 50 | 3 | 700 | 0.5 | 50 |
| 75 x 75 | 4 | 900 | 0.6 | 75 |
| Ground Rod Length (m) | Rod Diameter (mm) | Rod Resistance (Ω) | Soil Resistivity (Ω·m) | Notes |
|---|---|---|---|---|
| 1.5 | 16 | 20 | 100 | Typical rod resistance in medium resistivity soil |
| 2.4 | 16 | 12 | 100 | Longer rods reduce resistance significantly |
| 3.0 | 20 | 8 | 50 | Lower soil resistivity improves grounding |
| 1.8 | 12 | 25 | 200 | High resistivity soil increases rod resistance |
Detailed Real-World Examples of Grounding Grid Calculations
Example 1: Calculating Grounding Grid Resistance for a Medium-Sized Substation
A substation has a grounding grid of 50 m by 50 m with conductors spaced at 5 m intervals. The soil resistivity is measured at 100 Ω·m. The conductors are copper with a diameter of 16 mm. Calculate the approximate grounding grid resistance.
Step 1: Calculate total conductor length (L)
- Number of conductors per side = 50 m / 5 m + 1 = 11 conductors
- Total length of horizontal conductors = 11 × 50 m = 550 m
- Total length of vertical conductors = 11 × 50 m = 550 m
- Total conductor length, L = 550 + 550 = 1100 m
Step 2: Calculate the grid geometry factor (F)
Convert conductor diameter to meters: d = 16 mm = 0.016 m
Calculate F:
F = ln(2 × L / d) – 1 = ln(2 × 1100 / 0.016) – 1
Calculate inside the logarithm:
2 × 1100 / 0.016 = 137,500
ln(137,500) ≈ 11.83
Therefore, F = 11.83 – 1 = 10.83
Step 3: Calculate grounding grid resistance (Rg)
Rg = (ρ / L) × F = (100 / 1100) × 10.83 ≈ 0.985 Ω
The grounding grid resistance is approximately 0.985 Ω, which is acceptable for many substation applications.
Example 2: Step and Touch Voltage Calculation for a Fault Current
Consider a substation grounding grid with a resistance of 0.5 Ω. The maximum fault current expected is 10,000 A. Calculate the ground potential rise (GPR), step voltage, and touch voltage assuming step and touch voltage resistances of 0.03 Ω and 0.01 Ω respectively.
Step 1: Calculate Ground Potential Rise (GPR)
GPR = If × Rg = 10,000 × 0.5 = 5,000 V
Step 2: Calculate Step Voltage (Vstep)
Vstep = If × Rstep = 10,000 × 0.03 = 300 V
Step 3: Calculate Touch Voltage (Vtouch)
Vtouch = If × Rtouch = 10,000 × 0.01 = 100 V
According to IEEE Std 80, allowable touch voltage is typically limited to 50 V for dry conditions and 100 V for wet conditions. The calculated touch voltage is at the upper limit, indicating the need for mitigation measures such as increasing grid size or adding ground rods.
Additional Technical Considerations for Grounding Grid Design
- Soil Resistivity Profiling: Soil resistivity varies with depth and moisture content. IEEE Std 81 recommends using the Wenner or Schlumberger methods for accurate resistivity measurements.
- Layered Soil Models: When soil resistivity varies with depth, layered soil models must be used to calculate effective grounding resistance and voltage gradients.
- Grid Mesh Size Optimization: Smaller mesh sizes reduce step and touch voltages but increase material costs. A balance must be found based on safety and budget.
- Corrosion Protection: Grounding conductors and rods must be protected against corrosion, especially in aggressive soil environments, using coatings or sacrificial anodes.
- Thermal Stability: Conductors must withstand thermal stresses during fault currents without damage, requiring proper sizing and material selection.
- Use of Ground Rods and Plates: Supplementing the grid with rods or plates can significantly reduce resistance and improve safety.
- Bonding and Equipotential Grounding: All metallic structures must be bonded to the grounding grid to maintain equipotential surfaces and reduce shock hazards.
References and Further Reading
- IEEE Std 80-2013: IEEE Guide for Safety in AC Substation Grounding
- IEEE Std 81-2012: IEEE Guide for Measuring Earth Resistivity, Ground Impedance, and Earth Surface Potentials of a Ground System
- National Fire Protection Association (NFPA) – Electrical Safety Standards
- Occupational Safety and Health Administration (OSHA) – Electrical Safety Guidelines
Accurate grounding grid calculations following IEEE standards are vital for substation safety and reliability. Using the formulas, tables, and examples provided, engineers can design effective grounding systems that minimize hazards and comply with regulatory requirements.