Transferred voltages in grounding systems critically impact electrical safety and equipment reliability. Accurate calculation ensures compliance with IEEE and IEC standards.
This article explores advanced methods for calculating transferred voltages, including formulas, tables, and real-world examples. It covers IEEE and IEC guidelines comprehensively.
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- Calculate transferred voltage for a 10 Ω grounding resistance with 1000 A fault current.
- Determine transferred voltage using IEEE 80 with soil resistivity of 100 Ω·m and grid resistance 5 Ω.
- Find transferred voltage per IEC 62305 for a 50 kA lightning current and 2 Ω grounding resistance.
- Evaluate transferred voltage for a substation grounding system with 0.5 Ω resistance and 20 kA fault current.
Common Values for Transferred Voltages in Grounding Systems – IEEE and IEC Standards
| Parameter | Typical Range | Units | Standard Reference | Notes |
|---|---|---|---|---|
| Grounding Resistance (Rg) | 0.1 – 10 | Ω | IEEE 80, IEC 62305 | Depends on soil resistivity and grounding system design |
| Fault Current (If) | 1,000 – 100,000 | A | IEEE 80, IEC 62305 | Short-circuit or lightning current magnitude |
| Transferred Voltage (Vt) | 10 – 100,000 | V | IEEE 80, IEC 62305 | Voltage appearing on equipment or structures due to grounding |
| Soil Resistivity (ρ) | 10 – 10,000 | Ω·m | IEEE 81, IEC 62561 | Influences grounding resistance and voltage distribution |
| Touch and Step Voltages | 10 – 1,000 | V | IEEE 80, IEC 62305 | Safety limits for human exposure |
| Grid Potential Rise (GPR) | 100 – 50,000 | V | IEEE 80 | Voltage rise of grounding grid during fault |
Fundamental Formulas for Transferred Voltages in Grounding Systems
Understanding transferred voltages requires precise formulas derived from grounding system theory and fault current behavior. Below are the essential equations used in IEEE and IEC standards.
1. Transferred Voltage (Vt) Calculation
The transferred voltage is the voltage appearing on a conductive object connected to the grounding system during a fault or lightning strike.
- Vt = Transferred voltage (Volts, V)
- If = Fault current magnitude (Amperes, A)
- Rg = Grounding resistance (Ohms, Ω)
This formula assumes a simple grounding system where the transferred voltage is directly proportional to the product of fault current and grounding resistance.
2. Grid Potential Rise (GPR)
Grid potential rise is the voltage increase of the grounding grid relative to remote earth during a fault.
- GPR = Grid potential rise (Volts, V)
- If = Fault current (Amperes, A)
- Rg = Grounding resistance of the grid (Ohms, Ω)
Note: GPR is often used interchangeably with transferred voltage but specifically refers to the grounding grid potential.
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 = Touch voltage (Volts, V)
- Rg = Grounding resistance (Ohms, Ω)
- Rb = Body resistance (Ohms, Ω), typically 1000 Ω for dry skin
This formula accounts for the human body resistance in series with the grounding resistance.
4. Step Voltage (Vstep)
Step voltage is the voltage difference between two feet of a person standing near the grounding system during a fault.
- Vstep = Step voltage (Volts, V)
- Rg = Grounding resistance (Ohms, Ω)
- Rs = Soil resistance between feet (Ohms, Ω), typically 1000 Ω
Step voltage is critical for safety assessments in substations and industrial sites.
5. Transferred Voltage Considering Mutual Coupling
In complex grounding systems, transferred voltage can be influenced by mutual coupling between grounding grids.
- Vt = Transferred voltage (Volts, V)
- Rg = Grounding resistance of the local grid (Ohms, Ω)
- Rm = Mutual resistance between grids (Ohms, Ω)
Mutual resistance accounts for voltage transfer between interconnected grounding systems.
Detailed Real-World Examples of Transferred Voltages Calculation
Example 1: Transferred Voltage in a Substation Grounding System (IEEE 80)
A substation grounding grid has a measured grounding resistance of 0.5 Ω. During a fault, a current of 20,000 A flows into the grid. Calculate the transferred voltage appearing on a metallic structure connected to the grid.
- Given:
- Rg = 0.5 Ω
- If = 20,000 A
- Find: Transferred voltage (Vt)
Solution:
Using the formula:
The transferred voltage on the metallic structure is 10,000 V, which is significant and requires mitigation measures such as equipotential bonding and insulation.
Example 2: Transferred Voltage Due to Lightning Current (IEC 62305)
A lightning strike induces a current of 50 kA into a grounding system with a resistance of 2 Ω. Calculate the transferred voltage on a nearby structure connected to the grounding system.
- Given:
- Rg = 2 Ω
- If = 50,000 A
- Find: Transferred voltage (Vt)
Solution:
Applying the formula:
This extremely high transferred voltage necessitates advanced grounding design, including low-resistance grids and surge protection devices.
Additional Technical Considerations for Transferred Voltages
- Soil Resistivity Impact: Soil resistivity directly affects grounding resistance and thus transferred voltages. Layered soil models and seasonal variations must be considered.
- Frequency Dependence: Lightning currents have high-frequency components, influencing grounding impedance differently than power frequency faults.
- Mutual Coupling Effects: Adjacent grounding systems can induce voltages in each other, requiring detailed network analysis.
- Safety Limits: IEEE 80 and IEC 62305 specify maximum allowable touch and step voltages to prevent injury.
- Measurement Techniques: Fall-of-potential and clamp-on methods are standard for determining grounding resistance.
Authoritative References and Further Reading
- IEEE Std 80-2013 – Guide for Safety in AC Substation Grounding
- IEC 62305 – Protection Against Lightning
- IEEE Std 81-2012 – Guide for Measuring Earth Resistivity, Ground Impedance, and Earth Surface Potentials of a Ground System
- Analysis of Transferred Voltages in Grounding Systems
Accurate calculation and mitigation of transferred voltages are essential for electrical safety and system reliability. Utilizing IEEE and IEC standards ensures best practices in grounding system design.