To calculate tolerable voltages, IEEE 80 models the person as a 1000 ohm resistance in series with the ground resistance of the feet. For touch the two feet act in parallel and for step in series. With a foot represented as a disk of 0.08 m radius, the equivalent impedance is 1.5 times the soil resistivity for touch and 6 times for step.
Short answer. When a person touches a structure or walks on ground with a potential gradient, a circuit closes with the person in the middle. IEEE Std 80-2013 calls it the accidental ground circuit. It is represented with a voltage source (the one appearing between the contact points), the body resistance, set at 1000 Ω, and the ground resistance of the feet. From that circuit comes the maximum voltage that can be tolerated.
Body resistance
For direct current and for 50 Hz or 60 Hz, clause 7.1 allows the body to be represented by a resistance. The path considered is from one hand to both feet or from one foot to the other. The internal body resistance is about 300 Ω, and with the skin included the values vary between 500 Ω and 3000 Ω. Damage to or puncture of the skin at the contact point reduces the resistance.
In tests with salt water on hands and feet, Dalziel obtained for men a let-go current of 9.0 mA with 21.0 V between hand and hand and 10.2 V between hand and feet. From this come about 2330 Ω from hand to hand and 1130 Ω from hand to feet.
For the guide’s calculations, the contact resistances of hands and feet, and those of gloves and shoes, are assumed to be zero. A single value is used for every path considered:
R_B = 1000 Ω (equation 10)
It is a conservative value: it does not count series resistances that in reality exist.
Which paths matter
The 1000 Ω value corresponds to paths such as hand to one foot or to both, where a good part of the current passes through areas with vital organs, including the heart. It is generally accepted that current from one foot to the other is much less dangerous. Tests carried out in Germany indicated that, to produce the same current in the heart, a foot-to-foot current up to 25 times larger than hand to foot was needed.
This would suggest allowing higher resistances in that path, but the guide asks not to do so lightly, for two reasons. A voltage between the feet, painful but not deadly, can make the person fall and open a more dangerous current path through the chest. Also, a person may be working or resting lying down when the fault occurs. Deaths from the fall have been recorded, so the risk must not be ignored.
The equivalent circuit
With the body’s tolerable current (equations 8 and 9 of the guide, from Dalziel), the tolerable voltage between two points is determined. The guide uses these quantities: the total fault current, the current flowing through the grid, the body current, the body resistance and the total effective voltage of the accidental circuit. That voltage is the touch or step voltage, as the case may be.
Thevenin’s theorem makes it possible to reduce the whole network to a source and an impedance. The Thevenin voltage is the voltage between the two contact points when the person is not there. The Thevenin impedance is the one seen from those points with the sources short-circuited. The body current is:
I_b = V_Th / (Z_Th + R_B) (equation 11)
In practical cases the system impedance, the grid resistance and the mutual resistance between the grid and the feet can be neglected. The Thevenin impedance is then determined only by the person’s feet.
Touch and step: feet in parallel or in series
For touch, the hand touches a structure at grid potential and the two feet are together at one point on the ground. The two feet are in parallel and the impedance is half that of one foot. For step, the current enters through one foot and leaves through the other, and the two feet are in series: the impedance is twice that of one foot.
| Circuit | Thevenin impedance | With the foot as a 0.08 m disk |
|---|---|---|
| Touch | Z_Th = R_f / 2 (equation 12) | 1.5 ρ (equation 15) |
| Step | Z_Th = 2 R_f (equation 13) | 6.0 ρ (equation 16) |
Here R_f is the ground resistance of one foot, without considering the grid, and ρ is the soil resistivity in Ω·m. The guide represents the foot as a metallic disk of radius b on the surface of a homogeneous soil. Its resistance is R_f = ρ / (4b) (equation 14). Traditionally a disk of 0.08 m radius is taken, which makes R_f approximately 3 ρ. The resistance of shoes and socks is neglected.
The standard itself warns that equations 15 and 16 are conservative: they underestimate the Thevenin impedance in uniform soil and therefore give larger body currents than the real ones.
From current to tolerable voltage
The maximum voltage of the accidental circuit is the one that produces a body current equal to the tolerable I_B. With the previous equations:
- Touch: E_touch = (R_B + 1.5 ρ) · I_B (equation 17).
- Step: E_step = (R_B + 6.0 ρ) · I_B (equation 18).
With soil without a surface layer and as an illustrative example, for a 100 Ω·m soil, 0.5 s and 70 kg (I_B ≈ 0.222 A), the tolerable touch voltage is about 255 V and the step voltage about 355 V. The tolerable step voltage is higher because the foot-to-foot path is less dangerous and the feet in series offer more resistance.
When there is gravel or another surface material, the resistivity entering these expressions is corrected with the factor C_s. That correction is in clause 7.4 of the guide.
We carry out your grounding study
The accidental circuit is calculated with your site data: soil resistivity, surface material, clearing time and reference weight. Our team performs that calculation for each zone of your substation and verifies that the voltages of your grid remain below the tolerable ones. In the “Tolerable” tab of our free grounding resistance tool you can see the touch and step limits that result from these assumptions. See the engineering design and studies service or write to us through contact.
Related guides
- IEEE 80: Safety in Substation Grounding
- Tolerable Body Current According to IEEE 80
- Gravel Layer in Substations: Cs Factor and Safety
- Step and touch voltage: difference and IEEE 80
- Substation ground grid: what it is, design and tests
References
- IEEE Std 80-2013, IEEE Guide for Safety in AC Substation Grounding: clauses 7.1 (human body resistance), 7.2 (current paths) and 7.3 (accidental circuit equivalents); equations (10) to (18).
- C. F. Dalziel, salt water tests on hands and feet, cited in IEEE Std 80-2013, clause 7.1.
Frequently asked questions
Why does IEEE 80 use 1000 Ω for the body if other values are lower or higher?
The guide cites an internal resistance of about 300 Ω and values from 500 Ω to 3000 Ω with the skin included. It adopts 1000 Ω for paths from hand to one foot or to both feet, hand to hand and one foot to the other, and it does not count contact resistance of hands, feet, gloves or shoes. It is a simplification on the safe side, because skin damage lowers the resistance.
Is step voltage less dangerous than touch voltage?
By the path, yes: the current from one foot to the other passes less through the heart. The guide cites tests in which a foot-to-foot current up to 25 times larger was needed to produce the same current in the heart region. It still reminds that deaths have occurred from contact between feet, because a fall or a prone position changes the path.
What role does soil resistivity play in the accidental circuit?
It defines the ground resistance of the foot. A more resistive soil, or a high-resistivity surface layer, increases that resistance and reduces the current through the body for the same voltage. That is why resistivity appears in the tolerable voltage expressions.