Electrical Safety Engineering of Renewable Energy Systems. Rodolfo Araneo
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path left hand to feet, and Ih is the fibrillation current for different body paths, as shown in Table 1.1.
Table 1.1 Heart-current factor F for different current paths
| Path | Heart-Current Factor F | |
|---|---|---|
| IEC | Simulated | |
| Left hand–feet | 1 | 1 |
| Hands–feet | 1 | 0.85 |
| Left hand–right hand | 0.4 | 0.75 |
| Right hand–feet | 0.8 | 0.88 |
| Hands–seat | 0.7 | 0.84 |
| Left foot–right foot | 0.04 | 0.01 |
| Left hand–right foot | 1.00 | 1.00 |
| Left hand–left foot | 1.00 | 1.00 |
| Right hand–right foot | 0.88 | – |
| Right hand–left foot | 0.8 | 0.89 |
The larger is the heart-current factor; the more dangerous is the current pathway through the body.
As an example, a current of 225 mA hand-to-hand has the same likelihood of producing ventricular fibrillation as a current of 90 mA left hand-to-both feet. Therefore, the hand-to-hand pathway is less hazardous than the left hand-to-both feet.
The IEC does advise that the published heart-current factors must be considered as a rough estimation of the relative danger of the various current paths with regard to ventricular fibrillation. The IEC formulation of the heart-current factor is, in fact, based on experiments on corpses, animals and volunteers, or data from electrical accidents. Trials on animals produce results whose extrapolation to humans may not always be reliable, due to the obvious anatomical differences. In addition, exhaustive information about electrical accidents may not be available; therefore, it may not be possible to evaluate the magnitude of the body current affecting the injured and have reliable data.
A possible alternative computation for F can be obtained through human phantoms, which are computerized models that allow the numerical simulation [13] of the current pathways through the human body when subjected to external stimuli, as shown in the last column of Table 1.1.
The comparison between the two sets of heart-current factors shows that the IEC may underestimate the magnitude of F for pathways involving the right hand, probably due to the extrapolation of the results of measurements on animals to humans.
The same heart current factors are also applicable to d.c. currents.
1.3 The Electrical Impedance of the Human Body
The electrical impedance ZB of the human body is capacitive in nature [14] due to the capacitance Cs of the skin (Figure 1.3); therefore, it depends on the frequency of the applied touch voltage.RBi is the internal body resistance; Rcs represents the resistance of the skin at the surface area of contact, which takes into account the presence of the pores, which are small conductive elements; Rcs is strongly variable with environmental and physiological conditions (e.g., sweaty hands).
Figure 1.3 Impedances of the human body.
The model of Figure 1.3 has been validated on cadavers by analyzing the current response to a d.c. voltage V [15] (Figure 1.4).
Figure 1.4 Current response of human body to d.c. voltage.
When the d.c. touch voltage occurs, the capacitances Cs are not charged, and become short-circuits during the initial transient, bypassing the contact resistances Rcs; therefore, the ratio of the touch voltage V to the current peak equals RBi. After the transient expires, the capacitances of the skin become an open circuit, and the current reaches the steady-state value of V /(RBi +2Rcs ), where the denominator is the total body resistance.
The impedance of the skin is the primary barrier against the flow of the body current, providing that the voltage is not high enough to puncture it (i.e., below 200 V), and the skin is not wet. Voltages greater than 200 V exceed the dielectric strength of the skin, Cs “fails” and short-circuits the contact resistance Rcs, reducing the resistance of the human body to RBi: the body current can cause greater damages to the internal organs.
In addition, at 50/60 Hz, the capacitive reactance of the skin is practically an open circuit, and ZB ≈RBi+2Rcs.
1.3.1 The Internal Resistance of the Human Body
RBi in Figure 1.3 represents the internal resistance of the human body, which depends on the chosen current pathway [16]. IEC 60479-1 expresses the resistance Ri of different segments of the body, ignoring the skin contribution at 50/60 Hz, as a percentage of the internal resistance of the human body related to the path hand-to-foot (Figure 1.5).
Figure 1.5 Internal partial impedances of the human body (no skin contribution).
For example, the partial impedance of the trunk (i.e., segment D-E) is only 1.3% of the total body impedance hand-to-foot, due to large amount of conductive fluids normally present in the trunk.
The resistance Ri of the segment are determined as Ri = ρl/S, where is the segment tissue mean resistivity, l the mean length of the segment, and S its mean cross-sectional area. The cross-sectional area of the body segment plays a crucial role in determining its resistance: fingers and joints, such as elbow and knee, have higher resistance values due to their relatively small cross-sectional areas, even though they are made of well-conductive tissues.
The resistance Ri of the segment are determined as Ri = ρl/S, where is the segment tissue mean resistivity, l the mean length of the segment, and S its mean cross-sectional area. The cross-sectional area of the body segment plays a crucial role in determining its resistance: fingers and joints, such as elbow and knee, have higher resistance values due to their relatively small cross-sectional areas, even though