危险就在你脚下: 深入探讨接触电压和跨步电压

介绍

当我们想到电气危险时, 我们经常想象与高压电线或火花机械的直接接触. 然而, 电气工程中一些最隐蔽的危险是在不直接接触带电导体的情况下发生的. 变电站或电力线路发生接地故障时, 大电流涌入大地. 这种电流的涌入会在地面上产生电压梯度, 将人脚下的土壤变成潜在的死亡陷阱. 这种现象受到两个关键安全概念的控制: 阶跃电压 和接触电压.

理解这些概念不仅仅是一项学术练习; 它是变电站设计和公用设施安全的基石. 正如行业标准所指出的, 安全接地系统的主要目标是确保接地设施附近的人员不会面临严重电击的危险[1][3]. 本文探讨了这些电压的定义, 它们如何影响人体背后的科学, 规定安全限度的国际标准, 以及用于减轻这些无形威胁的工程方法.

定义危险: 步 vs. 接触电压

了解风险, 首先必须了解一个人在发生故障时可能遇到的两种电位差之间的区别.

阶跃电压 是一个人跨越一定距离时可能感受到的表面电势差 1 仪表 (大约一步) 用他们的脚, 无需接触任何接地 [1][4] . Imagine a fault where current dissipates into the ground. The voltage is highest at the point where the current enters the earth (例如, a downed conductor or a transmission tower) and decreases as the distance from that point increases[3] . If a person walks in the area, one foot might be at a point of higher voltage (closer to the fault) and the other foot at a lower voltage (further away). The voltage difference between those two points is the step voltage. If this voltage is high enough, it will drive a current through a person’s legs and lower body, potentially causing loss of muscle control or ventricular fibrillation[2][5]..

接触电压, on the other hand, involves a path from hand to feet. It is defined as the potential difference between theGround Potential Rise (GPR) of a grounded structure (such as a substation fence or a metal enclosure) and the surface potential at the point where a person is standing while simultaneously touching that structure[1][4]. . 例如, during a fault, a substation fence might rise to a dangerously high voltage relative to “true earth.” If a person standing a few feet away touches that fence, their body completes the circuit. The voltage trying to drive current through their chest (from hand to feet) is the touch voltage[2].

A third, related concept isTransferred Voltage, a special case of touch voltage. This occurs when a voltage is transferred into or out of a substation from or to a remote point via conductive paths like pipes, rails, or communication [1][3] . A person touching this “energized” remote object while standing on local ground could be exposed to the full force of the remote fault.

The Physics of a Shock: Body Current and Fibrillation

Why are these voltages dangerous? The human body is essentially a large resistor. When a voltage difference appears across it, current flows. The primary cause of death from electric shock isventricular fibrillation, a condition where the heart’s rhythmic pumping action ceases and it begins to quiver chaotically, rendering it unable to pump blood[5][2].

The severity of an electric shock depends on three main factors: the magnitude of the current, the duration of the exposure, and the path the current takes through the body (with hand-to-foot being the most dangerous because it crosses the heart) .

Standards like the IEEE (电气与电子工程师学会) 和IEC (国际电工委员会) have established mathematical models to determine safe voltage limits based on these factors. IEEE标准 80 uses a formula derived from studies by Dalziel, which assumes a body weight and a fixed body resistance of1000 Ž  [1][5]. The allowable body current for a 50 kg (110 lb) person is calculated as:

${我}_{乙}=\frac{0.116}{\sqrt{{ţ}_{\mathrm{小号}}}}\text{ <span class="tr\_" id="tr\_62" data-source="" data-orig="Amperes">Amperes</span>}$我乙​=ţ小号​​0.116​ Amperes

哪里${ţ}_{\mathrm{小号}}$ts​ is the duration of the shock in seconds. For a 70 kg person, the constant changes from 0.116 至 0.157[5] .

Using this, the tolerable touch and step voltages can be calculated. The formulas incorporate the body resistance (1000 Ž) and the resistance of the feet, which is modeled as a conducting disc. The foot resistance is dependent on the resistivity of the surface material (${\mathrm{<span\; class="tr\_"\; id="tr\_76"\; data-source=""\; data-orig="\rho ">\rho </span>}}_{\mathrm{小号}}$ρ小号​) on which the person stands. The standard equations are:

• 阶跃电压: ${它}_{\mathrm{小号}ţ和p}=(1000+6{Ç}_{\mathrm{小号}}{\mathrm{<span\; class="tr\_"\; id="tr\_80"\; data-source=""\; data-orig="\rho ">\rho </span>}}_{\mathrm{小号}})\frac{0.116}{\sqrt{{ţ}_{\mathrm{小号}}}}$它小号ţ和p​=(1000+6Ç小号​ρ小号​)ţ小号​​0.116​
• 接触电压: ${它}_{ţ该您ÇĤ}=(1000+1.5{Ç}_{\mathrm{小号}}{\mathrm{<span\; class="tr\_"\; id="tr\_84"\; data-source=""\; data-orig="\rho ">\rho </span>}}_{\mathrm{小号}})\frac{0.116}{\sqrt{{ţ}_{\mathrm{小号}}}}$它ţ该您ÇĤ​=(1000+1.5Ç小号​ρ小号​)ţ小号​​0.116​

The factor of “6” in the step equation accounts for two feet in series (the resistance of two foot contacts on the same surface), while the factor of “1.5” in the touch equation accounts for two feet in parallel [1][3] .

The IEC standard (符合IEC 60479-1) takes a more complex approach, considering body impedance as a variable dependent on voltage and population percentile, and introducing a “heart current factor” for different current paths. 通常, the IEC standard allows for higher safe limits for fault durations shorter than 400 毫秒, acknowledging the timing of the heart’s vulnerable T-wave phase[2][5] .

Engineering Mitigation and Design

Because the earth itself cannot be relied upon to clear a fault (a ground rod alone cannot reduce touch potential to a safe level[3])), engineers must design grounding systems to actively protect personnel. The design process involves measuring soil resistivity, calculating the maximum fault current, and then designing a grounding grid that ensures actual touch and step voltages remain below the calculated tolerable limits[1][3] .

Several key strategies are employed to achieve this:

1. The Grounding Grid: The primary defense is a well-designed grounding grid. This consists of a network of bare copper conductors buried in a grid pattern (often spaced 10 至 20 feet apart) and securely bonded to all above-ground metallic structures. This grid helps to keep the entire area at a more uniform potential and provides a low-impedance path for fault current[1][3][4].

2. High-Resistivity Surface Layers: This is one of the most visible and effective mitigation measures. In substations, a layer of crushed rock (gravel) is spread over the surface. This material has a very high resistivity (${\mathrm{<span\; class="tr\_"\; id="tr\_123"\; data-source=""\; data-orig="\rho ">\rho </span>}}_{\mathrm{小号}}$ρs​) compared to regular soil. By placing this layer between a person’s feet and the underlying earth, it adds significant series resistance to the shock circuit, thereby reducing the current that can flow through the body[1][4]. The effectiveness of this layer is accounted for in the safety equations by the scaling factor${Ç}_{\mathrm{小号}}$Cs​[1].

3. Equipotential Zones: For workers who must be in direct contact with grounded equipment, creating anequipotential zone is critical. This is often achieved using a temporaryground mat (a metallic mesh) that is bonded to the equipment. When a worker stands on the mat and touches the equipment, both their feet and hands are at the same potential, effectively reducing the touch voltage to zero [4] . Bonding all conductive objects in the immediate work area serves a similar purpose[3].

4. Faster Protection Clearing: 耐受电压限值与冲击持续时间的平方根成反比 ($\sqrt{{ţ}_{\mathrm{小号}}}$ţ小号​​). 因此, 保护继电器清除故障的速度越快, 理论上一个人可以生存的电压越高. 通过减少故障清除时间, 工程师可以显着提高安全边际.

结论

跨步电压和接触电压代表了电气安全方面的独特挑战: 危险是看不见的，存在于我们行走的地面上. 危险不是电源线本身的电压, 但是地球作为导体产生的电压梯度. 经过数十年对电对人体影响的研究, 标准如 IEEE Std 80 和IEC 60479 为工程师提供了量化这些风险并设计系统来减轻风险的工具[1][2]..

From the high-resistivity gravel beneath our feet in a substation to the complex computer models used to design grounding grids, every element works in concert to ensure that when a fault occurs, the invisible voltage gradient remains just that—invisible and, most importantly, harmless. As distributed energy resources and smart grids evolve, maintaining the integrity of these grounding systems remains paramount to protecting both the public and utility workers [3][4].

参考文献

1. IEEE Standard 80,Guide for Safety in AC Substation Grounding .
2. IEC 60479-1, *Effects of current on human beings and livestock – 部分 1: General aspects*.
3. IEEE Standard 81,Guide for Measuring Earth Resistivity, Ground Impedance, and Earth Surface Potentials of a Grounding System .
4. OSHA (Occupational Safety and Health Administration) guidance on electrical safety.
5. Dalziel, Ç. F., & Lee, 在. ŕ. (1960s-1970s). 致命电流。IEEE 工业和通用应用汇刊 .
6. IEC 62305，防雷保护 .

内容由人工智能辅助起草并由作者根据以下内容进行验证 30 多年电能质量领域经验.