Iec 61000 2 10 1998

INTERNATIONALE IEC INTERNATIONALSTANDARD 61000-2-10 Première éditionFirst edition1998-11 Compatibilité électromagnétique CEM – Partie 2-10: Environnement – Description de l’environnement

Remarques introductives

The electromagnetic field produced by a high-altitude nuclear explosion, as outlined in IEC 61000-2-9, induces voltages and currents in all metallic structures These currents and voltages, which propagate through conductors, create a conducted environment Consequently, the conducted environment is a secondary phenomenon that arises solely from the radiated field.

All metallic structures, including cables, conductors, pipes, and wires, will be impacted by the IEMN-HA The conductive environment is crucial as it can transmit IEMN-HA energy to sensitive electronics through interconnections such as signals, power, and ground There are two categories of conductors: external conductors and internal conductors (within a building and other enclosures) Although this distinction may seem simplistic, it is essential for the information provided in the subsequent sections of this standard.

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The pulse width is defined as the time interval between the leading and trailing edges of a pulse, measured at the point where the instantaneous value reaches 50% of the peak pulse amplitude, unless specified otherwise.

4.17 rectified impulse (RI) the integral of the absolute value of a time waveform’s amplitude over a specified time interval

The rise time of a pulse, defined as the time interval between when the instantaneous amplitude first reaches 10% and 90% of the peak pulse amplitude, is a critical parameter in signal analysis.

The short-circuit current, denoted as 4.19, refers to the current that flows when the output terminals of a circuit are directly connected This value is crucial for evaluating the effectiveness of surge protection devices.

4.20 source impedance the impedance presented by a source of energy to the input terminals of a device or network

Vertical polarization occurs when the electric field vector of an electromagnetic wave lies within the incidence plane, while the magnetic field vector is perpendicular to this plane and parallel to the ground This polarization is also referred to as transverse magnetic (TM) or parallel polarization.

5 Description of HEMP environment, conducted parameters

The electromagnetic field generated by a high-altitude nuclear explosion described in

IEC 61000-2-9 can generate currents and voltages in metallic structures, which represent the conducted environment This indicates that the conducted environment is a secondary effect, arising solely from the radiated field.

All metallic structures (i.e wires, conductors, pipes, ducts, etc.) will be affected by the HEMP.

The conducted environment plays a crucial role in directing HEMP energy to sensitive electronics via signal, power, and grounding connections It is essential to recognize the two main categories of conductors: external and internal conductors, particularly concerning buildings or enclosures This distinction, while seemingly straightforward, is vital for the information outlined in this standard.

Electromagnetic topology explains the differences between external and internal conductors External conductors, such as power cables, communication lines, antenna cables, and metallic water or gas pipes, are located outside buildings and are fully exposed to the total electromagnetic interference (EMI) environment These conductors can be either aerial, positioned at a certain height above the ground, or buried In contrast, internal conductors are found within partially or fully shielded buildings, where electromagnetic fields from EMI are significantly reduced This creates a more complex situation, as the waveforms of the electromagnetic field are notably altered by the building's shielding, making it challenging to calculate coupling to internal wires and cables, despite some usable results from EMI simulation tests.

This standard calculates common mode conducted environments on external conductors using simplified geometries and specified IEMN-HA environments for initial, intermediate, and final waveforms The external conducted environments are designed to assess the performance of protective devices outside a building, without considering variations in power systems, transformer effects, or telephone distribution This method yields well-defined approximate waveforms suitable for normative testing of protective elements on external conductors For internal conductors, a procedure is established to estimate appropriate conducted environments for equipment testing For unshielded multi-core cables, the ground return currents are assumed to be equal to the common mode current.

Environnement externe conduit généré par l'IEMN-HA initiale

The intense electric field of the initial IEMN-HA effectively couples with antennas and exposed lines, such as telephone and power transmission lines The coupling mechanism to an antenna is highly variable and significantly influenced by the antenna's parameters It is often recommended to conduct continuous wave (CW) tests on an antenna and combine its response function with the incident IEMN-HA environment Simple equations in paragraph 5.5 allow for the calculation of responses for thin antennas For long lines, a comprehensive series of reliable calculations can be performed in common mode, depending on a few parameters, including conductor length, positioning (above ground or buried), and surface soil conductivity (ranging from 0 m to 5 m depth) Additionally, the coupling of IEMN-HA is influenced by site angle and polarization, enabling a statistical evaluation of the probability of achieving a specific current level.

Table 1 below outlines the calculated common mode short-circuit currents and the source impedances of the equivalent Thévenin model, which are essential for determining open-circuit voltages These results are applicable for calculating common mode currents flowing through bare wires, insulated aerial cables, and the shields of shielded or coaxial cables For shielded cables, it is important to use the measured or specified transfer impedance to ascertain the currents and voltages on the internal wires Although the waveform varies with orientation, a single waveform is specified for aerial lines, characterized by its rise time (from 10% to 90%) and its half-height duration; this is typically denoted as ∆t_r/∆t_pw when describing the rise time and half-height duration of a pulse together.

Electromagnetic topology distinguishes between external and internal conductors External conductors, found outside buildings, are fully exposed to the HEMP environment and include power lines, metallic communication lines, antenna cables, and metallic water and gas pipes These conductors may be either elevated above ground or buried underground.

Internal conductors are found within buildings that are partially or fully shielded, leading to a reduction in HEMP fields This scenario complicates the situation, as the building's shielding significantly alters the HEMP field waveforms, making it challenging to accurately calculate the coupling to internal wires and cables However, some measured data from simulated HEMP tests are available to inform these calculations.

This standard outlines the calculation of external conducted common mode environments using simplified conductor geometries and specified HEMP environments for various time waveforms These environments are designed to assess the performance of protection devices located outside buildings, while excluding the effects of transformers and telephone splice boxes due to variations in telecom and power systems The resulting waveforms, though approximate, are well-defined and essential for standardized testing of protective elements on external conductors Additionally, a procedure is established to estimate the conducted environments for internal conductors, assuming that line-to-ground currents for unshielded multiconductor wires are equivalent to the common-mode current.

5.2 Early-time HEMP external conducted environment

In the context of early-time High-Altitude Electromagnetic Pulse (HEMP), the high-amplitude electric field effectively couples with antennas and exposed lines, such as power and telephone lines The efficiency of this coupling varies significantly based on antenna design, making continuous wave (CW) testing advisable to combine the antenna's response with the HEMP environment through convolution techniques Simple equations are available for calculating the response of thin antennas, while comprehensive common mode calculations for long lines rely on a few key parameters, including conductor length, exposure situation (above ground or buried), and surface ground conductivity at depths between 0 m and 5 m Additionally, the coupling of HEMP is influenced by the angle of elevation and polarization, allowing for a statistical analysis of the likelihood of generating specific current levels.

Table 1 below describes the calculated, coupled, common-mode short-circuit currents and the

The Thévenin equivalent source impedances, which are essential for determining open-circuit voltages, depend on factors such as severity level, conductor length, and ground conductivity These findings are relevant for common-mode currents on bare wires, overhead insulated wires, and the shields of shielded cables or coaxial transmission lines For shielded cables, it is crucial to utilize measured or specified cable transfer impedances to accurately assess internal wire currents and voltages While waveform variations may arise from different exposure geometries, a standardized time waveform is provided for elevated lines, characterized by its rise time (from 10% to 90%) and pulse width (at half maximum).

Table 1 indicates that a severity level of 99% means that 99% of induced currents will be below this threshold The calculated currents for buried lines show minimal variation with the angle of incidence and exhibit a broad probability distribution, with little difference between the 10% and 90% severity levels; thus, they are not described in terms of severity levels but rather in relation to soil conductivity The currents for overhead conductors in Table 1 apply to heights above 5 m, while those for buried conductors pertain to conductors slightly above or below the ground (h < 30 cm) For conductor heights below 5 m, the values for overhead cables in Table 1 can be linearly interpolated between 0.3 m and 5 m In cases where overhead lines transition into the ground (aerial-to-buried transition), the currents initially resemble those of waveform 1 and then decrease based on the length of the buried section until they reach waveform 2, which takes approximately 20 m For further details on obtaining these waveforms, refer to Appendix A.

Table 1 illustrates the common mode short-circuit currents generated by the initial IEMN-HA, where the peak value \$I_{pk}\$ and the temporal shape are influenced by the severity level of the length \$L\$ in meters and the soil conductivity \$\sigma_g\$.

1) Pourcentage de courants dont la valeur est inférieure à la valeur indiquée.

Table 1 shows that a severity level of 99% means that 99% of the produced currents will be below this threshold The calculated buried line currents exhibit minimal variation with the angle of incidence, demonstrating a broad probability distribution with small differences between 10% and 90% severity, and are not categorized by severity levels; instead, variations are presented based on ground conductivity For practical use, the elevated conductor currents are reliable for heights exceeding 5 meters, while the buried currents are applicable for conductors at slightly lower heights.

For conductor heights less than 30 cm above or below the surface, and specifically for heights below 5 m, values can be linearly interpolated between 0.3 m and 5 m as shown in Table 1 In scenarios where elevated lines enter the ground insulated, the initial current waveform will resemble waveform 1, which diminishes with burial distance until it transitions to waveform 2, typically requiring about 20 m For additional details on the derivation of these waveforms, please refer to Annex A.

Table 1 – Early-time HEMP conducted common-mode short-circuit currents including the time history and peak value I pk as a function of severity level, length L in metres and ground conductivity σ g

1) Percentage of currents smaller than the indicated value.

Environnement externe généré par l'IEMN-HA intermédiaire

The intermediate IEMN-HA only couples effectively with conductors longer than 1 km, making it relevant primarily for external conductors like energy transmission lines and telecommunication lines The pulse width of the intermediate IEMN-HA is significantly greater than that of the initial IEMN-HA, resulting in less variation in coupling based on site angle Consequently, the statistical variation is less pronounced compared to coupling with the initial wave However, soil conductivity plays a crucial role and impacts coupling for both overhead and underground lines For more details, refer to Appendix B.

Le tableau 2 décrit l'environnement externe conduit en fonction du type de ligne, de la conductivité du sol (à des profondeurs de 1 km) et de la longueur de la ligne.

Table 2 presents the short-circuit currents (common mode) induced by the intermediate IEMN-HA, where the peak value I pk and the temporal shape depend on the length L in meters and the soil conductivity σ g Table 2a illustrates the characteristics of the overhead conductor.

5.3 Intermediate-time HEMP external conducted environment

The intermediate-time HEMP environment effectively couples with long conductors exceeding 1 km, making it particularly relevant for external power and communication lines Unlike the early-time environment, the wider pulse width in this context results in less variation in coupling based on the angle of elevation, reducing the significance of statistical variation However, ground conductivity plays a crucial role in influencing coupling to both elevated and buried lines For a more comprehensive analysis, refer to annex B.

Table 2 describes the conducted external environment as a function of line length and ground conductivity (to depths of 1 km).

Table 2 – Intermediate-time HEMP conducted common-mode short-circuit currents including the time history and peak value I pk as a function of length L in metres and ground conductivity σ g

Environnement externe conduit généré par l'IEMN-HA finale

The coupling of the final IEMN-HA is significant primarily for long external conductors, such as energy transmission lines or telecommunication lines However, calculating short-circuit currents for typical configurations is challenging, as the final IEMN-HA is represented by a voltage source generated in the ground.

This voltage source generates currents only in conductors connected to the ground at two or more points As the current flow is highly dependent on the circuit's impedance, an analytical method is proposed to develop a normative conductive environment.

The method is demonstrated through an example, with a star/triangle three-phase configuration shown in Figure 4a and its equivalent circuit in Figure 4b (where E₀ represents the peak value of the final IEMN-HA) Given that the highest frequencies in the final IEMN-HA environment are around 1 Hz, it is reasonable to treat the problem as a quasi-continuous current issue, where the voltage source is directly calculated from the final IEMN-HA environment Consequently, it can be assumed that the voltage source Vₛ shares the same temporal dependence as E₀ Since the resistances in Figure 4b (the winding resistance Rᵧ and the grounding resistance Rₓ) are frequency-independent for f < 1 Hz, the induced current Iₚₖ will also exhibit the same temporal dependence as E₀.

Figure 4a – Ligne triphasée et transformateur

Figure 4b – Circuit équivalent simple dans lequel Eo est le champ électrique induit par l'IEMN-HA finale

Figure 4 – Ligne triphasée et circuit équivalent permettant de calculer le courant induit par l'IEMN-HA finale

5.4 Late-time HEMP external conducted environment

The late-time HEMP environment plays a crucial role in coupling with long external conductors, including power and communication lines However, calculating short circuit currents for typical scenarios in this context presents significant challenges.

The HEMP environment acts as a voltage source generated by the Earth, causing currents to flow exclusively in conductors connected to the Earth at multiple points The flow of this current is significantly influenced by the resistance within the circuit This article presents an analytical approach to establish a standard conducted environment.

This article illustrates the method through a specific example, featuring a three-phase Y-delta power configuration depicted in Figure 4a, alongside its equivalent circuit represented in Figure 4b.

The peak value of the late-time HEMP, denoted as Eo, can be analyzed as a quasi-d.c problem, with the voltage source derived directly from the late-time HEMP environment Since the highest frequencies in this environment are around 1 Hz, this approach is valid Consequently, the voltage source V s is assumed to share the same time dependence as Eo Additionally, the resistances in the system, including the parallel Y winding resistances R y and the grounding resistances R f, are frequency independent for frequencies below 1 Hz, leading to the conclusion that the induced current I pk will also exhibit the same time dependence as Eo.

Figure 4a – Three-phase line and transformer configuration

Figure 4b – Simple equivalent circuit where Eo is the induced late-time HEMP electric field

Figure 4 – Three-phase line and equivalent circuit for computing late-time HEMP conducted current

Dans l'exemple ci-dessus, le courant crête peut être calculé:

= 2( + O )+ (1) ó r L est la résistance de ligne parallèle par unité de longueur (Ω/m);

R f est la résistance de mise à la masse (Ω);

R y est la résistance parallèle d'enroulement dans un transformateur (Ω);

L est la longueur de la ligne (m).

In North America, a long 500 kV transmission line has a resistance per unit length of \$8.3 \times 10^{-6} \, \Omega/m\$, a winding resistance of \$0.06 \, \Omega\$, and a ground resistance of \$0.75 \, \Omega\$ For a line measuring \$10^5 \, m\$, the peak induced current is approximately \$40,000 \times E_o\$, where \$E_o\$ is \$0.04 \, V/m\$ as specified in IEC 61000-2-9 for deep soil conductivity (where \$d >> 10 \, km\$).

The peak current is approximately 1,600 A, corresponding to a conductivity of $10^{-4} \, \text{S/m}$ This peak value allows the current waveform to be approximated as a unipolar pulse with a rise time and half-duration of $1/50 \, \text{s}$ To simulate this waveform, a voltage source of 4 kV and an internal resistance of 2.45 Ω should be used It is essential for the transformer to be grounded to utilize the circuit shown in Figure 4, as some transformers are configured in a delta/delta arrangement and lack a direct ground connection.

The equation presented can be easily extended to other scenarios beyond energy transmission lines by calculating the total resistance of the circuit and dividing the total voltage induced along the conductor by this resistance This equation is applicable for long cables positioned above ground; however, for underwater cables, the calculated currents may be reduced by a factor of 100 This reduction is necessary because the electric field $E_0$ is inversely proportional to the square root of the soil's conductivity.

(pour des profondeurs de 10 km à 100 km) Pour les lacs d'eau douce ou les mers peu profondes, les courants ne peuvent pas être réduits d'autant.

Courants antennaires

Les antennes peuvent avoir différentes tailles et formes Dans la bande de fréquences VLF et LF

(3 kHz à 300 kHz), les antennes sont souvent de très longs fils qui peuvent être parfois enterrés.

In the frequency range of 300 kHz to 3,000 kHz, antennas are typically designed as vertical towers positioned above a buried mesh counterpoise For HF and VHF bands (3 MHz to 30 MHz and 30 MHz to 300 MHz), antennas usually take the form of center-fed dipoles At higher frequencies, such as UHF and SHF, antennas increasingly resemble distributed systems that incorporate reflectors and radiating apertures.

Antenna performance is typically optimized within a narrow band around their designed fundamental frequency To enhance narrowband performance, antennas are often tuned by incorporating impedance matching networks, adding passive elements near the active antenna, or integrating the antenna into an array configuration.

Given the wide variety in antenna configurations, it is challenging to provide a precise specification for the response of all antenna types However, the simple dipole antenna model, as illustrated in Figure 5, can serve as an approximate model, offering insights into the expected responses of more complex antennas It is important to note that this model is only applicable to antennas classified as electric dipoles; magnetic loop antennas and apertures are not accurately represented by this simple structure.

Pour des antennes plus complexes, il est recommandé d’effectuer des illuminations en CW ou des essais d’impulsions à haut niveau pour évaluer les réponses de ces antennes.

Using the example provided, the peak current can be calculated as:

= 2( + O )+ (1) where r L is the parallel wire resistance per unit length (Ω/m);

R y is the parallel winding resistance in one transformer (Ω);

In North America, a long 500 kV transmission line exhibits a resistance of 8.3 × 10⁻⁶ Ω/m, along with a transformer winding resistance of 0.06 Ω and a grounding resistance of 0.75 Ω For a line length of 10⁵ m, this configuration results in a peak current of approximately [insert peak current value].

The peak current value is approximately 1,600 A, calculated using the formula 40,000 × Eo, where Eo is specified as 0.04 V/m in IEC 61000-2-9 for deep ground conductivity of 10⁻⁴ S/m This current time waveform can be modeled as a unipolar pulse with a rise time and pulse width of 1/50 s.

To simulate the waveform effectively, utilize a 4 kV voltage source with a source impedance of 2.45 Ω It is crucial to ground transformers for the circuit depicted in figure 4, as some delta-delta transformers lack a direct grounding path.

Equation 1 can be adapted to various scenarios beyond power lines by calculating the total resistance in the circuit and dividing it by the total voltage induced along the conductor Specifically, this equation applies to long cables on land, while deep undersea cables may experience current reductions of up to 100 times This significant decrease is attributed to the electric field E o, which is inversely related to the square root of deep ground conductivity, extending to depths of 10 km to 100 km In contrast, freshwater lakes or shallow seas may not exhibit such substantial current reductions.

Antennas come in many different sizes and shapes At frequencies in the VLF and LF range

Antennas operating in the frequency range of 3 kHz to 300 kHz are typically designed as long wires, with some installations buried underground In the medium frequency (MF) band, spanning from 300 kHz to 3,000 kHz, antennas are commonly structured as vertical towers, which utilize a buried counterpoise grid for effective grounding.

In the HF (3 MHz to 30 MHz) and VHF (30 MHz to 300 MHz) bands, antennas are commonly designed as center-fed dipoles However, at higher frequencies such as UHF and SHF, the antenna systems evolve into more complex structures, utilizing reflecting dishes and radiating apertures.

Usually, antennas are operated in a narrow band of frequencies located around a fundamental design frequency In order to enhance their narrow-band performance, such antennas are often

“tuned” by adding lumped impedance elements, by adding additional passive elements near the active antenna, or by locating the antenna in an array.

Due to the wide variety of antenna configurations, accurately specifying current and voltage waveforms for every type is challenging However, the simple thin-wire vertical dipole antenna can serve as a basic model to approximate the responses of more complex antennas This model is limited to electric dipole class antennas, as it does not adequately represent loop or aperture antennas For evaluating the responses of more intricate antennas, it is advisable to conduct continuous wave (CW) illumination or high-level pulse testing.

Ces types de méthodes d’essai sont décrites dans la CEI 61000-4-23 *

The antenna depicted in Figure 5 is assumed to be loaded with a nominal resistance of 50 Ω, which is a typical load resistance for antennas within its bandwidth It is modeled as a cylinder with a length $ l $ (from end to end) and a radius $ a $, which together define the form factor $ \Omega = 2 \ln (l/a) $ The quality factor $ Q $ of the antenna's load current can be approximated by $ Q = \Omega/3.6 $ For non-ideal antennas, it is important to derive the $ Q $ parameter from antenna response measurements.

Figure 5 – Antenne dipôle chargée par le centre de longueur l et de rayon a, excitée par un champ incident de l'IEMN-HA initiale

Typically, the antenna shown in Figure 5 is positioned near other conductive objects, which alters the incident field and consequently affects the antenna's response compared to that of an isolated antenna For instance, the antenna may be located on or near the ground plane, where the reflected field can enhance the antenna's excitation Additionally, if the dipole is mounted on a mast, the scattered field from the mast and the feed cables will also modify the antenna's excitation.

It is challenging to account for all variations in antenna geometry when developing a standardized waveform of its response However, this issue is somewhat alleviated since, in many cases, the reflected field reaches the antenna after the incident field has already excited it Therefore, the response to the incident field can still provide a sufficient specification of the antenna's response In this simplified approach, all excitations caused by scattered fields will be disregarded.

* CEI 61000-4-23: Compatibilité électromagnétique (CEM) – Partie 4-23: Techniques d'essai et de mesure –

Méthodes d'essais pour les dispositifs de protection pour les perturbations rayonnées IEMN-HA Publication fonda- mentale en CEM (en préparation).

These types of test methods are described in IEC 61000-4-23 *

The antenna depicted in Figure 5 is modeled with a nominal load resistance of 50 Ω, representing a standard in-band load Its dimensions include an end-to-end length of $ l $ and a radius of $ a $, which are utilized to calculate the form parameter $ \Omega = 2 \ln(l/a) $.

The resonance bandwidth factor Q of the load current of this antenna may be approximated by

Q = Ω/3,6 For non-ideal antennas, the Q parameter should be derived from antenna response measurements.

Figure 5 – A centre-loaded dipole antenna of length land radius a, excited by an incident early-time HEMP field

The antenna depicted in figure 5 is typically situated near other conductive structures, which alter the incident field and affect the antenna's response compared to when it is isolated For instance, when positioned on or close to the ground, the antenna experiences additional excitation from the earth-reflected field Similarly, if the dipole is installed on a tall mast, the scattered fields from the mast and support wires will also influence its excitation.

Introductory remarks

The electromagnetic field generated by a high-altitude nuclear explosion described in

IEC 61000-2-9 can generate currents and voltages in metallic structures, which propagate through conductors, representing the conducted environment This indicates that the conducted environment is a secondary effect, arising solely from the radiated field.

All metallic structures (i.e wires, conductors, pipes, ducts, etc.) will be affected by the HEMP.

The conducted environment plays a crucial role in directing HEMP energy to sensitive electronics via signal, power, and grounding connections It is essential to distinguish between two types of conductors: external and internal conductors, particularly concerning buildings or enclosures This differentiation, while seemingly straightforward, is vital for the information outlined in this standard.

Electromagnetic topology explains the differences between external and internal conductors External conductors, located outside buildings, are fully exposed to the total electromagnetic interference (EMI) environment and include power cables, metallic communication lines, antenna cables, and metallic water or gas pipes These conductors can be either aerial, positioned at a certain height above the ground, or buried In contrast, internal conductors are found within partially or fully shielded buildings, where electromagnetic fields from EMI are reduced, creating a more complex situation The waveforms of the electromagnetic field are significantly altered by the building's shielding, making it challenging to calculate coupling to internal wires and cables, although some simulation test results for EMI can be applied.

This standard calculates common mode conducted environments on external conductors using simplified geometries and specified IEMN-HA environments for initial, intermediate, and final waveforms The external conducted environments are designed to assess the performance of protective devices outside buildings, without considering variations in power systems, transformer effects, or telephone distribution This method yields well-defined approximate waveforms suitable for normative testing of protective elements on external conductors For internal conductors, a procedure is established to estimate appropriate conducted environments for equipment testing For unshielded multi-core cables, the ground return currents are assumed to be equal to the common mode current.

5.2 Environnement externe conduit généré par l'IEMN-HA initiale

The intense electric field of the initial IEMN-HA effectively couples with antennas and exposed lines, such as telephone and power transmission lines The coupling mechanism to an antenna is highly variable and significantly influenced by the antenna's parameters It is often advisable to conduct continuous wave (CW) tests on an antenna and combine its response function with the incident IEMN-HA environment Simple equations in paragraph 5.5 allow for the calculation of responses for thin antennas For long lines, a comprehensive series of reliable calculations can be performed in common mode, depending on a few parameters, including conductor length, positioning (above ground or buried), and surface soil conductivity (ranging from 0 m to 5 m depth) Additionally, the coupling of IEMN-HA is influenced by site angle and polarization, enabling a statistical evaluation of the probability of achieving a specific current level.

Table 1 below outlines the calculated common mode short-circuit currents and the source impedances of the equivalent Thévenin model, which are essential for determining open-circuit voltages These results are applicable for calculating common mode currents flowing through bare wires, insulated aerial cables, and the shields of shielded or coaxial cables For shielded cables, it is important to use the measured or specified transfer impedance to ascertain the currents and voltages on the internal wires Although the waveform varies with orientation, a single waveform is specified for aerial lines, characterized by its rise time (from 10% to 90%) and its half-duration When describing the rise time and half-duration of a pulse together, the notation ∆t_r/∆t_pw is typically used.

Electromagnetic topology distinguishes between external and internal conductors External conductors, found outside buildings, are fully exposed to the HEMP environment and include power lines, metallic communication lines, antenna cables, and metallic water and gas pipes These conductors may be either elevated above ground or buried underground.

Internal conductors are found within buildings that are partially or fully shielded, leading to a reduction in HEMP fields This scenario complicates the situation, as the building's shielding significantly alters the HEMP field waveforms Consequently, calculating the coupling to internal wires and cables becomes challenging, despite the availability of some measured data from simulated HEMP tests.

This standard outlines the calculation of external conducted common mode environments using simplified conductor geometries and specified HEMP environments for various time waveforms These environments are designed to assess the performance of protection devices located outside buildings, while excluding the effects of transformers and telephone splice boxes due to variations in telecom and power systems The resulting waveforms, although approximate, are well-defined and essential for standardized testing of protective elements on external conductors Additionally, a procedure is established to estimate the conducted environments for internal conductors, assuming that line-to-ground currents for unshielded multiconductor wires are equivalent to the common-mode current.

Early-time HEMP external conducted environment

High-amplitude electric fields from early-time HEMP couple effectively with antennas and exposed lines, such as power and telephone lines, with the coupling mechanism varying based on antenna design Continuous wave (CW) testing is recommended to combine the antenna's response function with the HEMP environment using convolution techniques Simple equations are available for calculating the response of thin antennas For long lines, reliable common mode calculations can be performed based on a few key parameters, including conductor length, exposure situation (above ground or buried), and surface ground conductivity at depths of 0 to 5 meters Additionally, HEMP coupling is influenced by angle of elevation and polarization, allowing for statistical analysis of the likelihood of generating specific current levels.

Table 1 below describes the calculated, coupled, common-mode short-circuit currents and the

The Thévenin equivalent source impedances, which are essential for determining open-circuit voltages, depend on factors such as severity level, conductor length, and ground conductivity These findings are relevant for common-mode currents in bare wires, overhead insulated wires, and the shields of shielded cables or coaxial transmission lines For shielded cables, it is crucial to utilize measured or specified cable transfer impedances to accurately assess internal wire currents and voltages While waveform variations may arise from different exposure geometries, a standardized time waveform is provided for elevated lines, characterized by its rise time (from 10% to 90%) and pulse width (at half maximum).

Table 1 indicates that a severity level of 99% means that 99% of induced currents will be below this threshold The calculated currents for buried lines show minimal variation with the angle of incidence and exhibit a broad probability distribution, with little difference between the 10% and 90% severity levels; thus, they are not described in terms of severity levels but rather in relation to soil conductivity The currents for overhead conductors in Table 1 apply to heights above 5 m, while those for buried conductors pertain to conductors slightly above or below the ground (h < 30 cm) For conductor heights below 5 m, the values for overhead cables in Table 1 can be linearly interpolated between 0.3 m and 5 m In cases where overhead lines transition into the ground (aerial-to-buried transition), the currents initially resemble those of waveform 1 and then decrease based on the length of the buried section until they reach waveform 2, which takes approximately 20 m For further details on obtaining these waveforms, refer to Appendix A.

Table 1 illustrates the common mode short-circuit currents generated by the initial IEMN-HA, where the peak value I pk and the temporal shape depend on the severity level of the length L in meters and the soil conductivity σ g.

1) Pourcentage de courants dont la valeur est inférieure à la valeur indiquée.

Table 1 shows that a severity level of 99% means that 99% of the produced currents will fall below this threshold The calculated currents for buried lines exhibit minimal variation with the angle of incidence, resulting in a broad probability distribution with small differences between 10% and 90% severity, and are therefore not categorized by severity levels; instead, variations are presented based on ground conductivity For practical use, the elevated conductor currents are reliable for heights exceeding 5 meters, while the buried currents are applicable for conductors at slightly lower heights.

For conductor heights less than 30 cm above or below the surface, and specifically for heights below 5 m, values can be linearly interpolated from table 1 between 0.3 m and 5 m When elevated lines enter the ground insulated, the initial current waveform resembles waveform 1, which diminishes with burial distance until reaching waveform 2, typically after about 20 m For additional details on the derivation of these waveforms, refer to annex A.

Table 1 – Early-time HEMP conducted common-mode short-circuit currents including the time history and peak value I pk as a function of severity level, length L in metres and ground conductivity σ g

1) Percentage of currents smaller than the indicated value.

5.3 Environnement externe généré par l'IEMN-HA intermédiaire

The intermediate IEMN-HA only couples effectively with conductors longer than 1 km, making it relevant primarily for external conductors like energy transmission lines and telecommunication lines The pulse width of the intermediate IEMN-HA is significantly greater than that of the initial IEMN-HA, resulting in less variation in coupling based on site angle Consequently, the statistical variation is less pronounced compared to coupling with the initial wave However, soil conductivity plays a crucial role and impacts coupling for both overhead and buried lines For more details, refer to Appendix B.

Le tableau 2 décrit l'environnement externe conduit en fonction du type de ligne, de la conductivité du sol (à des profondeurs de 1 km) et de la longueur de la ligne.

Table 2 illustrates the short-circuit currents (common mode) induced by the intermediate IEMN-HA, where the peak value I pk and the temporal shape depend on the length L in meters and the soil conductivity σ g Table 2a presents data on aerial conductors.

Intermediate-time HEMP external conducted environment

The intermediate-time HEMP environment effectively couples with long conductors exceeding 1 km, making it particularly relevant for external power and communication lines Unlike the early-time environment, the wider pulse width in this context results in less variation in coupling based on the angle of elevation, reducing the significance of statistical variation However, ground conductivity plays a crucial role in influencing coupling to both elevated and buried lines For a more comprehensive analysis, refer to annex B.

Table 2 describes the conducted external environment as a function of line length and ground conductivity (to depths of 1 km).

Table 2 – Intermediate-time HEMP conducted common-mode short-circuit currents including the time history and peak value I pk as a function of length L in metres and ground conductivity σ g

5.4 Environnement externe conduit généré par l'IEMN-HA finale

The final coupling of the IEMN-HA is significant primarily for long external conductors, such as energy transmission lines or telecommunication lines However, calculating short-circuit currents for typical configurations is challenging, as the IEMN-HA is represented by a voltage source generated in the ground.

This voltage source generates currents only in conductors connected to the ground at two or more points The current flow is highly dependent on the circuit's impedance Therefore, an analytical method is proposed to develop a normative conductive environment.

The method is demonstrated through an example, with a star/triangle three-phase configuration shown in Figure 4a and its equivalent circuit in Figure 4b (where \$E_o\$ represents the peak value of the final IEMN-HA) Given that the highest frequencies in the final IEMN-HA environment are around 1 Hz, it is reasonable to treat the problem as a quasi-continuous current issue, where the voltage source is directly calculated from the final IEMN-HA environment Consequently, it can be assumed that the voltage source \$V_s\$ shares the same temporal dependence as \$E_o\$ Since the resistances in Figure 4b (the winding resistance \$R_y\$ and the grounding resistance \$R_f\$) are frequency-independent for \$f < 1\text{ Hz}\$, the induced current \$I_{pk}\$ will also exhibit the same temporal dependence as \$E_o\$.

Figure 4a – Ligne triphasée et transformateur

Figure 4b – Circuit équivalent simple dans lequel Eo est le champ électrique induit par l'IEMN-HA finale

Figure 4 – Ligne triphasée et circuit équivalent permettant de calculer le courant induit par l'IEMN-HA finale

Late-time HEMP external conducted environment

The late-time HEMP environment plays a crucial role in connecting to long external conductors, including power and communication lines However, calculating short circuit currents for typical scenarios in this context presents significant challenges.

The HEMP environment acts as a voltage source generated by the Earth, causing currents to flow exclusively in conductors connected to the Earth at multiple points The flow of this current is significantly influenced by the resistance within the circuit This article presents an analytical approach to establish a standard conducted environment.

This article illustrates the method through a specific example, featuring a three-phase Y-delta power configuration depicted in Figure 4a, alongside its equivalent circuit represented in Figure 4b.

The peak value of the late-time High-Altitude Electromagnetic Pulse (HEMP) is denoted as Eo, which can be analyzed as a quasi-direct current (d.c.) problem The voltage source is derived directly from the late-time HEMP environment, where the highest frequencies are approximately 1 Hz, making this approach suitable It is assumed that the voltage source V s shares the same time dependence as Eo Additionally, the resistances in the system, including the parallel Y winding resistances (R y) and the grounding resistances (R f), are not frequency dependent for frequencies below 1 Hz Consequently, the induced current I pk will exhibit the same time dependence as Eo.

Figure 4a – Three-phase line and transformer configuration

Figure 4b – Simple equivalent circuit where Eo is the induced late-time HEMP electric field

Figure 4 – Three-phase line and equivalent circuit for computing late-time HEMP conducted current

Dans l'exemple ci-dessus, le courant crête peut être calculé:

= 2( + O )+ (1) ó r L est la résistance de ligne parallèle par unité de longueur (Ω/m);

R f est la résistance de mise à la masse (Ω);

R y est la résistance parallèle d'enroulement dans un transformateur (Ω);

L est la longueur de la ligne (m).

In North America, a long 500 kV transmission line has a resistance per unit length of \$8.3 \times 10^{-6} \, \Omega/m\$, a winding resistance of \$0.06 \, \Omega\$, and a ground resistance of \$0.75 \, \Omega\$ For a line measuring \$10^5 \, m\$, the peak induced current is approximately \$40,000 \times E_o\$, where \$E_o\$ is \$0.04 \, V/m\$ as specified in IEC 61000-2-9 for deep soil conductivity (where \$d >> 10 \, km\).

The peak current is approximately 1,600 A, with the temporal shape of the current resembling a unipolar pulse characterized by a rise time and a half-duration of 1/50 s To simulate this waveform, a voltage source of 4 kV and an internal resistance of 2.45 Ω should be used It is essential for the transformer to be grounded to utilize the circuit shown in Figure 4, as some transformers are configured in a delta/delta arrangement and lack a direct ground connection.

The equation presented can be easily extended to other scenarios beyond energy transmission lines by calculating the total resistance of the circuit and dividing the total voltage induced along the conductor by this resistance This equation is applicable for long cables positioned above ground; however, for underwater cables, the calculated currents may be reduced by a factor of 100 This reduction is necessary because the electric field $E_0$ is inversely proportional to the square root of the soil's conductivity.

(pour des profondeurs de 10 km à 100 km) Pour les lacs d'eau douce ou les mers peu profondes, les courants ne peuvent pas être réduits d'autant.

Les antennes peuvent avoir différentes tailles et formes Dans la bande de fréquences VLF et LF

(3 kHz à 300 kHz), les antennes sont souvent de très longs fils qui peuvent être parfois enterrés.

In the frequency range of 300 kHz to 3,000 kHz, antennas are typically designed as vertical towers positioned above a buried mesh counterpoise For the HF and VHF bands, which span from 3 MHz to 30 MHz and 30 MHz to 300 MHz respectively, antennas are commonly configured as center-fed dipoles At higher frequencies, such as UHF and SHF, antennas increasingly resemble distributed systems that incorporate reflectors and radiating apertures.