Magnetic Field Analysis of Unconventional High Surge Impedance Loading (HSIL) Transmission Lines with Different Subconductor Configurations: Numerical Comparisons and Performance Evaluation

Abstract

High-voltage transmission lines are the backbone of modern power systems, facilitating the delivery of electricity from diverse generation sources, including conventional power plants and renewable energy systems, to consumers. As the electricity demand grows, the expansion of transmission infrastructure becomes essential to connecting new consumers with power suppliers. However, traditional transmission lines require significant right-of-way, posing challenges related to land use and environmental impact, as well as limited loadability. To address this issue, compact unconventional High Surge Impedance Loading (HSIL) transmission lines offer a viable solution by reducing right-of-way requirements while enhancing line natural power, mainly leading to less voltage drop. Before the implementation of the new unconventional HSIL lines, it is crucial to assess key parameters, such as magnetic field distribution under the lines, to ensure compliance with environmental and safety standards. This paper presents a numerical analysis of the magnetic field characteristics of compact unconventional HSIL transmission lines with different subconductor configurations. The results show that the proposed HSIL designs can reduce the magnetic field at ground level by up to 71.74% compared to a conventional 500 kV line near the center, as well as by up to 74% at the right-of-way edge, while maintaining magnetic field levels well below the limits set by ICNIRP and state-specific regulations. This study evaluates the magnetic field distribution within the right-of-way, providing insights into the electromagnetic performance and potential implications for transmission line design.

1. Introduction

Overhead transmission lines play a crucial role in transferring electrical energy within power systems, serving as the primary pathways for electricity distribution. Although underground cables offer an alternative, they are considerably more expensive, costing between three to ten times as much as overhead lines, with costs rising for higher-voltage installations. For example, Dominion Energy reports that underground lines range from $5.7 million to $10.3 million per mile, whereas overhead lines typically cost between $1 million and $2 million per mile [1,2]. In addition to high installation costs, underground systems pose challenges such as limited heat dissipation, difficulty in fault detection and repair, and significantly lower surge impedance, which reduces their suitability for bulk power transmission over long distances [3,4]. Consequently, overhead lines continue to be the preferred solution for high-voltage transmission in most scenarios. As electricity demand rises and urban expansion intensifies, optimizing overhead transmission line design becomes increasingly important to ensure cost-effectiveness, land use efficiency, and compliance with electromagnetic safety standards [5].

Since their introduction in 1953, tools such as the St. Clair curves have guided transmission planners in estimating line loadability by considering thermal, voltage-drop, and stability limits [6]. These curves help engineers determine the maximum deliverable power based on line length and operating conditions. For short lines (under 80 km at 60 Hz), thermal ratings typically limit transmission capacity. In contrast, for medium-length lines (80–300 km), voltage drop becomes the dominant factor, while long-distance lines exceeding 300 km are typically constrained by steady-state stability limits [6,7]. These loadability boundaries have since been investigated, validated, and refined in several studies that incorporate more detailed modeling of system inertia, load sensitivity, and reactive power support [8,9,10,11]. To improve transmission line performance, utilities often use series compensation to reduce impedance and enhance stability [12,13]. However, this method poses risks, such as sub-synchronous resonance, and requires complex protection systems. Additionally, the high cost of up to $150 million for a 30% compensation on a 500 kV line limits its practicality [14].

High-Voltage Direct Current (HVDC) technology provides an efficient solution for long-distance power transfer, particularly beyond 600 km, and is well suited for delivering renewable energy from remote sources, such as offshore wind farms [15]. However, its broader deployment faces barriers, including the lack of reliable circuit breakers for multi-terminal systems and issues with ground return modes in high-resistivity soils, which can cause stray currents in nearby AC systems [16,17]. These challenges underscore the enduring importance of AC overhead lines and the necessity to enhance their design to meet growing power demands safely and efficiently.

The restructuring of the electricity supply industry, particularly in the U.S., has placed additional pressure on transmission systems. Deregulation and the rise of renewable and distributed energy sources have led to transmission overloads, with some lines being underutilized while others carry excessive loads. Legal and environmental challenges in acquiring new rights-of-way (ROWs) also delay investments in new transmission infrastructure, further complicating the situation. The U.S. power grid is approaching its maximum load capacity, and events like the 2003 Northeast blackout emphasize the urgent need for reliable transmission systems that can handle grid disruptions [18,19,20,21].

To address these issues, two primary strategies have been adopted: upgrading existing transmission lines and creating compact transmission line designs. Innovations such as composite insulators, polymer-insulated arms, and cross-arms have facilitated the development of compact lines with reduced right-of-way (ROW) requirements [22]. These designs reduce phase-to-phase distances and tower sizes while maintaining mechanical strength. The BOLD design, which has earned multiple awards, is one such example. While these compact designs reduce ROW needs, it remains uncertain whether they can also enhance transmission capacity at a lower cost [23,24].

High Surge Impedance Loading (HSIL) lines have emerged as a potential solution to address transmission challenges. These lines, with unique configurations, enable higher power transfer capacity while reducing the need for extensive rights-of-way (ROWs) [25]. Compared to traditional transmission lines, HSIL designs can achieve the same power transfer (whether thermal or surge impedance) on a smaller ROW, all while meeting electric field and audible noise standards. Additionally, research has explored high-phase order transmission lines, such as six-phase or twelve-phase lines, as alternatives to the traditional three-phase design [26]. However, despite their promise, only a few pilot projects, like the 93 kV six-phase line in New York, have been implemented. HSIL lines demonstrate considerable potential for enhancing power transmission efficiency, minimizing environmental impacts, and offering a cost-effective means to meet the growing demands of modern power systems.

Before implementing a newly designed line, such as unconventional HSIL, it is necessary to evaluate the human exposure limits of the EMF (Electromagnetic Field). The electric and magnetic fields of the recently designed unconventional line in the right-of-way have been assessed, demonstrating the line’s reliability in terms of environmental impact and human exposure limits [27,28]. This paper focuses on the newly designed compact HSIL transmission lines with varying subconductor configurations (n = 2, 3, and 4 subconductors per phase) [29,30,31]. This paper focuses solely on calculating the magnetic field at the right-of-way of these lines. The results are compared with existing safety standards, offering a comprehensive understanding of the potential implications for the design and implementation of HSIL lines in future power systems.

2. Magnetic Field in High-Voltage Transmission Lines

High-voltage transmission lines generate time-varying electromagnetic fields due to the alternating current (AC) flowing through their conductors. The magnetic field ($B$-field) is directly proportional to the magnitude of the current and depends on the spatial arrangement of conductors, phase spacing, and subconductor configurations. The magnetic field produced by a transmission line is typically evaluated at various points within the right-of-way (ROW) and in its surrounding environment to ensure compliance with safety regulations. The fundamental equation governing the magnetic field due to a long straight conductor carrying AC, as shown in Figure 1, is derived from Ampere’s Law:

$$\oint B.dl={\mu }_{0}I$$

(1)

where $B$ is the magnetic field vector (in Tesla), ${\mu }_0$ is the permeability of free space ($4\pi \times {10}^{-7}$), and $I$ is the current flowing through the conductor (in Amperes).

The superposition principle is used to calculate the resultant magnetic field at any given point when multiple conductors are involved. The magnetic field produced by each individual conductor is calculated separately and then combined vectorially.

Overhead lines produce magnetic fields at frequencies of 50 or 60 Hz due to the electric current passing through them. For $N_c$ horizontal conductors, the formula for magnetic flux density also considers the induced eddy currents in the conductive earth [18,32,33]:

$$B_{rms}=0.2\times \sum _{n=1}^{N_c}{I}_n\left\{\left[{\displaystyle \frac{\left(y-d_n\right)}{r_{cn}^2}}-{\displaystyle \frac{\left(y+d_n+\alpha \right)}{r_{in}^2}}\right]{\overrightarrow{a}}_x-\left[{\displaystyle \frac{\left(x-h_n\right)}{r_{cn}^2}}-{\displaystyle \frac{\left(x-h_n\right)}{r_{in}^2}}\right]{\overrightarrow{a}}_y\right\}\hspace{1em}\mu T$$

(2)

$$\begin{gathered} r_{cn}=\sqrt{{\left(x-h_n\right)}^2+{\left(y-d_n\right)}^2}, \\ {r}_{in}=\sqrt{{\left(x-h_n\right)}^2+{\left(y+d_n+\alpha \right)}^2} \\ \alpha =\sqrt{2}{\delta }_g{e}^{-j\pi /4}, \\ {\delta }_g=503\sqrt{{\rho }_g/f} \end{gathered}$$

where ${\rho }_g$ denotes earth resistivity (Ω.m), $f$ denotes the frequency in Hz, $I_n$ denotes the conductor current (Amps-rms), and ${\overrightarrow{a}}_x$ and ${\overrightarrow{a}}_y$ refer to the unit vectors indicating the directional components of the magnetic field in the $x$ and $y$ axes. The factor $0.2$ is a conversion coefficient derived from ${\displaystyle \frac{{\mu }_0}{2\pi }}$ and appropriate unit scaling to express the result in micro Tesla (µT). All distances are considered in meters. The $n$-th conductor is positioned at $\left(x,y\right)=\left(h_n,d_n\right)$. Each conductor’s earth current, as shown in Figure 2, equals its magnitude and runs in the opposite direction. Furthermore, each earth current is buried in the earth with a complex depth proportional to ${\delta }_g$, Earth’s skin depth.

The lateral profile of the magnetic field can be computed using the measured currents in the conductors and the line diameters. Figure 3a denotes magnetic field measurements for a 735-kV transmission line arrangement [34]. Figure 3b shows the transmission line’s lateral profile of the magnetic field. Compared to Figure 3a, the code we wrote for calculating the magnetic field around the transmission line is verified. The magnetic field profiles in Figure 3 are at a height of 1 m above the ground.

3. Considered Transmission Line

In this paper, we analyze four 500 kV transmission lines: one is the conventional Chang-An line, as described in [35] and shown in Figure 4, and the other three are newly designed unconventional lines developed using the optimization methods outlined in [29,30,31]. The conventional line is a three-phase, four-subconductor configuration, with its specifications summarized in

Table 1. Conductor and ground wire of the 500-kV conventional No.2 Chang-An Line.

	Type	Dia (mm)	Sub-Cond. Spacing (m)	Sag (m)
Conductor	LGJ-400/35	26.82	0.45	13.5
Ground Wire	GJ-70	11.0	---	11.25

[35]. Although additional details such as conductor sag and ground wire positions are available in Table 1, these factors were not included in the magnetic field calculations. Specifically, the current in the ground wire was neglected, and instead of accounting for conductor sag, a fixed conductor height corresponding to the tower height was used in the simulations.

The arrangement of the line is as follows:

Figure 4. Configuration and dimensions of the head of the 500-kV conventional Chang-An line tower [35].

Figure 4. Configuration and dimensions of the head of the 500-kV conventional Chang-An line tower [35].

The other three conductors are derived from an optimization problem that aims to maximize the line’s surge impedance loading (SIL) while considering the essential constraints of the transmission line. The optimization scenario was designed in the following way [27,28]

$$\mathrm{m}\mathrm{a}\mathrm{x}\left\{SIL\right\}$$

(3)

with constrained

$$E_i^{max}<E_{th},\hspace{1em}i\in \left\{1,2,3\right\}$$

(3a)

$$D_{i,j}^{p2p}>D_{min}^{p2p},\hspace{1em}i,j\in \left\{1,2,3\right\} \& i\ne j$$

(3b)

$$H_i^{p2g}>H_{min}^{p2g},\hspace{1em}i\in \left\{1,2,3\right\}$$

(3c)

Equation (3) defines the primary objective function of the optimization problem, while Equation (3a–c) represent the associated constraints that govern the feasible design space. The first constraint ensures that the electric field on the surface of the subconductors does not exceed a specified threshold, thereby preventing corona discharge. The second constraint enforces a minimum phase-to-phase clearance to satisfy arc flash protection requirements and maintain electrical safety. The third constraint sets a minimum ground clearance. The rationale behind the selection of these constraints, along with their specific threshold values, is discussed in detail in the subsequent paragraphs.

The natural power of a transmission line is determined using the equation $SIL=P_n=3V_{\phi }^2/Z_c$, where $V_{\phi }$ represents the phase voltage and $Z_c$ denotes the surge impedance. Typically, the phases comprise subconductor bundles, which are multiple conductors arranged in a circular pattern in conventional overhead lines. Modifying this symmetrical subconductor arrangement to asymmetrical configurations can result in narrower corridor widths (CW) and increased $SIL$ values. Transmission lines incorporating such designs are referred to as unconventional lines. In this paper, CW refers to the horizontal distance between the outermost subconductors of the outer phases, not the total right-of-way required by regulation. This definition was adopted for comparative design analysis only, not as a prescriptive corridor definition. In conventional setups, grounded tower sections occupy interphase gaps, resulting in substantial phase-to-phase distances that account for twice the phase-to-ground distances. However, unconventional designs often eliminate this feature, reducing tower width and creating a more compact structure [25].

The goal was to minimize the inductance per unit length ($L$) while increasing the capacitance per unit length ($C$), thereby reducing the surge impedance ($Z_c$) and enhancing the system’s $SIL$. This can be accomplished by enlarging the bundled conductors’ geometric mean radius ($GMR$) and reducing the geometric mean distance ($GMD$) between phases. However, implementing such a design requires meeting specific constraints. The primary requirement is that, for each phase, $i\in \left\{1,2,3\right\}$, the maximum conductor surface electric field ($E_i^{max}$) must remain below a designated threshold ($E_{th}$), which is set at 20 kV/cm for this analysis [27,28]. Exceeding this limit can lead to significant corona discharges, resulting in various issues, including high-power losses, audible noise (AN), and electromagnetic interference (EMI), such as radio interference (RI) and television interference (TVI). We previously studied audible noise (AN) as well as radio and television interference (RI and TVI) from unconventional HSIL lines, as reported in our earlier papers [36]. Empirical formulas are commonly used to estimate AN, RI, and TVI in conventional transmission lines, where the maximum electric field on subconductors plays a key role. We understand that these formulas were developed specifically for conventional lines with symmetrical bundles and validated against experimental data for such configurations. For accurate estimation of AN, RI, and TVI in unconventional lines, it is indeed essential to measure these emissions from full-scale HSIL prototypes and evaluate the applicability of existing empirical models against the measured data. This step is critical and should be completed before finalizing any new line design. However, in the absence of experimental data for unconventional configurations—due to the high cost and limited availability of full-scale outdoor HV testing facilities (e.g., the EPRI lab in Lenox, MA, USA)—design studies and research still need to proceed. In this context, it is important to recall that AN, RI, and TVI are caused by corona discharges around subconductors, which are triggered when the electric field on the surface exceeds the breakdown strength of air, approximately 20 kV/cm in dry conditions. Therefore, if the maximum electric field on each subconductor is kept below this threshold, it is reasonable to expect that the resulting AN, RI, and TVI will remain comparable to those observed in conventional line designs. This principle underpins our use of the 20 kV/cm limit in designing the unconventional HSIL configurations presented in this paper.

Moreover, the distances between phases and between the phases and ground must comply with the minimum clearances.

The next phase of the design process involves selecting a suitable conductor and determining the number of subconductors per bundle. The objective was to use a configuration with $N=2,3\&4,$ where $N$ represents the number of subconductors in each phase. According to [37], recent trends in 500 kV transmission lines with two subconductors per bundle indicate a preference for ACSR conductors ranging in size from 2032 to 2036 AWG. Based on this, conductors are selected to accommodate the cost and weight, and the chosen conductors are listed in

Table 2. Selected conductor’s details.

N	Conductor	SIZE (AWG)	OD (mm)	Ampacity × N	Total Weight (kg/km)
2	Mockingbird	2034.5	42.7	3102	6428
3	Bittern	1272	34.2	3495	6393
4	Rail	954	29.6	4480	6399

.

With the conductor choice established, the bundle spacing ($B$) was determined. The parameter $R$ represents the radius of an idealized circle on which all subconductors in a conventional bundle are positioned. The initial bundle spacing was selected based on standard industry practice, with $B=0.457$ m and $R=B/2\mathrm{s}\mathrm{i}\mathrm{n}\left(\pi /N\right)$ [37]. A minimum phase-to-phase distance of 6.7 m was maintained, consistent with an actual conventional HSIL 500 kV line [35]. We adopted this value because it has already been implemented successfully in a real-world HSIL application. However, studies such as [18] indicate that even smaller clearances may be acceptable under specific conditions. Furthermore, our previous work [38], based on the arc propagation model developed by Rizk and Gallimberti, supports the feasibility of reduced phase-to-phase distances. We validated our selected spacing through detailed numerical analyses of switching overvoltages and arc flashover behavior [38,39]. In summary, while we fully agree that any proposed phase-to-phase distance for a new line design should ideally be verified through full-scale testing under switching and lightning overvoltages, we believe the 6.7 m value used in our design is conservative and likely exceeds the actual minimum distance that would be found acceptable through such tests. A further point supporting our assumption is the physics of air breakdown, which is initiated by corona discharges at subconductors and occurs when the surface electric field exceeds the air breakdown threshold. Since our design explicitly constrains the maximum electric field on each subconductor to 20 kV/cm, this further reduces the risk of underestimating the required clearance. Thus, we do not expect that the 6.7 m spacing will lead to any unforeseen performance issues.

For the reference case, a conventional 500 kV line [35] with horizontally arranged phases at a height of 28 m was considered. This height was adopted as the baseline for the unconventional designs, with a constraint that phase heights must range between 21 m and 35 m above ground level. After establishing these base values, the subconductors were arranged adjacent to form bundles, preserving the conventional circular bundle shape, and the phases were positioned horizontally. The maximum electric field ($E_i^{max}$) for each phase was found to be within the 20 kV/cm limit, as discussed in the following section.

To enhance the geometric mean radius ($GMR$) of the outer phases while reducing the geometric mean distance ($GMD$), one subconductor from the outer phases, $A_1$ and $C_1$, was placed as close as possible to the central phase. To determine the optimal placement for the remaining subconductors, a series of arcs with varying radii, starting from the base $rad=0.457$ m, was centered on $A_1$ and $C_1$. The corresponding subconductors, $A_2$ and $C_2$, were positioned along these arcs while ensuring compliance with the minimum phase-to-phase distance constraint $D_{min}^{p2p}$. The values of $E_i^{max}$ and $SIL$ were calculated for each configuration and plotted. The final configuration was selected based on achieving the highest possible $SIL$ while adhering to the $E_{th}$ constraint. Using this algorithm described in earlier sections, we obtained the positions of the subconductors with their achieved $SIL$. The positions of the subconductors are given in

Table 3. Subconductors’ position of the designed transmission line.

Number of Subconductor	Phase A		Phase B		Phase C		CW	SIL
N = 2	x	y	x	y	x	y	13.857	1137.9
	−4.716	32.9807	−0.2285	28	4.716	32.9807
	−6.9285	28.0	0.2285	28	6.9285	28
N = 3	−6.4638	30.477	−0.2285	27.868	6.4638	30.4770	13.857	1303.6
	−6.9285	27.868	0.0	28.2638	6.9285	27.868
	−6.4638	25.2591	0.2285	27.8681	6.9285	27.868
N = 4	−6.7593	30.3854	−0.3231	28	6.7593	30.3854	18.85	1414.2
	−7.0231	28.0	0.0	27.6769	7.0231	28
	−9.4231	28	0	28.3231	9.4231	28
	−6.7593	25.6146	9.4231	28	6.7593	25.6146

, with the achieved $SIL$, and shown in Figure 5.

To determine the SIL of transmission lines, it is first necessary to calculate the surge impedance ($Z_c$), which is influenced by the line’s inductance and capacitance. However, for accurate calculations, the transmission line must be fully transposed to ensure balanced inductances and capacitances. Figure 6 illustrates a fully transposed three-phase line, where each phase shifts through all three positions along one-third of the total line length.

The transposition process occurs at two points along the line, ensuring that each phase occupies every position for equal segments of the total length. Additionally, within each phase, the subconductors also cycle through all possible positions within the bundle, resulting in a fully transposed configuration for both the phases and the bundles.

The distance between any two positions $x$ and $y$, where $x,y\in \{1,2,3\}$, is represented as $D_{xy}$. Meanwhile, the geometric mean radius ($GMR$) of phase $y$ is denoted by $D_{sy}$. Assuming balanced positive-sequence currents ($I_A,I_B,I_c$), the condition $I_A+I_B+I_c=0$ holds. The magnetic flux linking phase A when it occupies positions 1, 2, and 3 can be expressed as follows:

$${\lambda }_{A1}=2\times {10}^{-7}\left[I_{A}ln{\displaystyle \frac{1}{D_{s1}}}+I_{B}ln{\displaystyle \frac{1}{D_{12}}}+I_{C}ln{\displaystyle \frac{1}{D_{31}}}\right]$$

(4)

$${\lambda }_{A2}=2\times {10}^{-7}\left[I_{A}ln{\displaystyle \frac{1}{D_{s2}}}+I_{B}ln{\displaystyle \frac{1}{D_{23}}}+I_{C}ln{\displaystyle \frac{1}{D_{12}}}\right]$$

(5)

$${\lambda }_{A3}=2\times {10}^{-7}\left[I_{A}ln{\displaystyle \frac{1}{D_{s3}}}+I_{B}ln{\displaystyle \frac{1}{D_{31}}}+I_{C}ln{\displaystyle \frac{1}{D_{23}}}\right]$$

(6)

The average of the above flux linkages is

$$\begin{array}{cc}\hfill {\lambda }_A& ={\displaystyle \frac{{\lambda }_{A1}+{\lambda }_{A2}+{\lambda }_{A3}}{3}}={\displaystyle \frac{2\times {10}^{-7}}{3}}\left[I_A\ln {\displaystyle \frac{1}{D_{s1}{D}_{s2}{D}_{s3}}}+(I_B+I_C)\ln {\displaystyle \frac{1}{D_{12}{D}_{23}{D}_{31}}}\right]\hfill \\ & ={\displaystyle \frac{2\times {10}^{-7}}{3}}\left[I_A\ln {\displaystyle \frac{1}{D_{s1}{D}_{s2}{D}_{s3}}}+\left({-I}_A\right)\ln {\displaystyle \frac{1}{D_{12}{D}_{23}{D}_{31}}}\right]={\displaystyle \frac{2\times {10}^{-7}}{3}}{I}_A\left[\ln {\displaystyle \frac{D_{12}{D}_{23}{D}_{31}}{D_{s1}{D}_{s2}{D}_{s3}}}\right]\hfill \\ & =2\times {10}^{-7}{I}_A\left[\ln {\displaystyle \frac{\sqrt[3]{D_{12}{D}_{23}{D}_{31}}}{\sqrt[3]{D_{s1}{D}_{s2}{D}_{s3}}}}\right]\hfill \end{array}$$

(7)

and the average inductance of the phase $a$ is

$$L_A=2\times {10}^{-7}\left[\ln {\displaystyle \frac{\sqrt[3]{D_{12}{D}_{23}{D}_{31}}}{\sqrt[3]{D_{s1}{D}_{s2}{D}_{s3}}}}\right]$$

(8)

Similarly, $L_B$ and $L_C$ are found to be the same as $L_A$. Only one phase is sufficient for a balanced, completely transposed three-phase line. For the above equations,

$$D_{12}={\left(\prod _{i=1}^N\prod _{j=1}^N{D}_{iA,jB}\right)}^{1/N^2}$$

(9)

$$D_{13}={\left(\prod _{i=1}^N\prod _{j=1}^N{D}_{iA,jC}\right)}^{1/N^2}$$

(10)

where $D_{iA,jB}$ is the distance between the subconductors $i$ in phase $A$ and subconductor $j$ in phase $B$, regarding the first $l/3$ length of the line and the same approach is used for $D_{iA,jC}$. For the lines shown in Figure 3, $D_{23}=D_{12}$. $D_{s1}$ is obtained by

$$D_{s1}={\left(\prod _{i=1}^N\prod _{j=1}^N{D}_{iA,jA}\right)}^{1/N^2}$$

(11)

where $D_{iA,jA}$ is the distance between the subconductor $i$ in phase $A$ and subconductor $j$ in phase $A$, regarding the first $l/3$ length of the line shown in Figure 3, and $D_{1A,1A}$ is the conductor GMR. $D_{s2}$ and $D_{s3}$ phases B and C can be obtained using the same approach.

The capacitance, $C$ of the lines can be obtained by

$$C={\displaystyle \frac{2\pi \times 8.854\times {10}^{-12}}{\ln \frac{\sqrt[3]{D_{12}{D}_{23}{D}_{31}}}{\sqrt[3]{D_{sc1}{D}_{sc2}{D}_{sc3}}}}}$$

(12)

where $D_{sc1}$ can be calculated the same way as $D_{s1}$. However, in this case, $D_{1a,1a}$ that is replaced with the outer radius of the subconductors.

That transposition of both phase and bundle arrangement (Equations (4)–(12)) indeed leads to equal inductance and capacitance among phases. In other words, although bundle arrangements in phases are not the same, via bundle transposition we will indeed have balanced currents in phases. We agree that when subconductors in a bundle are arranged asymmetrically, the currents in each subconductor are no longer perfectly equal—though they remain approximately equal under steady-state balanced conditions. In an asymmetric bundle, the unequal spacing between subconductors leads to variations in mutual inductance and in capacitance both to ground and between subconductors. These differences result in an uneven distribution of current across the bundle, with the subconductor closest to ground or nearest to another phase potentially carrying slightly more or less current. However, this imbalance is typically small, often just a few percent. Importantly, metallic spacers between subconductors play a significant role in mitigating such imbalances. These spacers, made of conductive materials, create low-resistance paths at discrete locations within the bundle. This enforces near-equipotential conditions among subconductors, especially at power frequencies, which naturally promotes equal current distribution. Even in physically asymmetric bundles, the presence of metallic spacers significantly improves current uniformity. For this reason, it is generally acceptable in steady-state power system studies to assume equal current distribution among subconductors within each phase, provided spacers are properly installed and the bundle is electrically continuous. Additionally, the magnetic field at ground level or evaluated at a height of 1 m from ground is a common design criterion. Although the subconductor spacing in the unconventional lines presented in this paper is larger than in conventional designs, it remains much smaller than the distance from the subconductors to the ground. This geometric relationship further diminishes the effect of minor current imbalances on the calculated magnetic field at ground level or evaluated at a height of 1 m from ground. Therefore, based on the above considerations, the assumption of equal current distribution among subconductors in each phase is well justified for the purposes of this study.

While the designs introduced in this paper are novel and not yet implemented, other designs of unconventional HSIL were indeed implemented and are in service. For instance, Russia’s 330 kV and 500 kV lines have utilized non-conventional subconductor placements such as positioning subconductors outside the typical circular array to optimize performance [40,41,42,43,44]. Additionally, elements such as the use of spacers between subconductors of each of the phases have been practically demonstrated, confirming mechanical feasibility. In particular, [25] provides a detailed review of both conventional and unconventional HSIL lines and addresses the question: How many lines of this kind have been commissioned worldwide? In summary, unconventional HSIL lines are indeed feasible, and several are already in service around the world.

4. Results and Discussion

In this study, four high-voltage transmission line configurations were analyzed—one conventional 500 kV line and three newly designed unconventional High Surge Impedance Loading (HSIL) lines, each with two, three, or four subconductors per phase. Each configuration was modeled under identical conditions to ensure a fair and consistent comparison. In the first analysis (Figure 7 and

Table 4. Magnetic field comparison of the designed transmission line at ground level.

Line Type	Number of Subconductors (N)	Corridor Width (CW) (m)	SIL (MW)	Max Magnetic Field Through the ROW (µT)	% Reduction Compared to Conventional	Magnetic Field at the 30 m Distance from the Center (µT)	% Reduction at the Edge Compared to Conventional
Conventional	4	24.6	996	8.8129	-	2	-
HSIL-1	2	13.857	1137.9	2.87	67.43%	0.757	62.15%
HSIL-2	3	13.857	1303.6	2.69	69.47%	0.565	71.75%
HSIL-3	4	18.85	1414.2	2.49	71.74%	0.52	74%

), all lines were assessed with a uniform phase current of 2000 A, whereas in the second scenario (Figure 8 and

Table 5. Magnetic field comparison of the designed transmission line at the calculated SIL condition.

Line Type	Number of Subconductors (N)	SIL (MW)	Loading Current (A)	Max Magnetic Field Through the ROW (µT)	% Reduction Compared to Conventional	Magnetic Field at the 30 m Distance from the Center (µT)	% Reduction at the Edge Compared to Conventional
Conventional	4	996	1151	5.06	-	1.15	-
HSIL-1	2	1137.9	1316	1.85	63.43%	0.48	58.28%
HSIL-2	3	1303.6	1509	2.0308	59.86%	0.48	58.28%
HSIL-3	4	1414.2	1632	2.0366	59.75%	0.426	62.95%

), the lines were analyzed under their respective surge impedance loading (SIL) conditions, reflecting realistic loading behavior. In practice, when a transmission line is in service within a power grid, the current flowing through it varies throughout the year depending on the grid’s loading conditions—from peak load to light load. Moreover, the current also fluctuates over the course of a single day. As such, there is no fixed or constant value that can universally represent the current in the line. For transmission lines operating at 500 kV, which are typically long, the maximum current is often limited by voltage drop constraints rather than by thermal limits. This means that, in practice, the thermal limit or the so-called “natural power” cannot be taken as the definitive maximum current for the line. The 2000 A current used in our studies is a typical value for this voltage level. Additionally, with respect to magnetic field calculations, as seen in Equation (2), the current magnitude affects only the amplitude of the magnetic field—not its spatial distribution. Since our goal is to compare different designs, using a different current value (e.g., 1000 A instead of 2000 A) would scale the magnetic field magnitude proportionally but would not alter the relative comparison, as long as the same current is assumed across all designs.

The primary objective of this evaluation was to assess the effectiveness of HSIL designs in reducing magnetic field exposure at ground level while enhancing power transfer capability through increased SIL. Magnetic field intensity at ground level is a critical parameter in transmission design, particularly in terms of compliance with public and occupational exposure regulations. As shown in Figure 7 and Table 4, all HSIL configurations significantly reduce the magnetic field across the right-of-way compared to the conventional 500 kV line. At a fixed current of 2000 A per phase, the maximum magnetic field across the ROW is reduced by 67.43%, 69.47%, and 71.74% for HSIL-1, HSIL-2, and HSIL-3, respectively. At 30 m from the line center (commonly the ROW boundary), the reductions are 62.15%, 71.75%, and 74%, respectively.

These results confirm that the compact HSIL configurations, despite occupying narrower physical corridors (as low as 13.857 m), can dramatically suppress magnetic field exposure while offering higher surge impedance loading, reaching up to 1414.2 MW in the HSIL-3 design. To provide a more realistic perspective, Table 5 presents the magnetic field performance under each line’s respective SIL-based loading current, which better reflects the natural loading capacity of each configuration. Under these conditions, the conventional line carries 1151 A, while HSIL-1, HSIL-2, and HSIL-3 carry 1316 A, 1509 A, and 1632 A, respectively. Even at these higher currents, HSIL designs continue to outperform the conventional design, reducing the maximum magnetic field by 63.43% (HSIL-1), 59.86% (HSIL-2), and 59.75% (HSIL-3). At the 30 m mark, the field reductions remain substantial: 58.28% for both HSIL-1 and HSIL-2, and 62.95% for HSIL-3.

Crucially, all magnetic field levels for the HSIL designs remain well below the thresholds defined by the International Commission on Non-Ionizing Radiation Protection (ICNIRP) [45]. The ICNIRP sets a public exposure limit of 100 µT, and the 2010 update increases this to 200 µT. Occupational limits are even higher, ranging from 500 to 1000 µT. In both evaluation scenarios, the maximum fields recorded for the HSIL lines remain below 3 µT, which is comfortably within the allowable limits. Furthermore, many U.S. states (e.g., Florida, New York) impose limits at the edge of the right-of-way (ROW), commonly around 15–20 µT. The HSIL designs meet these standards with considerable margin, typically registering below 1 µT at 30 m from the centerline.

To further evaluate the electromagnetic behavior of the proposed transmission lines, the magnetic field intensity was analyzed at multiple vertical heights above the ground: 0 m, 5 m, 10 m, and 15 m. Figure 9, Figure 10, Figure 11 and Figure 12 and

Table 6. Magnetic field comparison of the designed transmission line at different height levels.

Height from Ground Level	Conventional Line		HSIL-1 (N = 2)		HSIL-2 (N = 3)		HSIL-3 (N = 4)
	Max Magnetic field throughout the ROW (µT)	Magnetic field 30 m away center (µT)	Max Magnetic field throughout the ROW (µT)	Magnetic field 30 m away center (µT)	Max Magnetic field throughout the ROW (µT)	Magnetic field 30 m away center (µT)	Max Magnetic field throughout the ROW (µT)	Magnetic field 30 m away center (µT)
0 m	8.8	2	2.87	0.75	2.69	0.56	2.49	0.52
5	11.9	2.1	4	0.8	3.71	0.59	3.47	0.55
10	16.47	2.2	6	0.85	5.32	0.63	5.1	0.58
15	24.8	2.36	10.67	0.89	8.806	0.65	8.47	0.6

present the lateral magnetic field distribution across the right-of-way for the conventional line and each of the three HSIL configurations at these elevations. As expected, the magnetic field intensity increases with height due to two main factors: the decreasing distance between the observation points and the energized conductors, and the reduced influence of the ground-reflected image currents. However, the HSIL configurations consistently demonstrate significantly lower magnetic field levels than the conventional line at every height and lateral position considered. At ground level (0 m), the conventional line exhibits a maximum field of 8.8 µT, while HSIL-1, HSIL-2, and HSIL-3 yield 2.87 µT, 2.69 µT, and 2.49 µT, respectively. At a lateral distance of 30 m, representative of typical ROW boundaries, the field drops to 2.0 µT for the conventional line and further declines to 0.75 µT, 0.56 µT, and 0.52 µT for the HSIL designs.

At ground level (0 m), the conventional line exhibits a maximum field of 8.8 µT, while HSIL-1, HSIL-2, and HSIL-3 yield 2.87 µT, 2.69 µT, and 2.49 µT, respectively. At a lateral distance of 30 m, representative of typical ROW boundaries, the field drops to 2.0 µT for the conventional line and further declines to 0.75 µT, 0.56 µT, and 0.52 µT for the HSIL designs. At 5 m above ground, the trend remains consistent: the conventional line rises to 11.9 µT, while HSIL-1, HSIL-2, and HSIL-3 measure 4.0 µT, 3.71 µT, and 3.47 µT, respectively. At 10 m, the conventional line reaches 16.47 µT, whereas the HSIL alternatives remain significantly lower at 6.0 µT, 5.32 µT, and 5.1 µT. Finally, at 15 m, the conventional line peaks at 24.8 µT, while the HSIL configurations register 10.67 µT, 8.806 µT, and 8.47 µT, respectively.

Notably, at a 30 m horizontal distance, the field remains below 1 µT for all HSIL lines across all evaluated heights, reinforcing their advantage in low-exposure applications. This is a key consideration for multi-use right-of-way (ROW) environments that may include elevated infrastructure, such as overpasses, platforms, or residential buildings, near transmission corridors.

The ability of the HSIL designs to maintain suppressed magnetic field intensities at multiple heights highlights their versatility and potential for compliance in diverse environmental settings. Furthermore, these field levels are far below internationally accepted exposure limits. According to ICNIRP guidelines, the public magnetic field exposure limit is 100 µT (1998) and 200 µT (2010), while occupational limits reach 1000 µT. Similarly, several U.S. states, including Florida and New York, impose stricter limits in the range of 15–20 µT at ROW edges.

5. Conclusions

In conclusion, this paper presents a comprehensive analysis of magnetic field performance for a conventional 500 kV transmission line and three newly designed unconventional High Surge Impedance Loading (HSIL) lines with two, three, and four subconductors per phase, respectively. The optimized HSIL configurations not only enhanced surge impedance loading, reaching up to 1414.2 MW, but also demonstrated substantial reductions in magnetic field intensity. At ground level under 2000 A loading, the maximum magnetic field was reduced by up to 71.74%, and at the 30 m ROW boundary, reductions reached up to 74% compared to the conventional line. Even when evaluated under SIL-based loading currents, the HSIL lines continued to show reductions of over 59% in maximum field and over 62% at the ROW edge. Additionally, magnetic field levels remained below 11 µT at all evaluated heights (0–15 m) and below 1 µT at 30 m lateral distance, far under ICNIRP’s public exposure limits of 100–200 µT. These results confirm that the HSIL designs not only comply with international and regional electromagnetic field standards but also support increased power transfer and reduced corridor width, making them viable alternatives for safe and efficient future transmission line development.