Corona Effect and Dielectric Losses in High Voltage Lines

Electrodynamic and Thermodynamic Fundamentals of the Corona Effect

The corona discharge phenomenon in high-voltage (HV), extra-high-voltage (EHV), and ultra-high-voltage (UHV) transmission lines represents a complex manifestation of the disruptive ionization of the surrounding gaseous medium—predominantly atmospheric air—when the local electric potential gradient at the conductor surface exceeds the critical dielectric strength of the air. At a macroscopic level, this phenomenon translates into continuous active power loss, audible noise generation, electromagnetic interference (EMI), progressive degradation of insulating materials via surface erosion, and the secondary production of highly corrosive ozone and nitrogen oxides.

From the perspective of electromagnetic field theory, the electric field surrounding a cylindrical conductor of radius $r$ subjected to an alternating or direct potential is determined by solving Laplace's equation for the spatial distribution of the electrostatic potential. For an infinitely long, straight, and isolated cylindrical conductor, the surface electric field gradient $E_s$ is expressed by the classical formulation:

Where $V$ is the phase-to-ground potential of the conductor, $r$ is the outer radius of the conductor, and $D$ is the equivalent distance to the ground plane or to adjacent phase conductors. When the conductor is of the bundle type (bundle conductors), the calculation of the surface electric field becomes significantly more complex due to the electrostatic interaction among the subconductors. The maximum surface gradient in a bundle of $n$ subconductors separated by a distance $A$ (bundle radius $R$ where R = \frac{A}{2 \sin(\pi/n)} ) is evaluated precisely using Maxwell's proximity correction factor and the modified Peek equation for bundles:

The ionization of air does not occur instantaneously or uniformly throughout the inter-electrode space; rather, it initiates in microscopic regions where the local electric field exceeds the dielectric strength of standard air, known as the disruptive strength or critical disruptive gradient ($E_0$). Physically, air is never a perfect insulator; it always contains a small concentration of free ion pairs generated by cosmic radiation and the natural radioactivity of the Earth's crust. When these free electrons are accelerated by the intense electric field, they acquire sufficient kinetic energy between successive collisions with neutral nitrogen ($N_2$) and oxygen ($O_2$) molecules to trigger impact ionization.

Townsend's criterion for the self-sustainability of an avalanche discharge is defined by the impact ionization coefficient \alpha (the number of ion pairs generated by an electron per unit path length in the direction of the field):

Where \eta is the electron attachment coefficient (capture of free electrons by electronegative oxygen molecules, forming negative ions), $x_c$ is the critical length of the ionization zone where the local electric field exceeds the critical threshold, and $K$ is a critical ionization constant (approximately $18.0$ to $20.0$ for discharges in air at normal atmospheric pressure). The dielectric strength of dry air under standard temperature and pressure conditions (STP: $T_0 = 20 °C$ or $293.15 K$, and barometric pressure $P_0 = 760 mmHg$) is given empirically by Peek's celebrated law:

Where $g_0$ is the basic disruptive dielectric gradient for ideal flat or smooth air ($30 kV/cm peak$ or $21.2 kV/cm RMS$), $m_0$ is the conductor surface irregularity factor ($m_0 = 1.0$ for perfectly polished cylindrical conductors; m_0 = 0.8 \dots 0.98 for stranded or corroded conductors), $r$ is the conductor radius in centimeters, and \delta is the relative air density, calculated thermodynamically as:

Where $P$ is the barometric pressure in centimeters of mercury (cmHg) and $T$ is the ambient temperature in degrees Celsius (°C). Altitudinal variations drastically reduce the air density \delta , decreasing $E_0$ and causing lines designed to operate without corona effects at sea level to suffer severe losses in high-mountain corridors.

Physical and Thermodynamic Mechanisms of Dielectric Losses

Corona losses are not limited solely to the dissipation of electrostatic energy in the luminous corona, but represent a complex coupling among thermodynamic phenomena, chemical ionization, and energy dissipation in the alternating electromagnetic field. When the voltage applied to the line exceeds the critical corona voltage ($V_c$), the corona current ceases to be in pure quadrature with the voltage (as occurs in the pure geometric capacitance of the line) and introduces an in-phase component, which directly degrades the line power factor and generates active power losses.

Analytically, power lost due to the corona effect under sinusoidal alternating voltage was initially modeled by F.W. Peek via empirical expressions based on extensive experimental campaigns. Peek's general formulation for corona power losses under favorable weather conditions (fair weather) is expressed as:

Where $f$ is the system frequency in Hertz ($50$ or $60 Hz$), $Vph$ is the RMS phase operating voltage ($kV$), and $V_c$ is the RMS critical disruptive phase voltage, formally defined as:

Where $m_v$ is the irregularity factor due to meteorological and surface conditions of the line. It is fundamental to emphasize that Peek's equation is highly accurate only under fair-weather regimes and standard industrial frequencies. However, under conditions of rain, snow, frost, or high relative humidity ( RH > 85\% ), the presence of water droplets suspended or adhered to the lower surface of the conductors drastically alters the local geometry of the electric field.

Under rainy conditions, water droplets deform into ellipsoidal or ovoid shapes due to the competition between the surface tension of water and local electrostatic forces. At the tip of these deformed droplets, the geometric amplification factor of the local field can exceed a factor of $3$ to $5$, locally reducing the ionization threshold. As a direct consequence, the critical corona voltage shifts downward, and dielectric losses increase exponentially, potentially multiplying nominal fair-weather losses by a factor of $10$ to $20$.

The most advanced analytical model for calculating corona losses under adverse weather conditions and in extra- and ultra-high-voltage (EHV/UHV) systems was developed by Peterson and subsequently refined by the Electric Power Research Institute (EPRI):

Where $Kepri$ is a specific conductor design constant, $V_0$ is the corona inception voltage under storm conditions, and $Fweather$ is a stochastic weather penalty factor that quantifies the intensity of rainfall in millimeters per hour ($mm/h$).

Side Effects and Degradation of Insulating Materials

The corona effect represents not only an energy inefficiency translated into operational economic losses of active power, but also triggers a series of highly destructive physical-chemical processes for the structural integrity of electric grid components, including metal conductors, porcelain or glass insulator strings, and synthetic polymeric materials of cables and hardware.

From a chemical standpoint, the continuous ionization of air via the dissociation of oxygen and nitrogen molecules generates highly reactive radical species, among which ozone ($O_3$), nitrogen oxides (mainly $NO$ and $NO_2$), and, in the presence of atmospheric humidity, nitric acid ($HNO_3$) stand out:

The formation of nitric acid on the surface of ceramic or polymeric insulators, combined with the deposition of saline and industrial contaminants (salt fog, carbonaceous pollution), creates a conductive surface electrolytic layer that facilitates the formation of surface leakage currents. These currents lead to the appearance of partial dry-band arcing, catastrophically degrading silicone rubber (HTV) or EPDM insulators via the phenomenon of tracking and erosion, or provoking stress corrosion cracking (SCC) in galvanized steel hardware.

Additionally, continuous ionic bombardment on the surface of the metal conductor (usually aluminum conductor steel-reinforced, ACSR) causes pitting corrosion, mechanical micro-abrasion, and the gradual loss of the useful cross-sectional area of the outer wire, reducing the mechanical tensile strength of the conductor against extreme wind loads and span tangential tension.

Forensic Failure Analysis in High-Voltage Equipment Associated with the Corona Effect

Partial discharges (PD) and the corona effect are the root cause of a high percentage of premature catastrophic failures in power transformers, gas-insulated switchgear (GIS), dry-insulation underground cables (XLPE), and capacitive bushings. A rigorous forensic analysis reveals the molecular degradation mechanisms operating inside this equipment when the electric field design is inadequate.

In power transformer windings submerged in mineral oil, internal corona manifests as partial discharges in gas cavities or bubbles dissolved in the dielectric liquid, or in zones of high tangential gradient at the edges of electrostatic shields. Under the action of intense alternating electric fields, accelerated electrons decompose the hydrocarbon molecules of the mineral oil, generating characteristic combustible gases (hydrogen $H_2$, methane $CH_4$, acetylene $C_2H_2$). This process is described by low-energy oil pyrolysis thermodynamics:

Dissolved gas chromatographic analysis (DGA, according to IEEE C57.104 and IEC 60599 standards) allows for the identification of low-energy partial discharges (corona) via gas concentration ratios (Key Gas Method and Duval triangles). If these discharges are not mitigated, the solid insulation of impregnated kraft paper suffers irreversible cellulosic degradation, losing its mechanical and dielectric strength until culminating in a disruptive failure between turns or to ground.

In high-voltage cross-linked polyethylene (XLPE) insulated cables, partial discharges and microscopic corona occur in micro-voids or at the interface between the extruded semiconductor and the main insulation due to geometric irregularities or thermal contraction during the manufacturing process. The mechanism of deterioration via "electrical treeing" initiates when the local electric field in the micro-cavity exceeds the dielectric strength of the surrounding polymer ( EXLPE \approx 300 -- 400 kV/mm for short pulses, but much lower for long-term fatigue):

Repetitive discharges inside the cavity generate erosion via high-energy electron bombardment, breaking covalent carbon polymer bonds and expanding tree-like branched channels that eventually short-circuit the total thickness of the insulation, causing dielectric breakdown of the cable.

Advanced Design and Mitigation Strategies in Transmission Lines

Effective mitigation of the corona effect and associated dielectric losses requires rigorous parametric optimization during the conceptual and detailed engineering stages of High, Extra, and Ultra-High Voltage transmission lines. Design methodologies are based on the analytical control of the maximum surface gradient of the electric field below critical thresholds established by international standards (IEEE Std 738, IEC 60525, CIGRE).

The primary mitigation strategies implemented in modern engineering comprise:

• Conductor Geometry Optimization (Bundle Conductors): In 500 kV systems and above, the use of a single conductor is unviable due to the excessive gradient. Two-, three-, four-, or six-subconductor configurations (bundle conductors) are employed. This increases the equivalent conductor radius $Req$, drastically reducing the surface electric field according to Maxwell-Peek equations.
• Conductor Diameter Increase: Use of conductors with high-strength steel cores and outer aluminum layers featuring special profiles (expanded ACSR/AS conductors or trapezoidal wire ACCC glass-fiber core conductors), which allow larger outer diameters without disproportionately increasing the mass weight per unit length.
• Design of Grading Rings and Anti-Corona Shields (Corona Rings): Installation of metallic aluminum toroidal rings on the end hardware of insulator strings in EHV/UHV. These rings modify the equipotential distribution of the electric field, drastically reducing the gradient at critical connection points between the metal conductor and the first ceramic or polymeric insulator, preventing the concentration of lines of force.
• Surface Treatments and Cleaning: Use of hydrophobic silicone rubber-based coatings on composite insulators to minimize leakage current and prevent the formation of wet conductive paths.

Parameter / Electrical Variable	Normative Limit (IEEE / IEC)	Critical Failure Condition	Operational and Dielectric Consequences
Maximum Surface Gradient ($Emax$)	\leq 15 -- 17 kV/cm (RMS) (500 kV Lines)	$Emax > E_0$ (Perturbed air dielectric strength)	Onset of disruptive discharges, elevated corona losses, and excessive audible noise.
Fair-Weather Corona Losses	\leq 1.0 kW/km/phase (Optimal EHV Design)	Operational losses exceeding project economic tolerance	Permanent energy inefficiency, localized heating, and accumulated voltage drop.
Audible Noise Level (AN)	\leq 52 dB(A) at Right-of-Way (RoW) edge	Heavy rainfall storms ($> 25 mm/h$)	Unacceptable acoustic pollution, community complaints, and regulatory operational restrictions.
Radio Interference Voltage (RIV)	\leq 50 dB \ above 1\mu V/m at $1 MHz$	Conductor surfaces with advanced corrosion or pitting	Severe disruption in communication systems, radio frequency, and SCADA telemetry.
Ozone Concentration ($O_3$)	\leq 0.05 ppm at ground level (Environmental standards)	Thermal inversion and low catenary height	Environmental toxicity, accelerated degradation of elastomeric seals and synthetic polymers in substations.

Practical Application and Engineering Analysis via Vexten Suite

To illustrate the analytical rigor demanded in the design of highly complex electric power systems, the standard automated computational calculation procedure within the Vexten Suite engineering environment is implemented below, applying international standards IEC 60909 / IEEE 141 for short-circuit and load-flow analyses incorporating dielectric loss components, as well as IEC 60287 / NEC 310 for high-voltage cable sizing under harmonic regimes and power factor conditions.

Consider an Extra-High-Voltage (EHV) three-phase transmission line of $500 kV$ nominal, industrial frequency $f = 60 Hz$, length $L = 120 km$, operating in a corridor at an altitude of $2200 m$ above sea level. The conductors are of the quad-bundle aluminum conductor steel-reinforced type ("Falcon" ACSR), with a subconductor radius $r = 1.828 cm$, subconductor spacing within the bundle $A = 45.7 cm$, and geometric equivalent phase-to-phase distance $Deq = 11.5 m$.

The first step executed by the Vexten Suite calculation engine consists of evaluating the relative air density \delta adjusted for altitude and design ambient temperature ($T = 35 °C$, local barometric atmospheric pressure corrected for altitude $P = 58.6 cmHg$):

With this relative air density value, the critical disruptive gradient $E_0$ is calculated via the modified Peek formula, considering a conservative surface roughness factor for in-service conductors of $m_0 = 0.88$:

The electromagnetic field analysis module of Vexten Suite calculates the actual maximum surface gradient of the conductor bundle $Emax$ under the maximum continuous system operating voltage ($Vmax = 550 kV$, meaning V_{ph\_max} = 317.54 kV peak phase-to-ground value):

Given that the calculated maximum surface gradient of 19.27 kV/cm (peak) is lower than the critical disruptive gradient of 24.77 kV/cm (peak) , the Vexten Suite algorithm verifies that the line operates under a safe regime without frank ionization during fair-weather conditions. However, upon activating the stochastic weather simulation module for heavy rain conditions ($Fweather$ rainfall penalty factor of $12.5$), the software recalculates active power corona losses:

For a total length of $120 km$, the total active power losses due to the corona effect under storm conditions amount to:

This critical result generated by Vexten Suite conclusively demonstrates that, during adverse weather events, corona losses in EHV lines can represent a parasitic load on the order of megawatts, impacting economic dispatch stability and requiring dynamic analysis within Automatic Generation Control (AGC) and reactive network compensation systems.

Likewise, in the complementary sizing analysis of high-voltage underground cables under harmonics according to IEC 60287, the software evaluates the reduction factor due to accumulated dielectric losses in the XLPE insulation and total voltage harmonic distortion ($THD _V$), applying the temperature correction factor and supplementary losses in metallic screens:

This level of analytical and computational integration ensures that designs endorsed by Vexten Academy comply with the strictest standards of reliability, operational safety, and energy efficiency within the global domain of high-power electrical engineering.