DC Injection Core Saturation in ATEX Zone 1 & DGA Duval Diagnosis

Electromagnetic Phenomenology of DC Offset Injection

In industrial chemical processing facilities classified as ATEX Zone 1, the widespread adoption of static power converters—such as Active Front End (AFE) rectifiers, Variable Frequency Drives (VFDs), and Battery Energy Storage Systems (BESS)—has introduced a critical electromagnetic degradation phenomenon: the unintentional injection of direct current (DC offset) into the alternating current distribution network. This DC injection, even when constrained to fractions of 0.5% to 1% of the transformer's nominal current, radically alters the magnetization regime of the core in power and isolation transformers.

The root cause of this phenomenon lies in the intrinsic switching asymmetries of power semiconductors (IGBTs/IGCTs), thermal drift of Hall-effect current sensors in inverter control loops, asymmetrical dead-time distortion during bridge leg firing, and voltage imbalances across the intermediate DC bus. From an electromagnetic standpoint, the direct current resistance of the transformer primary winding ($Rdc$) is extremely small. Consequently, a minimal residual DC voltage ($Vdc$) induces a significant direct current $Idc = Vdc / Rdc$, which flows through the winding and establishes a continuous, unidirectional magnetic flux ($\Phi_{dc}$).

The total magnetic flux within the transformer core becomes governed by the superposition of the fundamental-frequency alternating flux ($\Phi_{ac}$) and the continuous offset flux ($\Phi_{dc}$):

where $N$ represents the number of winding turns, $\omega$ is the fundamental angular frequency ($2\pi f$), and $\mathcal{R}_{m}$ is the equivalent magnetic reluctance of the core circuit, expressed by:

Given that the relative magnetic permeability of Cold-Rolled Grain-Oriented (CRGO) silicon steel $\mu_r(B)$ is highly non-linear and dependent on the instantaneous flux density $B(t)$, the presence of $Bdc = \Phi_{dc} / Aeff$ shifts the mean operating point on the $B-H$ hysteresis loop. This shift biases the curve into the deep magnetic saturation region during one half-cycle of the sinusoidal wave, while the opposing half-cycle remains within the linear region.

The direct consequence of this asymmetrical saturation is severe distortion of the magnetizing current ($imag(t)$). The behavior of the flux density and the resulting magnetizing current is mathematically described via the Fourier series of a heavily distorted wave exhibiting a loss of half-wave symmetry:

Unlike symmetrical saturation (which generates exclusively odd-order harmonics $3^{ rd }, 5^{ th }, 7^{ th }, \dots$), DC offset saturation induces a dense spectrum of even-order harmonics ($2^{ nd }, 4^{ th }, 6^{ th }, \dots$) alongside an exponential surge in the peak magnetizing current ($Ipeak$). Under severe saturation conditions, the magnitude of the magnetizing current can increase by a factor of 10 to 50 relative to its nominal no-load value, taking the form of narrow, high-amplitude pulses in each power frequency cycle.

This strongly distorted stray flux invalidates linear magnetic design models, causing parasitic inductive coupling with surrounding metallic structures, core clamping hardware, winding presses, and the transformer tank walls.

Thermal and Mechanical Impact in ATEX Zone 1 Hazardous Areas and IEC 61439-1/2 Assemblies

In the strict context of a chemical facility categorized as an ATEX Zone 1 explosion hazard area (pursuant to IEC 60079-0 and IEC 60079-14 directives), electrical equipment must not only operate within nominal performance boundaries, but must guarantee under any service fault condition that the temperature of its external surfaces never reaches the autoignition temperature of the gas, vapor, or mist mixture present in the atmosphere (Temperature Classes T1 to T6).

DC saturation of transformers and reactors located within or interfaced to Zone 1 invalidates the thermal design parameters defined by low-voltage switchgear assembly standards IEC 61439-1 and IEC 61439-2. Core saturation compromises the fundamental assumption that magnetic flux remains confined within the magnetic steel laminations. Upon reaching the saturation flux density of the material ($Bsat \approx 1.7 - 2.0 T$ in CRGO laminations), core permeability drops precipitously toward values approaching the permeability of air ($\mu_r \to 1$). This forces a critical fraction of the magnetic flux into external stray flux paths.

This magnetic stray flux impinges perpendicularly on non-laminated structural elements of the transformer and switchgear enclosures (doors, sheet steel support profiles, busbar enclosures per IEC 61439-2). According to Faraday-Lenz law and electromagnetic field diffusion equations, the time-varying stray flux induces massive parasitic eddy currents within the tank walls and switchgear framing structures:

where $\sigma$ is the electrical conductivity of the structural steel and $\vec{A}_{stray}$ is the magnetic vector potential of the stray flux. These eddy current losses concentrate within very small metallic volumes, producing localized hotspots. In an ATEX Zone 1 installation with a strict Temperature Class T4 requirement (maximum allowable surface temperature $Tmax \le 135^\circ C$), a localized hotspot on the outer wall of the transformer or assembly enclosure resulting from saturation leakage flux can easily exceed $160^\circ C - 200^\circ C$ within minutes of uncompensated DC operation, instantly invalidating the Ex protection method (e.g., Ex "d", Ex "eb", or Ex "p").

Furthermore, under IEC 61439-1/2 (Clause 10.10 Verification of Temperature Rise), busbar dimensioning and enclosure thermal dissipation capacity are calculated based on linear Joule losses and standard harmonic losses. DC saturation introduces a compound thermal-mechanical impact:

• Extreme Enclosure Thermal Derating: Total transformer iron losses escalate as a quadratic function of the high-frequency harmonic components induced in the flux ($PFe = Physt \cdot \frac{f}{50} + Peddy \cdot \left(\frac{f}{50}\right)^2$). The internal ambient air volume inside the enclosure will exceed maximum operating ambient temperature limits ($35^\circ C$ 24-hour average), inducing premature dielectric breakdown of busbar support insulators (polyamides, epoxy resins).
• Magnetostrictive Mechanical Stresses: The asymmetrical magnetic regime generates high-magnitude electromagnetic and reluctance forces varying at both fundamental and even harmonic frequencies ($100 Hz , 200 Hz$). Magnetostrictive distortion ($\lambda = \Delta L / L$) loses its half-cycle symmetry, inducing severe vibratory accelerations across core clamps and metallic enclosures:
  $$Fmag(t) = \frac{B(t)^2 \cdot Aeff}{2 \mu_0} = \frac{\left(Bac\sin(\omega t) + Bdc\right)^2 Aeff}{2 \mu_0}$$
  The cross-term $\frac{Bac Bdc \sin(\omega t) Aeff}{\mu_0}$ introduces a primary oscillatory force component at the fundamental frequency of $50 Hz$ (instead of the normal double-frequency pulsation at $100 Hz$), triggering structural mechanical resonances in IEC 61439 switchgear frames, loosening bolted joints, and compromising the mechanical integrity of ATEX environmental seals (Ex "d" or Ex "t" elastomeric gaskets).

Diagnostic of Dielectric Degradation via Dissolved Gas Analysis (DGA) and Duval Triangle

Localized overheating and severe electrical stress resulting from DC core saturation trigger thermal and photochemical degradation of liquid dielectrics (mineral oils or synthetic/natural esters) and solid insulation (Kraft paper, Pressboard) used in transformer insulation systems. The breakdown of hydrocarbon chains in the insulating fluid releases combustible gases that dissolve into the liquid matrix. Dissolved Gas Analysis (DGA), standardized by IEC 60599 and IEEE C57.104, serves as the primary forensic tool for detecting these anomalies.

The thermal mechanisms induced by stray flux under DC saturation yield highly characteristic gas decomposition patterns. Hotspot temperatures govern the cleavage of specific chemical bonds:

• Low temperatures ($T < 300^\circ C$): Cleavage of weak C-C bonds, primarily yielding Ethane ($C _2 H _6$) and Methane ($CH _4$).
• Medium temperatures ($300^\circ C < T < 700^\circ C$): Cleavage of C-H and C=C bonds, leading to the dominance of Ethylene ($C _2 H _4$).
• High temperatures ($T > 700^\circ C$) or secondary insulation breakdown arcing: Massive generation of Ethethylene ($C _2 H _4$) and the appearance of Acetylene ($C _2 H _2$).

To unequivocally diagnose degradation induced by DC offset saturation, Duval Triangle 1 methodology is applied, based on the relative proportions of three key hydrocarbon gases: Methane ($CH _4$), Ethylene ($C _2 H _4$), and Acetylene ($C _2 H _2$). The coordinates within the triangle are calculated as percentages from ppm concentrations using the following expressions:

The interpretation of DC saturation-induced degradation via Duval Triangle 1 spans the following thermal zones:

• Zone T1 (Thermal Fault $T < 300^\circ C$): Characterized by a high concentration of $CH _4$ and $C _2 H _6$. Occurs in the early stages of DC injection, where stray flux induces mild heating in core frames and tank walls.
• Zone T2 (Thermal Fault $300^\circ C < T < 700^\circ C$): Corresponds to the critical operating condition of permanent DC saturation. Ethylene ($C _2 H _4$) concentrations increase rapidly, positioning the coordinate point in the mid-right region of the triangle. This confirms the presence of hotspots on structural steel components or regions adjacent to the windings.
• Zone T3 (Thermal Fault $T > 700^\circ C$): Occurs when DC saturation causes extreme localized overheating in internal connections or destroys thermal insulation laminations on tie-rods, reaching extreme temperatures with $C _2 H _4 > 50\%$ concentration.

To refine the characterization of low- and medium-temperature thermal faults caused by stray flux versus cellulose insulation faults, Duval Triangle 4 and Triangle 5 (specifically tailored for low-temperature thermal faults and non-mineral fluid transformers in service) are utilized in a complementary manner:

A sustained rise in Carbon Monoxide ($CO$) and Carbon Dioxide ($CO _2$) gases, accompanied by a ratio of $CO _2 / CO < 3$, unequivocally confirms that the saturation stray-flux hotspot has extended to the paper insulation (Kraft paper), irreparably degrading its polymeric structure.

Forensic Failure Analysis of Power System Components

Continued DC injection from power electronics converters triggers a cascading degradation process across electrical system assets. Below is the itemized forensic dissection by component:

Power and Isolation Transformers

The primary failure mode is the pyrolytic decomposition of cellulosic insulation. Kraft paper consists of glucose polymer chains whose health metric is the Degree of Polymerization (DP). New cellulosic insulation exhibits a $DP \approx 1000 - 1200$. Under the impact of stray flux thermal hotspots ($T > 140^\circ C$), the rate of cellulose chain scission accelerates exponentially according to the Arrhenius relationship:

When the $DP$ drops below 200, the mechanical tensile strength of the paper degrades to 20% of its initial value, turning it brittle. Under subsequent electrodynamic forces (such as a through-fault short circuit), the winding turns suffer mechanical collapse, resulting in a turn-to-turn short circuit.

The secondary failure mode in transformers is anomalous acoustic noise and structural resonance. DC offset breaks the symmetry of the hysteresis loop, producing vibration components at the fundamental frequency ($50 Hz$) superimposed on harmonic vibration modes. This places sustained fatigue stress on transformer tank welds and cooling system piping (radiators and oil pumps).

Cables and Cable Trays / Raceways (IEC 60287 / NEC 310)

Medium- and low-voltage power cables connecting AFE inverters to transformers experience a severely altered thermal regime. The non-sinusoidal, highly asymmetric current rich in low-order even harmonics (particularly the $2^{ nd }$ and $4^{ th }$ harmonics) causes a drastic surge in effective AC conductor resistance ($Rac$) due to skin and proximity effects:

where $y_s$ and $y_p$ are the skin and proximity effect factors respectively, scaling proportionally with the square of the harmonic frequency induced by saturation ($y_s \propto f^2$). This causes an elevated conductor internal operating temperature, accelerating thermal aging of XLPE or EPR insulation beyond its maximum rated continuous operating temperature ($90^\circ C$), promoting water treeing and destructive partial discharges within underground chemical plant installations.

Switchgear and Protection Relays

The presence of DC components and core saturation distorts the operational integrity of protective relaying systems (IEC 60255):

• Instrument Current Transformer (CT) Saturation: The heavily distorted primary current containing DC offset transfers into the secondary circuit of measurement and protection CTs. The CT core saturates rapidly, introducing severe waveform distortion to secondary signals fed into protective relays. This induces underreaching or overreaching (unintended tripping) in overcurrent relays (50/51) and transformer differential relays (87T).
• Circuit Breakers Arc Interruption (IEC 60947-2 / IEC 62271-100): Current waveform distortion can shift the natural current zero-crossing points, or eliminate them entirely for multiple cycles during combined short-circuit and DC transient conditions. Circuit breakers rely on natural zero-crossings to extinguish the electric arc inside arc chutes. The absence or displacement of zero-crossings prolongs arc duration, severely damaging silver-cadmium/tungsten power contacts and causing catastrophic arc chute explosions within ATEX environments.

Comparative Matrix of Electromagnetic, Normative, and Diagnostic Parameters

Electronic / Thermal Parameter	Nominal Normal Operation (No DC Offset)	Severe DC Saturation (Offset > 0.5% $I_n$)	Standard Limit (IEC / IEEE / ATEX)	DGA Consequence & Forensic Diagnostic
Peak Magnetic Flux Density ($Bpeak$)	$1.50 - 1.68 T$ (Linear region of CRGO steel)	$1.90 - 2.15 T$ (Deep saturation in one half-cycle)	$Bmax < 1.75 T$ (Manufacturer design margin)	Triggers severe core losses; onset of degradation via localized hotspots.
Magnetizing Current ($Imag$)	$< 1\% - 2\%$ of $I_n$ (Quasi-sinusoidal waveform)	$10\% - 50\%$ of $I_n$ (High-amplitude periodic pulses)	IEEE Std C57.110 / IEC 60076-1	Accelerated generation of $H _2$ and $CH _4$ via surface partial discharges and local overheating.
External Tank / Enclosure Temperature	$55^\circ C - 70^\circ C$ (Mean elevation above ambient)	$> 140^\circ C - 180^\circ C$ (In concentrated stray flux zones)	IEC 60079-0 (ATEX T4: $Tmax \le 135^\circ C$) / IEC 61439-1 (Clause 10.10)	Imminent ATEX ignition risk. DGA diagnostic: Zone T2 or T3 in Duval Triangle ($C _2 H _4$ dominant).
Current Harmonic Content	THD$_i < 3\%$, odd harmonic dominance ($3^{ rd }, 5^{ th }$)	THD$_i > 25\%$, massive even harmonic presence ($2^{ nd }, 4^{ th }, 6^{ th }$) & DC	IEEE 519 / IEC 61000-3-6 (DC injection limit $< 0.5\%$ $I_n$)	Severe liquid insulation degradation; accelerated pyrolysis of solid paper insulation.
Acoustic Noise & Vibration Level	$55 - 65 dBA$ (Dominant vibration at $100 Hz$)	$> 85 - 95 dBA$ (Severe $50 Hz$ fundamental and odd components)	IEC 60076-10 (Sound pressure limits)	Mechanical fatigue failure of core clamps, structural leaks in ATEX seals and connections.
Degree of Polymerization of Paper (DP)	$1000 - 1200 (New condition)$	Drops to $< 200 (End of insulation life)$	IEC 60450 / IEEE C57.100	Massive generation of $CO$ and $CO _2$, $CO _2/ CO < 3$, presence of furanic compounds (2-FAL).

Mitigation Strategies and Anti-Saturation Design Criteria

Eliminating ATEX thermal ignition hazards and preventing insulation failure in converter-fed installations requires a combination of active control mitigation techniques, passive hardware modifications, and strict compliance with IEC 61439-1/2 enclosure design specifications.

Active Mitigation via Inverter Control

Advanced inverter control architectures must implement real-time DC offset suppression loops utilizing high-precision flux sensing or direct output current sampling. Closed-loop Fluxgate current sensors (with zero-drift $< 1 ppm/K$) are coupled to a mean-value compensation algorithm executed within the Digital Signal Processor (DSP):

This correction signal is subtracted directly from the Pulse-Width Modulation (PWM) modulator, dynamically trimming the switching dead-time between upper and lower power transistors of each bridge leg to nullify the net DC voltage equivalent $Vdc \to 0$.

Passive Mitigation and Magnetic Design

Where active DC suppression cannot be guaranteed to 100% under inverter fault conditions, passive hardware-level modifications must be integrated:

• Strategic Distributed Air Gaps (Core Gapping): Introducing small distributed air gaps ($\delta$) within the magnetic circuit of the transformer significantly increases core reluctance to DC components, heavily attenuating the offset flux $\Phi_{dc}$. The modified reluctance is expressed as:
  $$\mathcal{R}_{m, modified} = \frac{leff}{\mu_0 \mu_r Aeff} + \frac{\delta}{\mu_0 Aeff}$$
  While this slightly increases fundamental reactive magnetizing current at no-load, it shifts the knee point of the $B-H$ saturation curve, immunizing the core against substantial DC deviations.
• Zig-Zag (Zn) Winding Isolation Transformers: Incorporating a Zig-Zag winding topology establishes a natural DC component and zero-sequence/triplen harmonic canceller on the secondary side. Magnetic fluxes generated by DC current in opposing half-windings on the same core leg counteract each other, achieving a net cancellation of DC magnetomotive force ($MMF_{dc} = N Idc - N Idc = 0$).
• DC Blocking Capacitor Banks: Installing non-polarized capacitor banks in series with the transformer neutral or within low-voltage coupling phases provides infinite impedance to direct current ($Zdc = \infty$), completely blocking DC current entry from the converter.

Enclosure Design and Assemblies in ATEX Zone 1 (IEC 61439 / IEC 60079)

When engineering low-voltage power assemblies under IEC 61439-1/2 for ATEX Zone 1 applications, the following anti-heating stray flux mitigation rules must be strictly applied:

• Non-Magnetic Cable Gland Plates: Entry of high-current single-core cables through Ex "d" or Ex "e" enclosure walls must be routed exclusively through gland plates constructed from non-magnetic materials (austenitic stainless steel AISI 316L, aluminum, or brass). This prevents the formation of a closed magnetic loop around single conductors, suppressing eddy current induction in the enclosure chassis.
• Distributed Fiber Optic Temperature Sensing (DTS): To prevent external enclosure surface temperatures in Zone 1 from exceeding the ATEX T4 limit ($135^\circ C$), continuous Fiber Bragg Grating (FBG) optical sensors should be attached directly to core clamping frames, cable glands, and outer tank surfaces. These intrinsically safe (Ex "i") sensors interface with main breaker trip circuits to disconnect power if temperatures exceed $105^\circ C$.

Modeling and Technical Integration in Vexten Suite

Accurately predicting the impact of DC offset saturation across industrial electrical networks demands advanced simulation software. The Vexten Suite platform incorporates calculation modules engineered to evaluate the non-linear electromagnetic and hydrocarbon phenomena detailed above.

Short-Circuit Calculation Module (IEC 60909 / IEEE 141)

Core pre-saturation induced by DC injection modifies equivalent system impedances during short-circuit events. Under IEC 60909, the peak short-circuit current ($i_p$) depends on the factor $\kappa$ (peak factor), which is a function of the system $R/X$ ratio at the fault location:

When a transformer core is pre-saturated by DC offset, both magnetizing reactance and leakage reactance drop transiently ($Xsat < Xlinear$). This alters the overall $R/X$ ratio toward higher values while reducing zero-sequence reactance. Vexten Suite dynamically updates the system admittance matrix ($\mathbf{Y}_{bus}$) by recalculating the saturated subtransient reactance ($X_{d\_sat}''$) to provide an exact peak current estimate ($i_p$), preventing under-rating of the breaking capacity of circuit breakers deployed in ATEX zones.

Cable Sizing and Harmonic Derating Module (IEC 60287 / NEC 310)

The cable sizing module within Vexten Suite executes an iterative algorithm based on IEC 60287 for steady-state current carrying capacity, integrating a compound thermal derating factor for harmonic distortion and DC offset ($Kderating$):

The module computes AC conductor resistance across even harmonic frequencies ($Rac(h)$) resulting from DC saturation, evaluating skin depth penetration changes $\delta_s = \sqrt{\frac{2}{\omega \mu \sigma}}$. Consequently, Vexten Suite prevents dielectric breakdown of cables feeding critical chemical loads by verifying that maximum conductor operating temperatures remain below nominal design limits ($90^\circ C$).

Resonance Analysis and Harmonic Filter Module

DC offset injection and harmonic generation from saturated cores reshape network frequency response profiles. The equivalent magnetizing inductance of transformers drops to instantaneous minimum values during core saturation ($L_{mag\_sat} \ll L_{mag\_nom}$). This shifts parallel system resonance frequencies ($fres$) toward higher harmonic orders:

If the shifted resonant frequency aligns with even harmonics amplified by saturation (e.g., $2^{ nd }$ harmonic at $100 Hz$ or $4^{ th }$ at $200 Hz$), the busbar voltage in the IEC 61439-1/2 assembly will experience severe harmonic voltage amplification. Vexten Suite performs automated dynamic frequency scans as a function of DC injection levels, sizing damped passive filters (C-Type or High-Pass) or adjusting active inverter damping parameters to reliably suppress resonance risks in high-consequence hazardous environments.