Asymmetric CT Saturation and Optical Arc Flash Protection in Residential Complexes

Fault Dynamics in Next-Generation Distribution Networks

The decarbonization of modern residential complexes has driven the massive integration of high-energy-density technologies, primarily high-power Electric Vehicle Service Equipment (EVSE) and aerothermal HVAC systems (air-to-water heat pumps driven by variable frequency inverters). This technological transition fundamentally alters the nature of the electrical load, replacing traditional linear resistive and inductive loads with non-linear loads coupled through power electronics. During a close-in short-circuit fault on the medium-voltage (MV) or low-voltage (LV) side of the distribution substation, the system behavior is no longer governed solely by the sub-transient and transient impedances of traditional synchronous rotating machines. The massive presence of inverters with Active Front-End (AFE) stages and diode/thyristor rectifiers with massive capacitive DC-link filters introduces complex transient dynamics. The inverters of EVs and aerothermal compressors operate under high-speed closed-loop current control algorithms that actively limit their contribution to the fault current, typically to values between 1.1 and 1.5 times their rated nominal current. However, the ultra-fast discharge of the DC-link capacitors of these devices during the first few microseconds of the fault generates a high-frequency, high-amplitude transient current peak that is superimposed on the power-frequency component. Furthermore, the topology of the distribution network in these residential complexes typically exhibits a significantly altered X/R (reactance-to-resistance) ratio. The use of large-cross-section underground cables to minimize voltage drops caused by the high simultaneous demand of EVs, combined with the proximity to high-capacity distribution transformers (typically ranging from 1000 kVA to 2500 kVA to supply concentrated demand), results in an extremely low fault loop impedance with an exceptionally high DC decay time constant ($T_a$) at the Point of Common Coupling (PCC). This combination of factors promotes the occurrence of fault currents with a highly pronounced and slowly decaying asymmetrical DC offset, pushing protection systems to their physical limits—specifically, the current transformers (CTs) responsible for feeding the protection relays. ---

Physics of Asymmetrical Current Transformer (CT) Saturation

Current transformer saturation is an electromagnetic phenomenon governed by Faraday's Law of Induction and the magnetic properties of the core material (typically grain-oriented silicon steel alloys). When a short-circuit current flows through the primary winding, the magnetic flux in the core must increase to induce the electromotive force (EMF) required in the secondary winding to drive the secondary current through the total loop impedance (the CT secondary winding resistance plus the connecting lead resistance and the input impedance of the relay, collectively known as the CT burden). The generalized primary fault current, considering an equivalent linear system, is mathematically expressed as: Where:

• $Ipk$ is the peak value of the symmetrical component of the short-circuit current.
• $\omega$ is the angular frequency of the system ($2\pi f$).
• $\theta$ is the fault inception angle.
• $\phi$ is the phase angle of the short-circuit impedance of the system ($\tan^{-1}(\omega L / R)$).
• $T_a = L/R$ is the decay time constant of the unidirectional primary DC offset component.

The total magnetic flux in the CT core, $\Psi(t)$, is the sum of the symmetrical alternating flux $\Psi_{ac}(t)$, the asymmetrical transient flux produced by the DC component $\Psi_{dc}(t)$, and the pre-existing remanent flux in the core $\Psi_r$: The unidirectional transient flux component is obtained by integrating the primary DC offset component transferred to the secondary, assuming ideal behavior prior to saturation: Where:

• $R_s$ is the total resistance of the secondary circuit (the CT secondary winding resistance, $Rct$, plus the connection lead resistance, $Rlead$, plus the input burden of the relay, $Rburden$).
• $N_s$ is the number of turns of the secondary winding.

The Transient Flux Accumulation Mechanism

When a fault occurs with the maximum possible DC offset ($\theta - \phi = -\pi/2$), the unidirectional component of the flux accumulates monotonically during the first few cycles of the fault. Unlike the symmetrical flux $\Psi_{ac}(t)$, which oscillates around zero with a peak value proportional to $\frac{R_s Ipk}{\omega N_s}$, the component $\Psi_{dc}(t)$ accumulates a value that is proportional to $\omega T_a$ times the peak symmetrical flux. In networks with a high $T_a$ value (typical of massive residential substations equipped with large transformers and low-resistance distribution cables), the factor $\omega T_a$ can easily exceed values of 15 to 30. This means that the flux required to faithfully transform the DC component is 15 to 30 times greater than the flux required for the purely symmetrical AC component. Once the total flux $\Psi(t)$ exceeds the saturation flux of the core ($\Psi_{sat}$), the incremental magnetic permeability of the core ($\mu_{\Delta} = dB/dH$) collapses from its steady-state value (typically between $10,000\mu_0$ and $100,000\mu_0$) to a value close to the permeability of vacuum ($\mu_0$). At this instant, the CT enters deep asymmetrical saturation, losing its ability to transfer current to the secondary circuit during the half-cycle where the polarity of the primary current coincides with the direction of the accumulated flux. Under these conditions, the excitation current of the CT increases dramatically, absorbing almost the entire primary current and leaving the secondary current severely distorted or virtually non-existent during the saturated intervals. ---

Impact of Power Electronic Loads (EV & Aerothermal Systems) on Fault Dynamics

The penetration of DC electric vehicle fast chargers (fast-charging buses with three-level active rectifiers such as Vienna rectifiers or dual active bridges) and aerothermal heat pump systems drastically alters the classical short-circuit parameters of the distribution grid. These loads introduce non-linear dynamics that modify both the root-mean-square (RMS) value of the fault current and its transient waveform.

Dynamic Behavior of Power Electronic Converters

Unlike traditional induction motors (used in legacy HVAC systems) which contributed a high initial short-circuit current due to their residual back-electromotive force (back-EMF), modern inverter-based aerothermal systems limit their output current almost instantaneously using closed-loop Field-Oriented Control (FOC) algorithms. During a voltage sag caused by a close-in fault, the inverter's inner current control loop (with a typical bandwidth of 1 to 3 kHz) acts within 2 to 5 milliseconds to limit the output current of the converter. However, during the first 1 to 2 milliseconds, before the inverter's current control loops can react, the output filter capacitors of the EV chargers and aerothermal inverters discharge directly into the fault point. This sub-transient discharge generates a high-frequency, high-amplitude current transient with an extremely high rate of rise of current ($di/dt$): Where:

• $Vdc0$ is the pre-fault DC-link voltage.
• $Ceq$ and $Leq$ are the equivalent capacitance of the equipment filters and the inductance of the connection cables to the fault point, respectively.
• $\alpha = Req / (2 Leq)$ is the damping factor.
• $\omega_d = \sqrt{\frac{1}{LeqCeq} - \alpha^2}$ is the damped natural frequency of the discharge transient.

This high-frequency transient pulse from the capacitors, superimposed on the power-frequency DC offset of the medium-voltage distribution network feeding the substation transformer, drastically accelerates the saturation process of the CT cores. The high rate of change of magnetic flux induced by this initial discharge current transient can cause the CT core to reach saturation in a fraction of a cycle (less than 5 milliseconds), far sooner than predicted by standard saturation calculation methods based solely on power-frequency currents.

Modification of the System Time Constant ($T_a$)

The concentration of active harmonic filters, power factor correction capacitor banks, and the input stage topologies of EV chargers modify the equivalent positive-sequence and zero-sequence impedances of the grid. By decreasing the equivalent effective resistance of the grid (due to the overdimensioning of conductors to mitigate heating from high-frequency harmonic currents) while maintaining high inductance due to the coupling transformers, the overall $X/R$ ratio of the internal distribution network of the residential complex increases substantially. An increase in the $X/R$ ratio from, for example, 8 to 24, increases the decay time constant of the DC component ($T_a$) from 25 ms to 76 ms. Consequently, any fault occurring in the vicinity of the distribution substation will exhibit a DC component that persists for several cycles, exponentially increasing the probability of persistent asymmetrical saturation in the protection CTs. ---

Forensic Analysis of Failures in Protection Systems and Electrical Equipment

The asymmetrical saturation of CTs severely degrades the fidelity of the secondary current signal delivered to overcurrent (50/51), differential (87), and distance (21) protection relays. When a CT saturates asymmetrically, the secondary current collapses to zero during the saturated portion of each cycle, as illustrated in the following conceptual representation: This collapse of the secondary current introduces catastrophic consequences for the performance of protection systems and the physical integrity of substation equipment.

Malfunction of Overcurrent Protection (50/51)

Modern numerical overcurrent relays process the secondary signal from the CTs using parameter estimation algorithms based on the Fast Fourier Transform (FFT) or Kalman filters to extract the fundamental power-frequency component (50 Hz or 60 Hz). When the secondary current is distorted due to asymmetrical saturation, the fundamental component content calculated by the relay drops drastically compared to the actual primary current. This artificial reduction of the current measured by the relay produces two critical effects:

• Inacceptable delay in the tripping of time-delay overcurrent protection (51): By calculating a fundamental RMS current significantly lower than the actual value, the relay operates on a section of the inverse-time curve with a delay far exceeding the coordinated margin. This prolongs the duration of the fault on the network.
• Failure to operate of the instantaneous overcurrent unit (50): If the current estimated by the relay due to saturation distortion does not reach the pickup setting, the instantaneous protection simply fails to trip, leaving fault clearance to the upstream backup protection.

Incorrect Operation of Differential Protection (87)

Differential protection for busbars or transformers (87) is based on Kirchhoff's Current Law, comparing the vector sum of the currents entering and leaving the protected zone. Under normal conditions or during an external fault outside the protected zone, the theoretical differential current is zero. If a high-magnitude external fault occurs (for example, on an outgoing feeder supplying EV chargers) and the CT of that specific feeder saturates asymmetrically due to the high fault current and the DC component, the secondary current of that CT will collapse. However, the CTs of the other feeders and the main incomer, which handle smaller fractions of the total current or have different saturation characteristics, may not saturate. This generates a massive spurious differential current in the differential relay: This transient imbalance is erroneously interpreted by the relay as an internal fault in the busbar or distribution transformer, causing a nuisance trip and the total disconnection of the residential complex, unjustifiably compromising the continuity of service.

Thermal, Mechanical, and Dielectric Consequences

The delayed clearance or failure to clear a short-circuit fault due to CT saturation exposes substation assets to extreme physical stresses:

• Thermal Stresses in Cables and Windings: The thermal energy dissipated in conductors during a fault is proportional to the Joule integral ($I^2t$). A delay in fault clearance from 100 ms to 1.5 seconds increases the thermal energy by a factor of 15, exceeding the short-circuit thermal capacity of the XLPE insulation of the distribution cables and the transformer windings, leading to irreversible thermal degradation or direct melting.
• Mechanical Stresses and Electrodynamic Repulsion Forces: The mechanical forces between conductors and busbars are proportional to the square of the instantaneous peak current ($i_p^2$). Asymmetrical currents with high DC offsets generate massive electrodynamic force peaks that can physically deform busbars, shatter porcelain or epoxy resin support insulators, and mechanically destroy circuit breaker operating mechanisms.
• Dielectric Degradation due to Prolonged Arcing: If the circuit breaker attempts to interrupt the fault current under conditions where the current does not exhibit zero crossings due to an extreme DC offset (the "missing zero-crossing" phenomenon), the electric arc inside the breaker's interrupter chamber cannot extinguish at the natural zero-crossing instant. This prolongs the electric arc, generating extreme temperatures in the chamber that degrade the SF6 gas, vacuum, or interrupting medium, potentially resulting in a catastrophic explosion of the circuit breaker.

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Regulatory Framework and CT Design Parameters according to IEC 61869 and IEEE C57.13

The selection and dimensioning of current transformers for protection applications require a strict analysis of international standards to ensure adequate performance under transient short-circuit conditions. The two global reference standards are IEC 61869 (specifically Part 2 for measuring and protective current transformers) and IEEE C57.13.

Comparison of CT Classes for Protection

The IEC 61869 standard classifies protective CTs into several classes based on their steady-state and transient behavior. Standard classes for steady-state protection are Class P and Class PX, while transient behavior classes are defined as Class TPX, Class TPY, and Class TPZ. The IEEE C57.13 standard uses the classification of Class C (where secondary leakage reactance is negligible) and Class T (with significant secondary leakage reactance).

Parameter / Characteristic	Class P (IEC 61869-2)	Class PR / PX (IEC 61869-2)	Class TPX (IEC 61869-2)	Class TPY (IEC 61869-2)	Class TPZ (IEC 61869-2)	Class C (IEEE C57.13)
Core Construction	Closed core without air gaps.	Closed core with low remanence (PR) / No air gaps (PX).	High-precision closed core without air gaps.	Core with small air gaps (low remanence).	Core with large air gaps (linearized remanence).	Closed core with closely coupled windings.
Remanent Flux ($\Phi_r$)	Very high (up to 80% of saturation flux).	Low (< 10% for PR) / Not specified (PX).	Very high (up to 80%).	Extremely low (< 10%).	Negligible (~ 0%).	Not controlled by standard (typically high).
Transient Behavior	Not specified. High probability of rapid saturation.	Not specified for fast transients.	Designed to withstand transients without saturation (large iron volume).	Designed to withstand transients with rapid flux decay via air gap.	Excellent transient response. Does not saturate, but introduces phase error.	Not specified for transients. Based on steady-state knee-point voltage.
Error / Accuracy Limit	5% or 10% at the Accuracy Limit Factor ($ALF$).	Limited ratio error; specified knee-point voltage ($E_k$).	Peak instantaneous error limited during transient fault cycle ($\hat{\varepsilon} \le 10\%$).	Peak instantaneous error limited ($\hat{\varepsilon} \le 10\%$) with low secondary time constant ($T_s$).	AC component error limited ($\hat{\varepsilon}_{ac} \le 10\%$). Transmits AC only.	Maximum 10% error at 20 times nominal current with standard burden.
Recommended Application	Standard non-critical overcurrent protection.	High-impedance differential and distance protection.	High-voltage transmission line protection (autoreclose cycles).	Transformer and busbar differential protection with high DC components.	Generator and busbar differential protection with extreme time constants.	General protection systems in North American networks.

The Transient Dimensioning Factor ($Ktf$)

To prevent CT saturation during faults with a transient DC component, the IEC 61869-2 standard introduces the Transient Dimensioning Factor ($Ktf$). This factor multiplies the steady-state flux requirement to obtain the required CT core size under dynamic conditions. The factor $Ktf$ is theoretically calculated for a single fault cycle (without reclosure) using the relationship: Where:

• $T_a$ is the primary time constant of the distribution network.
• $T_s$ is the secondary time constant of the current transformer, defined as $T_s = L_s / R_s$, where $L_s$ is the secondary magnetizing inductance (unsaturated).
• $tal$ is the time-to-accuracy limit (the time during which the CT must not saturate to allow correct relay operation, typically 10 to 40 ms).

If the CT has a closed core without air gaps (Class TPX or standard Class P), the secondary time constant $T_s$ is extremely large ($T_s \gg T_a$), simplifying the $Ktf$ equation to: For a system with a grid time constant $T_a = 80 ms$ (common in massive residential complexes with concentrated fast EV chargers and high-capacity transformers) and a required accuracy time of $tal = 20 ms$ (one cycle at 50 Hz to ensure instantaneous tripping), the required transient factor is: This means the CT must be dimensioned to withstand a magnetic flux 6.56 times greater than the flux required to transform the steady-state symmetrical fault current. If the existence of a remanent flux ($\Psi_r$) due to previous uncleared faults is also considered, an additional correction factor for remanence must be applied, drastically increasing the physical size and cost of the CT if closed-core technologies without air gaps are selected. ---

Mitigation Strategies and Protection Engineering Design

To resolve the issue of asymmetrical CT saturation in distribution networks with high penetrations of EVs and aerothermal systems, design engineers must implement a combination of hardware strategies and advanced software-based protection algorithms.

Dimensioning Methodology for Air-Gapped CTs (Class TPY and TPZ)

The most effective physical solution to mitigate saturation due to remanent flux and the DC component is the use of air-gapped CT cores. Air gaps introduce a controlled magnetic reluctance into the magnetic circuit, which drastically reduces the equivalent magnetic permeability and, consequently, decreases the remanent induction to virtually negligible values ($B_r < 10\%$ of $Bsat$ for Class TPY, and $B_r \approx 0$ for Class TPZ). The secondary time constant ($T_s$) of a Class TPY CT is intentionally reduced to values on the order of 0.5 to 2 seconds. This allows accelerated demagnetization of the core after the fault has been cleared, preparing the CT for a rapid autoreclosure cycle. For Class TPZ CTs, the large air gap reduces the secondary time constant to extremely low values ($T_s \approx 60 ms$ at 50 Hz). This almost completely eliminates the DC component from the secondary current, delivering a signal to the relay that is essentially the derivative of the primary current. While this eliminates the DC saturation problem, it requires the protection relay to incorporate a numerical integration algorithm to reconstruct the original AC fault current waveform.

Saturation Compensation Algorithms in Modern Numerical Relays

Next-generation numerical relays incorporate high-speed microprocessors that execute real-time CT saturation detection and compensation algorithms. These algorithms can be classified into two main categories:

• Saturation Detection based on the Second Derivative: Since the secondary current collapses abruptly at the instant the CT enters saturation, the rate of change of the secondary current ($di_s/dt$) and its second derivative ($d^2i_s/dt^2$) exhibit high-magnitude peaks at the start and end points of the saturation interval. The relay detects these peaks and "freezes" the decision loops of the differential or distance protection units during the saturated portion of the cycle, preventing nuisance tripping.
• Artificial Reconstruction of the Secondary Current: By using real-time mathematical models of the magnetic core (based on the CT's characteristic magnetization curve entered into the relay configuration), the software estimates the instantaneous magnetic flux $\Psi(t)$. When saturation is detected, the algorithm calculates the missing magnetizing current ($i_{\mu}(t)$) from the core model and algebraically adds it to the measured secondary current ($i_s(t)$), reconstructing the actual primary current with high accuracy ($i_p(t) = N_s \cdot [i_s(t) + i_{\mu}(t)]$).

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Advanced Simulation and Dimensioning with Vexten Suite

Detailed engineering design for the integration of EV chargers and aerothermal systems in large-scale residential complexes requires the use of professional-grade simulation tools. Vexten Suite provides an integrated ecosystem that allows a unified approach to short-circuit calculations, thermal dimensioning of conductors, and transient validation of protection systems.

Step 1: Short-Circuit Analysis and Grid Parameter Determination with Vexten Short-Circuit

The first step consists of modeling the electrical system of the residential complex in the Vexten Short-Circuit module, configured under the IEC 60909 or IEEE 141 standard. The model of the residential complex under analysis has the following design parameters:

• Medium-Voltage Utility Connection: 20 kV, Short-circuit capacity of the distribution grid ($Scc$) = 500 MVA.
• Substation Transformer: 1600 kVA, 20 kV / 0.4 kV, $u_k = 6\%$, ratio $X_T / R_T = 12$.
• Concentrated Loads: 120 Level 2 EV charging points (7.4 kW each) and 40 DC fast chargers (50 kW each), coupled to a common low-voltage distribution busbar, along with 80 aerothermal heat pumps (15 kW thermal / 4.5 kW electrical each).

Upon executing the simulation of a symmetrical three-phase fault and a close-in single-phase-to-ground fault on the low-voltage busbars of the transformer, the Vexten Short-Circuit calculation engine yields the following critical results:

• Initial symmetrical short-circuit current: $I_k'' = 38.49 kA$.
• Short-circuit peak factor ($\kappa$): 1.82 (calculated according to Method B of IEC 60909).
• Peak short-circuit current: $i_p = \kappa \cdot \sqrt{2} \cdot I_k'' = 1.82 \cdot 1.414 \cdot 38.49 = 99.12 kA$.
• Equivalent $X/R$ ratio at the fault point: 22.4.
• Decay time constant of the grid DC component:
  $$T_a = \frac{X}{\omega R} = \frac{22.4}{2\pi \cdot 50} \approx 71.3 ms$$

These output data from Vexten Short-Circuit are automatically exported to the protection dimensioning module.

Step 2: CT Dimensioning with Vexten Protection & CT Sizing Tool

With the imported fault parameters ($I_k'' = 38.49 kA$, $T_a = 71.3 ms$), the performance of the CTs installed in the low-voltage incoming cubicle of the substation is evaluated. The existing CTs are standard protection class 5P20, 2000/5 A, 15 VA, $Rct = 0.5\ \Omega$. The load connected to the CT secondary ($Rburden$) is calculated considering the copper connection cabling ($2.5 mm ^2$, 15 meters round-trip length) and the input impedance of the numerical relay:

• Cable resistance:
  $$Rlead = \rho \frac{L}{S} = 0.0178 \frac{15}{2.5} = 0.1068\ \Omega$$
• Relay resistance: $Rrelay = 0.02\ \Omega$.
• Total secondary loop resistance: $R_s = Rct + Rlead + Rrelay = 0.5 + 0.1068 + 0.02 = 0.6268\ \Omega$.

The steady-state knee-point voltage required to meet the Accuracy Limit Factor ($ALF = 20$) with the rated CT burden ($S_n = 15 VA$, which equates to a rated burden resistance $R_n = S_n / Isn^2 = 15 / 25 = 0.6\ \Omega$) is: However, to verify the transient behavior during the calculated fault with a required accuracy time of $tal = 30 ms$ (to guarantee instantaneous overcurrent protection tripping before saturation occurs), the Vexten Protection & CT Sizing module calculates the transient factor $Ktf$: The required transient knee-point voltage ($E_{al,trans}$) to avoid asymmetrical saturation during the first 30 ms of the fault is: Since the design knee-point voltage of the installed CT under standard conditions (associated with its accuracy limit) is significantly lower than that required transiently ($110 V \ll 524.7 V$), the Vexten Suite software issues a Critical Transient Saturation Alert, indicating that the CT will saturate in just $tsat = 4.2 ms$ from fault inception, disabling the operation of the protection relay.

Proposed Solution via Vexten Suite

To resolve this engineering problem, the software proposes two redesign alternatives:

1. Replacement with a Class TPX CT (Oversized Closed Core): Select a CT with a transformation ratio of 2000/5 A, but with a specified knee-point voltage greater than 550 V. This requires a large-volume iron core, increasing the space required in the LV switchgear.
2. Replacement with a Class TPY CT (Air-Gapped, Low Remanence): Select a Class TPY CT with the following characteristics validated in the simulator: $Ktf = 8.70$, $T_s = 1.2 s$, which mitigates the effect of remanent flux and reduces the required knee-point voltage to an optimized safety value thanks to the rapid demagnetization of the core.

Step 3: Thermal Dimensioning of Conductors with Vexten Thermal Cable Sizing (IEC 60287 / NEC 310)

Due to potential delays in fault clearance and the massive injection of high-frequency harmonics generated by EV chargers and aerothermal compressors (5th, 7th, 11th, and 13th order harmonics, plus high inverter switching frequencies between 2 kHz and 15 kHz), distribution cables suffer accelerated thermal heating. The Vexten Thermal Cable Sizing module implements the equations of the IEC 60287 standard to calculate the continuous current-carrying capacity (ampacity) and applies thermal derating factors due to harmonic distortion. The effective AC resistance of a conductor ($Rac$) increases due to the skin effect ($y_s$) and proximity effect ($y_p$), both of which intensify exponentially with the frequency of harmonic currents: Where the skin effect ($y_s$) and proximity effect ($y_p$) factors for a harmonic of order $h$ are expressed as: The software calculates the harmonic derating factor ($Iderated$) using the total harmonic current distortion ($THD_I$) measured at the residential complex (typically 28% under maximum EV and aerothermal load conditions): For an aluminum XLPE distribution cable of $3 \times 240 mm ^2$ installed directly buried, whose nominal steady-state ampacity without harmonics is $385 A$, the simulation in Vexten Thermal Cable Sizing demonstrates that, due to the increase in resistance from skin and proximity effects at high harmonic frequencies, the cable experiences an actual thermal derating of 18.4%, reducing its maximum safe operating capacity to 314 A. Furthermore, if the calculated short-circuit fault of $38.49 kA$ is cleared with a delay of 1.2 seconds (due to unmitigated CT saturation) instead of the design 100 ms, the software calculates the transient temperature of the conductor using the adiabatic short-circuit equation: Since the maximum allowable short-circuit temperature for XLPE insulation is 250 °C, the software issues a Cable Insulation Thermal Degradation Failure Alert, warning that the cable will suffer permanent dielectric failure during the short-circuit if the CT dimensioning is not corrected to ensure instantaneous protection tripping. This integrated analysis demonstrates the vital importance of using advanced tools like Vexten Suite to guarantee the safety, reliability, and resilience of next-generation distribution networks against the challenges imposed by the energy transition and the electrification of transport and heating.