Asymmetric CT Saturation at High Altitude and 50/51 Selectivity per IEEE 519-2022

Physical and Environmental Context of High-Altitude Mining (>3000 m.a.s.l.)

The design and engineering of electrical power systems in mining facilities located at high altitudes (typically between 3,000 and 5,000 meters above sea level) impose severe operational challenges that distort the nominal performance of switching, transformation, and protection equipment. At these extreme elevations, the reduction in atmospheric pressure alters the thermophysical and dielectric properties of ambient air, directly degrading the dielectric constant and the convective thermal heat transfer capability of the medium.

According to Paschen's Law, the breakdown voltage of a gas between two electrodes is a non-linear function of the product of the gas pressure ( $p$ ) and the gap distance ( $d$ ):

V_B = \frac{B \cdot p \cdot d}{\ln(A \cdot p \cdot d) - \ln\left[\ln\left(1 + \frac{1}{\gamma_{se}}\right)\right]}

Where $A$ and $B$ are composition constants of the gas, and $\gamma_{se}$ is the secondary Townsend ionization coefficient. As altitude increases, atmospheric pressure decreases exponentially according to the barometric formula:

p(h) = p_0 \cdot \left(1 - \frac{L \cdot h}{T_0}\right)^{\frac{g \cdot M}{R \cdot L}}

Where $p_0$ is the standard sea-level atmospheric pressure (101,325 Pa), $L$ is the temperature lapse rate (0.0065 K/m), $h$ is the altitude in meters, $T_0$ is the standard sea-level temperature (288.15 K), $g$ is the acceleration due to gravity, $M$ is the molar mass of dry air, and $R$ is the universal gas constant. At 4,500 meters above sea level (m.a.s.l.), the relative air density ( $\delta$ ) drops to approximately 60% of its sea-level value. This reduction in air density severely degrades the dielectric strength of the air, facilitating the onset of corona discharge, reducing the flashover voltage across insulators and current transformer (CT) bushings, and requiring the application of insulation correction factors in accordance with IEC 60071-2 and IEEE C37.100.1 standards:

K_a = e^{m \cdot \left(\frac{h - 1000}{8150}\right)}

Where $m$ is a parameter that depends on the type of withstand voltage (power frequency, switching impulse, or lightning impulse). For a CT installed at 4,000 m.a.s.l., the creepage and clearance distances in air must be oversized by multiplying the nominal design clearances by the inverse factor of $K_a$ .

In parallel, the degradation of air density reduces the thermal dissipation capacity via both natural and forced convection. The convective heat transfer coefficient ( $h_c$ ) scales with air density according to the relationship:

h_c \propto \rho^n

Where $n \approx 0.5$ for laminar flow and $n \approx 0.8$ for turbulent flow. The reduced thermal dissipation increases the operating temperature of the copper windings in the CT under nominal and overload conditions. This temperature rise increases the internal ohmic resistance of the CT secondary winding ( $R_s$ ) in accordance with the thermal coefficient of copper ( $\alpha_{\text{Cu}} \approx 0.00393 K ^{-1}$ ):

R_s(T) = R_s(20^\circ C ) \cdot \left[1 + \alpha_{\text{Cu}} \cdot (T - 20)\right]

An increase in $R_s$ directly elevates the total internal burden of the secondary circuit of the CT, thereby reducing the safety margin against transient magnetic saturation of the iron core during fault conditions.

Thermal Degradation of Magnetic Cores

The elevated operating temperature in high-altitude CTs not only increases $R_s$ , but also affects the intrinsic magnetic properties of the core's ferromagnetic material (typically grain-oriented silicon steel). As the temperature rises, the magnetic saturation flux density ( $Bsat$ ) of the material decreases due to the thermal agitation of the magnetic domains (reduction of spontaneous saturation magnetization according to the Curie-Weiss law). A reduction in $Bsat$ lowers the saturation flux of the CT ( $\Psi_{sat}$ ), causing the core to saturate at significantly lower short-circuit current levels compared to its rated performance at sea level.

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Phenomenology of Asymmetric Saturation in Current Transformers (CTs)

The asymmetric saturation of a current transformer is a transient phenomenon governed by the presence of a decaying direct current (DC) offset component in the primary short-circuit current. When a fault occurs in a power system, the primary current $i_p(t)$ is modeled by solving the differential equation of an equivalent R-L circuit:

i_p(t) = Ipk \cdot \left[ \sin(\omega t + \theta - \phi) - \sin(\theta - \phi) \cdot e^{-\frac{t}{T_p}} \right]

Where $Ipk$ is the peak value of the symmetrical alternating current, $\omega$ is the angular frequency of the system, $\theta$ is the fault inception angle, $\phi = \arctan(\omega L_p / R_p)$ is the network impedance angle, and $T_p = L_p / R_p$ is the decay time constant of the DC component of the primary network. The maximum value of the DC component occurs when $\theta - \phi = \pm \pi/2$ , resulting in a fully asymmetrical current waveform.

The magnetic flux in the CT core, $\Psi(t)$ , required to induce the secondary voltage that drives the current through the total secondary loop impedance (comprising the secondary winding resistance $R_s$ , the interconnecting lead resistance $Rwire$ , and the relay input impedance $Zrelay$ ), is obtained by integrating the ideal secondary current:

\Psi(t) = \frac{1}{N} \int_0^t v_s(\tau) d\tau = \frac{Rct}{N} \int_0^t i_p(\tau) d\tau

Where $N$ is the CT turns ratio, and $Rct$ is the total secondary loop resistance ( $Rct = R_s + Rwire + Rrelay$ ). Integrating the asymmetrical primary current yields a magnetic flux that contains both a steady-state AC component and a massive, unidirectional transient DC offset component:

\Psi(t) = \Psi_{ac} \cdot \cos(\omega t + \alpha) + \Psi_{dc} \cdot e^{-\frac{t}{T_p}} - \Psi_{\text{offset}}

The transient component of the accumulated flux reaches a peak value that can be many times greater than the steady-state flux required at power frequency. To quantify this phenomenon, the IEC 61869-2 standard defines the Transient Dimensioning Factor ( $Ktf$ ), which represents the ratio of the maximum transient flux to the peak steady-state flux at fundamental frequency:

Ktf = \frac{\Psi_{max}}{\Psi_{ac, max}} = 1 + \frac{\omega \cdot T_p \cdot T_s}{T_p - T_s} \cdot \left( e^{-\frac{tmax}{T_p}} - e^{-\frac{tmax}{T_s}} \right)

Where $T_s$ is the secondary time constant of the CT, defined by the magnetizing inductance in the linear region $L_m$ and the total secondary loop resistance $Rct$ :

T_s = \frac{L_m}{Rct}

And the time at which the transient flux reaches its absolute maximum value ( $tmax$ ) is given by:

tmax = \frac{\ln(T_p / T_s)}{\frac{1}{T_s} - \frac{1}{T_p}}

If the primary system time constant $T_p$ is large (typical in medium-voltage mining networks with local generation or high-capacity transformers where the $X/R$ ratio is elevated), and the secondary time constant $T_s$ is also high, the value of $Ktf$ can easily exceed 15 to 20. This indicates that the CT requires an extremely large core cross-sectional area to prevent the magnetic flux density ( $B$ ) from exceeding the knee-point of the magnetization curve of the ferromagnetic material ( $Bsat \approx 1.6 - 1.8 T$ ).

Mechanism of Magnetic Operating Point Shift

When the transient flux component $\Psi_{dc}$ shifts the magnetic operating point beyond the knee-point of the saturation curve, the incremental magnetic permeability of the core ( $\mu_{\text{diff}} = dB/dH$ ) collapses abruptly from values exceeding $10,000 \cdot \mu_0$ to values approaching the permeability of free space ( $\mu_0$ ). Physically, the core loses its ferromagnetic properties and behaves as an air-core coil. At this instant, the magnetizing current ( $i_\mu$ ), which under normal conditions represents less than 1% of the load current, increases exponentially, absorbing almost the entirety of the primary current:

i_s(t) = \frac{i_p(t)}{N} - i_\mu(t)

Consequently, the secondary current measured by the protection relay experiences severe distortion, characterized by an almost complete loss of the signal during one half-cycle of the sinusoidal wave (the half-cycle polarized by the DC offset component), drastically reducing the root-mean-square (RMS) value calculated by the relay's filtering algorithms.

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Interaction with Power Quality and Harmonic Distortion under IEEE 519-2022

Modern mining environments are characterized by a massive penetration of high-power non-linear loads, such as medium-voltage variable frequency drives (VFDs) for main ventilation fans, high-capacity pumping systems, overland conveyors, and SAG (semi-autogenous) or ball mill drives operated by cycloconverters or Active Front End (AFE) systems. These loads inject a complex harmonic spectrum into the electrical distribution network, which is strictly regulated by the IEEE 519-2022 standard.

The IEEE 519-2022 standard defines the allowable limits for harmonic current distortion at the Point of Common Coupling (PCC), classifying them based on the ratio of the maximum short-circuit current ( $Isc$ ) to the maximum demand load current ( $I_L$ ). For distribution systems rated from 120 V to 69 kV, the Total Demand Distortion (TDD) limits range from 5.0% to 20.0%, requiring strict control over both individual odd and even harmonic components.

The continuous presence of harmonic currents interacts detrimentally with current transformers under both nominal load and fault conditions. The additional copper losses due to the skin effect and the eddy current losses in the CT's magnetic core under harmonic regimes are modeled using the eddy current loss rise factor ( $PEC$ ):

PEC = P_{EC-R} \cdot \sum_{h=1}^{hmax} h^2 \cdot \left(\frac{I_h}{I_R}\right)^2

Where $P_{EC-R}$ represents the eddy current losses at the fundamental frequency, $h$ is the harmonic order, and $I_h$ is the current of the $h$ -th harmonic order. In mining systems with high-frequency harmonics originating from VFD switching (carrier frequencies of 1 kHz to 5 kHz), the $h^2$ factor drastically amplifies the thermal losses within the CT, further elevating the internal temperature of the secondary winding and accelerating the increase in resistance $R_s$ .

In addition to thermal effects, harmonic and interharmonic currents distort the waveform of the CT magnetizing current under steady-state conditions. The residual magnetic flux ( $\Psi_{res}$ ) in the CT core is heavily influenced by the presence of current harmonics with zero-sequence components or phase imbalances that introduce continuous asymmetric biases. This phenomenon reduces the available saturation-free dynamic range for transients:

\Psi_{\text{disponible}} = \Psi_{sat} - \Psi_{res} - \Psi_{bias-harmonic}

A critical factor in high-altitude mining is the operation of cycloconverters for SAG mills, which modulate low frequencies (typically from 0 Hz to 15 Hz). These very low-frequency currents impose a severe saturation challenge because the required magnetic flux is inversely proportional to the frequency:

\Psi(t) \propto \frac{V_s}{f}

At sub-nominal operating frequencies (e.g., 5 Hz), the magnetic flux required to transform the same current is multiplied by a factor of 10 (for a 50 Hz system) or 12 (for a 60 Hz system), inducing almost instantaneous CT saturation even at nominal load currents.

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Impact on the Selectivity of Overcurrent Protections (50/51, 50N/51N)

Modern numerical overcurrent protection relays process analog secondary currents through signal conditioning that includes analog-to-digital conversion (ADC) and digital filtering, typically based on Fast Fourier Transform (FFT) or one-cycle Discrete Fourier Transform (DFT) algorithms. The DFT algorithm extracts the magnitude and phase angle of the fundamental power frequency component ( $I_1$ ) to evaluate the trip conditions for the 50 (instantaneous overcurrent) and 51 (inverse-time overcurrent) functions.

When the CT undergoes asymmetric saturation, the secondary current waveform is severely deformed, exhibiting unilateral clipping. Harmonic analysis of an asymmetrically saturated sine wave reveals a massive loss in the amplitude of the fundamental component and the appearance of a high content of even and odd harmonics, as well as a fictitious secondary transient DC component.

I_{1, measured} = \frac{2}{T} \int_0^T i_{s, sat}(t) \cdot \sin(\omega t) dt \ll I_{1, actual}

This collapse in the fundamental component measured by the relay has catastrophic consequences for the selectivity and operating speed of the protection system:

Effect on the Inverse-Time Overcurrent Function (51)

The operating time equation for standardized overcurrent curves (IEEE C37.112 or IEC 60255-151) is given by:

top = TD \cdot \left[ \frac{A}{\left(\frac{Imeasured}{Ipickup}\right)^p - 1} + B \right]

Where $TD$ is the time dial, and $Imeasured$ is the current measured by the relay. If the CT saturates, $Imeasured$ is artificially reduced below the actual fault current. Consequently:

The operating time calculated by the relay increases significantly (delayed tripping), resulting in a loss of coordination with downstream devices.
In extreme saturation cases, the measured current may drop below the pickup threshold ( $Ipickup$ ), completely preventing the protection from tripping (fail-to-trip condition).

Effect on the Instantaneous Overcurrent Function (50)

The 50 function is designed to operate without intentional delay during severe short-circuit faults. Numerical algorithms for the 50 function may utilize either the peak value of the signal or the DFT-filtered fundamental component. If the CT saturates asymmetrically within the first half-cycle of the fault, the current calculated by the relay will never reach the pickup threshold of the 50 function. This shifts fault clearance to the time-delayed 51 function or, worse, requires the operation of backup protections at the main substation, causing a widespread blackout of the mining plant.

Selectivity Issues due to Residual Current in Ground Schemes (50N/51N)

In mining distribution systems grounded through a Low-Resistance Grounding (LRG) system, single-phase-to-ground fault currents are limited (typically to 100 A, 200 A, or 400 A). Residual ground protection schemes (50N/51N) obtain the neutral current through the vector sum of the three secondary phase currents ( $3I_0 = I_a + I_b + I_c$ ).

During a high-magnitude external phase-to-phase or three-phase fault (not involving ground), the asymmetry of the fault current will cause unequal saturation of the CTs in the affected phases due to minor manufacturing tolerances or unequal secondary cable lengths. This differential asymmetric saturation generates a massive fictitious residual current in the secondary circuit:

3I_{0, error} = I_{a, sat} + I_{b, sat} + I_{c, sat} \neq 0

This error current is interpreted by the protection relay as an internal high-impedance ground fault, causing instantaneous, spurious tripping of the healthy feeder (loss of selectivity due to "sympathetic tripping").

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Comparative Analysis of Electrical and Regulatory Parameters

The following technical matrix compares the critical electrical parameters of CTs, regulatory limits, and operational/dielectric consequences under extreme conditions of altitude and harmonic distortion.

Parameter / Condition	Sea-Level Limits (Standard)	High-Altitude Limits (>3000 m.a.s.l.)	Regulatory Reference (IEEE/IEC)	Operational / Dielectric Consequences
Air Breakdown Voltage	100% of nominal design voltage (e.g., 95 kV BIL for 15 kV systems).	Reduction of up to 30% at 4,500 m.a.s.l. without correction (requires oversizing).	IEC 60071-2 / IEEE C37.100.1	Flashover on bushings, air ionization, internal arcing in medium-voltage switchgear.
Secondary Winding Resistance ( $R_s$ )	Specified at 75°C (typically $0.15 - 0.5 \ \Omega$ ).	Increase of 15% to 25% due to reduced thermal dissipation and higher operating temperature.	IEC 61869-2 / IEEE C57.13	Premature CT saturation due to the increase in total internal burden ( $Rct$ ).
Transient Dimensioning Factor ( $Ktf$ )	Typically calculated for networks with $X/R \le 15$ ( $Ktf \approx 5 - 10$ ).	Requires design for $X/R \ge 30$ ( $Ktf \ge 20$ ) due to the high inductance of the mining grid.	IEC 61869-2 (Classes TPX, TPY)	Transient saturation in less than 4 ms after fault inception, blocking fast relay operation.
Total Demand Distortion (TDD)	Limits from 5% to 15% depending on the $Isc/I_L$ ratio at the PCC.	Often exceeded by massive non-linear loads (VFDs, cycloconverters) without active filtering.	IEEE 519-2022	Additional thermal losses, thermal derating of the CT, induction of residual magnetic flux.
Knee-Point Saturation Voltage ( $V_k$ )	In accordance with the accuracy class (e.g., C400 or C800 under IEEE).	Requires physical oversizing of the core to compensate for the drop in $Bsat$ due to temperature.	IEEE C57.13	Loss of linearity in the secondary output current at low fault currents.

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Forensic Analysis of Electrical Failures in Mining Power Systems

To understand the destructive interaction of these phenomena, the following is a forensic reconstruction of a real catastrophic event that occurred at a copper processing plant located at 4,200 m.a.s.l. in the Andes.

System Description and Fault Scenario

The main distribution substation operates at 33 kV, feeding a 20 MVA, 33/4.16 kV step-down transformer (Dyn1 connection) that energizes a 15 MW SAG Mill controlled by a 12-pulse cycloconverter. The mill's 4.16 kV feeder is protected by a state-of-the-art multifunction numerical relay. The CTs installed in the vacuum circuit breaker of the feeder have a ratio of 3,000:5 A, with an IEEE C400 accuracy class (secondary winding resistance $R_s = 0.18 \ \Omega$ at 20°C).

A bolted phase-to-phase fault (Phase A to Phase B) occurred at the terminal box of the SAG mill motor, downstream of the feeder circuit breaker. The calculated symmetrical short-circuit current at the 4.16 kV busbar was 28 kA RMS, with an $X/R$ ratio of 28 at the fault location (primary time constant $T_p \approx 74 ms$ at 60 Hz).

Fault Chronology and Pathophysiology of the Collapse

The event unfolded according to the following millisecond (ms) sequence:

$t = 0 ms$ : Inception of the phase-to-phase fault at a voltage angle that caused maximum current asymmetry in Phase A. The peak primary current reached:
$i_{p, peak} = IRMS \cdot \sqrt{2} \cdot \left(1 + e^{-\frac{\pi}{\omega T_p}}\right) \approx 28 \cdot \sqrt{2} \cdot \left(1 + e^{-\frac{16.67}{74}}\right) \approx 71.3 kA$
$t = 3.5 ms$ : The severe DC component of the primary current, combined with the high resistance of the secondary loop (elevated by the internal ambient temperature of the medium-voltage switchgear at high altitude, where the CT winding operating temperature reached 95°C, increasing $R_s$ to $0.23 \ \Omega$ , plus a long secondary cable run of $4 mm ^2$ cross-section contributing $Rwire = 0.42 \ \Omega$ ), forced the magnetic flux in the core to exceed the saturation limit of 1.7 Tesla.
$t = 4.0 ms$ : The Phase A CT core entered deep saturation. The measured secondary current collapsed abruptly to zero during the positive half-cycle.
$t = 8.3 ms$ (First half-cycle): The DFT filtering algorithm of the feeder relay, designed to calculate the RMS value of the fundamental component over a one-cycle sliding window (16.67 ms), processed the distorted signal. Due to the asymmetry and wave clipping, the relay calculated a fundamental current of only 6.2 kA RMS, instead of the actual 28 kA.
$t = 15.0 ms$ : The threshold of the instantaneous overcurrent protection (50 function), set at 18 kA (600% of nominal current), was not reached by the calculated current of 6.2 kA. The relay failed to issue an instantaneous trip command.
$t = 100 ms$ : The fault remained active. The energy dissipated by the electric arc at the motor terminals generated violent overpressure and vaporization of dielectric materials.
$t = 450 ms$ : Due to the delay accumulated by saturation on the inverse-time curve (51 function), the feeder protection had still not operated. Finally, the protection relay at the upstream 33 kV main substation, set with an inverse-time coordination curve for backup faults, detected the fault and tripped the 33 kV main breaker at 520 ms.

Physical Consequences and Structural Damage

The delay of more than 500 ms in clearing a 28 kA short-circuit in a low air density environment (>3000 m.a.s.l.) had devastating consequences:

Medium-Voltage Switchgear Explosion: The prolonged electric arc overheated the air in the breaker's cable compartment. Due to the lower atmospheric pressure, the dielectric strength of the remaining air degraded instantly in the presence of hot ionized gases, triggering a generalized three-phase short-circuit across the switchgear busbars, completely destroying three adjacent cubicle sections.
Thermal Damage to Power Cables: The 4.16 kV XLPE-insulated cables suffered irreversible thermal degradation. The Joule integral of the fault ( $I^2 t$ ) far exceeded the allowable short-circuit thermal limit of the copper conductor with XLPE insulation ( $K^2 S^2$ ):
$I^2 t = (28,000)^2 \cdot 0.52 = 4.07 \times 10^8 A ^2 s$
For a $240 mm ^2$ cable, the limit is $2.38 \times 10^8 A ^2 s$ . The cables melted and the insulation carbonized over a length of 80 meters.
Structural Damage to the 20 MVA Transformer: Repulsive mechanical electrodynamic forces (proportional to the square of the peak current, $i_p^2$ ) acted on the transformer windings for an extended duration, causing physical deformation of the low-voltage coils (radial buckling) and loss of axial clamping pressure, requiring a complete rewind of the transformer.

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Design Methodology, Correct Dimensioning, and Mitigation

To prevent catastrophic failures due to asymmetric saturation in high-altitude mining environments, design engineering must apply a rigorous CT dimensioning procedure in accordance with IEC 61869-2 and IEEE C57.13 standards, adapted for extreme environmental conditions.

Selection of Specialized Accuracy Classes (IEC 61869-2)

Conventional metering and protection CTs (classes 5P and 10P) feature closed magnetic cores without air gaps, resulting in high inductance and extremely high magnetic remanence ( $\Psi_{res} \ge 80\%$ of saturation flux). These CTs are highly susceptible to transient saturation and are unsuitable for protecting critical systems in high-altitude mining.

The use of transient protection classes designed to withstand the DC offset component without saturating must be specified:

Class TPX: Current transformers without air gaps in the core, characterized by a large iron cross-section and a very high secondary time constant $T_s$ . Suitable for simple operating cycles where rapid auto-reclosing is not required, as core demagnetization is slow.
Class TPY: CTs with small air gaps in the magnetic core, which reduces the residual flux to less than 10% of $\Psi_{sat}$ . They exhibit excellent transient response and are mandatory for transmission lines or substations with high-speed auto-reclosing schemes (O-t-CO cycle).
Class TPZ: CTs with large air gaps that reduce the secondary time constant $T_s$ to extremely low values (typically 15 to 100 ms). They are virtually immune to saturation but exhibit a significant phase error at power frequency, limiting their use primarily to differential protection of generators and large power transformers.

Calculation of the Required Knee-Point Voltage considering Altitude and Transients

For a CT specified under the IEC standard (Class PX or TPY), the rated equivalent limiting secondary knee-point voltage ( $Eal$ ) must be calculated to satisfy the non-saturation transient condition under the most severe fault:

Eal \ge Ktf \cdot Kssc \cdot Isr \cdot \left( R_s(Tmax) + Rwire(Tmax) + Zrelay \right)

Where:

$Ktf$ is the transient dimensioning factor calculated previously.
$Kssc$ is the rated symmetrical short-circuit current factor, defined as the ratio of the primary short-circuit current ( $I_{f, max}$ ) to the rated primary current of the CT ( $Ipr$ ):
$Kssc = \frac{I_{f, max}}{Ipr}$
$Isr$ is the rated secondary current of the CT (typically 1 A or 5 A).
$R_s(Tmax)$ is the secondary winding resistance corrected for the maximum operating temperature at high altitude ( $Tmax$ ), calculated by considering thermal dissipation derating.
$Rwire(Tmax)$ is the resistance of the interconnecting leads corrected for temperature.

Practical Mitigation Strategies

If the calculation of $Eal$ results in a CT size that is physically impossible to install within standard medium-voltage switchgear cubicles, the following mitigation strategies must be adopted:

Adoption of 1-Ampere Secondary CTs: Reduce the rated secondary current of the CT from 5 A to 1 A. Since Joule losses in the secondary circuit scale with the square of the current ( $Isr^2$ ), the voltage drop across the secondary burden decreases by a factor of 25. This drastically reduces the required knee-point voltage and, consequently, the physical size of the CT core.
Utilization of Low-Burden Relays: Replace legacy protection relays with modern numerical relays whose input impedance is virtually negligible ( $Zrelay < 0.1 \ \Omega$ ).
Rogowski Coil Technology (Optical / Non-Conventional Sensors): For new mining installations, it is highly recommended to replace electromagnetic CTs with Non-Conventional Instrument Transformers (NCITs) based on Rogowski Coils or optical Faraday-effect sensors. Lacking a ferromagnetic core, these devices exhibit absolute linearity, complete elimination of magnetic saturation, immunity to altitude-related thermal derating, and an extremely wide bandwidth, making them ideal for environments with high harmonic distortion under IEEE 519-2022.

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Practical Application and Simulation with Vexten Suite

To validate and optimize the design of protection systems and mitigation strategies against asymmetric CT saturation in complex high-altitude mining environments, the advanced simulation platform Vexten Suite is utilized. This electrical engineering software suite integrates unified modules for multi-physics modeling, electromagnetic transient (EMT) analysis, short-circuit calculations, and protection coordination.

Short-Circuit Module (IEC 60909 / IEEE 141) in Vexten Suite

The first step in the Vexten Suite workflow involves detailed modeling of the mining network topology. The software calculates the symmetrical and asymmetrical short-circuit currents in accordance with IEC 60909 or IEEE 141 (Red Book) methodologies, automatically adjusting system parameters for high-altitude conditions.

The calculation engine of Vexten Suite precisely determines the decay of the DC component by analyzing the network decrement factor, obtaining the equivalent $X/R$ ratio at the fault point using the equivalent frequency method (per IEC 60909-0) or the complex impedance method. This allows the user to plot the actual primary transient current curve $i_p(t)$ to be injected into the CT model.

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

The secondary loop resistance ( $Rct$ ) is a critical input parameter for CT saturation. Vexten Suite incorporates a calculation engine based on the IEC 60287 standard for sizing power and control cables under severe thermal regimes. The software automatically applies correction factors for altitude, ambient temperature, and grouping:

Iadmissible = Itabulada \cdot Ftemp \cdot Faltitud \cdot Fagrupamiento

Additionally, the software calculates the increase in the effective ohmic resistance of the conductor due to skin and proximity effects induced by the harmonic spectrum injected by non-linear loads (such as the SAG mill VFDs), modeled according to IEEE 519-2022 guidelines. This ensures that the secondary loop resistance used in saturation simulations corresponds to the worst-case thermal and harmonic scenario in the mine.

Electromagnetic Transients and CT Saturation Simulation Module

Vexten Suite features an EMT simulation environment where the non-linear dynamic behavior of the current transformer core is modeled. The CT model implements the Jiles-Atherton magnetic hysteresis equation or magnetization curves represented by bilinear or multi-segment approximation functions.

The engineer inputs the parameters of the CT to be simulated:

Transformation ratio ( $N_p:N_s$ ).
Secondary winding resistance ( $R_s$ ) at the altitude-calibrated operating temperature.
Characteristic excitation curve of the core ( $V-I$ curve).
Initial residual magnetic flux ( $\Psi_{res}$ ).
Total secondary burden impedance (cables and relay).

Upon running the transient short-circuit simulation, Vexten Suite generates the following interactive diagnostic plots:

Comparison of Primary Current (Referred to the Secondary) vs. Actual Secondary Current: Visualizes the exact instant of saturation (wave clipping) and quantifies the instantaneous current error.
Magnetic Flux Trajectory ( $\Psi-t$ ) and Operating Curve on the B-H Plane: Allows observation of the dynamic shift of the operating point into the deep saturation region due to the DC offset.
Relay Algorithm Response (DFT): Simulates the digital signal processing of the protection relay. It plots the fundamental RMS current calculated by the relay in real-time, identifying delays in 51 function operation or the blocking of 50 functions.

Harmonic Mitigation and Resonance Module

To comply with IEEE 519-2022 limits and protect CTs from thermal effects and premature saturation caused by harmonics, Vexten Suite enables the design and simulation of mitigation systems, such as:

Passive Harmonic Filters (Tuned and Broadband): The software calculates the system impedance as a function of frequency to identify parallel resonance points between the capacitance of power factor correction capacitor banks and the inductance of the mining grid. Vexten Suite optimizes the filter's inductance and capacitance parameters to shift resonance frequencies away from the critical harmonic orders generated by cycloconverters.
Active Power Filters (APF): Simulates the injection of harmonic currents in anti-phase to cancel harmonic distortion at the PCC, verifying strict compliance with the TDD and IHD limits of IEEE 519-2022.

By utilizing Vexten Suite, design engineers can perform parametric sensitivity analysis ("What-If" scenarios), evaluating the impact of varying the turns ratio, secondary cable cross-section, CT protection class, or installation altitude, thereby guaranteeing absolute selectivity and safety of the mine's electrical system under the most extreme operating conditions on the planet.