Trip curves B, C, D, K, Z under IEC 60898 and IEC 60947-2

Introduction and Fundamental Regulatory Framework

The correct selection and coordination of overcurrent protective devices—specifically Miniature Circuit Breakers (MCBs under IEC 60898) and Molded Case / Air Circuit Breakers (MCCBs/ACBs under IEC 60947-2)—represents one of the critical pillars in low-voltage electrical power system engineering. The primary function of these apparatuses is not merely the interruption of bolted short-circuit currents, but the comprehensive protection of conductor insulation against thermal overheating and the preservation of the structural and dielectric integrity of components under severe electrodynamic stresses.

The international regulatory framework establishes fundamental distinctions in the design and testing of these devices. Standard IEC 60898-1 (Circuit-breakers for overcurrent protection for household and similar installations) regulates apparatus intended to be operated by ordinary persons, limiting their rated short-circuit capacities (typically up to $25 kA$) and establishing fixed, standardized magnetic tripping thresholds (Curves B, C, and D). On the other hand, standard IEC 60947-2 (Low-voltage switchgear and controlgear - Part 2: Circuit-breakers) governs circuit breakers intended for industrial, commercial, and heavy distribution applications, where they are operated by skilled or instructed electricians. This standard allows for complex parametric adjustments, higher ultimate ($Icu$) and service ($Ics$) breaking capacities, and contemplates additional high-precision tripping curves such as classes K and Z.

Understanding the dynamic interaction between the thermal profile of the bimetallic element and the transient response of the ferromagnetic core is indispensable to avoid nuisance tripping during transient starting regimes (inrush) while simultaneously guaranteeing strict compliance with the maximum disconnection times demanded by electrical safety codes for protection against indirect contact and earth faults.

Phenomenological Analysis of the Inrush Transient and its Behavior in Complex Loads

The magnetizing inrush current phenomenon constitutes the primary challenge in selecting magnetothermal tripping curves. This transient regime arises from the sudden excitation of inductive elements with ferromagnetic cores, coupling capacitors, or the initial charging of switched-mode power supplies (SMPS) and induction motors.

Current Transients in Distribution Transformers

When a single-phase or three-phase transformer is energized, the magnetic flux in the core must adjust to the instantaneous voltage applied at the moment of closing. Neglecting the resistive voltage drop in the primary winding $R_1$, the relationship between the applied voltage $v(t) = V_m \sin(\omega t + \alpha)$ and the magnetic flux in the core $\Phi(t)$ is given by Faraday-Lenz's law:

Where $\Phi_r$ is the residual flux in the core due to the magnetic hysteresis prior to de-energization, $N_1$ is the number of primary turns, and $\alpha$ is the voltage phase angle at the instant of closing. If the breaker closes at a voltage zero-crossing ($\alpha = 0$) and a residual flux $\Phi_r$ exists with the same polarity as the upcoming flux peak, the total flux will reach a theoretical maximum value that can double twice the nominal flux:

Given that silicon steel cores saturate rapidly at flux densities exceeding their saturation knee ($Bsat \approx 1.5 - 1.8 T$), the effective magnetizing inductance $L_m$ drops drastically to values close to the leakage inductance. Consequently, the primary circuit impedance is reduced almost exclusively to the ohmic resistance of the winding, generating inrush current peaks that can oscillate between $10I_n$ and $25I_n$ with a time decay constant $\tau = L/R$ ranging from tens of milliseconds to several seconds in large transformers.

Starting and Energization Currents in Induction Motors and Capacitive Loads

In IEC-standard three-phase induction motors, the Locked Rotor Current (LRC) typically oscillates between $6I_n$ and $14I_n$, depending on the motor design class (NEMA Design A/B or IEC equivalents). The initial asymmetrical component, driven by the stator DC current component, introduces an initial crest factor greater than $1.8$ in the first few half-cycles.

On the other hand, power factor correction capacitor banks and switched-mode power supplies exhibit capacitive charging currents whose peaks can exceed more than $20$ to $30$ times the RMS nominal current, due to the very low instantaneous impedance presented by discharged capacitors ($Z_c \to 0$ at $t=0$).

Mathematical and Physical Fundamentals of IEC 60898 and IEC 60947-2 Tripping Curves

The operation of a circuit breaker is divided into two clearly differentiated zones: the thermal protection zone (overload) and the magnetic protection zone (instantaneous short-circuit).

Thermal Mechanism (Bimetallic Tripper)

The thermal element consists of a calibrated bimetallic strip made of two metals with different linear thermal expansion coefficients ($\alpha_1 \neq \alpha_2$). The heat generated by the flow of electric current via the Joule effect heats the bimetal:

The mechanical deflection $d$ of the free end of the bimetal is directly proportional to the temperature increase $\Delta T$ and, therefore, to the square of the effective circulating current $I^2$ during a cumulative time interval:

IEC standards establish standardized operating bands that define thermal behavior:

• Conventional Non-Tripping Current ($I_n$): Current that the device must be able to carry indefinitely without tripping ($1.13 \cdot I_n$ according to IEC 60898 for a conventional time of 1 to 2 hours).
• Conventional Tripping Current ($I_2$): Current that must cause automatic tripping within the stipulated conventional time ($1.45 \cdot I_n$ for IEC 60898).

Magnetic Mechanism (Electromagnetic Tripper)

The magnetic tripper consists of a solenoid or air/iron core with a plunger restrained by a calibrated opposing spring. When the short-circuit current exceeds the nominal magnetic threshold $Iim$, the generated magnetromotive force exceeds the mechanical tension of the spring:

Where $N$ is the number of turns, $I$ is the fault current, and $\frac{dG}{dx}$ represents the variation of the magnetic circuit permeance with respect to the plunger displacement. The interruption time in this zone is extremely fast, typically under $10 ms$ (less than half a cycle in $50/60 Hz$ systems), severely limiting the integrated specific let-through energy.

Comprehensive Analysis of Curves B, C, D, K, and Z

The operational characteristics and regulatory ranges of each curve under IEC 60898 and IEC 60947-2 are detailed below:

Curve B

• Magnetic Tripping Range: $3 \cdot I_n$ to $5 \cdot I_n$ (IEC 60898) / $3.2 \cdot I_n$ to $4.8 \cdot I_n$ (IEC 60947-2).
• Main Application: Protection of long distribution circuits with high fault loop impedance, generators, and circuits with purely resistive loads (incandescent lighting, ohmic heating) where inrush currents are nonexistent or negligible.
• Technical Justification: Guarantees rapid disconnection against low-magnitude earth faults in networks with TN or TT earthing connection schemes where the short-circuit current is limited by the high impedance of long conductors.

Curve C

• Magnetic Tripping Range: $5 \cdot I_n$ to $10 \cdot I_n$ (IEC 60898) / $7 \cdot I_n$ to $10 \cdot I_n$ (IEC 60947-2).
• Main Application: The default industrial standard. Used for fluorescent lighting, LED lamps with massive electronic drivers, general socket outlets (residential and commercial plugs), and small motors with moderate starting currents.
• Technical Justification: Tolerates moderate inrush transients of up to $5$ to $10$ times the nominal current for brief periods without compromising selectivity or causing nuisance trips.

Curve D

• Magnetic Tripping Range: $10 \cdot I_n$ to $20 \cdot I_n$ (IEC 60898) / $10 \cdot I_n$ to $14 \cdot I_n$ (IEC 60947-2).
• Main Application: Heavy inductive loads with high and sustained inrush currents, such as power distribution transformers, arc welding machines, high-power motors with heavy direct-on-line (DOL) starting, and industrial capacitor banks.
• Technical Justification: Prevents magnetic tripping during severe magnetization or starting transients, ensuring that the circuit breaker only acts upon bolted short-circuits in the winding or load.

Curve K

• Magnetic Tripping Range: $8 \cdot I_n$ to $12 \cdot I_n$ (exclusive to IEC 60947-2).
• Main Application: Protection of circuits with high-inertia induction motors, transformers with very high magnetizing currents, and mixed industrial loads.
• Technical Justification: Offers a narrow magnetic tolerance window combined with high precision in thermal protection against prolonged overloads, optimizing protection coordination in complex industrial environments.

Curve Z

• Magnetic Tripping Range: $2 \cdot I_n$ to $3 \cdot I_n$ (exclusive to IEC 60947-2).
• Main Application: Protection of sensitive electronic devices, power semiconductors, control circuits with low overcurrent withstand capability, and critical analog/digital instrumentation.
• Technical Justification: Its extremely high magnetic sensitivity allows the interruption of minor fault currents that could destroy delicate electronic components before catastrophic thermal damage occurs in the silicon.

Comparative Matrix of Electrical and Regulatory Parameters

The following table consolidates the fundamental operational parameters, international regulatory limits, and critical fault conditions associated with each type of tripping curve:

Tripping Curve	Applicable Standard	Thermal Threshold ($I_n$ / $I_2$)	Magnetic Threshold (IEC 60898 / 60947-2)	Max Tolerated Inrush	Typical Industrial Application	Consequence of Improper Selection (Forensic Failure)
B	IEC 60898 / IEC 60947-2	$1.13 I_n$ / $1.45 I_n$	$3I_n$ to $5I_n$	Low ($< 3I_n$)	Long lines, heating, generators, resistive lighting.	Nuisance tripping due to minor transient currents; damage due to lack of selectivity in meshed networks.
C	IEC 60898 / IEC 60947-2	$1.13 I_n$ / $1.45 I_n$	$5I_n$ to $10I_n$	Moderate ($5I_n - 8I_n$)	General socket outlets, fluorescent/LED lighting, small motors.	If used on transformers, immediate trip due to inrush; if used on sensitive electronic loads, excessive clearing time.
D	IEC 60898 / IEC 60947-2	$1.13 I_n$ / $1.45 I_n$	$10I_n$ to $20I_n$	Very High ($10I_n - 15I_n$)	Power transformers, welding machines, heavy DOL motors.	Magnetic threshold too high for circuits with high loop impedance; risk of failing to clear distant earth faults (violation of maximum disconnection time).
K	IEC 60947-2	$1.05 I_n$ / $1.20 I_n$ (Adjustable)	$8I_n$ to $12I_n$	High and sustained	Industrial motors, inductive loads with high inertia and frequent switching.	Cumulative overheating of the bimetal if operated outside the motor's thermal class; winding insulation overstress.
Z	IEC 60947-2	$1.05 I_n$ / $1.20 I_n$ (Adjustable)	$2I_n$ to $3I_n$	Extremely low ($< 2I_n$)	Semiconductors, power rectifiers, delicate electronic control circuits.	Continuous nuisance trips from minimal load fluctuations or harmless magnetization currents in power supplies.

Forensic Failure Analysis in Distribution Systems Due to Incorrect Protection Selection

The incorrect selection of the tripping curve triggers catastrophic failures that can be classified into two main streams: nuisance trips due to transient undersizing and failure to clear faults due to magnetic oversizing.

Failure Due to Magnetic Oversizing (Improper Use of Curve D in Long Terminal Circuits)

When a designer installs a circuit breaker with a Curve D in a residential or commercial terminal circuit with excessive cable length, the fault loop impedance $Z_s$ increases significantly. According to Ohm's law, the bolted short-circuit current at the end of the line is limited by:

If the impedance $Z_s$ is such that the resulting short-circuit current is, for example, $12 \cdot I_n$, a Curve C breaker will trip magnetically in less than $10 ms$. However, a Curve D breaker requires a minimum current of $10$ to $20 \cdot I_n$ to guarantee instantaneous magnetic tripping. If $Isc$ is in the range of $8 \cdot I_n$, the breaker will not operate instantaneously magnetically, but will rely on its bimetallic thermal element. The time required for the bimetal to reach the tripping temperature at $8 \cdot I_n$ can be several seconds. During this interval:

• Thermal Damage to the Conductor: The specific let-through energy $I^2 t$ far exceeds the thermal rating of the cable insulation (PVC or XLPE), causing melting of the insulating material, toxic gas emission, secondary multi-phase short circuits, and initiation of fires due to sustained electric arcs.
• Severe Dielectric Stresses: Connected equipment suffers accelerated insulation degradation due to the prolonged maintenance of reduced voltages and elevated fault currents.

Failure Due to Transient Undersizing (Use of Curve B or C on Transformers or Capacitor Banks)

Selecting a Curve B to protect the primary of a distribution transformer generates systematic instantaneous trips every time the equipment is energized due to inrush current. In an industrial environment, the erroneous practice of repeatedly replacing the circuit breaker or resetting it without investigating the cause leads to thermal fatigue of the main breaker contacts, contact welding of the arcing contacts, and premature destruction of the spring tripping mechanism.

Practical Design Strategies, Mitigation, and Vexten Suite Sizing

To mitigate risks associated with inrush transients and strictly comply with IEC 60909 and IEC 60287 standards, the Vexten Academy engineering department recommends following the systematic calculation and selection protocol detailed below.

Calculation Methodology for Curve and Rating Selection

Step 1: Determine the continuous operating nominal current of the load $I_b$ considering power factors and harmonics:

Step 2: Calculate the peak inrush current and its estimated duration $tinrush$:

Step 3: Select the nominal rating of the circuit breaker $I_n$ complying with cable protection coordination according to IEC 60364-4-43:

Where $I_z$ is the allowable current-carrying capacity of the conductor corrected for ambient temperature, grouping, and harmonics according to IEC 60287 / NEC 310.

Step 4: Verify the short-circuit protection condition and maximum disconnection times to avoid dangerous touch voltages on metallic frames:

Where $k$ is the factor dependent on the conductor material and insulation, and $S$ is the conductor cross-sectional area in $mm ^2$.

Practical Application with Vexten Suite (Short-Circuit and Thermal Derating Study)

When using the advanced module Vexten Suite - ShortCircuit & Protection Analyzer, the design engineer must enter the following input parameters for a typical $1000 kA$, $400 V$ industrial substation:

1. Transformer Power: $S_n = 630 kVA$, Short-circuit voltage $u_k = 6\%$.
2. Primary and Secondary Nominal Current: $In2 = 909.3 A$.
3. Estimated Inrush Current: $12 \cdot In2 \approx 10,911 A$ with a time constant $\tau = 70 ms$.
4. Fault Loop Impedance calculated by the software: $Z_s = 0.024\,\Omega$.

The IEC 60909 calculation engine of Vexten Suite simulates the aperiodic and symmetric components of the three-phase and single-phase short circuit. When evaluating protection options on the low-voltage side of the transformer, the software automatically rejects the use of low-rating Curve C breakers due to the risk of spurious tripping, and validates a Molded Case Circuit Breaker (MCCB) under IEC 60947-2 with an electronic trip unit featuring adjustable time delays, or alternatively, a Curve D MCB with $I_n = 1000 A$ and an ultimate breaking capacity $Icu = 50 kA$.

Likewise, the power factor and harmonic mitigation module of Vexten Suite applies derating factors for XLPE conductors installed in perforated trays exposed to an ambient temperature of $45^\circ C$ and a current harmonic distortion of $25\%$ (massive presence of 3rd, 9th, and 15th order harmonics due to non-linear loads):

Where $f_T$ is the temperature correction factor, $f_G$ is the cable grouping factor, and $f_H$ is the harmonic content reduction factor stipulated by international standards. This ensures that the selected thermal curve ($I_2 = 1.45 I_n$) operates in perfect coordination with the new derated thermal limit of the cable, preventing premature degradation of the polymeric insulation and ensuring maximum operational reliability of the electrical power system.

Conclusion

The rigorous selection of tripping curves B, C, D, K, and Z under the guidelines of IEC 60898 and IEC 60947-2 does not constitute a mere regulatory exercise, but an advanced engineering discipline that requires the synchronous analysis of conductor thermodynamics, short-circuit electrodynamics, and the transient phenomenology of industrial loads. Mastery of these concepts prevents catastrophic failures, optimizes chronometric and amperometric selectivity, and ensures the safeguarding of human lives and high-value industrial assets.