Analysis of Rated Short-Time Thermal Current and Dynamic Stability Current Parameters for Current Transformers

Xiamen No.1 Instrument Transformer Co., Ltd.

Addtime: 2025-08-25 Clicknum

1. Introduction

Current transformers (CTs) are critical components in power systems, serving two primary functions: measurement (providing accurate current signals for metering) and protection (triggering protective relays during faults). During short-circuit faults, CTs are subjected to extreme electrical and mechanical stresses—specifically, high currents that generate excessive heat (thermal stress) and intense electromagnetic forces (mechanical stress). To ensure CTs survive such events without permanent damage, two key parameters are defined: rated short-time thermal current and dynamic stability current. These parameters are fundamental to CT design, selection, and validation, directly impacting the reliability and safety of power systems. This analysis explores their definitions, underlying principles, standards, calculations, and practical applications.

2. Rated Short-Time Thermal Current

2.1 Definition

The rated short-time thermal current (often denoted as

I_{t h}

) is the maximum rms current that a CT’s windings can withstand for a specified duration (typically 1s, 2s, or 3s) without exceeding permissible temperature limits. This parameter ensures the CT’s insulation and conductor materials do not degrade due to excessive heat generated during short circuits.

2.2 Thermal Stress Mechanism

Short-circuit currents, which can be 10–100 times higher than rated current, induce significant heat in CT windings via Joule-Lenz law:

Q = I^{2} Rt

, where

Q

is heat energy (in joules),

I

is current (rms),

R

is winding resistance, and

t

is duration (in seconds). This heat raises the winding temperature; exceeding the insulation’s maximum allowable temperature (e.g., 250°C for Class B insulation, 180°C for Class F) causes irreversible damage (e.g., insulation cracking, conductor annealing).

2.3 Key Concept: $I^{2} t$ Withstand Value

The thermal capability of a CT is better characterized by the

I^{2} t

withstand value (the product of the square of the rated short-time current and the duration). This value represents the total thermal energy the CT can absorb without failure. For example, a CT rated at

31.5 kA for 1s

has an

I^{2} t

value of

31. 5^{2} \times 1 = 992.25 kA^{2} s

When selecting a CT, its

I^{2} t

withstand value must exceed the

I^{2} t

of the actual short-circuit current in the system. The system’s short-circuit

I^{2} t

depends on the fault current magnitude and the time it takes for protective devices (e.g., circuit breakers) to clear the fault.

2.4 Standards and Duration

International standards (e.g., IEC 61869-2, ANSI C57.13) specify standard durations for

I_{t h}

1 second: Most common for medium-voltage (MV) and high-voltage (HV) systems, aligning with typical breaker clearing times.
2 seconds or 3 seconds: Used in systems where faults may persist longer (e.g., remote grids with slower protection).

Standards also define temperature limits: for example, IEC 61869-2 requires that after the short-time test, winding temperatures must not exceed 250°C (for Class B insulation) or 180°C (for Class F), measured by resistance methods or thermocouples.

2.5 Calculation and Validation

To determine

I_{t h}

, manufacturers consider:

Winding material (copper or aluminum) and cross-sectional area (affecting resistance $R$ ).
Insulation class (defining maximum temperature).
Heat dissipation (via conduction, convection, or radiation, though negligible during short durations).

The formula for

I_{t h}

is derived from thermal energy balance:

I_{t h} = \frac{C \cdot Δ T}{R \cdot t}

Where:

$C$ = thermal capacity of the winding (J/°C).
$Δ T$ = allowable temperature rise (°C).
$R$ = winding resistance at operating temperature (Ω).
$t$ = duration (s).

Validation involves short-time thermal tests: CTs are subjected to

I_{t h}

for the specified duration, and post-test inspections confirm no insulation breakdown or conductor damage.

3. Dynamic Stability Current

3.1 Definition

The dynamic stability current (denoted as

I_{d y n}

) is the maximum peak current a CT can withstand without mechanical damage (e.g., winding deformation, insulation displacement) due to electromagnetic forces generated during short circuits. Unlike

I_{t h}

, it focuses on mechanical stress rather than thermal effects.

3.2 Mechanical Stress Mechanism

Short-circuit currents produce intense magnetic fields, creating electromagnetic forces between parallel current-carrying conductors (Ampère’s law). For CTs, these forces act between primary and secondary windings, as well as between turns within a winding. The force magnitude is proportional to the square of the current and inversely proportional to the distance between conductors:

F \propto \frac{I ^{2}}{d}

Where

d

is the distance between conductors.

During symmetric short circuits, the fault current waveform has a peak value (due to AC asymmetry) equal to

22 I_{sc, r m s} \approx 2.828 I_{sc, r m s}

, where

I_{sc, r m s}

is the rms short-circuit current. For asymmetric faults (e.g., single-line-to-ground), the peak can be higher (up to

2.55 I_{sc, r m s}

for 50Hz systems, as defined by IEC). This peak current induces the maximum mechanical force, making

I_{d y n}

a peak value rather than an rms value.

3.3 Relationship to Short-Time Thermal Current

I_{d y n}

is often specified as a multiple of

I_{t h}

. For symmetric faults, the ratio is typically

2.55

(derived from

2 \times 1.8

, where 1.8 accounts for DC offset in asymmetric faults). For example, a CT with

I_{t h} = 31.5 kA

(rms, 1s) may have

I_{d y n} = 31.5 \times 2.55 \approx 80 kA

(peak).

3.4 Mechanical Design Considerations

To withstand

I_{d y n}

, CTs require robust mechanical design:

Winding bracing: Reinforcements (e.g., epoxy resin, glass fiber) prevent winding displacement.
Conductor rigidity: Thick, rigid conductors resist bending under force.
Insulation spacing: Adequate distance between windings reduces force intensity while maintaining insulation integrity.

3.5 Standards and Testing

Standards like IEC 61869-2 and ANSI C57.13 define

I_{d y n}

test procedures: CTs are subjected to a peak current equal to

I_{d y n}

(simulating the first half-cycle of a short circuit). Post-test checks include:

Visual inspection for winding deformation or insulation damage.
Electrical tests (e.g., turns ratio, insulation resistance) to confirm no performance degradation.

4. Distinction and Synergy Between the Two Parameters

Aspect	Rated Short-Time Thermal Current ( $I_{t h}$ )	Dynamic Stability Current ( $I_{d y n}$ )
Nature of Stress	Thermal (heat-induced insulation/conductor damage)	Mechanical (electromagnetic force-induced deformation)
Current Type	RMS value	Peak value
Key Factor	$I^{2} t$ (thermal energy)	$I_{p e ak}^{2}$ (force magnitude)
Duration	Specified (1s, 2s, etc.)	Instantaneous (first half-cycle of fault)
Failure Mode	Insulation breakdown, conductor melting	Winding deformation, structural damage

Despite their differences,

I_{t h}

and

I_{d y n}

are complementary: a CT must satisfy both to survive short circuits. For example, a CT with high

I_{t h}

but low

I_{d y n}

may avoid thermal damage but fail mechanically; conversely, a CT with high

I_{d y n}

but low

I_{t h}

may melt due to prolonged heat.

5. Application in CT Selection

Selecting a CT requires matching

I_{t h}

and

I_{d y n}

to the system’s short-circuit characteristics:

5.1 Step 1: Calculate System Short-Circuit Parameters

Determine the maximum rms short-circuit current ( $I_{sc, r m s}$ ) at the CT location (using software like ETAP or PSCAD).
Estimate the fault clearing time ( $t_{c l e a r}$ ) (e.g., 0.5s for fast-acting breakers).
Compute the system’s $I^{2} t$ value: $I_{sc, r m s}^{2} \times t_{c l e a r}$ .
Calculate the peak short-circuit current: $I_{sc, p e ak} = k \times I_{sc, r m s}$ , where $k \approx 2.55$ (asymmetric faults).

5.2 Step 2: Select CT Parameters

$I_{t h}$ : Choose a CT with $I_{t h}^{2} \times t_{r a t e d} \geq I_{sc, r m s}^{2} \times t_{c l e a r}$ . For example, if $I_{sc, r m s} = 40 kA$ and $t_{c l e a r} = 0.5 s$ , the system $I^{2} t = 4 0^{2} \times 0.5 = 800 kA^{2} s$ . A CT with $I_{t h} = 50 kA$ (1s) has $5 0^{2} \times 1 = 2500 kA^{2} s$ , which is sufficient.
$I_{d y n}$ : Ensure $I_{d y n} \geq I_{sc, p e ak}$ . For $I_{sc, p e ak} = 40 \times 2.55 = 102 kA$ , select a CT with $I_{d y n} \geq 125 kA$ (a common standard value).

6. Standards Overview

IEC 61869-2: Specifies requirements for CTs, including $I_{t h}$ (1s, 2s) and $I_{d y n}$ (peak, 2.55× $I_{t h}$ for symmetric faults).
ANSI C57.13: Defines thermal ratings (e.g., 10kA for 30s) and mechanical ratings (e.g., 200kA peak) for distribution and power CTs.
IEEE C57.13.1: Provides test procedures for verifying $I_{t h}$ and $I_{d y n}$ , including temperature rise and mechanical stress tests.

7. Conclusion

Rated short-time thermal current and dynamic stability current are critical metrics ensuring current transformers survive short-circuit faults.

I_{t h}

safeguards against thermal degradation, while

I_{d y n}

prevents mechanical failure. Proper selection, based on system short-circuit calculations and adherence to standards, is essential for maintaining power system reliability. Engineers must balance both parameters to avoid under-sizing (risk of CT failure) or over-sizing (increased cost). As power systems evolve with higher fault levels (e.g., due to renewable integration), these parameters will remain central to CT design and application.

XUJIA

I graduated from the University of Electronic Science and Technology, majoring in electric power engineering, proficient in high-voltage and low-voltage power transmission and transformation, smart grid and new energy grid-connected technology applications. With twenty years of experience in the electric power industry, I have rich experience in electric power design and construction inspection, and welcome technical discussions.

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Analysis of Rated Short-Time Thermal Current and Dynamic Stability Current Parameters for Current Transformers

1. Introduction