CT Composite Error Explained

Introduction

When a Current Transformer fails to accurately reproduce the primary fault current in its secondary circuit, protection relays receive distorted signals — and the consequences range from delayed tripping to complete protection failure. At the heart of CT accuracy specification lies a single parameter that engineers often reference but rarely fully understand: composite error. Composite error is the IEC-defined mathematical expression of total CT measurement inaccuracy, combining both current magnitude error and phase displacement into a single RMS percentage value — and it is the governing criterion that determines whether a protection CT passes or fails its accuracy class at the Accuracy Limiting Factor¹. For electrical engineers specifying protection CTs for medium voltage switchgear, substations, and industrial power distribution systems, a clear understanding of composite error is essential to ensure protection reliability under real fault conditions. This guide unpacks the IEC 61869-2² definition, the mathematical formulation, and the practical engineering implications of composite error in MV protection circuits.

Table of Contents

• What Is CT Composite Error and How Is It Defined by IEC Standards?
• How Is Composite Error Mathematically Calculated in Protection CTs?
• How Does Composite Error Influence CT Selection for MV Protection Applications?
• What Are the Common Misunderstandings and Testing Errors Around CT Composite Error?

What Is CT Composite Error and How Is It Defined by IEC Standards?

Composite error is the total accuracy deviation of a CT secondary output from its ideal theoretical value, expressed as a percentage of the primary current RMS value. It is defined under IEC 61869-2 (superseding IEC 60044-1) as the governing accuracy criterion for protection-class CTs at their rated Accuracy Limiting Factor (ALF).

Unlike ratio error and phase displacement — which are measured separately under normal sinusoidal conditions — composite error captures the combined effect of both magnitude and phase errors simultaneously, including the distortion introduced by core non-linearity and magnetic saturation³ at high fault current multiples. This makes it the most comprehensive and demanding accuracy metric for protection CT performance.

The IEC 61869-2 Definition

Per IEC 61869-2, composite error ($\varepsilon_c$) is defined as:

“The RMS value of the difference between the instantaneous values of the primary current and the secondary current multiplied by the rated transformation ratio, expressed as a percentage of the RMS value of the primary current.”

This definition has three critical implications for protection engineers:

• It is measured at ALF × rated primary current — not at normal load current
• It captures waveform distortion caused by core saturation, not just steady-state ratio error
• It is an RMS percentage — meaning harmonic distortion components from saturated core behavior are fully included

Accuracy Classes and Composite Error Limits

Accuracy Class	Composite Error Limit at ALF	Phase Displacement Limit	Typical Application
5P	≤ 5%	± 60 minutes	Differential, distance, overcurrent protection
10P	≤ 10%	Not specified	Overcurrent, earth fault protection
5PR	≤ 5%	± 60 minutes	Remanence-controlled protection schemes
10PR	≤ 10%	Not specified	General protection, remanence-limited
PX / PXR	Defined by knee-point voltage	Not by composite error	Unit protection, high-impedance schemes

Key Technical Parameters Governing Composite Error

• Core Material: Cold-rolled grain-oriented silicon steel (CRGO) — grain orientation determines saturation knee-point and therefore composite error behavior at high fault multiples
• Core Cross-Section: Larger core area delays saturation onset, reducing composite error at high ALF
• Secondary Winding Turns: Determines transformation ratio accuracy and leakage flux contribution to phase error
• Insulation System: Epoxy resin cast, rated 12kV / 24kV / 36kV — insulation class does not directly affect composite error but determines installation environment
• Rated Burden: Higher burden increases magnetizing current demand, increasing composite error — directly linked to ALF performance

How Is Composite Error Mathematically Calculated in Protection CTs?

The mathematical formulation of composite error integrates the instantaneous difference between ideal and actual secondary output over a complete cycle, capturing both fundamental frequency errors and harmonic distortion from core saturation.

The IEC Composite Error Formula

$\varepsilon_c = \frac{100}{I_1} \sqrt{\frac{1}{T} \int_0^T (K_n \cdot i_2 – i_1)^2 , dt} ,$

Where:

• $\varepsilon_c$ = composite error (%)
• $I_1$ = RMS value of primary current (A)
• $K_n$ = rated transformation ratio (N₂/N₁ or I₁ₙ/I₂ₙ)
• $i_1$ = instantaneous primary current (A)
• $i_2$ = instantaneous secondary current (A)
• $T$ = duration of one complete cycle (seconds)

Relationship to Magnetizing Current

In practical CT testing, composite error is most commonly derived from the magnetizing current method, which is simpler to implement than direct instantaneous waveform comparison:

$\varepsilon_c \approx \frac{I_0}{I_1} \times 100 ,$

Where $I_0$ is the RMS magnetizing current at the test point (ALF × $I_{1n}$). This approximation holds when the magnetizing current is primarily reactive — valid for well-designed protection CT cores operating below deep saturation.

Composite Error vs. Ratio Error vs. Phase Displacement

Understanding how composite error relates to — but differs from — the two individual error components is essential:

Ratio Error (Current Error):
$\varepsilon_i = \frac{K_n \cdot I_2 – I_1}{I_1} \times 100 ,$

This captures only the magnitude difference between actual and ideal secondary current under sinusoidal conditions.

Phase Displacement ($\delta$):
The angular difference in minutes between primary and secondary current phasors — relevant for power measurement accuracy but less critical for protection relay operation.

Composite Error:
Combines both, plus harmonic distortion from core saturation:

$\varepsilon_c^2 \approx \varepsilon_i^2 + \left(\frac{\delta}{3438}\right)^2 + \varepsilon_{harmonic}^2$

The harmonic distortion term $\varepsilon_{harmonic}$ becomes dominant when the CT core approaches saturation — which is precisely the condition at ALF × rated current. This is why composite error is always larger than ratio error alone at high fault current multiples.

Numerical Example

CT Specification: 400/5A, Class 5P20, 15VA, Rct = 0.4Ω

At ALF test point (20 × 400A = 8000A primary):

• Measured magnetizing current I₀ = 0.18A (RMS)
• Rated secondary current I₂ₙ = 5A
• Primary current at test = 8000A, referred to secondary = 100A

$\varepsilon_c = \frac{0.18}{100} \times 100 = 0.18$

Wait — this is the magnetizing current as a fraction of secondary current at ALF:

$\varepsilon_c = \frac{I_0}{K_n \cdot I_{2,ALF}} \times 100 = \frac{0.18}{100} \times 100 = 0.18$

Result: 0.18% composite error — well within the 5P class limit of 5%. This CT passes its accuracy class at ALF = 20.

Client Case — Quality-Focused Utility Engineer, 24kV Grid Substation:
A utility protection engineer in Eastern Europe received a batch of Class 5P20 CTs from a new supplier. Factory test certificates showed ratio error of 0.8% and phase displacement of 25 minutes — both within Class 5P limits at rated current. However, the engineer requested composite error test data at ALF = 20. The supplier could not provide it. Bepto was contacted for a replacement supply and provided full type test reports per IEC 61869-2 including composite error excitation curves at ALF, magnetizing current data, and knee-point voltage verification. The composite error at ALF = 20 measured 3.2% — within the 5% limit with margin. The engineer approved the specification with confidence. Composite error at ALF is the definitive protection CT acceptance criterion — ratio error at rated current alone is insufficient.

How Does Composite Error Influence CT Selection for MV Protection Applications?

Composite error limits directly determine which accuracy class is appropriate for each protection function. Selecting the wrong class — even if the CT physically fits the panel — can compromise the entire protection coordination scheme.

Step 1: Identify Protection Function Requirements

Different protection relay types have different tolerance for CT composite error:

• Differential Protection⁴ (transformer, busbar, motor): Requires Class 5P — composite error ≤ 5% essential to prevent false tripping on through-fault magnetizing inrush
• Distance Protection (line, feeder): Requires Class 5P — phase angle accuracy critical for impedance measurement
• Overcurrent / Earth Fault Protection: Class 10P acceptable — composite error ≤ 10% sufficient for time-overcurrent relay operation
• High-Impedance Differential (busbar protection): Class PX — composite error not the governing criterion; knee-point voltage and magnetizing current at Vk define performance

Step 2: Determine Required ALF Based on Fault Level

$ALF_{required} = \frac{I_{sc,max}}{I_{1n}}$

Then verify that the specified CT’s composite error remains within class limits at this ALF — not just at the nameplate ALF under rated burden, but at the actual ALF under real operating burden.

Step 3: Application-Specific Composite Error Considerations

• Industrial MV Distribution (6–12kV): Class 5P20, 15VA — motor and feeder differential protection demands tight composite error control at high fault multiples
• Power Grid Substation (33–36kV): Class 5P30, 30VA — distance relay schemes require composite error ≤ 5% maintained across full fault current range
• Solar Farm MV Collection (33kV): Class 10P10, 10VA — lower fault levels and simpler overcurrent protection tolerate higher composite error
• Urban Ring Main Unit (12kV): Class 5P20, compact epoxy-cast — space-constrained but protection accuracy non-negotiable
• Marine / Offshore (MV switchboard): Class 5P20, IP67 epoxy encapsulation — composite error performance must be verified at elevated temperature (50°C ambient)

Composite Error and Remanence: The PR Classes

Standard 5P and 10P CTs can retain residual flux (remanence) up to 80% of saturation flux after a DC offset fault current. This remanence reduces the effective ALF on the next fault event — potentially pushing composite error above class limits. For applications with:

• Auto-reclose protection schemes
• Repeated fault clearing sequences
• DC-biased fault currents (motor starting, transformer energization)

Specify Class 5PR or 10PR — these include a small air gap in the core that limits remanence to ≤ 10% of saturation flux, ensuring composite error remains within limits on successive fault events.

What Are the Common Misunderstandings and Testing Errors Around CT Composite Error?

Composite Error Verification Checklist

1. Request composite error test data at ALF — not just ratio error and phase displacement at rated current; these are different measurements
2. Verify test was performed at rated burden — composite error increases significantly if tested at lower burden than rated
3. Check Rct measurement at 75°C — not ambient temperature; winding resistance affects magnetizing current demand and therefore composite error
4. Confirm core excitation curve is provided⁵ — knee-point voltage and magnetizing current at Vk are the physical basis for composite error performance
5. For PR class CTs, verify remanence factor — confirm Kr ≤ 10% per IEC 61869-2 clause for remanence-controlled cores
6. Cross-check ALF on nameplate against test certificate — some manufacturers stamp optimistic ALF values not supported by actual composite error test data

Common Misunderstandings in Specification and Testing

• Confusing ratio error with composite error — ratio error is measured at rated current under sinusoidal conditions; composite error is measured at ALF × rated current including harmonic distortion. A CT can pass ratio error limits and fail composite error limits simultaneously
• Assuming composite error is constant across all burden values — composite error worsens as burden increases toward rated burden; always specify and test at rated burden
• Neglecting DC component in fault current — real fault currents contain a DC offset that drives the CT core into deeper saturation than AC-only composite error tests predict; IEC 61869-2 Annex 2C addresses transient performance separately
• Accepting measuring CT test data for protection CT specification — measuring CTs (Class 0.5, 1.0) are tested for ratio error and phase displacement only; composite error at high fault multiples is not a measuring CT requirement and is never tested
• Misinterpreting the magnetizing current approximation — the simplified formula $\varepsilon_c \approx I_0/I_1 \times 100$ is valid only when magnetizing current is predominantly reactive; for heavily saturated cores, the full instantaneous integral formula must be applied

Client Case — EPC Contractor, 11kV Industrial Substation Expansion:
An EPC contractor received CT test certificates from a local supplier showing ratio error of 1.2% at rated current — within Class 5P limits. The protection engineer accepted the certificates without requesting composite error data at ALF. During factory acceptance testing, Bepto’s application engineer performed a secondary injection test and measured composite error of 7.8% at ALF = 20 — exceeding the 5P class limit of 5%. The CTs were rejected. Replacement units from Bepto’s production, tested per full IEC 61869-2 type test protocol, measured 3.6% composite error at ALF = 20. The project avoided installing non-compliant protection CTs in a live 11kV industrial substation — a failure that could have compromised motor protection on critical process equipment.

Conclusion

Composite error is the single most important accuracy parameter for protection-class Current Transformers in medium voltage power distribution systems. By combining magnitude error, phase displacement, and harmonic distortion into one RMS percentage value measured at the Accuracy Limiting Factor, it provides the definitive assessment of whether a CT will deliver reliable signals to protection relays during actual fault conditions. For engineers specifying CTs for MV substations, industrial feeders, or power grid protection schemes, demanding full composite error test data per IEC 61869-2 — not just ratio error at rated current — is the non-negotiable standard for protection reliability.

FAQs About CT Composite Error

1. Understand how the Accuracy Limiting Factor determines protection CT performance under high fault conditions. ↩

2. Review the international standard governing accuracy and performance requirements for instrument transformers. ↩

3. Explore how magnetic saturation in the transformer core impacts the accuracy of secondary signals. ↩

4. Learn about the operation and requirements of differential protection schemes for power system components. ↩

5. Discover how to interpret excitation curves to verify current transformer performance and knee-point voltage. ↩