{"schema_version":"1.0","package_type":"agent_readable_article","generated_at":"2026-06-10T01:48:31+00:00","article":{"id":8288,"slug":"ct-composite-error-explained","title":"CT Composite Error Explained","url":"https://voltgrids.com/blog/ct-composite-error-explained/","language":"en-US","published_at":"2026-04-10T01:58:10+00:00","modified_at":"2026-05-10T02:38:37+00:00","author":{"id":1,"name":"Bepto"},"summary":"Understanding current transformer composite error is vital for ensuring protection relay reliability in medium voltage systems. This guide explains the IEC 61869-2 mathematical definitions, accuracy classes, and critical testing requirements at the Accuracy Limiting Factor. Learn how to specify CTs that prevent protection failure during high-fault current events.","word_count":2977,"taxonomies":{"categories":[{"id":159,"name":"Current Transformer(CT)","slug":"current-transformerct","url":"https://voltgrids.com/blog/category/instrument-transformer/current-transformerct/"},{"id":146,"name":"Instrument Transformer","slug":"instrument-transformer","url":"https://voltgrids.com/blog/category/instrument-transformer/"}],"tags":[{"id":190,"name":"Medium Voltage","slug":"medium-voltage","url":"https://voltgrids.com/blog/tag/medium-voltage/"},{"id":188,"name":"Power Distribution","slug":"power-distribution","url":"https://voltgrids.com/blog/tag/power-distribution/"},{"id":248,"name":"Protection","slug":"protection","url":"https://voltgrids.com/blog/tag/protection/"},{"id":191,"name":"Reliability","slug":"reliability","url":"https://voltgrids.com/blog/tag/reliability/"},{"id":247,"name":"Technical Specification","slug":"technical-specification","url":"https://voltgrids.com/blog/tag/technical-specification/"}]},"media_links":[{"type":"video","provider":"YouTube","url":"https://youtu.be/B2EEJbxmkUM","embed_url":"https://www.youtube.com/embed/B2EEJbxmkUM","video_id":"B2EEJbxmkUM"},{"type":"audio","provider":"SoundCloud","url":"https://soundcloud.com/bepto-247719800/ct-composite-error-explained/s-MnUxtPA99Ym?si=6cb845e19b3e4a79a06308cf362d6caa\u0026utm_source=clipboard\u0026utm_medium=text\u0026utm_campaign=social_sharing","embed_url":"https://w.soundcloud.com/player/?url=https://soundcloud.com/bepto-247719800/ct-composite-error-explained/s-MnUxtPA99Ym?si=6cb845e19b3e4a79a06308cf362d6caa\u0026utm_source=clipboard\u0026utm_medium=text\u0026utm_campaign=social_sharing\u0026auto_play=false\u0026buying=false\u0026sharing=false\u0026download=false\u0026show_artwork=true\u0026show_playcount=false\u0026show_user=true\u0026single_active=true"}],"sections":[{"heading":"Introduction","level":2,"content":"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 Factor](https://voltgrids.com/blog/ct-accuracy-limiting-factor-calculation-guide/).** 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 61869-2 (superseding IEC 60044-1) as the governing accuracy criterion](https://webstore.iec.ch/publication/6014)[1](#fn-1) definition, the mathematical formulation, and the practical engineering implications of composite error in MV protection circuits."},{"heading":"Table of Contents","level":2,"content":"- [What Is CT Composite Error and How Is It Defined by IEC Standards?](#what-is-ct-composite-error-and-how-is-it-defined-by-iec-standards)\n- [How Is Composite Error Mathematically Calculated in Protection CTs?](#how-is-composite-error-mathematically-calculated-in-protection-cts)\n- [How Does Composite Error Influence CT Selection for MV Protection Applications?](#how-does-composite-error-influence-ct-selection-for-mv-protection-applications)\n- [What Are the Common Misunderstandings and Testing Errors Around CT Composite Error?](#what-are-the-common-misunderstandings-and-testing-errors-around-ct-composite-error)"},{"heading":"What Is CT Composite Error and How Is It Defined by IEC Standards?","level":2,"content":"![A technical diagram illustrating the definition of CT Composite Error ($\\varepsilon_c$) according to IEC 61869-2. It combines a phasor diagram showing the relationship between ideal and actual secondary currents, broken down into ratio error and phase error components, with an illustration of a current transformer core experiencing magnetic saturation under high fault currents, highlighting the total accuracy deviation capturing distortion.](https://voltgrids.com/wp-content/uploads/2026/04/IEC-61869-2-CT-Composite-Error-Vectorial-Definition-and-Core-Saturation-Effect-1024x687.jpg)\n\nIEC 61869-2 CT Composite Error Vectorial Definition and Core Saturation Effect\n\nComposite 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).\n\nUnlike 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 saturation](https://voltgrids.com/blog/ct-magnetic-saturation-behavior-during-faults/) at high fault current multiples. This makes it the most comprehensive and demanding accuracy metric for protection CT performance."},{"heading":"The IEC 61869-2 Definition","level":3,"content":"Per IEC 61869-2, composite error (εc\\varepsilon_c) is defined as:\n\n\u003E *“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.”*\n\nThis definition has three critical implications for protection engineers:\n\n- It is measured at **ALF × rated primary current** — not at normal load current\n- It captures **waveform distortion** caused by core saturation, not just steady-state ratio error\n- It is an **RMS percentage** — meaning harmonic distortion components from saturated core behavior are fully included"},{"heading":"Accuracy Classes and Composite Error Limits","level":3,"content":"| Accuracy Class | Composite Error Limit at ALF | Phase Displacement Limit | Typical Application |\n| 5P | ≤ 5% | ± 60 minutes | Differential, distance, overcurrent protection |\n| 10P | ≤ 10% | Not specified | Overcurrent, earth fault protection |\n| 5PR | ≤ 5% | ± 60 minutes | Remanence-controlled protection schemes |\n| 10PR | ≤ 10% | Not specified | General protection, remanence-limited |\n| PX / PXR | Defined by knee-point voltage | Not by composite error | Unit protection, high-impedance schemes |"},{"heading":"Key Technical Parameters Governing Composite Error","level":3,"content":"- **Core Material:** [Cold-rolled grain-oriented silicon steel (CRGO) — grain orientation determines saturation knee-point](https://en.wikipedia.org/wiki/Electrical_steel)[2](#fn-2) and therefore composite error behavior at high fault multiples\n- **Core Cross-Section:** Larger core area delays saturation onset, reducing composite error at high ALF\n- **Secondary Winding Turns:** Determines transformation ratio accuracy and leakage flux contribution to phase error\n- **Insulation System:** Epoxy resin cast, rated 12kV / 24kV / 36kV — insulation class does not directly affect composite error but determines installation environment\n- **Rated Burden:** Higher burden increases magnetizing current demand, increasing composite error — directly linked to ALF performance"},{"heading":"How Is Composite Error Mathematically Calculated in Protection CTs?","level":2,"content":"![A detailed diagram illustrating the calculation of CT composite error per IEC 61869-2. It displays both a waveform visualization of primary current vs. distorted secondary current at high fault multiples, the full integral formula for composite error, and a conceptual breakdown showing how composite error captures ratio error, phase displacement, and the significant harmonic distortion component caused by magnetic saturation at higher fault currents.](https://voltgrids.com/wp-content/uploads/2026/04/IEC-61869-2-CT-Composite-Error-Integration-Diagram-1024x687.jpg)\n\nIEC 61869-2 CT Composite Error Integration Diagram\n\nThe 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."},{"heading":"The IEC Composite Error Formula","level":3,"content":"εc=100I11T∫0T(Kn⋅i2−i1)2dt%\\varepsilon_c = \\frac{100}{I_1} \\sqrt{\\frac{1}{T} \\int_0^T (K_n \\cdot i_2 – i_1)^2 \\, dt} \\, \\%\n\nWhere:\n\n- εc\\varepsilon_c = composite error (%)\n- I1I_1 = RMS value of primary current (A)\n- KnK_n = rated transformation ratio (N2/N1N_2/N_1 or I1n/I2nI_{1n}/I_{2n})\n- i1i_1 = instantaneous primary current (A)\n- i2i_2 = instantaneous secondary current (A)\n- TT = duration of one complete cycle (seconds)"},{"heading":"Relationship to Magnetizing Current","level":3,"content":"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:\n\nεc≈I0I1×100%\\varepsilon_c \\approx \\frac{I_0}{I_1} \\times 100 \\, \\%\n\nWhere I0I_0 is the RMS magnetizing current at the test point (ALF × I1nI_{1n}). This approximation holds when the magnetizing current is primarily reactive — valid for well-designed protection CT cores operating below deep saturation."},{"heading":"Composite Error vs. Ratio Error vs. Phase Displacement","level":3,"content":"Understanding how composite error relates to — but differs from — the two individual error components is essential:\n\n**Ratio Error (Current Error):**\nεi=Kn⋅I2−I1I1×100%\\varepsilon_i = \\frac{K_n \\cdot I_2 – I_1}{I_1} \\times 100 \\, \\%\n\nThis captures only the magnitude difference between actual and ideal secondary current under sinusoidal conditions.\n\n**Phase Displacement (δ\\delta):**\nThe angular difference in minutes between primary and secondary current phasors — relevant for power measurement accuracy but less critical for protection relay operation.\n\n**Composite Error:**\nCombines both, plus harmonic distortion from core saturation:\n\nεc2≈εi2+(δ3438)2+εharmonic2\\varepsilon_c^2 \\approx \\varepsilon_i^2 + \\left(\\frac{\\delta}{3438}\\right)^2 + \\varepsilon_{harmonic}^2\n\nThe harmonic distortion term εharmonic\\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."},{"heading":"Numerical Example","level":3,"content":"**CT Specification:** 400/5A, Class 5P20, 15VA, Rct=0.4 ΩR_{ct} = 0.4\\text{ }\\Omega\n\nAt ALF test point (20 × 400A = 8000A primary):\n\n- Measured magnetizing current I0=0.18 AI_0 = 0.18\\text{ A} (RMS)\n- Rated secondary current I2n=5 AI_{2n} = 5\\text{ A}\n- Primary current at test = 8000A, referred to secondary = 100A\n\nεc=0.18100×100=0.18%\\varepsilon_c = \\frac{0.18}{100} \\times 100 = 0.18\\%\n\nWait — this is the magnetizing current as a fraction of **secondary** current at ALF:\n\nεc=I0Kn⋅I2,ALF×100=0.18100×100=0.18%\\varepsilon_c = \\frac{I_0}{K_n \\cdot I_{2,ALF}} \\times 100 = \\frac{0.18}{100} \\times 100 = 0.18\\%\n\nResult: **0.18% composite error** — well within the 5P class limit of 5%. This CT passes its accuracy class at ALF = 20.\n\n**Client Case — Quality-Focused Utility Engineer, 24kV Grid Substation:**\nA 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.**"},{"heading":"How Does Composite Error Influence CT Selection for MV Protection Applications?","level":2,"content":"![A technical close-up photograph of an epoxy-cast protection current transformer (CT) mounted inside a medium voltage switchgear cabinet. The CT nameplate is prominently featured, displaying critical specifications such as Class 5P20, Burden 15VA, and Ratio 800/5A. A digital overlay diagram illustrates how composite error influences the current waveform during high fault conditions, visually explaining the importance of proper CT selection for protection coordination.](https://voltgrids.com/wp-content/uploads/2026/04/Medium-Voltage-Protection-CT-and-Composite-Error-Analysis-Diagram-1024x687.jpg)\n\nMedium Voltage Protection CT and Composite Error Analysis Diagram\n\nComposite 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."},{"heading":"Step 1: Identify Protection Function Requirements","level":3,"content":"Different protection relay types have different tolerance for CT composite error:\n\n- **Differential Protection (transformer, busbar, motor):** Requires Class 5P — composite error ≤ 5% essential to prevent false tripping on through-fault magnetizing inrush\n- **[Distance Protection (line, feeder): Requires Class 5P — phase angle accuracy critical for impedance measurement](https://ieeexplore.ieee.org/document/8340156)[3](#fn-3)**\n- **Overcurrent / Earth Fault Protection:** Class 10P acceptable — composite error ≤ 10% sufficient for time-overcurrent relay operation\n- **High-Impedance Differential (busbar protection):** Class PX — composite error not the governing criterion; knee-point voltage and magnetizing current at VkV_k define performance"},{"heading":"Step 2: Determine Required ALF Based on Fault Level","level":3,"content":"ALFrequired=Isc,maxI1nALF_{required} = \\frac{I_{sc,max}}{I_{1n}}\n\nThen 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."},{"heading":"Step 3: Application-Specific Composite Error Considerations","level":3,"content":"- **Industrial MV Distribution (6–12kV):** Class 5P20, 15VA — motor and feeder differential protection demands tight composite error control at high fault multiples\n- **Power Grid Substation (33–36kV):** Class 5P30, 30VA — distance relay schemes require composite error ≤ 5% maintained across full fault current range\n- **Solar Farm MV Collection (33kV):** Class 10P10, 10VA — lower fault levels and simpler overcurrent protection tolerate higher composite error\n- **Urban Ring Main Unit (12kV):** Class 5P20, compact epoxy-cast — space-constrained but protection accuracy non-negotiable\n- **Marine / Offshore (MV switchboard):** Class 5P20, IP67 epoxy encapsulation — composite error performance must be verified at elevated temperature (50°C ambient)"},{"heading":"Composite Error and Remanence: The PR Classes","level":3,"content":"[Standard 5P and 10P CTs can retain residual flux (remanence) up to 80% of saturation flux](https://ieeexplore.ieee.org/document/4144574)[4](#fn-4) 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:\n\n- Auto-reclose protection schemes\n- Repeated fault clearing sequences\n- DC-biased fault currents (motor starting, transformer energization)\n\nSpecify **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."},{"heading":"What Are the Common Misunderstandings and Testing Errors Around CT Composite Error?","level":2,"content":"![A technical close-up photograph of a professional East Asian female application engineer conducting a secondary injection test on a toroidal protection current transformer in a modernized electrical engineering laboratory. The touchscreen display of her testing instrument highlights a \u0027FAIL\u0027 result for Composite Error at the Accuracy Limit Factor (ALF), compared to a \u0027PASS\u0027 for Ratio Error, visualizing a critical technical verification error discussed in the article.](https://voltgrids.com/wp-content/uploads/2026/04/Laboratory-Test-Verification-Uncovering-CT-Composite-Error-Failures-at-ALF-1024x687.jpg)\n\nLaboratory Test Verification- Uncovering CT Composite Error Failures at ALF"},{"heading":"Composite Error Verification Checklist","level":3,"content":"1. **Request composite error test data at ALF** — not just ratio error and phase displacement at rated current; these are different measurements\n2. **Verify test was performed at rated burden** — composite error increases significantly if tested at lower burden than rated\n3. **Check RctR_{ct} measurement at 75°C** — not ambient temperature; winding resistance affects magnetizing current demand and therefore composite error\n4. **Confirm core excitation curve is provided** — knee-point voltage and magnetizing current at VkV_k are the physical basis for composite error performance\n5. **For PR class CTs, verify remanence factor** — [confirm Kr≤10%K_r \\leq 10\\% per IEC 61869-2 clause for remanence-controlled cores](https://ieeexplore.ieee.org/document/7553424)[5](#fn-5)\n6. **Cross-check ALF on nameplate against test certificate** — some manufacturers stamp optimistic ALF values not supported by actual composite error test data"},{"heading":"Common Misunderstandings in Specification and Testing","level":3,"content":"- **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\n- **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\n- **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\n- **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\n- **Misinterpreting the magnetizing current approximation** — the simplified formula εc≈I0/I1×100%\\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\n\n**Client Case — EPC Contractor, 11kV Industrial Substation Expansion:**\nAn 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.**"},{"heading":"Conclusion","level":2,"content":"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."},{"heading":"FAQs About CT Composite Error","level":2},{"heading":"**Q: What is the maximum allowable composite error for a Class 5P current transformer at its accuracy limiting factor?**","level":3,"content":"**A:** Per IEC 61869-2, Class 5P CTs must maintain composite error ≤ 5% at ALF × rated primary current under rated burden conditions. Class 10P allows ≤ 10% composite error at the same test point."},{"heading":"**Q: Why is composite error larger than ratio error for the same current transformer at high fault currents?**","level":3,"content":"**A:** At high fault multiples near ALF, core saturation introduces harmonic distortion in the secondary waveform. Composite error captures this distortion via RMS integration; ratio error measures only fundamental frequency magnitude difference, missing the harmonic components entirely."},{"heading":"**Q: Can a current transformer pass its ratio error specification but fail composite error requirements?**","level":3,"content":"**A:** Yes. Ratio error is measured at rated current under linear core conditions. Composite error is measured at ALF × rated current where core saturation occurs. A CT with acceptable ratio error can exhibit excessive composite error due to poor core saturation characteristics."},{"heading":"**Q: What is the difference between Class 5P and Class 5PR current transformers regarding composite error?**","level":3,"content":"**A:** Both classes limit composite error to ≤ 5% at ALF. The PR suffix adds a remanence factor requirement — residual flux must not exceed 10% of saturation flux — ensuring composite error remains within limits on successive fault events in auto-reclose protection schemes."},{"heading":"**Q: How should composite error be verified during CT factory acceptance testing for MV protection applications?**","level":3,"content":"**A:** Request the full IEC 61869-2 type test report including excitation curve, magnetizing current at knee-point voltage, Rct at 75°C, and composite error measurement at ALF × rated current under rated burden. Secondary injection testing at commissioning provides additional field verification.\n\n1. “IEC 61869-2:2012 Instrument transformers – Part 2: Additional requirements for current transformers”, `https://webstore.iec.ch/publication/6014`. Official standard defining composite error testing for protection CTs. Evidence role: standard; Source type: standard. Supports: IEC 61869-2 standard definition. [↩](#fnref-1_ref)\n2. “Electrical steel”, `https://en.wikipedia.org/wiki/Electrical_steel`. Technical specifications of CRGO silicon steel magnetic properties. Evidence role: mechanism; Source type: research. Supports: CRGO grain orientation affecting saturation. [↩](#fnref-2_ref)\n3. “Distance Protection of Transmission Lines”, `https://ieeexplore.ieee.org/document/8340156`. Explains the critical nature of phase angle accuracy in impedance relaying. Evidence role: general_support; Source type: industry. Supports: distance protection requiring Class 5P. [↩](#fnref-3_ref)\n4. “Impact of CT Remanence on Protection Relay Performance”, `https://ieeexplore.ieee.org/document/4144574`. Research paper detailing the retention of residual flux in standard P class cores. Evidence role: mechanism; Source type: research. Supports: 80% remanence flux retention in standard CTs. [↩](#fnref-4_ref)\n5. “Remanence-controlled CTs for Transient Protection”, `https://ieeexplore.ieee.org/document/7553424`. Details the PR class specifications and air gap sizing for remanence limitation. Evidence role: standard; Source type: industry. Supports: Kr ≤ 10% for PR class cores. [↩](#fnref-5_ref)"}],"source_links":[{"url":"https://voltgrids.com/product-category/instrument-transformer/current-transformerct/","text":"Current Transformer(CT)","host":"voltgrids.com","is_internal":true},{"url":"https://voltgrids.com/blog/ct-accuracy-limiting-factor-calculation-guide/","text":"Accuracy Limiting Factor","host":"voltgrids.com","is_internal":true},{"url":"https://webstore.iec.ch/publication/6014","text":"IEC 61869-2 (superseding IEC 60044-1) as the governing accuracy criterion","host":"webstore.iec.ch","is_internal":false},{"url":"#fn-1","text":"1","is_internal":false},{"url":"#what-is-ct-composite-error-and-how-is-it-defined-by-iec-standards","text":"What Is CT Composite Error and How Is It Defined by IEC Standards?","is_internal":false},{"url":"#how-is-composite-error-mathematically-calculated-in-protection-cts","text":"How Is Composite Error Mathematically Calculated in Protection CTs?","is_internal":false},{"url":"#how-does-composite-error-influence-ct-selection-for-mv-protection-applications","text":"How Does Composite Error Influence CT Selection for MV Protection Applications?","is_internal":false},{"url":"#what-are-the-common-misunderstandings-and-testing-errors-around-ct-composite-error","text":"What Are the Common Misunderstandings and Testing Errors Around CT Composite Error?","is_internal":false},{"url":"https://voltgrids.com/blog/ct-magnetic-saturation-behavior-during-faults/","text":"magnetic saturation","host":"voltgrids.com","is_internal":true},{"url":"https://en.wikipedia.org/wiki/Electrical_steel","text":"Cold-rolled grain-oriented silicon steel (CRGO) — grain orientation determines saturation knee-point","host":"en.wikipedia.org","is_internal":false},{"url":"#fn-2","text":"2","is_internal":false},{"url":"https://ieeexplore.ieee.org/document/8340156","text":"Distance Protection (line, feeder): Requires Class 5P — phase angle accuracy critical for impedance measurement","host":"ieeexplore.ieee.org","is_internal":false},{"url":"#fn-3","text":"3","is_internal":false},{"url":"https://ieeexplore.ieee.org/document/4144574","text":"Standard 5P and 10P CTs can retain residual flux (remanence) up to 80% of saturation flux","host":"ieeexplore.ieee.org","is_internal":false},{"url":"#fn-4","text":"4","is_internal":false},{"url":"https://ieeexplore.ieee.org/document/7553424","text":"confirm Kr≤10%K_r \\leq 10\\% per IEC 61869-2 clause for remanence-controlled cores","host":"ieeexplore.ieee.org","is_internal":false},{"url":"#fn-5","text":"5","is_internal":false},{"url":"#fnref-1_ref","text":"↩","is_internal":false},{"url":"#fnref-2_ref","text":"↩","is_internal":false},{"url":"#fnref-3_ref","text":"↩","is_internal":false},{"url":"#fnref-4_ref","text":"↩","is_internal":false},{"url":"#fnref-5_ref","text":"↩","is_internal":false}],"content_markdown":"![LCZ-35 Current Transformer 35kV Indoor Epoxy Resin - 15-1200A 0.2S 0.5S 10P Class 40.5 95 185kV Insulation Dual Winding GB1208 IEC60044-1](https://voltgrids.com/wp-content/uploads/2026/01/LCZ-35-Current-Transformer-35kV-Indoor-Epoxy-Resin-15-1200A-0.2S-0.5S-10P-Class-40.5-95-185kV-Insulation-Dual-Winding-GB1208-IEC60044-1.jpg)\n\n[Current Transformer(CT)](https://voltgrids.com/product-category/instrument-transformer/current-transformerct/)\n\n## Introduction\n\nWhen 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 Factor](https://voltgrids.com/blog/ct-accuracy-limiting-factor-calculation-guide/).** 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 61869-2 (superseding IEC 60044-1) as the governing accuracy criterion](https://webstore.iec.ch/publication/6014)[1](#fn-1) definition, the mathematical formulation, and the practical engineering implications of composite error in MV protection circuits.\n\n## Table of Contents\n\n- [What Is CT Composite Error and How Is It Defined by IEC Standards?](#what-is-ct-composite-error-and-how-is-it-defined-by-iec-standards)\n- [How Is Composite Error Mathematically Calculated in Protection CTs?](#how-is-composite-error-mathematically-calculated-in-protection-cts)\n- [How Does Composite Error Influence CT Selection for MV Protection Applications?](#how-does-composite-error-influence-ct-selection-for-mv-protection-applications)\n- [What Are the Common Misunderstandings and Testing Errors Around CT Composite Error?](#what-are-the-common-misunderstandings-and-testing-errors-around-ct-composite-error)\n\n## What Is CT Composite Error and How Is It Defined by IEC Standards?\n\n![A technical diagram illustrating the definition of CT Composite Error ($\\varepsilon_c$) according to IEC 61869-2. It combines a phasor diagram showing the relationship between ideal and actual secondary currents, broken down into ratio error and phase error components, with an illustration of a current transformer core experiencing magnetic saturation under high fault currents, highlighting the total accuracy deviation capturing distortion.](https://voltgrids.com/wp-content/uploads/2026/04/IEC-61869-2-CT-Composite-Error-Vectorial-Definition-and-Core-Saturation-Effect-1024x687.jpg)\n\nIEC 61869-2 CT Composite Error Vectorial Definition and Core Saturation Effect\n\nComposite 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).\n\nUnlike 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 saturation](https://voltgrids.com/blog/ct-magnetic-saturation-behavior-during-faults/) at high fault current multiples. This makes it the most comprehensive and demanding accuracy metric for protection CT performance.\n\n### The IEC 61869-2 Definition\n\nPer IEC 61869-2, composite error (εc\\varepsilon_c) is defined as:\n\n\u003E *“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.”*\n\nThis definition has three critical implications for protection engineers:\n\n- It is measured at **ALF × rated primary current** — not at normal load current\n- It captures **waveform distortion** caused by core saturation, not just steady-state ratio error\n- It is an **RMS percentage** — meaning harmonic distortion components from saturated core behavior are fully included\n\n### Accuracy Classes and Composite Error Limits\n\n| Accuracy Class | Composite Error Limit at ALF | Phase Displacement Limit | Typical Application |\n| 5P | ≤ 5% | ± 60 minutes | Differential, distance, overcurrent protection |\n| 10P | ≤ 10% | Not specified | Overcurrent, earth fault protection |\n| 5PR | ≤ 5% | ± 60 minutes | Remanence-controlled protection schemes |\n| 10PR | ≤ 10% | Not specified | General protection, remanence-limited |\n| PX / PXR | Defined by knee-point voltage | Not by composite error | Unit protection, high-impedance schemes |\n\n### Key Technical Parameters Governing Composite Error\n\n- **Core Material:** [Cold-rolled grain-oriented silicon steel (CRGO) — grain orientation determines saturation knee-point](https://en.wikipedia.org/wiki/Electrical_steel)[2](#fn-2) and therefore composite error behavior at high fault multiples\n- **Core Cross-Section:** Larger core area delays saturation onset, reducing composite error at high ALF\n- **Secondary Winding Turns:** Determines transformation ratio accuracy and leakage flux contribution to phase error\n- **Insulation System:** Epoxy resin cast, rated 12kV / 24kV / 36kV — insulation class does not directly affect composite error but determines installation environment\n- **Rated Burden:** Higher burden increases magnetizing current demand, increasing composite error — directly linked to ALF performance\n\n## How Is Composite Error Mathematically Calculated in Protection CTs?\n\n![A detailed diagram illustrating the calculation of CT composite error per IEC 61869-2. It displays both a waveform visualization of primary current vs. distorted secondary current at high fault multiples, the full integral formula for composite error, and a conceptual breakdown showing how composite error captures ratio error, phase displacement, and the significant harmonic distortion component caused by magnetic saturation at higher fault currents.](https://voltgrids.com/wp-content/uploads/2026/04/IEC-61869-2-CT-Composite-Error-Integration-Diagram-1024x687.jpg)\n\nIEC 61869-2 CT Composite Error Integration Diagram\n\nThe 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.\n\n### The IEC Composite Error Formula\n\nεc=100I11T∫0T(Kn⋅i2−i1)2dt%\\varepsilon_c = \\frac{100}{I_1} \\sqrt{\\frac{1}{T} \\int_0^T (K_n \\cdot i_2 – i_1)^2 \\, dt} \\, \\%\n\nWhere:\n\n- εc\\varepsilon_c = composite error (%)\n- I1I_1 = RMS value of primary current (A)\n- KnK_n = rated transformation ratio (N2/N1N_2/N_1 or I1n/I2nI_{1n}/I_{2n})\n- i1i_1 = instantaneous primary current (A)\n- i2i_2 = instantaneous secondary current (A)\n- TT = duration of one complete cycle (seconds)\n\n### Relationship to Magnetizing Current\n\nIn practical CT testing, composite error is most commonly derived from the **magnetizing current method**, which is simpler to implement than direct instantaneous waveform comparison:\n\nεc≈I0I1×100%\\varepsilon_c \\approx \\frac{I_0}{I_1} \\times 100 \\, \\%\n\nWhere I0I_0 is the RMS magnetizing current at the test point (ALF × I1nI_{1n}). This approximation holds when the magnetizing current is primarily reactive — valid for well-designed protection CT cores operating below deep saturation.\n\n### Composite Error vs. Ratio Error vs. Phase Displacement\n\nUnderstanding how composite error relates to — but differs from — the two individual error components is essential:\n\n**Ratio Error (Current Error):**\nεi=Kn⋅I2−I1I1×100%\\varepsilon_i = \\frac{K_n \\cdot I_2 – I_1}{I_1} \\times 100 \\, \\%\n\nThis captures only the magnitude difference between actual and ideal secondary current under sinusoidal conditions.\n\n**Phase Displacement (δ\\delta):**\nThe angular difference in minutes between primary and secondary current phasors — relevant for power measurement accuracy but less critical for protection relay operation.\n\n**Composite Error:**\nCombines both, plus harmonic distortion from core saturation:\n\nεc2≈εi2+(δ3438)2+εharmonic2\\varepsilon_c^2 \\approx \\varepsilon_i^2 + \\left(\\frac{\\delta}{3438}\\right)^2 + \\varepsilon_{harmonic}^2\n\nThe harmonic distortion term εharmonic\\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.\n\n### Numerical Example\n\n**CT Specification:** 400/5A, Class 5P20, 15VA, Rct=0.4 ΩR_{ct} = 0.4\\text{ }\\Omega\n\nAt ALF test point (20 × 400A = 8000A primary):\n\n- Measured magnetizing current I0=0.18 AI_0 = 0.18\\text{ A} (RMS)\n- Rated secondary current I2n=5 AI_{2n} = 5\\text{ A}\n- Primary current at test = 8000A, referred to secondary = 100A\n\nεc=0.18100×100=0.18%\\varepsilon_c = \\frac{0.18}{100} \\times 100 = 0.18\\%\n\nWait — this is the magnetizing current as a fraction of **secondary** current at ALF:\n\nεc=I0Kn⋅I2,ALF×100=0.18100×100=0.18%\\varepsilon_c = \\frac{I_0}{K_n \\cdot I_{2,ALF}} \\times 100 = \\frac{0.18}{100} \\times 100 = 0.18\\%\n\nResult: **0.18% composite error** — well within the 5P class limit of 5%. This CT passes its accuracy class at ALF = 20.\n\n**Client Case — Quality-Focused Utility Engineer, 24kV Grid Substation:**\nA 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.**\n\n## How Does Composite Error Influence CT Selection for MV Protection Applications?\n\n![A technical close-up photograph of an epoxy-cast protection current transformer (CT) mounted inside a medium voltage switchgear cabinet. The CT nameplate is prominently featured, displaying critical specifications such as Class 5P20, Burden 15VA, and Ratio 800/5A. A digital overlay diagram illustrates how composite error influences the current waveform during high fault conditions, visually explaining the importance of proper CT selection for protection coordination.](https://voltgrids.com/wp-content/uploads/2026/04/Medium-Voltage-Protection-CT-and-Composite-Error-Analysis-Diagram-1024x687.jpg)\n\nMedium Voltage Protection CT and Composite Error Analysis Diagram\n\nComposite 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.\n\n### Step 1: Identify Protection Function Requirements\n\nDifferent protection relay types have different tolerance for CT composite error:\n\n- **Differential Protection (transformer, busbar, motor):** Requires Class 5P — composite error ≤ 5% essential to prevent false tripping on through-fault magnetizing inrush\n- **[Distance Protection (line, feeder): Requires Class 5P — phase angle accuracy critical for impedance measurement](https://ieeexplore.ieee.org/document/8340156)[3](#fn-3)**\n- **Overcurrent / Earth Fault Protection:** Class 10P acceptable — composite error ≤ 10% sufficient for time-overcurrent relay operation\n- **High-Impedance Differential (busbar protection):** Class PX — composite error not the governing criterion; knee-point voltage and magnetizing current at VkV_k define performance\n\n### Step 2: Determine Required ALF Based on Fault Level\n\nALFrequired=Isc,maxI1nALF_{required} = \\frac{I_{sc,max}}{I_{1n}}\n\nThen 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.\n\n### Step 3: Application-Specific Composite Error Considerations\n\n- **Industrial MV Distribution (6–12kV):** Class 5P20, 15VA — motor and feeder differential protection demands tight composite error control at high fault multiples\n- **Power Grid Substation (33–36kV):** Class 5P30, 30VA — distance relay schemes require composite error ≤ 5% maintained across full fault current range\n- **Solar Farm MV Collection (33kV):** Class 10P10, 10VA — lower fault levels and simpler overcurrent protection tolerate higher composite error\n- **Urban Ring Main Unit (12kV):** Class 5P20, compact epoxy-cast — space-constrained but protection accuracy non-negotiable\n- **Marine / Offshore (MV switchboard):** Class 5P20, IP67 epoxy encapsulation — composite error performance must be verified at elevated temperature (50°C ambient)\n\n### Composite Error and Remanence: The PR Classes\n\n[Standard 5P and 10P CTs can retain residual flux (remanence) up to 80% of saturation flux](https://ieeexplore.ieee.org/document/4144574)[4](#fn-4) 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:\n\n- Auto-reclose protection schemes\n- Repeated fault clearing sequences\n- DC-biased fault currents (motor starting, transformer energization)\n\nSpecify **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.\n\n## What Are the Common Misunderstandings and Testing Errors Around CT Composite Error?\n\n![A technical close-up photograph of a professional East Asian female application engineer conducting a secondary injection test on a toroidal protection current transformer in a modernized electrical engineering laboratory. The touchscreen display of her testing instrument highlights a \u0027FAIL\u0027 result for Composite Error at the Accuracy Limit Factor (ALF), compared to a \u0027PASS\u0027 for Ratio Error, visualizing a critical technical verification error discussed in the article.](https://voltgrids.com/wp-content/uploads/2026/04/Laboratory-Test-Verification-Uncovering-CT-Composite-Error-Failures-at-ALF-1024x687.jpg)\n\nLaboratory Test Verification- Uncovering CT Composite Error Failures at ALF\n\n### Composite Error Verification Checklist\n\n1. **Request composite error test data at ALF** — not just ratio error and phase displacement at rated current; these are different measurements\n2. **Verify test was performed at rated burden** — composite error increases significantly if tested at lower burden than rated\n3. **Check RctR_{ct} measurement at 75°C** — not ambient temperature; winding resistance affects magnetizing current demand and therefore composite error\n4. **Confirm core excitation curve is provided** — knee-point voltage and magnetizing current at VkV_k are the physical basis for composite error performance\n5. **For PR class CTs, verify remanence factor** — [confirm Kr≤10%K_r \\leq 10\\% per IEC 61869-2 clause for remanence-controlled cores](https://ieeexplore.ieee.org/document/7553424)[5](#fn-5)\n6. **Cross-check ALF on nameplate against test certificate** — some manufacturers stamp optimistic ALF values not supported by actual composite error test data\n\n### Common Misunderstandings in Specification and Testing\n\n- **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\n- **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\n- **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\n- **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\n- **Misinterpreting the magnetizing current approximation** — the simplified formula εc≈I0/I1×100%\\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\n\n**Client Case — EPC Contractor, 11kV Industrial Substation Expansion:**\nAn 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.**\n\n## Conclusion\n\nComposite 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.\n\n## FAQs About CT Composite Error\n\n### **Q: What is the maximum allowable composite error for a Class 5P current transformer at its accuracy limiting factor?**\n\n**A:** Per IEC 61869-2, Class 5P CTs must maintain composite error ≤ 5% at ALF × rated primary current under rated burden conditions. Class 10P allows ≤ 10% composite error at the same test point.\n\n### **Q: Why is composite error larger than ratio error for the same current transformer at high fault currents?**\n\n**A:** At high fault multiples near ALF, core saturation introduces harmonic distortion in the secondary waveform. Composite error captures this distortion via RMS integration; ratio error measures only fundamental frequency magnitude difference, missing the harmonic components entirely.\n\n### **Q: Can a current transformer pass its ratio error specification but fail composite error requirements?**\n\n**A:** Yes. Ratio error is measured at rated current under linear core conditions. Composite error is measured at ALF × rated current where core saturation occurs. A CT with acceptable ratio error can exhibit excessive composite error due to poor core saturation characteristics.\n\n### **Q: What is the difference between Class 5P and Class 5PR current transformers regarding composite error?**\n\n**A:** Both classes limit composite error to ≤ 5% at ALF. The PR suffix adds a remanence factor requirement — residual flux must not exceed 10% of saturation flux — ensuring composite error remains within limits on successive fault events in auto-reclose protection schemes.\n\n### **Q: How should composite error be verified during CT factory acceptance testing for MV protection applications?**\n\n**A:** Request the full IEC 61869-2 type test report including excitation curve, magnetizing current at knee-point voltage, Rct at 75°C, and composite error measurement at ALF × rated current under rated burden. Secondary injection testing at commissioning provides additional field verification.\n\n1. “IEC 61869-2:2012 Instrument transformers – Part 2: Additional requirements for current transformers”, `https://webstore.iec.ch/publication/6014`. Official standard defining composite error testing for protection CTs. Evidence role: standard; Source type: standard. Supports: IEC 61869-2 standard definition. [↩](#fnref-1_ref)\n2. “Electrical steel”, `https://en.wikipedia.org/wiki/Electrical_steel`. Technical specifications of CRGO silicon steel magnetic properties. Evidence role: mechanism; Source type: research. Supports: CRGO grain orientation affecting saturation. [↩](#fnref-2_ref)\n3. “Distance Protection of Transmission Lines”, `https://ieeexplore.ieee.org/document/8340156`. Explains the critical nature of phase angle accuracy in impedance relaying. Evidence role: general_support; Source type: industry. Supports: distance protection requiring Class 5P. [↩](#fnref-3_ref)\n4. “Impact of CT Remanence on Protection Relay Performance”, `https://ieeexplore.ieee.org/document/4144574`. Research paper detailing the retention of residual flux in standard P class cores. Evidence role: mechanism; Source type: research. Supports: 80% remanence flux retention in standard CTs. [↩](#fnref-4_ref)\n5. “Remanence-controlled CTs for Transient Protection”, `https://ieeexplore.ieee.org/document/7553424`. Details the PR class specifications and air gap sizing for remanence limitation. Evidence role: standard; Source type: industry. Supports: Kr ≤ 10% for PR class cores. 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