How to Calculate CT Knee Point Voltage

Introduction

Every protection engineer eventually faces the same uncomfortable moment: a relay fails to operate during a fault, the post-incident investigation points to CT saturation, and the question becomes — was the knee point voltage ever correctly calculated in the first place? In the majority of cases I have reviewed across industrial and utility substation projects, the answer is no. The CT ratio was matched to the load current, the accuracy class was copied from a previous project, and the knee point voltage was accepted as whatever the manufacturer offered — without a single calculation to verify it was adequate.

CT knee point voltage (Vk) is the minimum secondary excitation voltage at which the core begins to saturate, and it must be calculated — not assumed — by determining the maximum secondary burden voltage under worst-case fault conditions, multiplying by the transient dimensioning factor to account for DC offset, and applying a safety margin to protect against remanence and measurement uncertainty.

I’ve worked with procurement teams and protection engineers across projects in Germany, Australia, the UAE, and Southeast Asia, and the knee point voltage calculation is consistently the most skipped step in CT specification. The consequences range from delayed relay operation to complete protection failure during close-in faults. This article walks you through every calculation method — from the fundamental IEC formula to application-specific worked examples — so you can specify CTs with full engineering confidence. 🔍

Table of Contents

• What Is CT Knee Point Voltage and How Is It Defined Under IEC Standards?
• How Do You Calculate the Required Knee Point Voltage Step by Step?
• How Does Knee Point Voltage Calculation Differ Across Protection Applications?
• How Do You Verify Knee Point Voltage Through Field Testing and What Are the Common Errors?
• FAQs About CT Knee Point Voltage Calculation

What Is CT Knee Point Voltage and How Is It Defined Under IEC Standards?

Before performing any calculation, you need a precise, standard-compliant understanding of what knee point voltage actually means — because the definition varies between standards, and using the wrong definition leads to systematic undersizing errors. ⚙️

The IEC 61869-2 Definition

Under iec 61869-2¹ (the current international standard for instrument transformers), the knee point voltage is defined through the V-I excitation curve measured with the primary open-circuited:

The knee point voltage (Vk) is the point on the secondary excitation characteristic (V-I curve) at which a 10% increase in excitation voltage produces a 50% increase in exciting current.

This definition identifies the boundary between the linear operating region and the onset of saturation. Below Vk, the core operates in its linear region with acceptable accuracy. Above Vk, the core is entering saturation and secondary output accuracy degrades rapidly.

The BS 3938 Definition (Still Widely Referenced)

The older BS 3938 standard — still referenced in many UK and Commonwealth project specifications — defines the knee point as:

The point on the excitation curve where the tangent makes an angle of 45° to the horizontal axis.

In practice, the BS 3938 knee point is typically 5–15% lower than the IEC 61869-2 knee point for the same core. When reviewing CT datasheets or comparing specifications from different suppliers, always confirm which standard’s definition was used to determine the published Vk value.

Key Parameters in the Knee Point Voltage Framework

Parameter	Symbol	Unit	Definition
Knee Point Voltage	Vk	Volts (V)	Excitation voltage at saturation onset
Exciting Current at Vk	Ie (or Imag)	Amperes (A)	Magnetizing current at knee point — lower is better
Secondary Winding Resistance	Rct	Ohms (Ω)	DC resistance of CT secondary winding
Connected Burden	Rb	Ohms (Ω)	Total external secondary circuit impedance
Accuracy Limiting Factor	ALF	—	Max overcurrent multiple before error limit exceeded
Transient Dimensioning Factor	Ktd	—	DC offset flux demand multiplier = 1 + (X/R)
Remanence Factor	Kr	%	Residual flux as percentage of saturation flux
Rated Secondary Current	In	Amperes (A)	Nominal secondary current (1A or 5A)

The Relationship Between Vk, ALF, and Accuracy Class

For Class P CTs, the knee point voltage is not directly specified — instead, the Accuracy Limiting Factor (ALF) and rated burden are specified. The implied minimum knee point voltage is:

$V_{k,\text{implied}} \geq ALF \times I_{n} \times \left(R_{ct} + R_{b,\text{rated}}\right)$

However, this implied Vk is calculated at rated burden — if the actual installed burden differs from the rated burden, the effective ALF changes. This is one of the most common sources of CT undersizing in practice.

For Class PX and Class TP CTs, Vk is specified directly and independently of burden, giving the protection engineer explicit control over the saturation threshold.

How Do You Calculate the Required Knee Point Voltage Step by Step?

The knee point voltage calculation follows a logical sequence that builds from system fault data through to a final specified Vk value. Each step must be completed in order — skipping any step produces an unreliable result. 📐

The Master Formula

The complete knee point voltage requirement for a protection CT subject to DC offset transients is:

$V_{k,\text{required}} = K_{td} \times I_{f,\text{sec}} \times \left(R_{ct} + R_{b}\right) \times SF$

Where:

• $K_{td} = 1 + \frac{X}{R}$
• $I_{f,\text{sec}} = \frac{I_{f,\text{primary}}}{CTR}$
• $R_{ct} = \text{CT secondary winding resistance } (\Omega)$
• $R_{b} = \text{Total connected burden resistance } (\Omega)$
• $SF = 1.2 \text{ to } 1.5$

Step 1: Determine Maximum Fault Current

Obtain the maximum symmetrical fault current at the CT installation point from the network fault study:

• Use the maximum fault infeed condition (all sources in service)
• For generator-connected CTs, include subtransient fault contribution²
• Convert to secondary amperes: $I_{f,\text{sec}} = \frac{I_{f,\text{primary}}}{CTR}$

Example:

• Maximum fault current: 12,500A (primary)
• CT ratio: 200/1A → CTR = 200
• $I_{f,\text{sec}} = \frac{12{,}500}{200} = 62.5,\text{A}$

Step 2: Determine the System X/R Ratio

Obtain the x/r ratio³ at the fault point from the network impedance data:

System Location	Typical X/R Range	Ktd Range
LV industrial distribution	3 – 8	4 – 9
MV distribution substation	8 – 15	9 – 16
HV subtransmission	15 – 25	16 – 26
EHV transmission	25 – 50	26 – 51
Generator terminals	30 – 80	31 – 81

Example:

• System X/R at 33kV bus = 18
• Ktd = 1 + 18 = 19

Step 3: Calculate Total Secondary Burden

Measure or calculate every resistance element in the secondary circuit:

$R_b = R_{\text{cable}} + R_{\text{relay}} + R_{\text{contacts}} + R_{\text{test switch}}$

Burden Component	Typical Value	How to Determine
Relay input impedance	0.01 – 0.5Ω	Relay technical manual
Secondary cable (loop)	0.02Ω/m × length	Measure cable length and CSA
Test switch contacts	0.01 – 0.05Ω	Manufacturer datasheet
Terminal block contacts	0.005 – 0.02Ω	Estimated or measured
CT secondary winding (Rct)	0.5 – 10Ω	CT datasheet or measured

Example:

• Relay input: 0.1Ω
• Cable (20m loop, 2.5mm²): 20 × 0.0072 = 0.144Ω
• Test switch + terminals: 0.04Ω
• Rb = 0.1 + 0.144 + 0.04 = 0.284Ω
• Rct (from datasheet) = 2.1Ω
• Total (Rct + Rb) = 2.384Ω

Step 4: Apply the Master Formula

$V_{k,\text{required}} = K_{td} \times I_{f,\text{sec}} \times (R_{ct}+R_b) \times SF$

$V_{k,\text{required}} = 19 \times 62.5 \times 2.384 \times 1.3 = 3494,\text{V}$

This result immediately reveals whether a standard catalogue CT is adequate or whether a custom specification is required.

Step 5: Apply the Remanence Correction

If the CT core has a known remanence factor Kr, the effective available knee point voltage is reduced:

$V_{k,\text{effective}} = V_{k,\text{rated}} \times (1 – K_{r})$

Rearranging to find the required rated Vk:

$V_{k,\text{rated required}} = \frac{V_{k,\text{required}}}{1 – K_{r}}$

Example with Kr = 0.70 (standard GOES core):

$V_{k,\text{rated required}} = \frac{3494}{1 – 0.70} = \frac{3494}{0.30} = 11647\,\text{V}$

This calculation demonstrates why standard silicon steel cores are frequently inadequate for high-voltage protection applications with significant DC offset — and why low-remanence core materials are not a luxury but a necessity.

With Kr = 0.08 (nanocrystalline core⁴):

$V_{k,\text{rated required}} = \frac{3494}{1 – 0.08} = \frac{3494}{0.92} = 3798,\text{V}$

The difference between a 70% remanence core and an 8% remanence core translates to a 3× difference in required knee point voltage — a specification gap that determines whether a standard CT is adequate or whether a custom high-Vk unit is required.

Customer Story: Thomas, a senior protection engineer at a utility contractor in the Netherlands managing a 110kV substation refurbishment, had inherited CT specifications from a 1990s design that specified Vk ≥ 400V for the busbar differential protection. Running the full calculation with the current fault level (18kA), X/R ratio (22), actual cable burden (0.31Ω), and the installed GOES core remanence (Kr = 72%), the required Vk came out at 9,200V. The installed CTs were rated 400V. The protection had been technically non-compliant for decades. Bepto supplied Class TPY replacement CTs with nanocrystalline cores (Vk = 4,100V, Kr = 7%), bringing the scheme into full IEC 61869-2 compliance. ✅

How Does Knee Point Voltage Calculation Differ Across Protection Applications?

The master formula provides the universal framework, but each protection function introduces specific modifications to the calculation methodology. Applying the wrong calculation approach for a given protection function is as dangerous as skipping the calculation entirely. 🔧

Overcurrent Protection (ANSI 50/51) — Class P or PX

For time-delayed overcurrent protection, the full transient Ktd factor is often not required because the relay can tolerate some degree of CT saturation without maloperation. The simplified calculation uses:

$V_{k,\text{required}} = ALF \times I_{n} \times (R_{ct} + R_{b})$

Where ALF is selected to ensure the CT remains accurate up to the relay’s instantaneous pickup setting. For instantaneous elements (50), the full Ktd formula applies.

Transformer Differential Protection (ANSI 87T) — Class PX or TPY

Differential protection requires matched performance from CTs on both sides of the protected transformer. The calculation must be performed for each CT separately, and the results must be compatible:

$V_{k,\text{HV}} \geq K_{td} \times I_{f,\text{sec,HV}} \times (R_{ct,\text{HV}} + R_{b,\text{HV}}) \times SF$

$V_{k,\text{LV}} \geq K_{td} \times I_{f,\text{sec,LV}} \times (R_{ct,\text{LV}} + R_{b,\text{LV}}) \times SF$

Additionally, the magnetizing inrush current must be considered — transformer energization produces inrush currents of 8–12× rated current with significant DC offset, which can drive CTs into saturation and produce false differential current even without a fault.

Distance Protection (ANSI 21) — Class TPY

Distance relays are sensitive to both magnitude and phase angle accuracy. The knee point voltage calculation must ensure the CT remains in its linear region throughout the fault duration — not just at fault inception:

$V_{k,\text{required}} = K_{td} \times I_{f,\text{sec}} \times (R_{ct} + R_{b}) \times SF \times K_{\text{angle}}$

Where Kangle (typically 1.1–1.2) accounts for the additional phase angle accuracy requirement of distance relay impedance measurement algorithms.

Busbar Differential Protection (ANSI 87B) — Class TPZ

Busbar protection operates at the highest speed (typically 8–12ms) and has zero tolerance for CT saturation. The calculation uses the full Ktd factor with no simplifications, and Class TPZ air-gapped cores are specified to eliminate remanence entirely:

$V_{k,\text{required}} = \left(1 + \frac{X}{R}\right) \times I_{f,\text{sec max}} \times (R_{ct} + R_{b}) \times 1.5$

The 1.5 safety factor is mandatory for busbar protection — no reduction is acceptable.

Application-Specific Calculation Summary

Protection Function	Ktd Applied	Remanence Critical	Typical Vk Range	CT Class
Time-delayed OC (51)	Optional	No	50 – 300V	Class P
Instantaneous OC (50)	Full (1+X/R)	Moderate	200 – 800V	Class P or PX
Transformer differential (87T)	Full	Yes (Kr<30%)	400 – 2000V	Class PX or class tpy5
Distance relay (21)	Full + Kangle	Yes (Kr<10%)	500 – 3000V	Class TPY
Busbar differential (87B)	Full + 1.5 SF	Critical (Kr<1%)	1000 – 5000V+	Class TPZ
Auto-reclose scheme	Full × 2 cycles	Critical (Kr<10%)	800 – 4000V	Class TPY

Customer Story: Maria, a procurement manager at a switchgear OEM in Milan, Italy, was sourcing CTs for a batch of 24kV gas-insulated switchgear destined for a refinery project in Saudi Arabia. The project specification required Class TPY CTs for feeder differential protection with a minimum Vk of 1,200V. Two competing suppliers quoted standard Class PX CTs with Vk = 800V, claiming equivalence. Bepto’s engineering team provided a full worked calculation demonstrating that the 1,200V requirement was correctly derived from the 40kA fault level and X/R = 24 at that bus — and supplied certified Class TPY units with Vk = 1,450V and Kr = 6.8%. The client’s protection consultant accepted the Bepto submission without qualification. 💡

How Do You Verify Knee Point Voltage Through Field Testing and What Are the Common Errors?

A calculated knee point voltage is only as reliable as the CT that gets installed. Field verification through the magnetization test is the non-negotiable final step that confirms the installed CT matches its specification — and catches manufacturing deviations, transport damage, and incorrect unit identification before the protection system is energized.

The Secondary Injection Magnetization Test Procedure

1. Isolate the CT — open all primary connections and confirm primary is de-energized
2. Short-circuit all unused secondary windings — prevents dangerous open-circuit voltages
3. Connect test equipment — variable autotransformer to secondary terminals, precision ammeter in series, voltmeter across terminals
4. Apply increasing AC voltage — start from zero, increase in small steps (5–10V increments near the knee point)
5. Record V and I at each step — continue until exciting current increases sharply (typically 2–3× the knee point current)
6. Plot the V-I curve — on log-log paper or software; identify the knee point using the IEC 10%/50% criterion
7. Compare against factory certificate — measured Vk must be within ±10% of the certified value

Acceptance Criteria

Test Parameter	Acceptance Criterion	Action if Failed
Measured Vk vs. certified Vk	Within ±10%	Reject CT — return to supplier
Exciting current at Vk	≤ datasheet value	Investigate core damage or wrong unit
Curve shape	Smooth, consistent with class	Investigate lamination damage
Winding resistance Rct	Within ±5% of datasheet	Check for shorted turns

Common Calculation and Specification Errors

• Using rated burden instead of actual burden — the nameplate burden is a maximum rating, not the installed burden; always calculate actual Rb from measured cable resistance and relay input data
• Omitting the Ktd multiplier for instantaneous protection — time-delayed relays may tolerate some saturation, but instantaneous elements (50) operate in the first cycle and require the full transient calculation
• Applying a single X/R value across the entire network — X/R varies by location; a value appropriate for the HV bus may be significantly wrong for a downstream MV feeder
• Ignoring Rct in the burden calculation — the CT’s own winding resistance is part of the total burden and can be the dominant term for long secondary cable runs; it must always be included
• Accepting manufacturer’s standard catalogue Vk without verification — catalogue CTs are designed for typical applications; your specific fault level, X/R ratio, and burden combination may require a non-standard specification
• Forgetting to derate for remanence — calculating Vk_required without applying the (1 – Kr) correction factor produces a result that assumes a perfectly demagnetized core — an assumption that is never valid in service

Post-Calculation Verification Checklist

1. ✅ Maximum fault current obtained from current network fault study
2. ✅ X/R ratio confirmed at the specific CT installation bus
3. ✅ Actual burden measured — not estimated from nameplate
4. ✅ Rct included in total burden calculation
5. ✅ Ktd applied using full (1 + X/R) formula
6. ✅ Remanence correction applied using actual Kr for specified core material
7. ✅ Safety factor of minimum 1.2 applied
8. ✅ Field magnetization test performed and results within ±10% of specification
9. ✅ Test certificate retained for maintenance baseline comparison

Conclusion

Calculating CT knee point voltage correctly is not a bureaucratic compliance exercise — it is the engineering foundation that determines whether your protection system operates in 20 milliseconds or fails entirely during the fault it was designed to clear. The master formula is straightforward, but every input must be derived from actual system data: real fault currents, measured burdens, confirmed X/R ratios, and verified core remanence factors. Apply the calculation rigorously, verify through field testing, and document the results as a permanent maintenance baseline. Get the knee point voltage right from the start, and your protection CTs will perform exactly as designed when it matters most. 🔒

FAQs About CT Knee Point Voltage Calculation

1. Access the official IEC standards for instrument transformers to ensure compliance. ↩

2. Explore technical data on subtransient fault contributions for accurate protection calculations. ↩

3. Understand how system reactance and resistance affect fault transients and CT sizing. ↩

4. Review the performance benefits of nanocrystalline materials in reducing remanence. ↩

5. Detailed specifications for transient protection class CTs used in high-speed schemes. ↩