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CT Selection & Sizing

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Nominal Current *

Load nominal current (motor FLC, feeder current, etc.)

Maximum Fault Current *

Maximum fault current at CT location (from fault study)

System Voltage (V)

Line-to-line voltage

Frequency (Hz)

CT Primary Current *

CT primary winding rated current

CT Secondary Current (A) *

CT Accuracy Class *

CT Rated Burden *

CT rated burden at secondary current

Knee Point Voltage Vk

From CT datasheet (optional)

CT Internal Resistance

Ω

CT secondary winding resistance (optional)

Cable Length *

One-way cable length from CT to relay

Conductor Area (mm²) *

Relay Burden *

Relay/meter burden at rated secondary current

Cable Temperature (°C)

Expected cable operating temperature

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CURRENT TRANSFORMER (CT) SELECTION & SIZING

IEC 60044-1 / IEC 61869-2 - Current Transformer Suitability Assessment

This calculation verifies CT suitability for protection applications through:
1. BURDEN ANALYSIS - VA load must not exceed CT rated burden
2. ALF VERIFICATION - Accuracy Limit Factor ensures accuracy during faults
3. SATURATION CHECK - Knee point voltage prevents core saturation
4. RATIO SELECTION - Optimal ratio for nominal current

**Protection CT Classes:**
* 5P/10P - 5% or 10% composite error at accuracy limit
* ALF Suffix (5, 10, 20) - Current multiple maintaining accuracy
* PX/TPX/TPS - Special classes for differential protection

1. INPUT PARAMETERS

System parameters and CT specifications for suitability assessment.

Parameter	Symbol	Value	Notes
Nominal Primary Current	I_nom	50 A	Load nominal current
Maximum Fault Current	I_fault	5 kA	From fault study
System Voltage	V_LL	415 V	Line-to-line
CT Ratio		50:5	n = 10.0
CT Accuracy Class		5P10	ALF = 10x
CT Rated Burden	VA_rated	10 VA	CT nameplate rating
CT Knee Point Voltage	V_k	Not specified	From datasheet
Cable Length	L	20 m	One-way distance
Conductor Area	A	2.5 mm2	Cable cross-section
Relay Burden	VA_relay	500 mVA	Relay/meter burden

2. CT TRANSFORMATION RATIO

The CT ratio determines the relationship between primary and secondary currents.

2.1 CT Ratio Calculation

CT Ratio: 50:5 CT Class: 5P10 (Accuracy Limit Factor = 10x) The ALF defines the current multiple at which the CT maintains specified accuracy. Beyond this point, the CT may saturate.

Formula: $$ n = \frac{I_{primary}}{I_{secondary}} = \frac{50}{5} = 10 $$

3. SECONDARY CIRCUIT RESISTANCE

The total secondary circuit resistance includes cable, relay, and CT internal resistance.

3.1 Resistance Calculations

Where: * rho(75.0C) = 0.020968 Ohm*mm2/m (copper @ 75.0C) * L = 20.0 m (one-way length) * A = 2.5 mm2 R_cable = 0.335482 Ohm (94.4% of total) R_relay = 0.020000 Ohm (5.6% of total) R_CT = 0.000000 Ohm (0.0% of total)

Formula: $$ R_{cable} = \frac{\rho(T) \times 2L}{A} $$

Cable resistance typically dominates for long cable runs. Use larger conductor area to reduce cable resistance.

Formula: $$ R_{total} = R_{cable} + R_{relay} + R_{CT} = 0.335482 + 0.020000 + 0.000000 = 0.355482 \text{ Ohm} $$

4. BURDEN ANALYSIS - PASS

The burden represents power consumed by the secondary circuit. It must not exceed the CT rated VA.

4.1 Burden Calculation

**Burden Assessment:** * CT Rated Burden: 10.0 VA * Actual Burden: 8.887 VA * Utilization: 88.9% * Margin: 1.113 VA **Result: PASS** Actual burden is within CT rated burden. Recommended: 50-80% utilization for safety margin.

Formula: $$ VA_{actual} = I_{sec}^2 \times R_{total} = 5^2 \times 0.355482 = 8.887 \text{ VA} $$

6. FAULT CURRENT ANALYSIS

STEP 7: FAULT CURRENT TRANSFORMATION TO SECONDARY

During fault conditions, the CT must accurately reproduce the
fault current on the secondary side without saturating.

Fault Multiple Calculation (IEC 60044-1 cl. 3.4.202):
    Fault_Multiple = I_fault / I_rated_primary

Where:
    I_fault = 5,000 A (maximum fault current from fault study)
    I_rated_primary = 50.0 A (CT rated primary current)

Calculation:
    Fault_Multiple = 5,000 / 50.0
    Fault_Multiple = 100.0x

This indicates the fault current is 100.0 times the CT rated primary current.

---

STEP 8: SECONDARY FAULT CURRENT

The secondary fault current is determined by the CT ratio:

Formula:
    I_sec_fault = I_fault / n

Where:
    I_fault = 5,000 A
    n = 10.0 (CT ratio factor)

Calculation:
    I_sec_fault = 5,000 / 10.0
    I_sec_fault = 500.0 A

The secondary circuit will experience 500.0 A during maximum fault.

---

STEP 9: REQUIRED SECONDARY VOLTAGE DURING FAULT

The voltage required to drive the fault current through the
secondary circuit resistance determines saturation risk:

Formula:
    V_required = I_sec_fault x R_total

Where:
    I_sec_fault = 500.0 A
    R_total = 0.355482 Ohm

Calculation:
    V_required = 500.0 x 0.355482
    V_required = 177.7 V

CRITICAL REQUIREMENT:
This voltage MUST be less than the CT knee-point voltage (Vk)
to prevent core saturation during fault conditions.

If V_required > Vk:
* The CT core will saturate
* Secondary current will be distorted
* Protection relay may fail to detect fault correctly
* Relay operating time will be extended (dangerous!)

VOLTAGE BUDGET ANALYSIS:
* Required Secondary Voltage: 177.7 V
* CT Knee Point Voltage: Not specified
* Utilization: Cannot calculate (Vk not specified)

7. ACCURACY LIMIT FACTOR (ALF) VERIFICATION - FAIL

STEP 10: ALF COMPLIANCE CHECK

The Accuracy Limit Factor (ALF) defines the maximum current
multiple at which the CT maintains its specified accuracy.

Per IEC 60044-1:
* The CT is guaranteed to have <= specified composite error
  up to (ALF x rated primary current)
* Beyond ALF, the CT may saturate and produce errors > specified limit

Verification Formula:
    Fault_Multiple <= ALF

Values:
    Fault_Multiple = 100.0x
    ALF = 10x (from CT class 5P10)

Check:
    100.0 <= 10?
    UNACCEPTABLE

Margin: -90.0x (Negative margin - INADEQUATE!)

---

ALF INTERPRETATION:

For CT class 5P10:
* Rated primary current: 50.0 A
* Accuracy maintained up to: 500 A (10x rated)
* Maximum fault current: 5,000 A

COMPOSITE ERROR DEFINITION:
The composite error combines:
* Ratio error (deviation from ideal transformation ratio)
* Phase displacement (angular error between primary and secondary)

For 5P10 class:
* Composite error <= 5% at 10x rated current

WARNING: ALF EXCEEDED!
The fault current exceeds the CT's accuracy limit.
Possible consequences:
* CT may saturate during fault
* Protection relay may malfunction
* Fault clearance time may be extended
* Equipment damage risk increased

CORRECTIVE ACTIONS (if ALF check fails):
* Option 1: Specify higher ALF class (e.g., 5P20 instead of 5P10)
* Option 2: Increase CT ratio to 100:5.0 (adjust relay settings)
* Option 3: Use PX/TPX class with higher knee-point voltage
* Option 4: Review fault study - verify maximum fault current

8. KNEE POINT VOLTAGE CHECK - DATA NOT AVAILABLE

STEP 11: KNEE POINT VOLTAGE NOT PROVIDED

The CT knee-point voltage (V_k) has not been specified.
This parameter is essential for accurate saturation assessment.

Required Secondary Voltage: 177.7 V
Estimated Saturation Risk: HIGH

ESTIMATION METHOD (without V_k):

Rule of thumb for protection CTs:
* 5P class at rated VA: V_k ~ 75-150 V (typical range)
* 10P class at rated VA: V_k ~ 50-100 V (typical range)
* PX class: V_k >= 200 V (manufacturer specified)

Saturation Risk Estimation:
* V_required < 50 V: LOW risk (typical)
* V_required 50-150 V: MEDIUM risk (verify from datasheet)
* V_required > 150 V: HIGH risk (likely saturation)

For this application:
* Required voltage: 177.7 V
* Estimated risk: HIGH

IMPORTANT - ACTION REQUIRED:

Obtain the CT knee-point voltage from:
1. Manufacturer's datasheet (most reliable)
2. Excitation curve (V_k is at 10%V -> 50%I point)
3. Type test report (if available)
4. Factory test certificate

Cannot accurately verify CT suitability without V_k!

INTERIM RECOMMENDATION:

Specify minimum V_k requirement in procurement:
* Minimum V_k >= 267 V (with 50% margin)
* Recommended V_k >= 355 V (with 100% margin)

For critical protection applications:
* Specify Class PX with minimum V_k
* Request excitation curves from manufacturer
* Perform acceptance testing to verify V_k

9. OVERALL SUITABILITY ASSESSMENT

STEP 12: OVERALL CT SUITABILITY ASSESSMENT

Overall Status: NOT SUITABLE

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DETAILED SUITABILITY CHECKS:

PASS - Burden Check
    VA burden (8.89 VA) ≤ CT rated VA (10.0 VA)

FAIL - ALF Check
    Fault multiple (100.0×) exceeds ALF (10×)

WARNING - Knee Point Check
    Knee point not provided. Required voltage: 177.7 V

---

SUITABILITY CRITERIA SUMMARY:

For a CT to be suitable for protection application:

Burden Check: VA_actual <= VA_rated
  - Ensures CT operates within thermal limits
  - Maintains specified accuracy

ALF Check: Fault_Multiple <= ALF
  - Ensures accuracy during fault conditions
  - Prevents saturation up to rated fault current

Knee Point Check: V_required <= V_k
  - Prevents core saturation
  - Ensures linear operation during faults

CT SUITABILITY ASSESSMENT: NOT SUITABLE

One or more critical checks have FAILED.
This CT should NOT be used for this application without modifications.
Review the recommendations below for corrective actions.

10. WARNINGS & RECOMMENDATIONS

WARNINGS:

The following warnings have been identified:

1. Verify knee-point voltage from CT datasheet
2. Cable resistance dominates burden - consider shorter cable run or larger conductor

---

RECOMMENDATIONS:

Consider the following options to improve CT suitability:

1. Use higher ALF class (e.g., 5P20) or increase CT ratio
2. Option 2: Use CT with ALF ≥ 100 (e.g., 5P20)
3. Option 3: Increase CT ratio to 100:5 (adjust relay settings)

---

GENERAL RECOMMENDATIONS FOR CT SELECTION:

Burden Optimization:
* Minimize cable length where possible
* Use adequate conductor size (2.5mm2 minimum for 5A secondary)
* Select modern digital relays (low burden < 0.5 VA)
* Consider 1A secondary for long cable runs (1/25th the burden)

Protection Class Selection:
* Overcurrent/earth fault: 5P10 or 5P20 typically adequate
* Differential protection: Class PX or TPX preferred
* High fault current systems: Use 5P20 or PX class
* Generator protection: TPX or TPS class for stability

Ratio Selection:
* Choose next standard ratio above nominal current
* Typical guideline: I_primary = (1.2 to 1.5) x I_nominal
* For motors: Consider 1.25 x I_FLC as minimum
* For feeders: Consider load growth and diversity

Specification Best Practices:
* Always specify minimum knee-point voltage
* Request excitation curves from manufacturer
* Specify maximum secondary winding resistance
* Include acceptance testing requirements
* Verify accuracy class and ALF in datasheet

11. CT RATIO SELECTION RECOMMENDATION

STEP 13: CT RATIO SELECTION RECOMMENDATION

Optimal CT ratio selection balances:
* Adequate range for maximum fault current
* Sufficient sensitivity at nominal current
* Standard available ratios

Selection Guideline:
Choose the next standard ratio above nominal current.

Your System:
* Nominal Current: 50.0 A
* Current CT Ratio: 50:5
* Recommended Ratio: 50:5

RATIO SELECTION: OPTIMAL

The current CT ratio matches the recommended ratio.
This provides good balance between sensitivity and range.

Relay Sensitivity Check:
* Nominal secondary current: 5.00 A
* Minimum pickup setting: ~2.50 A (typical 50%)
* Maximum fault secondary: 500.0 A

Verify relay settings can accommodate this range.

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STANDARD CT RATIOS (5A Secondary):

Low Current:
* 5:5, 10:5, 15:5, 20:5, 25:5, 30:5, 40:5, 50:5

Medium Current:
* 60:5, 75:5, 100:5, 150:5, 200:5, 250:5, 300:5, 400:5, 500:5

High Current:
* 600:5, 750:5, 800:5, 1000:5, 1200:5, 1500:5, 2000:5

1A Secondary (for long cable runs):
* 50:1, 100:1, 200:1, 500:1, 1000:1

12. CALCULATION SUMMARY & COMPLIANCE

CALCULATION SUMMARY

Input Parameters:
* Nominal Current: 50.0 A
* Fault Current: 5,000 A (100.0x nominal)
* CT Ratio: 50:5 (Class 5P10)
* Secondary Circuit: 20.0m x 2.5mm2 + 0.5VA relay

Key Results:
* Secondary Burden: 8.887 VA (Rated: 10.0 VA) - PASS
* Required Voltage: 177.7 V (Vk: Not specified) - N/A
* ALF Compliance: Fault 100.0x vs ALF 10x - FAIL
* Overall Status: NOT SUITABLE

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STANDARDS & REFERENCES

International Standards:
* IEC 60044-1 (2003) - Instrument transformers - Current transformers
* IEC 61869-2 (2012) - Instrument transformers - Additional requirements for current transformers
* IEC 60255 - Measuring relays and protection equipment

Regional Standards:
* AS 60044.1 (Australian adoption of IEC 60044-1)
* IEEE C57.13 (American standard for instrument transformers)
* BS 3938 (British standard for current transformers)

Protection Standards:
* IEC 60255-151 - Overcurrent protection
* IEEE C37.91 - Guide for protective relay applications
* ANSI/IEEE C37.110 - Guide for application of current transformers

CALCULATION RESULTS - CT NOT SUITABLE

Final assessment of CT suitability for this application.

**Overall Result: NOT SUITABLE**
One or more checks failed

Parameter	Symbol	Value	Notes
Cable Resistance	R_cable	335 mOhm	@ 75.0C
Total Secondary Resistance	R_total	355 mOhm	Cable + relay + CT
Actual Burden	VA_actual	8.89 VA	88.9% of rated
Burden Check		PASS	Margin: 1.11 VA
Fault Multiple		100 x	I<sub>fault</sub> / I<sub>rated,primary</sub>
Required Voltage (Fault)	V_req	178 V	During fault
ALF Check		FAIL	Fault multiple vs ALF
Saturation Check		N/A	V<sub>req</sub> vs V<sub>k</sub>
Overall Suitability		NOT SUITABLE	One or more checks failed

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