Accurate measurement of current and voltage is critical for power system protection and metering. Errors in transformers can significantly impact system reliability and billing accuracy.
This article explores error calculation methods for current and voltage transformers based on IEC and IEEE standards. It covers formulas, tables, and practical examples for engineers and technicians.
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- Calculate current transformer error for 100 A primary, 5 A secondary, 1.5% burden, 0.5% excitation error.
- Determine voltage transformer error at 11 kV primary, 110 V secondary, 0.2% ratio error, 1.0 degree phase error.
- Find combined error of CT and VT for 50 Hz system with 200 A primary, 5 A secondary, 0.3% ratio error.
- Evaluate CT error under 120% rated current with 1.0% ratio error and 0.2 degree phase displacement.
Common Values for Error in Current and Voltage Transformers – IEC, IEEE
| Transformer Type | Rated Primary Current (A) | Rated Secondary Current (A) | Typical Ratio Error (%) | Typical Phase Displacement (minutes) | Burden (VA) |
|---|---|---|---|---|---|
| Protection Class CT (IEC 60044-1) | 5 – 6000 | 1 or 5 | 0.1 – 0.5 | 10 – 60 | 1 – 15 |
| Metering Class CT (IEC 60044-1) | 5 – 600 | 1 or 5 | 0.1 – 0.3 | 5 – 20 | 1 – 10 |
| Voltage Transformer (IEC 60044-2) | 3.3 kV – 765 kV | 100 V or 110 V | 0.1 – 0.5 | 1 – 10 | 10 – 50 |
| Instrument Transformer (IEEE C57.13) | 5 – 6000 | 1 or 5 | 0.1 – 0.6 | 5 – 30 | 1 – 20 |
| Parameter | Typical Range | IEC Standard Reference | IEEE Standard Reference |
|---|---|---|---|
| Ratio Error (%) | 0.1 – 0.6 | IEC 60044-1, 60044-2 | IEEE C57.13 |
| Phase Displacement (minutes) | 1 – 60 | IEC 60044-1, 60044-2 | IEEE C57.13 |
| Burden (VA) | 1 – 50 | IEC 60044-1, 60044-2 | IEEE C57.13 |
| Frequency (Hz) | 50 or 60 | IEC 60044-1, 60044-2 | IEEE C57.13 |
Fundamental Formulas for Error Calculation in Current and Voltage Transformers
1. Current Transformer Ratio Error
The ratio error of a current transformer (CT) quantifies the deviation between the actual secondary current and the ideal secondary current.
- I2,actual: Actual secondary current (A)
- I2,ideal: Ideal secondary current based on rated ratio (A)
Alternatively, using primary current and rated transformation ratio:
- N: Rated transformation ratio (primary/secondary)
- I1: Primary current (A)
2. Current Transformer Phase Displacement Error
Phase displacement error represents the angular difference between primary and secondary currents, expressed in minutes or degrees.
- θ1: Phase angle of primary current (degrees)
- θ2: Phase angle of secondary current (degrees)
3. Voltage Transformer Ratio Error
Voltage transformer (VT) ratio error is the difference between actual secondary voltage and ideal secondary voltage.
- V2,actual: Actual secondary voltage (V)
- V2,ideal: Ideal secondary voltage based on rated ratio (V)
4. Voltage Transformer Phase Displacement Error
Phase displacement error for VT is the angular difference between primary and secondary voltages.
- φ1: Phase angle of primary voltage (degrees)
- φ2: Phase angle of secondary voltage (degrees)
5. Combined Error of CT and VT
When both CT and VT are used in measurement, the combined error is the sum of their individual ratio and phase errors.
<strong>Total Phase Displacement (minutes) = Phase DisplacementCT + Phase DisplacementVT</strong>
6. Burden Effect on CT Error
The burden connected to the CT secondary affects the error magnitude. The burden is the load impedance expressed in VA at rated secondary voltage.
- IEC 60044-1 specifies maximum burden for each CT class.
- Operating beyond rated burden leads to saturation and nonlinear error increase.
Detailed Real-World Examples of Error Calculation
Example 1: Calculating CT Ratio and Phase Error for Protection Class CT
A protection class CT has a rated primary current of 1000 A and secondary current of 5 A. The actual secondary current measured is 4.95 A when the primary current is 1000 A. The phase angle difference between primary and secondary currents is 0.2 degrees. Calculate the ratio error and phase displacement error.
Step 1: Calculate Ratio Error
Rated transformation ratio, N = 1000 / 5 = 200
Using the formula:
Substitute values:
The CT secondary current is 1% less than ideal, indicating a -1% ratio error.
Step 2: Calculate Phase Displacement Error
Given phase angle difference θ2 – θ1 = 0.2 degrees
Convert to minutes:
The phase displacement error is 12 minutes, within typical protection class limits.
Example 2: Voltage Transformer Error Calculation for Metering Class VT
A metering class VT has a rated primary voltage of 11 kV and secondary voltage of 110 V. The actual secondary voltage measured is 109.5 V at rated primary voltage. The phase angle difference between primary and secondary voltages is 0.05 degrees. Calculate the ratio error and phase displacement error.
Step 1: Calculate Ratio Error
Using the formula:
Substitute values:
The VT secondary voltage is 0.4545% less than ideal, indicating a -0.45% ratio error.
Step 2: Calculate Phase Displacement Error
Given phase angle difference φ2 – φ1 = 0.05 degrees
Convert to minutes:
The phase displacement error is 3 minutes, suitable for metering class VT.
Additional Technical Considerations for Transformer Error Analysis
- Frequency Dependence: Both CT and VT errors vary with frequency deviations from rated 50/60 Hz. IEC and IEEE standards specify test frequencies and correction factors.
- Burden Impact: The connected burden affects CT accuracy. Exceeding rated burden causes core saturation, increasing ratio and phase errors nonlinearly.
- Temperature Effects: Transformer errors can change with ambient temperature due to core and winding resistance variations.
- Harmonic Distortion: Non-sinusoidal currents and voltages introduce additional errors not covered by fundamental frequency calculations.
- Standards Compliance: IEC 60044 series and IEEE C57.13 provide detailed test procedures, accuracy classes, and permissible error limits for instrument transformers.
References and Further Reading
- IEC 60044-1: Instrument Transformers – Part 1: Current Transformers
- IEC 60044-2: Instrument Transformers – Part 2: Voltage Transformers
- IEEE C57.13-2016 – Standard Requirements for Instrument Transformers
- Electrical Engineering Portal – Instrument Transformers