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Transformer Differential Protection Calculator — IEC 60255-111

CT ratio matching, biased differential characteristic, and inrush/overflux harmonic restraint per IEC 60255-111.

IEC 60255-111 IEC 60255-151 IEEE C37.91
Presets
Transformer Parameters
Primary CT Ratio
Secondary CT Ratio
Protection Settings
Harmonic Restraint
CT Ratio Matching
Biased Differential Characteristic
Inrush Restraint (2nd Harmonic)
Overflux Restraint (5th Harmonic)
Slope Setting Recommendations
Export Report
Related Tools
Transformer Protection (IEC 60255-151) Protection Coordination (IDMT TCC) Short Circuit (IEC 60909) Voltage Regulation
Methodology
CT Ratio Matching+
Primary and secondary rated currents are calculated from transformer MVA and voltages. CT turns ratios are applied to derive relay-side currents. Mismatch below 5% is acceptable per IEC 60255-111 §5.3.
Dual-Slope Biased Characteristic+
The operate threshold Id_thresh(Ir) follows a dual-slope piecewise linear function: Id = I_pu + k1·Ir for Ir ≤ Ir_bp, and Id = I_pu + k1·Ir_bp + k2·(Ir − Ir_bp) for Ir > Ir_bp (IEC 60255-111 §7.3).
Inrush Restraint+
Energisation inrush is estimated at 8×I_nom (conservative, IEEE C37.91). The relay measures the 2nd harmonic ratio in the differential current. If the ratio exceeds h2_threshold_pct, the relay asserts the BLOCK (restrain) output, preventing false trips (IEC 60255-111 §9.1).
Overflux Restraint+
Transformer overfluxing (V/Hz > 1.1 p.u.) generates 5th harmonic in the magnetising current. If the 5th harmonic ratio in the differential current exceeds h5_threshold_pct, the relay blocks tripping (IEC 60255-111 §9.2). Typical threshold: 10% for generator-transformers, 12% for distribution.
Frequently Asked Questions
What is transformer differential protection?+
Transformer differential protection compares the currents entering and leaving a transformer. Under normal load or through-faults, these currents balance. During an internal fault, the difference (differential current Id) exceeds the biased operate threshold and the relay trips.
What does IEC 60255-111 specify?+
IEC 60255-111 specifies the performance requirements for transformer differential protection relays, including CT ratio matching criteria (§5.3), phase compensation (§5.4), biased differential characteristic (§7.3), minimum operating current sensitivity (§8.2), and harmonic restraint methods (§9).
How are CT ratios matched for a transformer?+
The CT ratios are selected so that the secondary currents delivered to the relay are equal on both sides at rated load. Any residual mismatch under 5% is acceptable per IEC 60255-111 §5.3; larger mismatches require software correction or different CT ratios.
Why does Dyn11 vector group require phase compensation?+
The Dyn11 vector group introduces a 30° phase displacement between primary and secondary currents due to the delta/star winding connection. Without compensation, the relay sees a 30° current difference even at rated load, causing false tripping. Compensation is applied in software (digital relays) or via interposing CTs.
What is the purpose of 2nd harmonic inrush restraint?+
When a transformer is energised, it can draw magnetising inrush currents up to 8–10× rated current. These are rich in 2nd harmonic content (typically 15–40%). The relay measures the 2nd harmonic ratio — if it exceeds the threshold (usually 15–20%), it blocks tripping to distinguish inrush from an internal fault.
How do slope 1 and slope 2 differ?+
Slope 1 (k1, typically 20–30%) governs the low-restraint region (0 to Ir_breakpoint) and is set to accommodate CT errors, saturation, and ratio mismatch at normal load. Slope 2 (k2, typically 40–60%) governs the high-restraint region above the breakpoint, providing stability under heavy through-fault conditions where CT saturation is more severe.