The differential protection of a transformer is based on the principle of current vector sum balance. In theory, within the protection zone (encompassing the CTs), if the transformer windings are intact and no internal faults exist, the vector sum of currents on the high-voltage and low-voltage sides should be zero:
where 
and 
are the high-voltage and low-voltage currents, respectively, scaled to the same side for comparison.
Key Challenges in Practice
1. Magnitude Compensation (Ratio Correction)
The rated currents of the transformer’s high and low-voltage sides usually differ. The relay must correct the CT secondary currents for the magnitude difference to prevent load current from creating false differential currents.
2. Phase Compensation
For example, a transformer with a Yd11 (star-delta) vector group has a 30° phase shift between high and low-voltage sides. The relay must compensate for this inherent phase difference to avoid false tripping.
3.Zero-Sequence Compensation
When an external ground fault occurs, zero-sequence currents appear only on the star-connected side. This can lead to “false differential currents” because the delta side circulates zero-sequence currents internally and doesn’t show them externally. The relay must filter out these zero-sequence components to avoid misoperation.
Example Analysis
Consider a 63/20 kV, 40 MVA transformer with a Yd11 connection group:
High-voltage side rated current:
During normal operation, with ratio and phase compensation applied, the differential current should be nearly zero. If an internal fault occurs (e.g., short-circuit between turns), the differential relay will detect an abnormal differential current and trigger a trip command to isolate the transformer.
When setting the differential protection, additional factors must be considered:
✅ CT errors and potential saturation
✅ Transient current changes caused by the on-load tap changer (OLTC)
✅ Reasonable definition of the protection zone boundaries to avoid misoperation due to external faults
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