Transformer Differential Protection Calculation


Transformer differential protection is a protective scheme used to detect internal faults within a power transformer. It operates based on the principle of current differential protection, where currents entering and leaving the transformer are compared. If a fault occurs within the transformer, the difference in current between the primary and secondary windings will increase, causing the protection relay to trip and isolate the transformer from the system.

Here's an outline of the main calculations and considerations involved in transformer differential protection:

1. Current Transformers (CTs) Selection and Matching

  • Differential protection requires CTs on both sides of the transformer (high-voltage and low-voltage sides).
  • The CT ratios must be chosen carefully to ensure that the secondary currents are properly scaled and aligned for accurate comparison.
  • For transformers with multiple windings or different voltage ratings on the primary and secondary sides, CT ratios are adjusted accordingly.

2. Current Ratio Matching

  • Due to the transformer turns ratio, the current magnitudes will differ on each side of the transformer.
  • To compensate, the relay settings or CT ratios are adjusted so that, under normal conditions, the secondary currents from both sides are equal when referred to the relay.
  • The relay's algorithm can incorporate compensation factors to balance these values correctly.

3. Calculation of Differential and Restraint Currents

  • Differential current (I_diff): Calculated by summing the currents on the primary and secondary sides. If there's no fault, the differential current should be close to zero. Idiff=∣Iprimary+Isecondary∣I_{\text{diff}} = |I_{\text{primary}} + I_{\text{secondary}}|
  • Restraint current (I_restraint): Used to stabilize the protection and prevent misoperation under load or external faults. The restraint current is typically the average or sum of the magnitudes of the currents from both sides: Irestraint=∣Iprimary∣+∣Isecondary∣2I_{\text{restraint}} = \frac{|I_{\text{primary}}| + |I_{\text{secondary}}|}{2} or Irestraint=∣Iprimary∣+∣Isecondary∣I_{\text{restraint}} = |I_{\text{primary}}| + |I_{\text{secondary}}|
  • The restraint current helps prevent the relay from tripping due to inrush currents or other transient events that might cause temporary, non-fault-related differences.

4. Setting the Differential Protection Characteristic

  • The differential protection relay uses a characteristic curve to determine if the differential current warrants tripping. This curve typically has two or more slopes:
    • Low slope: Allows higher sensitivity for small differential currents under normal load or small faults.
    • High slope: Increases stability for high-through fault currents, especially during external faults or high magnetizing inrush conditions.
  • The trip decision is based on whether the differential current exceeds the threshold set by the restraint current and characteristic curve.

5. Inrush Current Detection and Harmonic Restraint

  • During transformer energization, a high inrush current can occur, which is not due to an internal fault.
  • To distinguish between inrush current and internal faults, the differential relay uses harmonic restraint, typically detecting the second harmonic component of the current.
  • If the second harmonic content exceeds a certain threshold (indicating inrush), the relay restrains from tripping.

6. Through Fault Stability

  • Transformers often experience through-faults, where high currents flow through the transformer from one side to another during external faults.
  • The protection relay uses the restraint mechanism to prevent tripping for these through-faults, as they do not indicate an internal fault within the transformer.

7. Relay Settings and Coordination

  • Relay settings, such as the percentage restraint, minimum pickup, and harmonic thresholds, need to be carefully set to ensure reliable operation.
  • Factors like transformer winding configuration (Y-Y, Y-Delta, etc.), vector group, and tap changer position can affect the settings, as these impact current flow and balance under different conditions.

Example Calculation

Assume a transformer has the following data:

  • Primary current: Iprimary=100 AI_{\text{primary}} = 100 \, \text{A}
  • Secondary current: Isecondary=95 AI_{\text{secondary}} = 95 \, \text{A}
  • CT ratios adjusted to produce equal currents for the relay comparison.

  1. Calculate the differential current:

    Idiff=∣100−95∣=5 AI_{\text{diff}} = |100 - 95| = 5 \, \text{A}

  2. Calculate the restraint current (average method):

    Irestraint=∣100∣+∣95∣2=97.5 AI_{\text{restraint}} = \frac{|100| + |95|}{2} = 97.5 \, \text{A}

  3. Check the characteristic curve. If IdiffI_{\text{diff}} exceeds a preset threshold relative to IrestraintI_{\text{restraint}}, the relay will trip; otherwise, it remains stable.

In practice, these calculations are automated within the relay itself, which performs the necessary comparison and issues a trip signal if an internal fault is detected. Proper configuration of the transformer differential protection is essential for accurate fault detection and prevention of unwanted trips.

You have to wait 10 seconds.

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