Differential Protection Relay: Average Scaling

Table of Contents

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Minimum operate current
Initial Slope
Initial Slope Boundary Limit
Second Slope
Unrestrained operate current
References

The percentage biased differential protection relay operates on the ratio of operate-to-restraint current according to a defined slope. This slope is calculated by considering the potential sources of differential current. These are the following:

transformer excitation current
tap variation
CT error, and
relay measurement error

In our discussion on percentage biased differential protection, we showed how these sources of differential current stack-up and estimated the minimum slope setting. We also showed how to determine the minimum operating current setting for a typical transformer differential protection relay based on CT error and tap variation in a through-current condition. The minimum operating current and slope are used to define the differential protection slope characteristic curve. A typical slope characteristic curve for a dual-slope percentage biased transformer differential protection is shown below.

Figure 1. Slope Characteristic Curve

To draw the slope characteristic curve, one will need the following parameters.

Minimum operate current

This is the minimum level of differential current required for operation.

Initial Slope

This is the operate-to-restraint current ratio calculated based on the steady-state through-currents.

Initial Slope Boundary Limit

This is the restraint current value where the initial slope ends and the second slope starts. This can be based on 100%-200% of the FLA rating but could extend to as much as 300%.

Second Slope

This is the operate-to-restraint current ratio calculated based on the transient through-currents. This can be based on close-in external faults that may result to CT saturation.

Unrestrained operate current

This is the value of the differential current that when exceeded will operate the differential protection irrespective of the restraint current.

Biased Differential Protection for Transformers

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Vector Group of Transformer Dyn1|Dyn11|Ynd1|Ynd11

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These parameters define only the slope characteristic curve as shown in figure 1. However, when you visualize this on secondary injection test sets, like Omicron 356 or Doble F6150, you will see a diagonal line apart from the slope-characteristic curve.

Figure 2. Slope Characteristic Curve. Omicron (left); Doble (right)

This line implies the maximum slope ratio limit and is defined by how the restraint current is quantified. In our previous discussion on percentage biased differential protection, we introduced the concept of minimum slope setting in order to define the slope characteristic curve.

The above equation is commonly referred to as average restraint. For a two-winding transformer differential protection, this results to the average current entering and exiting the zone. We also showed in our previous discussion that using the restraint current equation to calculate the minimum slope setting will yield the general equation.

The constant, k, in the above equation is commonly referred to as the scaling factor. The general equation to calculate the maximum slope ratio limit is

With an average scaling factor of k = 0.5, the maximum slope ratio limit is calculated to be 200%. Take note that the above calculations are applicable for differential protection relays using the average restraint scaling factor.