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# Description

This model implements a transformer differential relay (87T) with harmonic restraint and harmonic blocking functions. A differential relay operates when the difference between

two or more input electrical quantities exceeds a predefined value. It comprises up to three CT inputs (assuming there can be 3 transformer windings). A 2-slope restraint characteristic is available in this model. The model works for both 50 Hz and 60 Hz system.

# Model Overview

The differential relay trips whenever the difference between two (or three) input currents exceeds a predefined value. It is sensitive to faults within the differential zone, and it should be set to make it insensitive to external faults.
This model implements two types of differential functions – unrestraint (87U) and restraint (87R) differential elements. The differential current is calculated as a phasor summation of the current inputs from the CTs. First, the current magnitudes are adapted
to the primary side based on the winding voltage levels of the transformer. Then, the magnitudes and angles of the currents are corrected from Y side to delta side according to the transformer winding connections in order to ensure the currents used by the differential element are in phase. It has to be noted that the input CT current polarity should be either “looking towards the transformer” for all inputs or “looking away the transformer” for all inputs and all the CTs are considered to be Y connected. Based on the rated current specified in the relay control panel, the per unit values of the currents are calculated. The rated current can be considered as the current seen at the secondary side of the CT at winding 1 during normal operating condition. The same current base is used for differential current settings.

The protection logic of 87T relay is shown in the figure below:

## 87U

The 87U element compares the differential current directly with the predefined 87U pickup current. The output of the 87U element operates when the differential current of one or more phases exceeds the pickup current.

## 87R

The 87R element adds a 2-slope characteristic to the fixed operating current, as shown in Figure 1. The horizontal axis of this figure is the restraint current in pu whereas the vertical axis is the differential current in pu.

Two types of restraints are available:

Where Ii are the per unit input current phasors from each CT.
If and only if the differential current is larger than the pickup current and falls in the operating region (calculated from the two slopes), the 87R element will operate.

Harmonic restraint function is also provided in this model. This model implements a 2nd and 4th order harmonic restraint for better operation security. If the harmonic restraint function is enabled, the restraint current is calculated as follows:

Where  and  are the magnitudes of the second and fourth-order harmonics in the differential current.  and  are the harmonic blocking levels in percentage, which respect to fundamental signal.

## Harmonic Blocking

Harmonic blocking function is supported either for the 2nd, 4th, 5th harmonics individually or a combination of 2nd +4th or 2nd +5th harmonics. If the maximum level of the selected harmonics is reached, the 87R element operation is blocked as long as this
condition is satisfied. Internally, the comparison is made between the magnitude of the selected harmonics and the fundamental signal times the maximum harmonic levels in percentage, for example, IH2 is compared with IFund*L2 . If the former is larger, differential protection is blocked. Otherwise, harmonic blocking is not active.

# Mask and Parameters

## General parameters

NameUnitDescription

Enable

-

Enable/Disable for the relay operation

Frequency

Hz

The frequency of the measured current signals. Both 50 and 60 Hz are supported within the model.

Primary/Secondary

connection

-

Transformer connection between winding 1 and winding 2.

Primary/Tertiary

connection

-

Transformer connection between winding 1 and winding 3.

Winding 1 voltage

(L-L)

V

The L-L voltage of winding 1.

Winding 1 CT ratio

-

The ratio of the CT connected at winding 1.

Winding 2 voltage

(L-L)

V

The L-L voltage of winding 2.

Winding 2 CT ratio

-

The ratio of the CT connected at winding 2.

Winding 3 voltage

(L-L)

V

The L-L voltage of winding 3.

Winding 3 CT ratio

-

The ratio of the CT connected at winding 3.

Rated current

A

The base current (RMS) of the input signals and differential current settings. User can use the CT secondary current at winding 1 during normal operating condition.

87U pickup

pu

The pickup current for 87U element.

Restraint type

-

Select how the restraint current is calculated:

Sum:

Max:

87R pickup

pu

The pickup current for 87R element.

Breakpoint

pu

Threshold current between slope 1 and slope 2.

Slope 1

-

Value of the first slope in the 2-slope characteristics curve.

Slope 2

-

Value of the second slope in the 2-slope characteristics curve.

Trip Delay

s

Delay time before tripping if tripping conditions are

met, for both 87U and 87R

Reset Delay

s

Delay time before the relay is reset, for both 87U and 87R

## Harmonic Blocking and Restraint

NameUnitDescription

87U Harmonic blocking

To enable the harmonic blocking function for 87U, enabled if checked.

87R Harmonic blocking

-

To enable the harmonic blocking function for 87R, enabled if checked.

2nd Harmonic

-

To enable the 2nd order harmonic blocking option, enabled if checked.

2nd Harmonic

%

The maximum 2nd harmonic level in percentage, with respect to the fundamental harmonic.

4th Harmonic

-

To enable the 4th order harmonic blocking option, enabled if checked.

4th Harmonic

%

The maximum 4th harmonic level in percentage, with respect to the fundamental harmonic.

5th Harmonic

-

To enable the 5th order harmonic blocking option, enabled if checked.

5th Harmonic

%

The maximum 5th harmonic level in percentage, with respect to the fundamental harmonic.

2nd+4th Harmonic

-

2nd+4th Harmonic enable

2nd+4th Harmonic

%

The maximum 2nd+4th harmonic level in percentage, with respect to the fundamental harmonic.

2nd+5th Harmonic

-

2nd+5th Harmonic enable

2nd+5th Harmonic

%

The maximum 2nd+5th harmonic level in percentage, with respect to the fundamental harmonic.

Harmonic Restraint:

2nd+4th Harmonic

-

To enable the harmonic restraint function, enabled if checked

# Inputs and Outputs

## Inputs

NameDescription

Iabc1

Three-phase currents of CT1.

Iabc2

Three-phase currents of CT1.

Iabc3

Three-phase currents of CT1.

Reset

The reset signal for the relay. The relay will be reset when this signal becomes 1.

## Outputs

NameDescription

87U

The output of unrestraint differential relay. By default it is 0, if a differential scenario is detected, it becomes 1.

87R

The output of restraint differential relay. By default it is 0, if a differential scenario is detected, it becomes 1.

# Reference

1. SEL-487E-3, -4 Relay Current Differential and Voltage Protection Instruction Manual
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