Testing of Differential Protection Relay: Stability Test, Pickup Test, Slope Test, & Harmonic Blocking

Differential protection relays are the primary protective devices used for power transformers, generators, busbars, and large motors in electrical power systems. These relays operate based on Kirchhoff’s current law by comparing the currents entering and leaving a protected zone. Testing of differential protection relay is a mandatory activity during commissioning and periodic maintenance to verify that the relay will operate correctly during internal faults while remaining stable during external faults and normal operating conditions.

In this technical guide, we will discuss everything you need to know about testing differential protection relays. We will discuss the step by step test procedures, pickup current calculations, stability tests, slope characteristic verification, harmonic blocking tests, and real examples from actual commissioning reports.

1. What is a Differential Protection Relay?

A differential protection relay works on a simple principle. It compares the current entering a protected equipment with the current leaving it. Under normal conditions and external fault conditions, the current entering equals the current leaving. The difference between these two currents is zero or very small. During an internal fault within the protected zone, some current flows to the fault point and does not exit through the other side. This creates a difference between the entering and leaving currents which the relay detects and initiates tripping.

For transformer differential protection, the relay receives current signals from CTs installed on both HV (High Voltage) and LV (Low Voltage) sides of the transformer. Modern numerical differential relays like the Siemens 7UT85 series automatically compensate for transformer vector group, CT ratio mismatch, and tap changer position. These relays use percentage bias characteristics to remain stable during through faults while being sensitive to internal faults.

The relay calculates two quantities from the input currents. The differential current (Idiff) is the vector sum of all currents entering the protected zone. The bias or restraint current (Ibias) is proportional to the through current flowing in the protected equipment. The relay trips when the differential current exceeds a set percentage of the bias current.

2. Why Testing of Differential Protection Relay is Necessary

Testing of differential protection relay serves multiple purposes in power system protection. First, it verifies that the relay settings match the transformer or equipment parameters. Second, it confirms that the relay correctly calculates differential and bias currents from the CT inputs. Third, it validates that the relay remains stable during external faults and through current conditions.

During commissioning of a new transformer or substation, differential relay testing is performed before the equipment is energized. This pre-commissioning test identifies any wiring errors, CT polarity mistakes, or setting errors that could cause protection failure or unwanted tripping during normal operation.

Periodic testing during maintenance outages helps detect relay degradation over time. Component aging, environmental factors, and firmware issues can affect relay performance. Regular testing catches these problems before they cause protection failures during actual faults.

3. Equipment Required for Differential Relay Testing

The testing of differential protection relay requires specialized test equipment. A relay test set capable of injecting multiple current channels simultaneously is the primary requirement. For transformer differential relay testing, the test set must have at least six current output channels – three for HV side CTs and three for LV side CTs.

The test set must be capable of producing:

• Six-channel current injection up to 30A per channel
• Precise control of phase angles between channels
• Independent magnitude control for each channel
• Harmonic current injection capability (2nd and 5th harmonics)
• Accurate timing measurement for trip time verification
• Synchronized injection with adjustable angles

Additional equipment includes a laptop computer with relay configuration software, appropriate connecting cables, and isolation equipment to prevent backfeed during testing. The relay configuration software is needed to read relay settings, verify configuration, and download test results.

4. Pre-Test Preparations and System Parameters

Before conducting differential relay tests, you must verify all system parameters and relay configurations. The following example uses actual data from a differential relay testing project I completed in 2023 to demonstrate the testing procedure and provide practical context for understanding the process.

Transformer Details:

• Rating: 20 MVA
• HV Voltage: 132 kV
• LV Voltage: 33 kV
• Vector Group: Delta-Star

CT Ratios:

• HV Side CT Ratio: 300 A / 1 A
• LV Side CT Ratio: 1000 A / 1 A

Relay Information:

• Relay Model: Siemens 7UT85
• Auxiliary Supply: 120 V DC
• Differential Setting (Idiff>): 0.2 (20% of rated current)

These parameters are used to calculate the full load currents and pickup values for testing.

5. Current Measurement Verification Test

The first step in differential relay testing is verifying that the relay correctly measures injected currents from both HV and LV sides. This test confirms proper wiring connections, validates CT ratio settings in the relay, and checks for any phase identification errors.

5.1 HV Side Current Measurement Test:

Individual phase currents are injected one at a time on the HV side inputs. The relay display shows the primary current value after applying the CT ratio.

The relay converts 1A secondary current to 300A primary using the 300/1 CT ratio. When all three phases are injected with balanced currents, the zero sequence current (3I0) should be zero. Minor differences like 299A instead of 300A are acceptable within measurement tolerances.

5.2 LV Side Current Measurement Test:

Similar verification is performed for LV side current inputs:

The relay converts 1A secondary current to 1000A primary using the 1000/1 CT ratio. This test confirms that both HV and LV side current inputs are correctly wired and the relay is properly configured for the CT ratios.

6. Stability Test Procedure

The stability test is one of the most important tests for differential protection relays. This test verifies that the relay does not operate during normal load conditions or external through faults. During these conditions, equal currents flow into and out of the protected zone, and the differential current should be negligible.

6.1 Stability Test Setup

For this test, currents are injected on both HV and LV sides simultaneously. The currents must be adjusted for the transformer ratio and must have correct phase relationship. For a transformer with 132 kV / 33 kV voltage ratio, the current ratio is inverse of the voltage ratio.

The test uses the following calculated values:

• HV Side Full Load Current (Secondary): 0.292 A
• LV Side Full Load Current (Secondary): 0.349 A

The phase angles must account for the transformer vector group. The LV side currents are shifted by 180 degrees from HV side to simulate the current flowing through the transformer.

6.2 Stability Test Results

The test results show that with proper phase angles, the differential current (Idiff) is nearly zero (0.003 to 0.005) while the bias current (Ibias) is close to 1.0 per unit. The relay correctly identifies this as a through current condition and does not trip. This confirms the relay stability for external faults and normal load conditions.

7. Instability Test Procedure

The instability test verifies that the relay operates correctly when an internal fault occurs. During an internal fault, the currents on HV and LV sides are no longer balanced, creating a high differential current. This test is performed by changing the phase angle of the LV side currents to be in phase with HV side currents instead of 180 degrees apart.

7.1 Instability Test Results

When the LV side currents are in phase with HV side currents (simulating an internal fault), the differential current jumps to approximately 1.92 per unit. The relay correctly detects this high differential current and trips in 30.40 milliseconds. This fast operating time is important for limiting damage during internal transformer faults.

8. Pickup Current Calculation for HV Side

Before performing pickup tests, the expected pickup current values must be calculated based on transformer rating, CT ratios, and relay settings.

8.1 HV Side Full Load Current Calculation

Using the power equation \(P = \sqrt{3} \times V \times I\):

Primary Full Load Current \(= \frac{P}{(\sqrt{3} \times V)}\)
\(= \frac{20,000,000}{(\sqrt{3} × 132,000)}\)
\(= 87.477 A\)

Secondary Full Load Current \(= \frac{\text{Primary Current}}{\text{CT Ratio}}\)
\(= \frac{87.477}{300}\)
\(= 0.292 A\)

8.2 Three-Phase Pickup Calculation

\(\text{3-Phase Pickup} = \text{Secondary Full Load Current} \times \text{Diff Setting}\)
\(= 0.292 \times 0.2\)
\(= 0.0584 A\)

8.3 Single-Phase Pickup Calculation

For single-phase faults, a zero sequence compensation factor is applied:

\(\text{1-Phase Pickup} = \text{Sec FLC} \times \text{Diff Sett.} \times \text{Zero Comp.}\)
\(= 0.292 \times 0.2 \times 1.5\)
\(= 0.0876 A\)

The zero sequence compensation factor of 1.5 accounts for the different current distribution during single-phase-to-ground faults.

9. HV Side Pickup Test Results

The pickup test verifies that the relay operates at the calculated pickup current values. Current is injected on the HV side only (simulating an internal fault with no current on LV side) and gradually increased until the relay trips.

9.1 HV Side Three-Phase Pickup Test

The actual pickup of 0.0586 A is very close to the calculated value of 0.0584 A. The small difference of 0.0002 A (about 0.3%) is well within acceptable limits for numerical relays.

9.2 HV Side Single-Phase Pickup Tests

All three phases show actual pickup values of 0.0878 A against the calculated value of 0.0876 A. The operating times vary slightly between phases (41 to 48 ms) but are all within acceptable limits for fast differential protection.

10. Pickup Current Calculation for LV Side

Similar calculations are performed for the LV side of the transformer.

10.1 LV Side Full Load Current Calculation

Primary Full Load Current \(= \frac{P}{(\sqrt{3} \times V)}\)
\(= \frac{20,000,000}{(\sqrt{3} \times 33,000)}\)
\(= 349.909 A\)

\(\text{Secondary Full Load Current} = \frac{\text{Primary Current}}{\text{CT Ratio}}\)
\(= \frac{349.909}{1000}\)
\(= 0.349 A\)

10.2 Three-Phase Pickup Calculation

\(\text{3-Phase Pickup} = \text{Secondary Full Load Current} \times \text{Diff Setting}\)
\(= 0.349 × 0.2\)
\(= 0.0692 A\)

Single-Phase Pickup Calculation:

\(\text{1-Phase Pickup} = \text{Sec FLC} \times \text{Diff Sett.} \times \text{Zero Comp.}\)
\(= 0.349 \times 0.2 \times 1.5\)
\(= 0.1038 A\)

11. LV Side Pickup Test Results

11.1 LV Side Three-Phase Pickup Test

11.2 LV Side Single-Phase Pickup Tests

The LV side pickup tests show slightly higher actual values compared to calculated values. This small difference is acceptable and may be due to relay measurement tolerances. The operating times on the LV side are similar to HV side, confirming consistent relay performance.

12. Slope Characteristic Test Procedure

The differential slope characteristic is a key feature of percentage differential protection. The relay uses a biased or percentage restraint characteristic where the pickup threshold increases with increasing through current. This provides stability during external faults with high through currents while maintaining sensitivity for internal faults at low load conditions.

Modern transformer differential relays have dual slope characteristics:

• Slope 1: Lower slope (typically 25-30%) active at lower bias currents
• Slope 2: Higher slope (typically 50-70%) active at higher bias currents

The transition between slopes occurs at a defined bias current level (typically 2.5 to 5 times rated current).

12.1 Slope 1 Test (25% Slope)

12.1.1 Test Procedure

Full load current is applied on both HV and LV sides with balanced angles (180 degrees apart). Then one side current is gradually increased until the relay trips. The differential and restraint currents at the trip point are recorded.

12.1.2 Slope 1 Test Results (25% Setting)

12.1.3 Slope Calculation

\(\text{Slope} = \frac{I_{diff}}{I_{bias}}\)
\(= \frac{0.249}{0.99}\)
\(= 0.25 (25\%)\)

The operated slope of 25% matches the set value of 25%. This confirms correct operation of the first slope region of the differential characteristic.

12.2 Slope 2 Test (50% Slope)

12.2.1 Test Procedure

For testing the second slope region, higher currents (typically 5-6 times rated) are injected. Two test points are taken to calculate the slope using the incremental method.

12.2.2 First Test Point (5 times rated current)

12.2.3 Second Test Point (6 times rated current)

12.2.4 Slope 2 Calculation

\(\text{Slope} = \frac{(Id_2 – Id_1)}{(Ir_2 – Ir_1)}\)
\(= \frac{(3.995 – 2.998)}{(9.979 – 7.984)}\)
\(= \frac{0.997}{1.995}\)
\(= 0.499 (49.9\%)\)

The operated slope of 49.9% is very close to the set value of 50%. This confirms correct operation of the second slope region which provides increased stability during high through fault currents.

13. Harmonic Blocking Test – 2nd Harmonic

Transformer magnetizing inrush current contains high levels of second harmonic component (100 Hz for 50 Hz systems). This inrush current flows only on one side of the transformer and appears as differential current to the relay. Without harmonic blocking, the relay would trip during transformer energization.

The second harmonic blocking function measures the ratio of second harmonic current to fundamental current. If this ratio exceeds the set threshold, the differential protection is blocked.

13.1 2nd Harmonic Blocking Test Procedure

Both 50 Hz (fundamental) and 100 Hz (second harmonic) currents are injected in parallel on the HV side. The 100 Hz current is then reduced until the relay trips. The ratio at which tripping occurs indicates the operated blocking threshold.

13.2 2nd Harmonic Test Results

The relay blocks differential tripping when the second harmonic content is above 15% of fundamental. When the second harmonic drops below 14.53%, the blocking is removed and the relay trips. The operated value of 14.53% is close to the set value of 15%, confirming correct harmonic blocking operation.

14. Harmonic Blocking Test – 5th Harmonic

Fifth harmonic component (250 Hz for 50 Hz systems) is present during transformer over-excitation conditions. Over-excitation occurs when the transformer operates above rated V/Hz ratio due to overvoltage or underfrequency. The fifth harmonic blocking prevents unwanted tripping during over-excitation conditions.

14.1 5th Harmonic Blocking Test Procedure:

Both 50 Hz (fundamental) and 250 Hz (fifth harmonic) currents are injected in parallel on the HV side. The 250 Hz current is reduced until the relay trips.

14.2 5th Harmonic Test Results

The test results show the relay blocks when fifth harmonic content exceeds the set threshold of 50%. When the fifth harmonic drops below 50%, the blocking is removed and the relay trips.

15. Over-Excitation Protection Test

Over-excitation protection is an additional function in transformer differential relays. It protects against excessive magnetic flux in the transformer core due to high V/Hz conditions. The over-excitation element operates on an inverse time characteristic where higher V/Hz ratios result in faster operation.

15.1 Over-Excitation Stage-1 Test Results

The test results show good correlation between calculated and operated times. At lower voltage (79.387 V), the relay operates in 50.24 seconds. As voltage increases, the operating time decreases rapidly. At 95.265 V, the relay operates in just 1.046 seconds.

16. Additional Functional Tests

Several other tests are performed to verify complete relay functionality:

• Check of LED Indicators: All front panel LED indicators are tested to verify they illuminate correctly for different alarm and trip conditions.
• Check of Trip Relays: Trip output contacts are tested for proper operation when tripping conditions are met.
• Check of Signal Output Relays: Alarm and indication output relays are verified for correct operation.
• Check of Binary Inputs: All digital inputs for CB status, blocking signals, and other functions are tested.
• Alarm and Trip Functions: The complete logic from fault detection to output operation is verified.

17. Conclusion

Testing of differential protection relay is a mandatory activity that every protection engineer must perform with precision. The test procedures covered in this guide show how systematic testing verifies relay performance for both stability during external faults and correct operation during internal faults. From basic current measurement verification to advanced slope characteristic and harmonic blocking tests, each test serves a specific purpose in validating relay operation.

18. Frequently Asked Questions (FAQs)