End-to-end testing for line differential protection

Electrical Tester - 27 November 2020

Author: Sughosh Kuber, Relay Applications Engineer


Line differential protection is one of the most popular forms of transmission line protection. This type of protection is based on Kirchoff’s current law, which states that the current flowing into a line must be equal to the current flowing out of the line. With line differential protection, the zone of protection is defined by the location of the current transformers (CTs) monitoring the currents at each end of the line. When a fault occurs, it is essential for the protective relays at the ends of the line to communicate with each other and issue a trip signal for in-zone faults.

In Figure 1, a single line diagram shows the arrangement of line current differential relays (87L) installed at the ends of a transmission line. The relays, which are referred to as the local relay and the remote relay, monitor current from their associated CTs and communicate with each other via optical fiber cables. When a fault occurs on the line, the relays see the fault at the same time. Based on information received from the other end of the line, the relays decide what needs to be done – trip or restrain. Relay manufacturers use various methods to measure and compare currents in differential protection relays: magnitude comparison, phasor comparison, phase comparison, charge comparison, and various combinations of these. One popular method is to use the alpha-plane characteristic to determine line differential condition.

This article discusses line differential protection, the importance of end-to-end testing, and the procedure for testing alpha-plane characteristics using the end-toend test method. Specifically, testing the 87L element is considered in relation to pick-up accuracy, time of operation, dependability (by simulating internal faults) and security (by simulating external faults).


Understanding alpha-plane characteristics

When the ratio of phase currents (or sequence currents) entering or leaving a transmission line is geometrically represented on a complex plane, this constitutes the alpha-plane characteristic. Currents considered for the ratio calculation can be either monitored values of phase currents at remote and local relays, or currents calculated from equations that use real and imaginary components of the differential and restrain currents obtained from monitored phase currents. Different models of relays use different algorithms. In Figure 2, k represents the ratio of the currents.

Figure 1: Line differential protection implementation

The area of stability and trip can be determined by the characteristic parameters with which any percentage differential characteristic can be mapped onto the alpha plane. The restrain region is defined by the radius of the greater arc (R), the radius of the inner arc (1/R) and the angle (α). The radius of the greater arc and inner arc determines the radius of the restrain region (stability area) and the angle (α) represents the angular extent of the restrain region. Each phase has its own alpha-plane characteristics. In the example of Figure 1, if the A phase current monitored by the local relay is 3∠0 °, the remote relay will record 3∠180 °. The ratio of the remote current to local current will be:

On the alpha plane, this ratio will plot on the real axis to the left of the imaginary axis. As can be seen in Figure 2, this falls in the restrain region, which is also the stability area. This case can be related to nominal load condition or to an external fault, depending on the current levels.

Figure 2: Alpha plane characteristics

In the case of an internal fault, the currents read by both the relays for their respective phases tend to be in phase as they monitor the currents feeding the fault. This will plot the resultant ratio at 0 °, which falls in the trip region of the alpha-plane characteristics shown above.

The significance of end-to-end testing

End-to-end testing is the evaluation of a relay protection scheme by simulating fault conditions simultaneously at both ends of the transmission line. It is essential for the test systems at each of the lines to be synchronized so that the test currents can be injected into all of the relay terminals simultaneously. Line differential relays receive currents from their own terminals and they also receive, via various modes of communication, data about currents at the remote relay. Since the relays send time-stamped information packets to each other, even a small timing error during injection can incorrectly stamp the packets, which can cause incorrect or unintended operation.

To avoid this, a time signal from a Global Positioning System (GPS) clock is used to synchronize the test systems at each end of the line. Time signals are available in various forms such as pulse per second (1 PPS), IRIG-B, Precision time protocol (PTP), etc. In this article, only the IRIG-B time sync standard is considered. The endto- end testing method requires two sets of relay test equipment with the ability to decode IRIG-B signal so that the injection of analogue signals can be triggered simultaneously in both sets of equipment. (See Figure 3).

Figure 3: End-to-end testing: the whole picture

The IRIG-B signal from the GPS receiver, with its associated antenna, is also made available to the relays under test. This type of testing is used to evaluate new protection schemes during substation commissioning, troubleshoot malfunctioning relays, verify relay setting changes, and for other purposes.

The items needed to perform end-to-end tests include:

  • Two sets of relay test equipment with the ability to decode IRIG-B signals and generate currents with the magnitudes and phase angles specified in the test plan
  • GPS receivers
  • Co-axial cables (to connect GPS receiver and relay test sets and relays)
  • Two computers (to drive the relay test sets at respective substations)
  • A means of communication between the test technicians (cell phones or other voice communication equipment)
  • Test software with pre-built test plans

When implemented correctly, communication-based protection schemes provide more efficient and more reliable protection for transmission lines than schemes based on multiple relays that do not communicate with each other. And, while it is undoubtedly simpler to test individual relays in a scheme, it is better to test the entire scheme as a whole as this not only validates the individual components, but also the communication system.


Test procedure

A test set up can be arranged to simulate a system similar to that shown in Figure 3. IRIG-B signals should be provided to the appropriate inputs of the relay test equipment and to the relays under test. Test connections to inject analogue signals into the relays should be made at both ends. Spare output contacts on both the relays should be programmed for 87L element. Phase differential pick-up tests, radius check tests, angular extent boundary tests and timing tests for an internal fault will be discussed. For the purposes of this article, the protection relay is a type having an algorithm that works with currents derived from calculations that use the real and imaginary parts of differential and restrain currents obtained from monitored phase currents.


Relay settings

Phase Differential Element Pick-up: 0.72 pu

Phase Differential Element Radius ( R ): 6

Phase Differential Element Block Angle ( α ): 195 °

Phase differential pick-up test

The phase differential pick-up test validates the 87L logic and pick-up setting when the injected current is above the pick-up setting. This test can be performed on each phase at each end separately and does not need the time synchronization. Based on a relay setting of 0.72 pu and a nominal current of 5 A, the calculated pick-up value is 3.6 A. Therefore, the 87L element should pick up at 3.6 A. 

Figure 4: Alpha plane characteristic plot: inner arc radius test


Radius check test

The radius check test is performed to validate the boundary of the restrain region in the alpha plane with respect to the radius from origin. Initially, the test should be conducted to verify the radius setting pick-up of the inner arc of the restrain region. The distance from the origin to the inner arc of the restrain region is defined by 1/R as shown in Figure 2. Based on the relay settings, 1/R = 1/6 = 0.16. Once the test sets are synchronized during pre-fault, the test values should be varied during the fault state. The test value at which the 87L element trips should be 0.80∠0 ° amps. This value translates to 0.16 pu distance from the origin to the inner arc. In Figure 4, to validate the 1/R setting, the alpha-plane characteristic shows the changes in the complex ratio plot as the test current is varied. Table 1 lists the phase A currents to be injected into the local and remote relays in the pre-fault and fault states. Based on the currents injected, the relays use differential and restrained equations to calculate derived currents, and the ratio of these derived currents is plotted on alpha plane to define the 87L element operation.


After validating the 1/R setting, the next test verifies the radius setting of the outer arc of the restrain region. In Figure 2, this radius setting is shown as R. To verify the R setting, the same pre-fault values as before are injected. However, the fault state currents on local relay are varied up to 30 A. This is equivalent to 6 pu, the radius of the restrain region. As soon as the current is increased to more than 30 A, the complex ratio on the alpha plane crosses the restrain region and the relay should trip. The test procedure described is for the A phase, but the same procedure is followed to test the B and C phases.

Angular extent boundary check test 

This test is performed to validate the angular extent of the restrain region on the alpha plane. The angular extent setting is shown as α in Figure 2. The α setting of the relay under test in this example is 195 °. Therefore, prefault current injection with phase angle ∠0 ° on the local relay and ∠180 ° on the remote relay should be done. In the fault state, the phase angle of the analogue currents to the local relay should be varied in a counterclockwise direction. The relay should trip at a phase angle of 98 °.

In Figure 5, the alpha-plane characteristic shows changes in complex ratio plot based on the phase angle variation. This validates the angular extent of restrain region. The next test should be performed to validate the angular extent in the opposite direction from origin. The phase angle in fault state should be varied in a clockwise direction for the local relay. The relays should trip at a value of -98 °. The difference of angular extents between first and second test is 98 °- (-98 °) = 196 °. This result closely corresponds to the angular extent setting of the relay (195 °). The test procedure described above is for A phase, but the same procedure is used for the B and C phases.

Figure 5: Alpha plane characteristic plot: angular extent boundary check test

Timing test (for an internal fault)

An internal fault can be simulated to carry out a timing test on the 87L element. Pre-fault and fault states are set up with the values shown in Table 5. Ideally, the local relay and remote relays should trip within a cycle of seeing an internal fault. In Figure 6, the alpha-plane characteristic shows the path of complex ratio plot transitioning from the restrain region to the operate region based on current injection switching from the prefault to the fault state.

Figure 6: Alpha plane characteristic plot - internal fault timing test

A similar setup of pre-fault and fault states can be used to simulate external fault currents. The relays should restrain from tripping, as the complex ratio of the currents plots on to the restrain region of the alpha plane.

Relays may also have settings enabled for 87L negative sequence and 87L zero sequence elements to provide protection for single line-to-ground faults and unbalanced fault conditions. The tests discussed for phase elements in this article should also be performed to validate the negative sequence and zero sequence elements.



The vast majority of utilities all over the world implement line differential protection. It is important to validate the protection scheme for correct operation under fault conditions. End-to-end testing validates the entire communication-based protection scheme, including the operation of the relays as well as the communication between the relays. Knowledge of end-to-end test methods and field experience help technicians carry out testing more efficiently. This article has provided an insight into the testing of line differential protection using the end-to-end test method, as well as the testing of alpha-plane characteristics to validate the line differential element with pick-up, radius and angular-extent tests.