Cable Differential Protection (87L): Design, Settings, Communications and Testing

Cable differential protection is one of the most selective ways to
protect a medium-voltage cable. It compares the current entering the
cable with the current leaving it and trips when the difference
indicates a fault inside the CT-defined zone. The principle is simple; a
dependable scheme is not. CT performance, channel behaviour, cable
charging current, terminal configuration and trip logic all affect
security and sensitivity.

Core principle: 87L protects a zone, not merely a
length of cable. The zone begins at the current transformers at one
terminal and ends at the current transformers at the other. Every cable
termination, joint, earthing lead, reactor, transformer and tee must be
deliberately placed inside or outside that zone.

This guide covers the design inputs, relay characteristic,
communications, settings, trip matrix and end-to-end tests needed for a
practical line-current-differential scheme.

1. Where cable
differential protection fits

An 87L scheme is especially attractive when:

• fast, unit protection is required over the whole cable length;
• fault-current direction or magnitude changes with network
  topology;
• converter-based generation makes conventional overcurrent grading
  difficult;
• both cable ends have circuit breakers and numerical relays;
• pilot protection is already justified by system importance;
• distance protection would have a very short reach or would be
  affected by cable parameters, fault resistance or infeed.

Unlike a time-graded 50/51 element, 87L does not have to wait for a
downstream delay. Unlike a distance element, it does not estimate
impedance to a fault. Correctly applied, it can trip both cable ends
rapidly for an internal fault and remain stable for through-fault
current.

It should still be backed up. Local phase and earth overcurrent,
directional earth fault, breaker failure and a communications-failure
strategy remain necessary.

2. The differential
measuring principle

Relay currents are referred to a common base and assigned a polarity
pointing into the protected zone. A simplified two-terminal phase
calculation is:

I_operate = |I_L +
I_R|

I_restraint = (|I_L| + |I_R|) /
2

For normal load and an external fault, one terminal current enters
the zone and the other leaves it. After polarity alignment, their sum is
approximately zero. For an internal fault, currents flow into the zone
from one or both terminals and the operate quantity rises.

Modern relays may use alpha-plane comparison, multiple slopes, phase
and sequence quantities, adaptive restraint or proprietary
charging-current compensation. The equations above explain the concept;
they are not a substitute for the selected relay’s exact
characteristic.

Why percentage restraint
is necessary

The two measured currents are never perfectly equal. Error comes from
CT ratio and phase error, relay input accuracy, channel alignment,
unequal CT saturation, analogue filtering and cable charging current. A
biased characteristic permits more differential current as through
current increases.

A generic two-slope characteristic may be visualised as:

Trip when I_operate > I_minimum +
Slope × I_restraint

Many relays implement the slopes piecewise and add an unrestrained
high-set stage. Use the manufacturer’s curve, definitions and base
quantities when proving any setting.

3. Information required
before design

Collect and freeze the following before setting the relay:

• single-line diagram and exact CT locations at every terminal;
• cable conductor size, construction, length and
  positive-/zero-sequence parameters;
• calculated steady-state and switching charging current;
• sheath bonding, single-point bonding or cross-bonding
  arrangement;
• maximum load, overload and emergency transfer current;
• minimum and maximum internal fault current;
• maximum external through-fault current and X/R ratio;
• number of line terminals and any tapped load or embedded
  generation;
• CT ratios, classes, knee-point data, secondary burden and lead
  resistance;
• relay sampling, time-synchronisation and channel requirements;
• available direct fibre, multiplexed, Ethernet or pilot-wire
  path;
• breaker operating times, intertripping requirements and
  breaker-failure clearing paths;
• auto-reclose philosophy, which is normally restrictive for
  underground cable faults.

If a transformer, series reactor or grounding transformer lies
between the terminal CTs, confirm that the relay can compensate its
ratio, vector group, zero-sequence behaviour and inrush—or move the zone
boundary.

4. CT selection and
circuit integrity

Differential security depends on the pair of CT systems, not on
either CT in isolation.

Ratio and phase matching

Numerical relays can compensate different CT ratios, but avoid
unnecessary mismatch. Enter primary and secondary ratings exactly and
check whether the relay normalises to nominal current, rated current or
a user-defined reference. Polarity must be proved from the primary
conductor through every terminal block to the relay.

Saturation during external
faults

The most demanding stability case is commonly a high-current external
fault where one CT saturates more than the other. The study should
include:

• symmetrical and asymmetrical fault current;
• system X/R and remanent flux assumption;
• CT knee voltage or class data;
• secondary winding resistance;
• relay and lead burden;
• fault duration until primary protection clears.

Increasing slope is not the only remedy for a weak CT. A higher-ratio
or higher-performance CT, shorter/heavier secondary wiring, adaptive
saturation logic or a separate protection core may provide better
sensitivity and security.

CT secondary supervision

An open CT circuit is hazardous and can imitate differential current.
Use shorting-type test blocks, single-point secondary earthing and relay
CT-circuit supervision where available. Route the two end systems
independently so one wiring error cannot affect both measurements.

5. Cable charging current

A cable draws capacitive current even when no load is connected.
Because each relay measures its local terminal current, the charging
current can appear in the differential quantity. Its importance
increases with voltage, cable length and capacitance.

For one phase, a simplified steady-state estimate is:

I_charging = 2πfCV_phase

where C is the total phase-to-earth capacitance
represented by the model. Use the cable manufacturer’s data or a
validated study for actual settings.

Available remedies include:

• selecting minimum pickup above the worst uncompensated charging
  spill plus error margin;
• enabling the relay’s charging-current compensation;
• using positive-sequence or phase-segregated algorithms as provided
  by the relay;
• checking energisation and de-energisation transients
  explicitly.

Do not enable compensation without confirming the capacitance units,
reference voltage and status logic. A tenfold data-entry error can make
the scheme less secure than leaving compensation disabled.

6.
Communications are part of the protection system

The current vectors or processed comparison quantities must arrive
within the relay’s permitted delay and asymmetry. Therefore the
communications path is a protection component with its own design,
supervision and tests.

Common channel arrangements

• dedicated point-to-point fibre;
• IEEE C37.94 or other relay interface through telecom equipment;
• synchronous digital hierarchy or packet transport engineered for
  protection;
• Ethernet channels supported by the relay, possibly with PRP/HSR
  redundancy;
• legacy pilot wire for compatible schemes.

The relay supplier should state permitted latency, latency variation,
asymmetry, bit-error behaviour and recovery time. Confirm what happens
during route switching and whether the network can introduce unequal
forward and reverse delay.

Channel failure philosophy

On loss or degradation of the differential channel, a typical scheme
will:

1. block 87L before stale or misaligned data can cause a trip;
2. raise a high-priority alarm with channel identity;
3. retain independent local backup protection;
4. change to an approved permissive or directional scheme only if that
   mode has been designed and tested;
5. record the event and channel statistics.

Automatic fallback must never be assumed. It is relay- and
design-specific.

Time synchronisation used for event records is not necessarily the
same mechanism used for differential alignment. Confirm whether the
algorithm relies on channel echo timing, PTP, IRIG-B, GNSS or an
internal method and test the actual architecture.

7. Special applications

Multi-terminal cables

A tee with three or more sources requires a relay designed for the
required number of terminals and a communications topology that remains
available after a single failure. All terminal currents must be aligned
and included in the operate and restraint quantities. A hidden tapped
load outside the calculation becomes permanent spill current.

In-zone transformer

Where supported, the scheme must compensate transformer ratio and
phase shift and manage zero-sequence current. Magnetising inrush and
overexcitation restraint or blocking may also be required. Treat this as
transformer differential applied through a communications-assisted zone,
not as an ordinary two-end cable setting.

Sheaths and screens

Sheath current is not normally measured by phase CTs, but sheath
bonding affects zero-sequence network behaviour and fault distribution.
Ground CT placement must avoid unintentionally including parallel sheath
return current in one terminal but not the other. Review cross-bonding
boxes and sheath-voltage limiters in the earth-fault study.

One-end-fed operation

An internal fault may be fed from only one end. The differential
scheme should still see the local contribution and the remote current
near zero. Check minimum source strength, converter current limiting and
the relay’s minimum operate threshold.

8. Worked two-terminal
example

Consider a 33 kV, 20 km cable with 800/1 A CTs at both ends and a
normal load of 450 A. The following values are deliberately simplified
and use a common per-unit base after polarity and ratio
compensation.

Normal load

Assume the local relay receives:

• left current: +0.563 pu;
• right current, aligned into the zone: −0.550
  pu.

Then:

I_operate = |0.563 − 0.550| = 0.013 pu

I_restraint = (0.563 + 0.550) / 2 = 0.557
pu

The small operate current represents combined measurement and
charging-current spill. It should remain below the characteristic with
margin.

Internal three-phase fault

Assume both systems feed a fault inside the CT zone:

• left current: +2.40 pu;
• right current: +1.80 pu.

Then:

I_operate = |2.40 + 1.80| = 4.20 pu

I_restraint = (2.40 + 1.80) / 2 = 2.10
pu

The operating point should be well inside the trip region.

What the example does not
prove

These two points do not establish a setting. A study must also test
minimum internal earth and phase faults, maximum load plus charging
current, single-end infeed, CT errors, transformer inrush where
applicable, and the worst external fault with severe CT saturation. Plot
every case on the manufacturer’s actual characteristic.

9. Setting workflow

Use the following sequence:

1. Define the zone. Mark every CT and breaker on the
   single-line and identify all in-zone plant.
2. Choose common bases. Enter CT ratios, nominal
   frequency and phase rotation; verify terminal naming and polarity.
3. Calculate standing spill. Include CT accuracy,
   ratio mismatch, cable charging current and maximum load.
4. Set minimum pickup. Place it above credible
   standing and transient spill with a documented margin, while retaining
   sensitivity to the minimum internal fault.
5. Set restraint slopes. Prove stability for the
   maximum external fault and CT saturation using the relay-specific
   algorithm.
6. Review high-set operation. If an unrestrained stage
   is used, secure it against CT saturation and energisation
   transients.
7. Configure channel supervision. Define alarm delay,
   blocking, fallback mode and restoration behaviour.
8. Coordinate backup. Grade local 50/51, 50N/51N,
   67/67N or 21 elements with adjacent protection.
9. Build trip logic. Trip both required ends, initiate
   local breaker failure and transfer trip where necessary.
10. Document evidence. Record study cases, relay
    equations, firmware, settings file checksum and test tolerances.

10. Example trip and alarm
matrix

Initiating condition	Local breaker	Remote breaker	Lockout	Auto-reclose	Alarm/record
87L internal fault	Trip	Trip	Normally yes	Normally block for cable fault	Yes
Local backup phase/earth fault	Trip	Per coordination/intertrip design	Project-specific	Usually block if cable fault inferred	Yes
Communications channel failed	No immediate trip	No immediate trip	No	Block or constrain as designed	High priority
CT circuit supervision operated	Block affected 87L channel/terminal as designed	No direct trip	No	Review scheme availability	High priority
Local breaker failure after 87L	Re-trip	Transfer trip if needed	Yes	Block	Yes
Relay hardware failure	No protection trip unless failsafe design says otherwise	No	No	Scheme-specific	High priority

The actual matrix must include disconnectors, bypass arrangements,
bus couplers, maintenance states and every terminal.

11. FAT and configuration
checks

Factory testing should prove more than a pickup number:

• settings-file version, logic diagrams and terminal names;
• CT ratio and phase-rotation compensation;
• through-current stability at several restraint levels;
• internal phase and earth faults at several locations/infeeds;
• operating and restraining characteristic boundary points;
• external fault with simulated CT saturation;
• cable charging-current compensation and energisation logic;
• channel latency, asymmetry, interruption, error and recovery;
• terminal data mismatch and swapped communications channels;
• trip to both terminals and correct breaker-failure initiation;
• fallback and blocking behaviour after channel loss;
• SOE, disturbance records, time stamps, IEC 61850 GOOSE and SCADA
  indications;
• setting-group change and maintenance/bypass logic.

12. SAT and end-to-end
commissioning

The most valuable commissioning test injects all line terminals
synchronously. GPS- or PTP-synchronised test sets can create realistic
through faults and internal faults while the actual communications
network is in service.

A minimum SAT programme should include:

1. primary CT ratio and polarity checks at every end;
2. end-to-end phase identification and phase rotation;
3. secondary burden and CT-earthing inspection;
4. synchronized load/current stability test;
5. synchronized internal and external phase-fault tests;
6. internal and external earth-fault tests, including weak infeed;
7. maximum expected channel delay and planned route switchover;
8. loss of each channel, power supply and time source;
9. actual trip of every breaker, including remote transfer trip;
10. breaker-failure timer and upstream clearing output;
11. SCADA, alarms, event reports and disturbance retrieval;
12. as-left settings and comparison with approved files.

For new cables, compare measured steady-state charging current and
phase angle with the study once energised. Investigate a significant
mismatch before lowering pickup.

13. Common engineering
mistakes

• Reversing one CT polarity and trying to correct it by raising
  pickup.
• Treating a telecom path as ideal without testing delay asymmetry and
  failover.
• Ignoring cable charging current because the load current is much
  larger.
• Applying a two-terminal relay to a tee or tapped load not included
  in the current sum.
• Selecting slopes from another relay whose restraint definition is
  different.
• Proving internal faults but not the severe
  external-fault/CT-saturation case.
• Forgetting that a remote breaker must also trip and initiate its own
  breaker-failure logic.
• Allowing auto-reclose after a confirmed underground-cable
  differential trip without an explicit policy.
• Using event-record synchronisation as proof of differential-channel
  timing.
• Completing relay secondary injection but omitting synchronized
  end-to-end tests.

14. Design review checklist

Before issue for construction, verify that the package states:

• exact CT-to-CT zone and terminal count;
• CT data and worst through-fault performance;
• cable charging-current calculation and compensation data;
• relay operate/restraint equations and setting base;
• channel type, routing, latency budget, redundancy and failure
  response;
• trip, intertrip, breaker-failure and reclose matrix;
• backup protection during planned or unplanned channel outage;
• cyber, access-control and configuration-management
  requirements;
• FAT, synchronized end-to-end SAT and periodic maintenance
  tests.

Conclusion

Cable differential protection delivers fast and highly selective
clearing only when the complete measuring chain is engineered as one
system. The CTs define the zone, the communications path transports the
comparison, and the relay characteristic must tolerate charging current
and measurement error without losing minimum-fault sensitivity. A
synchronized end-to-end test is the final proof that all three parts
work together.

Authoritative
references and further reading

• IEC 60255-187-3, Functional
  requirements for biased differential protection of transmission
  lines
• ABB
  RED615 line differential protection and control
• Hitachi
  Energy RED670 line differential protection
• Siemens
  SIPROTEC 7SD82 line differential protection
• SEL-411L Advanced Line
  Differential Protection, Automation, and Control System

Application note: Relay algorithms, channel limits
and terminology vary by manufacturer and firmware. Verify every
equation, data unit, timer and test tolerance against the exact relay
manual and approved protection study.

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