Ground-fault voltage protection is often described using several
overlapping terms: 59N, 59G, 64, neutral overvoltage, neutral
displacement, residual voltage, zero-sequence voltage, open delta, and
broken delta. The confusion begins when an ANSI function number
is treated as if it defined the relay’s physical input.
It does not.
The most important distinction is the measurement
path:
- The relay can calculate residual voltage from three phase-to-ground
voltages. - The relay can measure residual voltage directly from a broken-delta
VT circuit or a neutral-to-ground VT.
Both methods may respond to the same earth fault, but their wiring,
scaling, supervision, and failure modes are different. Depending on the
relay manufacturer, either method may be assigned to an element labelled
59N, 59G, 64, residual overvoltage, or neutral displacement. The relay
manual and input-assignment diagram therefore take precedence over the
ANSI label.
Short answer
- 59N normally means neutral or residual overvoltage
protection. It operates when the magnitude of a neutral-related voltage
exceeds a setting. - 64 is a broad ground-detection designation. In many
applications, a voltage-operated 64 element uses a directly measured
neutral or residual voltage, but 64 is not universally limited to one
measurement principle. - Calculated residual voltage is obtained internally
as VA + VB + VC = 3V0 and requires three valid
phase-to-ground voltage inputs. - Broken-delta voltage is formed physically by the VT
secondary windings and is connected to a suitable relay voltage
input. - A broken-delta input is not inherently “59N” or “64.” Its function
depends on how the specific relay maps the analogue input to its
protection elements. - Neither a basic 59N nor a basic voltage-operated 64 element is
directional. Directional earth-fault protection normally requires
current and a polarising quantity.
1. The electrical
quantity behind both methods
For the three phase-to-ground voltage phasors VA, VB, and VC, the
zero-sequence voltage is:
V0 = (VA + VB + VC) / 3
The residual voltage is:
3V0 = VA + VB + VC
In a balanced system, the three phase-to-ground voltage phasors are
displaced by 120 degrees and their vector sum is approximately zero. An
earth fault or neutral displacement introduces zero-sequence voltage, so
the vector sum increases.
The word phasor is essential. The relay does not add
three RMS magnitudes:
|VA + VB + VC| is not equal to |VA| + |VB| +
|VC|
A numerical relay normally samples the voltage waveforms, extracts
the fundamental-frequency phasors, calculates their complex vector sum,
and compares the magnitude with the pickup setting.
V0 and 3V0 are not
interchangeable
Some relays display or set the element in V0, while others use 3V0.
This creates a possible factor-of-three error:
3V0 = 3 × V0
Before calculating any setting, confirm whether the relay parameter
represents:
- V0;
- 3V0;
- raw broken-delta secondary voltage;
- a primary-referred value; or
- a per-unit value.
2.
Method A: residual voltage calculated from three phase voltages
The signal path is:
Three phase-to-ground VT inputs → phasor extraction → VA + VB
+ VC → overvoltage pickup → timer → alarm or trip
The operating quantity is normally:
Ures,calc = |VA + VB + VC| = |3V0|
What is required?
- Three phase-to-ground voltage inputs, not merely two phase-to-phase
voltages. - Correct VT ratio and nominal secondary-voltage configuration.
- Correct phase identification, phase sequence, and polarity.
- A valid neutral reference and correct secondary grounding.
- Healthy VT circuits on all three phases.
- VT fuse-failure or secondary-MCB supervision where practical.
- A pickup setting above the maximum standing residual voltage in the
healthy system.
No dedicated residual-voltage winding is required for this method.
The same three voltage inputs can also support metering, undervoltage,
overvoltage, negative-sequence voltage, synchronism-check, and other
functions.
Why two
line-to-line voltages are insufficient
Zero-sequence voltage is common to all three phase-to-ground voltages
and cancels in a line-voltage subtraction:
VAB = VA − VB
Therefore, true 3V0 cannot be reconstructed from VAB and VBC alone. A
relay may offer a model-specific estimation method using current and
system impedance, but that is an estimated quantity rather than an
independent residual-voltage measurement.
Advantages
- No separate broken-delta wiring or residual-voltage input is
needed. - Individual phase voltages remain available in metering and
disturbance records. - The three phase-voltage channels can be supervised
individually. - One VT set can support several protection and control
functions.
Limitations
- Small VT ratio and phase-angle errors are added as a residual
quantity. - A blown fuse, open circuit, or incorrect phase connection can create
false residual voltage. - The result depends on all three voltage channels being healthy.
- It cannot be derived directly from a two-VT V–V connection.
3.
Method B: residual voltage measured from a broken delta
A broken-delta circuit uses residual-voltage windings from three VTs.
The windings are connected in series with one corner left open, and the
voltage across the open terminals is proportional to the phasor sum of
the three secondary voltages.
The signal path is:
Residual VT windings → broken-delta output → dedicated relay
voltage input → overvoltage pickup → timer → alarm or trip
The measured quantity is:
Ures,meas = |Ubroken-delta|, proportional to
|3V0|
In a healthy balanced system, the three residual-winding voltages
largely cancel. During an earth fault, the broken-delta output
rises.
Open
delta and broken delta: an important terminology warning
“Open delta” is sometimes used for two different circuits:
- A two-VT V–V connection used to obtain
phase-to-phase voltages. - A three-winding residual or broken-delta connection
used to obtain voltage proportional to 3V0.
These circuits are not functionally equivalent. A two-VT V–V
connection does not provide a true zero-sequence-voltage measurement. In
this article, broken delta means the residual-voltage
connection in item 2.
What is required?
- VTs with suitable residual-voltage windings or another approved
residual-voltage arrangement. - Correct series connection and polarity of all residual
windings. - A relay voltage input suitable for the expected broken-delta
voltage. - Correct residual-winding ratio and relay input scaling.
- Confirmation that maximum earth-fault voltage remains within the
relay input rating. - Secondary fuse or MCB protection and suitable circuit
supervision. - A damping or stabilising resistor when required by the VT
manufacturer or ferroresonance study. - End-to-end commissioning from the VT terminals to the relay
logic.
Advantages
- Residual voltage is formed directly by the VT circuit instead of
being calculated from three relay channels. - The residual winding can be designed specifically for earth-fault
detection. - The residual-voltage phasor can often be used as a polarising
quantity for directional earth-fault protection. - It remains available even when the relay has no three
phase-to-ground voltage channels, provided a compatible residual input
exists.
Limitations
- Additional VT windings, wiring, protection, and a relay voltage
input are required. - Incorrect polarity can reduce the output or reverse its angle.
- An open secondary circuit may make the protection insensitive during
a real fault. - A fuse failure or wiring defect can generate false residual
voltage. - Ferroresonance and resistor thermal duty must be considered.
4. What do 59N and 64
actually mean?
59N
ANSI 59 is an overvoltage function. The suffix N is commonly used for
a neutral-related quantity. A 59N element therefore normally operates
when neutral or residual voltage exceeds its setting.
However, the designation alone does not tell us whether the relay
obtains that voltage by:
- calculating VA + VB + VC;
- measuring a broken-delta input;
- measuring voltage between a machine or transformer neutral and
ground; or - receiving a calculated value through another internal or digital
signal path.
64
ANSI 64 is a ground detector. Its implementation is
application-dependent and can include voltage-based or other
ground-detection principles. Suffixes and manufacturer terminology may
further distinguish stator ground, rotor ground, restricted earth fault,
neutral displacement, or other schemes.
For this reason, it is unsafe to assume that every 64 element is a
broken-delta overvoltage element. When a relay offers a voltage-operated
64 stage supplied from a residual or neutral-voltage input, its
behaviour may resemble 59N, but its actual input and algorithm must
still be checked.
5. Practical comparison
| Engineering question | Calculated residual-voltage element | Direct residual-voltage element |
|---|---|---|
| Typical labels | 59N, 59G, residual overvoltage | 59N, 59G, 64, ground overvoltage |
| Measured quantity | Internally calculated 3V0 | Physical residual or neutral voltage input |
| Where 3V0 is formed | Relay software | VT secondary circuit |
| Required analogue inputs | VA, VB, and VC phase-to-ground | One suitable residual-voltage input |
| Broken-delta VT required | No | Yes, when broken delta is the selected source |
| CT required for basic overvoltage operation | No | No |
| Main scaling risk | V0 versus 3V0 and phase-VT ratio | Residual-winding ratio and raw input voltage |
| Main wiring risk | Missing phase, fuse failure, phase or polarity error | Series polarity, open circuit, fuse failure |
| Directional by itself | No | No |
The table compares the measurement methods, not
universal ANSI definitions. The exact relay logic may use different
labels.
6. Influence of system
grounding
The usefulness and expected magnitude of residual voltage depend
strongly on the grounding method.
Solidly grounded systems
Earth-fault current is normally high, so overcurrent and differential
protection are usually the principal fault-clearing methods. Residual
overvoltage may be used for supervision, backup, or special zones.
Resistance-grounded systems
Residual voltage can provide sensitive detection of earth faults,
while the grounding resistor limits fault current. Settings must
coordinate with the neutral-grounding resistor protection and feeder
earth-fault elements.
Isolated-neutral systems
During a single earth fault, the neutral shifts and the healthy
phase-to-ground voltages rise. Residual overvoltage is effective for
detecting the presence of a fault, but a non-directional element
generally cannot identify the faulty feeder.
Resonant-grounded systems
Fault current may be very small because a Petersen coil compensates
the network capacitive current. Residual voltage is useful for fault
detection, but feeder selection may require sensitive directional
wattmetric, admittance, transient, or other specialised earth-fault
functions.
7. How to
calculate and select the pickup setting
There is no universal percentage suitable for every installation. The
setting must satisfy both security and sensitivity:
Maximum healthy residual voltage + margin < pickup <
minimum target-fault residual voltage − margin
Use the following process:
- Identify the exact relay operating quantity: V0, 3V0, raw secondary
voltage, primary voltage, or per unit. - Confirm which analogue inputs or calculated signals feed the
element. - Establish the applicable VT ratios separately for the phase-voltage
and residual-winding circuits. - Measure or estimate the maximum healthy residual voltage, including
VT errors and normal system unbalance. - Calculate the minimum residual voltage for the highest-resistance or
most remote fault that must be detected. - Add security margin for measurement tolerance, frequency variation,
harmonics, and transient conditions. - Select the delay according to whether the function provides an
alarm, primary trip, or time-coordinated backup trip. - Define blocking for VT fuse failure, open secondary MCBs,
maintenance, and invalid measurement conditions.
Scaling the calculated
method
If the phase-to-ground VT ratio is:
nP = primary phase-to-ground voltage / secondary
phase-to-ground voltage
then:
3V0(primary) = nP × 3V0(secondary calculated)
Scaling the broken-delta
method
The broken-delta conversion must be taken from the residual-winding
nameplate data and connection diagram. Do not automatically apply the
normal phase-VT ratio: residual windings are frequently specified with a
different secondary voltage.
8. Numerical example
Assume the relay receives three phase-to-ground voltages containing a
zero-sequence component:
V0 = 8∠30° V secondary
The calculated residual voltage is:
3V0 = 24∠30° V secondary
A calculated residual-overvoltage element therefore measures 24
V.
Assume the broken-delta VT circuit is designed so that the same
primary-system condition produces 24 V at the relay residual-voltage
input. A directly measured element also sees 24 V. With a 20 V pickup,
both elements start.
The two raw readings will only be equal if their scaling is
equivalent. In practice, compare them on a common primary 3V0 or
per-unit base.
9. When directional
protection is required
59N and voltage-operated 64 elements normally indicate that an earth
fault or neutral displacement exists, but they do not determine the
fault direction.
In systems with several feeders, ring operation, parallel sources,
distributed generation, isolated neutrals, or resonant grounding,
selectivity may require a directional earth-fault element such as 67N or
67G. Directional operation requires:
- a suitable residual or zero-sequence current quantity;
- a valid polarising voltage, often 3V0 from a calculated or
broken-delta source; - correct current and voltage polarity;
- a defined characteristic angle or directional method; and
- commissioning tests that verify both magnitude and angle.
Connecting a broken-delta voltage to a relay does not by itself make
the protection directional.
10. Commissioning tests
Calculated 3V0 path
- Apply balanced nominal three-phase voltages and verify that
calculated 3V0 is close to zero. - Add the same in-phase zero-sequence component to all three voltage
inputs and verify the expected factor of three. - Test pickup, reset ratio, operating time, and every enabled
stage. - Simulate each VT fuse or secondary-MCB failure and verify alarm or
blocking logic. - Confirm phase sequence, phase labels, VT ratio, event records, and
oscillography.
Broken-delta path
- Inject voltage directly into the residual-voltage input and test
pickup, reset, and timing. - Verify continuity from the VT terminal box to the relay.
- Check the polarity and series connection of all residual
windings. - Confirm the residual-winding ratio and relay scaling.
- Test the fuse or MCB supervision logic.
- Verify any damping resistor value, connection point, voltage rating,
and thermal rating. - If the voltage polarises a directional element, test the operating
and restraining directions.
Cross-checking both methods
When calculated and directly measured residual voltages are both
available, compare them after conversion to a common base:
Mismatch = |3V0(calculated) − K × Ubroken-delta|
An abnormal mismatch can indicate a ratio error, polarity error,
blown fuse, broken wire, or failed voltage channel. The conversion
factor K and the permitted tolerance must be established from the VT
ratios and accuracy classes.
11. Common engineering
mistakes
- Assuming every 59N element uses calculated VA + VB + VC.
- Assuming every broken-delta input belongs to a 64 element.
- Treating ANSI 64 as a universal definition of voltage-operated
ground protection. - Confusing V0 and 3V0 and creating a factor-of-three setting
error. - Adding RMS magnitudes instead of voltage phasors.
- Expecting true 3V0 from a two-VT V–V connection.
- Applying the normal phase-VT ratio to a residual winding without
checking its nameplate. - Entering a primary value into a setting expressed in secondary
volts. - Ignoring VT fuse failure, an open residual circuit, or loss of a
relay voltage channel. - Assuming residual overvoltage is feeder-selective or
directional. - Selecting a damping resistor without VT-manufacturer data and system
studies.
12. Selection guide
Use a calculated residual-voltage element when three
reliable phase-to-ground voltage inputs already exist, the relay
calculation is fully documented, and eliminating additional residual
wiring is desirable.
Use a direct broken-delta measurement when a
dedicated residual winding is provided, the relay has a compatible
input, direct residual measurement is required, or the voltage will also
be used as a polarising quantity.
Use both methods when independent measurement paths,
cross-supervision, or enhanced diagnostics justify the additional
equipment. Remember that two paths using the same primary VT set are not
fully independent.
Use a directional earth-fault function when the
protection must identify the faulty feeder or fault direction rather
than merely detect neutral displacement.
Conclusion
59N and 64 cannot be compared reliably by ANSI number alone. The
decisive questions are:
- What electrical quantity does the element use?
- Is residual voltage calculated inside the relay or measured from a
physical input? - Does the relay work with V0, 3V0, or raw broken-delta voltage?
- Which VT ratio applies?
- How are voltage-circuit failures supervised?
- Is simple fault detection sufficient, or is directional selectivity
required?
Calculated residual voltage and broken-delta voltage are two valid
methods of observing zero-sequence voltage. Their power-system meaning
may be similar, but their measurement paths and engineering requirements
are different. Always verify the relay manual, input matrix, VT
nameplate, wiring diagram, grounding study, and protection-coordination
report before selecting the function and its settings.
References
- IEEE
C37.2-2022 – Device Function Numbers, Acronyms, and Contact
Designations. - IEC 60255-127
– Functional requirements for over/undervoltage protection. - SEL – Protection for
Unexpected Delta Sources, including broken-delta 3V0 and
voltage-circuit supervision considerations. - SEL – Automatic
Reconfiguration of Zones for Three-Phase and Spare Transformer
Banks, including comparison of calculated and broken-delta 3V0. - ABB
– SafePlus 36 Product Catalogue, residual-winding ratios and
damping-resistor application.