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Neutral Grounding Resistor Sizing: Current, Rating and Detection

Size an NGR from fault current or assess an existing resistor. Check 3·I_c0, hot-current detection, short-time energy and relay grading—and compare with 400 A.

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Published 29. October 2026 · version 3 of 6. November 2026

#fault detection #IEEE 142-2007 #IEEE 242-2001 #medium voltage #NGR #protection coordination #resistance grounding

Size a neutral grounding resistor for a medium-voltage, three-phase system and examine the protection consequences of reducing the ground fault current. This NGR sizing calculator is for power engineers, students and engineers comparing resistance-grounding options. It calculates the resistor value, neutral voltage duty, power and short-time energy, then checks the charging-current and relay-sensitivity constraints entered by the user.

Start with the line-to-line RMS voltage. Enter the total phase-to-ground capacitance of the connected network per phase, or switch to a known per-phase charging current. Include cables, connected machines, surge capacitors and other relevant equipment in the largest credible operating configuration. A measured system ground charging current is normally 3·I_c0, so divide that total by three before entering it as I_c0.

Choose a target NGR let-through current or enter an existing resistor resistance. The target is the resistive current component at full phase voltage, rather than the magnitude of the complete ground fault current. The calculator also reports the total bolted-fault magnitude, with capacitive and resistive components combined in quadrature. Enter the manufacturer's hot-to-cold resistance ratio: heating can reduce the fault current and make detection less dependable.

For the protection screen, enter the sensing CT ratio and relay pickup in secondary amperes. The minimum-fault fraction represents a separately studied reduction due to fault resistance or winding location. The minimum fault current must be strictly above pickup: equality is a theoretical boundary, and an inverse-time relay has no finite operating time there. Provide operating margin and check pickup against the largest healthy-feeder residual or spill current. Core-balance CTs, residually connected phase CTs, bus differential and transformer ground differential have different accuracy and sensitivity limits. Repeat this screen for each relevant protection zone.

Enter downstream and backup relay operating times at the same studied fault, breaker interrupting time and the required grading margin. Clearing time and energy are conditional planning values from these inputs; they do not establish operation at or below pickup. The proposed NGR time rating must cover that duration; energy alone does not establish a manufacturer's temperature-rise or insulation rating.

Is 400 A always the correct answer? No. The required current depends on connected capacitance and protection sensitivity. A smaller candidate can reduce resistor duty while still meeting the entered screens; a larger current may be needed for another protection arrangement. The resistance sweep shows cold and hot let-through current alongside charging and detection limits.

This is a single-source, fixed-frequency screening calculation with resistor-dominated fault impedance. It does not perform a full sequence-network study, relay-curve coordination, arc-flash analysis, grounding-grid design or insulation-coordination assessment. Verify voltage extremes, resistance tolerances, repeated duty and all operating configurations separately. IEEE 142-2007 and IEEE 242-2001 provide the named historical grounding and coordination background; check against the standard in force. Installation work belongs to a qualified person.

How it is calculated

For a balanced, single-source system with negligible source and fault impedance compared with the NGR, $V_{LN}=V_{LL}/\sqrt{3}$ and $R_N=V_{LN}/I_R$ . With total phase-to-ground capacitance $C_0$ per phase, $I_{c0}=2\pi f C_0 V_{LN}$ and the ground-fault charging contribution is $I_C=3I_{c0}$ . Check $I_{R,hot}\ge I_C$ , using $R_{hot}=k_{hot}R_N$ . The cold total bolted-fault magnitude is $\sqrt{I_R^2+I_C^2}$ ; a neutral CT senses the resistor branch rather than that total.

Refer secondary pickup to primary with $I_{pickup}=I_{sec}(CT_p/CT_s)$ . The detection scenario is $I_{min}=k_{fault}I_{R,hot}$ , with no credit for capacitive current. Detection requires $I_{min}>I_{pickup}$ , or $M=I_{min}/I_{pickup}>1$ . The displayed theoretical nominal current boundary is $k_{hot}\max(3I_{c0},I_{pickup}/k_{fault})$ ; it is not a passing selection. When detection controls this boundary, nominal current must be strictly greater than it. At exactly one times pickup, an inverse-time relay has no finite operating time. Provide study-specific operating margin and verify the actual relay curve even when $M>1$ . Pickup must also exceed the entered healthy-feeder residual/spill current.

Resistor power is $P=V_{LN}^2/R_N$ . The assumed backup clearing time is $t_c=t_{up}+t_{breaker}$ , giving the conditional constant-cold-resistance duty $W=P t_c$ . These are planning values from entered times, not predicted relay operation; at or below pickup, clearing is not established and this energy is not an upper bound on actual fault duty. Also report $P t_{duty}$ for the proposed short-time duration. The available grading interval is $t_{up}-t_{down}-t_{breaker}$ ; compare it with the entered requirement. Enter times for the same fault current and operating configuration.

The charging and total-current method is supported by Chang (2015), sections 2.3 and 4.1, DOI 10.1080/22348972.2015.1110878, and I-Gard, NGR Application and Design, pages 2–4. Littelfuse's attached catalog page 1 (printed page 61) supplies independent resistance benchmarks. Helfrich, El-Mahayni and Alhumoud (2026), DOI 10.1109/MIAS.2026.3682226, motivates checking each protection zone before reducing current. Power, energy and the two-level timing screen follow basic circuit and timing relations.

SEL, PowerSystemProtection Instruction Manual, Date Code 20180920, page 6, Equation 1, defines inverse-time operating time only for $M>1$ . This supports the strict detection check; no relay curve constants or tables are reproduced.

Assumptions

Balanced three-wire system; one directly connected neutral resistor and one source; sinusoidal steady-state RMS quantities. Capacitance is the connected total for one phase, including the chosen operating configuration. Resistance is treated as constant for each cold/hot current calculation. The hot-resistance ratio and minimum-fault fraction are user inputs, not a transient thermal model or predicted fault resistance. The default ratio 1.20, fault fraction 0.50 and grading margin 0.20 s are illustrative study assumptions. The diagram omits the faulted-phase capacitor because it is shorted by the bolted fault. Resistor energy uses cold power throughout, conservatively neglecting its reduction as resistance rises.

Where it applies

For preliminary sizing and review of tripping resistance-grounded systems, approximately 0.2–35 kV and 45–65 Hz. Confirm that source and sequence impedances are small relative to 3·R_N; otherwise use a full single-line-to-ground fault model. The entered nominal-current target limits the resistive component, not total fault magnitude. Check voltage extremes, cold resistance tolerance, hot resistance, insulation level/BIL, temperature rise, altitude, enclosure, repeated faults and manufacturer's tested current/time duty. The displayed voltage is the minimum nominal RMS requirement, not an insulation-test voltage or an approved equipment class.

A passing screen does not establish selective coordination. Verify relay curves at minimum and maximum fault current, CT burden, saturation and residual errors, feeder charging-current distribution, and every 50G/51N/87B/87TG zone. A neutral CT cannot locate a feeder fault by itself. Continuously monitor the NGR and neutral-to-ground path where required; an open resistor can defeat current-only detection. No alarm-only continuous-duty, multiple grounded sources, grounding-transformer design, arc-flash, transient-overvoltage magnitude, touch/step voltage or code-compliance assessment is provided. IEEE Std 142-2007 and IEEE Std 242-2001 are historical reference editions (both listed inactive-reserved by IEEE); check against the standard in force and the applicable local rules.

References

Helfrich, C. A., El-Mahayni, R., and Alhumoud, A. (2026). Evaluating Neutral Grounding Resistor Sizing in Medium-Voltage Systems: Is 400 A Always the Correct Answer? IEEE Industry Applications Magazine, September/October 2026. DOI: https://doi.org/10.1109/MIAS.2026.3682226
Chang, C.-K. (2015). Optimal neutral ground resistor rating of the medium voltage systems in power generating stations. Journal of International Council on Electrical Engineering 5(1), 55–63. Open access. DOI: https://doi.org/10.1080/22348972.2015.1110878
I-Gard. Neutral Grounding Resistors: Application and Design, pages 2–4. https://i-gard.com/site/assets/files/1073/ngr_application_and_design.pdf
Littelfuse (2017). Protection Relays & Controls Catalog, NGR sizing chart, printed page 61; attached source page 1. Manufacturer document hosted by Steven Engineering: https://cdn.stevenengineering.com/wordpressprd/wp-content/uploads/2019/08/28PRC_RESISTANCE-GROUNDING.pdf
IEEE Std 142-2007. IEEE Recommended Practice for Grounding of Industrial and Commercial Power Systems (Green Book), 2007 edition. https://standards.ieee.org/ieee/142/3548/ — check against the standard in force.
IEEE Std 242-2001. IEEE Recommended Practice for Protection and Coordination of Industrial and Commercial Power Systems (Buff Book), 2001 edition. https://standards.ieee.org/ieee/242/426/ — check against the standard in force.
SEL (2018). PowerSystemProtection Instruction Manual, Date Code 20180920, page 6, Equation 1: inverse-time operating-time domain M > 1. https://cdn.selinc.com/assets/Literature/Miscellaneous/RTAC%20Library%20Extension%20Manuals/PowerSystemProtection.pdf?v=20181019-202244

Inputs

Input	Symbol	Unit	Default
System voltage, line to line (RMS) Use the operating system voltage. Resistor neutral voltage is V_LL / √3.	`V_LL`	kV	4.16
Charging-current data A measured total ground charging current is 3·I_c0; divide it by three before entering per-phase current.	`charge_basis`		Total capacitance per phase
Power frequency	`f_line`	Hz	60
Total phase-to-ground capacitance per phase Sum connected cable, machine, surge-capacitor and other capacitances for one phase in the largest credible connected system. This is not the sum of all three phases.	`C_zero`	uF	6.4
Charging current per phase at phase voltage I_c0 at normal line-to-neutral voltage. The ground-fault charging contribution is three times this value.	`I_c0_known`	A	5.8
Choose current or assess a resistor	`size_basis`		Size from target NGR current
Target NGR let-through current (cold) Allowed resistive component at full phase voltage. The total fault current also includes charging current in quadrature.	`I_target`	A	200
Existing NGR resistance (cold)	`R_entered`	ohm	12
Hot-to-cold resistance ratio Use manufacturer maximum resistance increase over the duty. 1.20 is an illustrative 20% rise, not a material rating. Minimum bolted resistor current is cold current / this ratio.	`k_hot`		1.2
Proposed NGR short-time rating Manufacturer-rated duration at the calculated cold current and neutral voltage. This tool treats a tripping system, not continuous alarm-only duty.	`t_duty`	s	10
Sensing CT rated primary current Enter the CT that supplies this ground element. For residual phase-CT sensing, use the phase CT ratio and verify spill and accuracy separately.	`CT_primary`	A	200
Sensing CT rated secondary current	`CT_secondary`	A	5
Ground-element secondary pickup Actual relay setting in secondary amperes. CT ratio converts it to primary pickup; this is not an automatically recommended setting.	`I_pick_sec`	A	0.5
Minimum fault current / hot bolted current A study-derived sensitivity scenario for fault resistance or winding location. Detection uses this fraction of the hot resistor current, without credit for charging current.	`k_fault`		0.5
Largest healthy-feeder residual or spill current Worst primary current seen by a healthy feeder element, including its charging current and CT spill. Pickup must exceed this value; obtain it from the protection study.	`I_spill`	A	5
Downstream relay operating time at studied fault	`t_down`	s	0.1
Backup relay operating time at studied fault For inverse-time devices, enter the actual curve time at the minimum studied fault, strictly above pickup. Include intentional delay. This calculator does not predict relay operating time.	`t_up`	s	0.4
Breaker interrupting time Used for both devices in this simple two-level screen; use the slower interrupting time if they differ.	`t_breaker`	s	0.08
Required grading margin after downstream clearing User-selected coordination margin for relay tolerances, overshoot and engineering practice. It is not a universal IEEE setting.	`dt_grade`	s	0.2

Results

With the default inputs above, the calc gives:

Result	Value
Cold NGR resistance	12.01 Ω
Theoretical nominal current boundary	48 A
Charging-current limit: 3·I_c0	17.38 A
Minimum hot bolted NGR current	166.67 A
Cold total ground-fault magnitude	200.75 A
Minimum nominal resistor voltage duty	2.402 kV
Maximum cold resistor power	480.36 kW
Conditional energy for assumed backup clearing	0.231 MJ
Relay pickup on primary side	20 A
Minimum fault / pickup multiple	4.1667
Assumed backup clearing time; verify operation	0.48 s
Available grading interval	0.22 s
Conservative energy for proposed time rating	4.804 MJ
400 A energy for assumed backup clearing	0.461 MJ
Entered screening result	Entered screens pass
400 A comparison	400 A passes current screens; verify margin

Checked against sources

Each case below was calculated by this calc and agrees with the value from its source (within the tolerance where one is shown).

Littelfuse: 4.16 kV, 10 A resistor

Source: Littelfuse 2017 Protection Relays & Controls catalog, printed p. 61 (attached p. 1): 4,160 V line to line, 10 A, 240 Ω. Published values are rounded; the ideal result is about 240.18 Ω.

Inputs: Hot-to-cold resistance ratio = 1; Total phase-to-ground capacitance per phase = 0.1 uF; Sensing CT rated primary current = 50 A; Ground-element secondary pickup = 0.1 A; Minimum fault current / hot bolted current = 1; Largest healthy-feeder residual or spill current = 0 A; Target NGR let-through current (cold) = 10 A; the others as above.

Result	Source	This calc
Cold NGR resistance	240 ± 0.6 Ω	240.2 Ω

Littelfuse: 13.8 kV, 200 A resistor

Source: Littelfuse 2017 catalog, printed p. 61 (attached p. 1): 13,800 V line to line, 200 A, 40 Ω, 10 s. Allow rounding of the published resistance.

Inputs: Hot-to-cold resistance ratio = 1; Total phase-to-ground capacitance per phase = 0.1 uF; Sensing CT rated primary current = 50 A; Ground-element secondary pickup = 0.1 A; Minimum fault current / hot bolted current = 1; Largest healthy-feeder residual or spill current = 0 A; System voltage, line to line (RMS) = 13.8 kV; the others as above.

Result	Source	This calc
Cold NGR resistance	40 ± 0.2 Ω	39.837 Ω

IEEE MIAS 2026: residual phase CT sensitivity example

Source: Helfrich, El-Mahayni and Alhumoud, IEEE Industry Applications Magazine 2026, DOI 10.1109/MIAS.2026.3682226, 51N protection discussion (printed p. 26): the worked example gives 300 A primary pickup for a 3000:5 CT and 0.5 A secondary setting. Used here only as a pickup-conversion benchmark; it does not verify selectivity.

Inputs: Hot-to-cold resistance ratio = 1; Total phase-to-ground capacitance per phase = 0.1 uF; Sensing CT rated primary current = 3,000 A; Largest healthy-feeder residual or spill current = 0 A; Target NGR let-through current (cold) = 800 A; the others as above.

Result	Source	This calc
Relay pickup on primary side	300 A	300 A

Chang: fault magnitude at the charging-current boundary

Source: Chang (2015), section 4.1, DOI 10.1080/22348972.2015.1110878: published limiting result I_F = 1.414 I_R when I_R = 3 I_c0. With a chosen 200 A resistor component this gives the independent rounded ratio benchmark 282.8 A. This is a boundary case, not a recommended operating margin.

Inputs: Hot-to-cold resistance ratio = 1; Charging-current data = Known charging current per phase; Sensing CT rated primary current = 50 A; Ground-element secondary pickup = 0.1 A; Minimum fault current / hot bolted current = 1; Largest healthy-feeder residual or spill current = 0 A; Charging current per phase at phase voltage = 66.667 A; the others as above.