Exercise set

Protection Coordination, Relay Settings, and Selectivity Exercises

Worked protection-coordination exercises for pickup windows, CT scaling, selectivity, inverse curves, differential trips, ZSI and reclosers.

Branch: Electrical Engineering
Content: Exercise set
Updated: Jul 03, 2026
Revision: v1.0.0 · reviewed

These exercises practise protection coordination as a setting, selectivity and release-evidence problem. They cover pickup windows, CT secondary conversion, motor-start restraint, ground-fault pickup, time-current selectivity, inverse-time margins, CT saturation, differential restraint, zone-selective interlocking, recloser-fuse sequences, maintenance settings, backup clearing and coordination release gates.

The focus is narrower than fault-current duty. Fault-current studies ask whether equipment can survive and interrupt; protection coordination asks whether the right protective device trips, at the right time, for the right fault, without unnecessary upstream outages.

How to Use These Exercises

For each calculation, define:

the protected zone and downstream/upstream device pair;
normal load, inrush, minimum fault, maximum fault and arcing-current cases;
CT ratio, burden, relay scaling and setting file revision;
the coordination margin, sensitivity margin or security margin;
the commissioning evidence needed before the setting is released.

The common mistake is proving selectivity at one curve point. Protection coordination should be checked at credible bolted, arcing, ground-fault, weak-source, inrush and backup conditions.

Release Evidence Notes

Relay settings should be traceable to the exact device file and one-line revision. A correct pickup value in a spreadsheet is weak if the installed relay file, CT ratio or device model differs.

CT evidence should include ratio, polarity, burden, saturation, remanence and secondary wiring. A relay that calculates correctly on paper can misoperate if the CT cannot reproduce the current during a through fault.

Selectivity evidence should cover more than normal service. Maintenance settings, ZSI wiring, fuse substitutions, recloser shot sequence and source-mode changes can all change which device trips first.

Backup evidence should remain visible. A scheme that preserves selectivity too long can damage equipment or increase arc energy; a scheme that trips too fast can create unnecessary outages.

Engineering Boundary Notes

These exercises are simplified training screens. Real relay settings and protective-device coordination require manufacturer time-current curves, device tolerances, CT accuracy data, short-circuit study, arc-flash study, grounding method, system operating modes, commissioning tests and qualified review.

A passing coordination screen does not prove equipment duty. Breakers, panels, cables and switchgear must still have adequate interrupting, withstand, making and SCCR ratings for the available current.

Scenario Map

Scenario	Exercises	Primary calculation	Engineering decision
Pickup and sensitivity	1-5, 11-12	load restraint, fault sensitivity, CT scaling, inrush and ground-fault margin	Decide whether settings detect faults without nuisance trips.
Selectivity and relay behavior	6-10, 13-15	time-current margins, inverse curves, CT saturation, differential restraint and ZSI	Decide whether the intended device trips first and backup remains available.
Release and operating modes	16-18	recloser sequence, maintenance mode, setting-file evidence and release gates	Decide whether the protection package can be released.

Exercise 1: Protection Pickup Window

A feeder has maximum normal load:

I_L=360\ \text{A}

Expected minimum fault current is:

I_F=1450\ \text{A}

The local rule requires pickup at least $125\%$ of load and at most $70\%$ of minimum fault. Find the pickup window.

Solution

Minimum pickup for load security:

I_{p,min}=1.25(360)=450\ \text{A}

Maximum pickup for sensitivity:

I_{p,max}=0.70(1450)=1015\ \text{A}

The acceptable pickup window is:

450\ \text{A}\le I_p\le 1015\ \text{A}

Engineering Comment

The window is only a first screen. Motor starting, transformer inrush, cold-load pickup, CT errors and source-mode changes can narrow it.

Plausibility Check

The minimum fault is roughly four times load, so a usable pickup window should exist.

Exercise 2: CT Secondary Pickup Conversion

A relay uses a:

600:5

current transformer. The relay secondary pickup is set to:

4.2\ \text{A}

Calculate primary pickup.

Solution

CT ratio:

R=\dfrac{600}{5}=120

Primary pickup:

I_p=4.2(120)=504\ \text{A}

Engineering Comment

The arithmetic is simple, but setting release also needs CT wiring, polarity, burden, relay input scaling and setting-file verification.

Plausibility Check

Five secondary amps represent $600$ primary amps, so a little over four secondary amps should represent about $500$ primary amps.

Exercise 3: Motor Starting Security

A motor feeder has normal full-load current:

I_{FL}=180\ \text{A}

Starting current is:

5.8I_{FL}

The short-time pickup is set to:

I_{ST}=1250\ \text{A}

Calculate starting current and security margin.

Solution

Starting current:

I_{start}=5.8(180)=1044\ \text{A}

Security margin:

M=1250-1044=206\ \text{A}

Percentage margin relative to starting current:

M_{\%}=\dfrac{206}{1044}=19.7\%

Engineering Comment

The pickup clears this simple current screen. The time delay still has to ride through acceleration time without losing protection for stalled or faulted conditions.

Plausibility Check

Starting current near six times full-load current is about $1000$ A, so a $1250$ A pickup leaves moderate margin.

Exercise 4: Ground-Fault Pickup and Normal Leakage

A distribution panel has measured normal leakage:

I_{leak}=7.5\ \text{A}

The ground-fault pickup is:

I_{GF}=30\ \text{A}

The security rule requires pickup at least three times normal leakage. Check the setting.

Solution

Security ratio:

R=\dfrac{30}{7.5}=4.0

The rule requires $R\ge 3$ , so the setting passes.

Engineering Comment

Normal leakage should be measured in representative operating states. Variable-speed drives, filters, moisture and connected loads can change the residual current.

Plausibility Check

Thirty amps is four times $7.5$ A, so the margin is clear.

Exercise 5: Minimum Fault Sensitivity Margin

A relay pickup is:

I_p=520\ \text{A}

The minimum protected-zone fault current is:

I_{min}=760\ \text{A}

The project sensitivity rule requires:

I_{min}\ge 1.4I_p

Check the margin.

Solution

Required current:

1.4I_p=1.4(520)=728\ \text{A}

Margin:

M=760-728=32\ \text{A}

The setting passes with narrow margin.

Engineering Comment

Narrow sensitivity margins should be tested against source tolerance, CT error, arcing current and weak-source operation before release.

Plausibility Check

The minimum fault is only slightly above the required value, so the narrow pass is plausible.

Exercise 6: Selectivity Margin from Curve Readings

For a downstream fault, the downstream breaker clears in:

t_d=0.18\ \text{s}

The upstream breaker trip time at the same current is:

t_u=0.42\ \text{s}

The required coordination margin is:

0.20\ \text{s}

Check selectivity.

Solution

Coordination margin:

M=t_u-t_d=0.42-0.18=0.24\ \text{s}

The margin exceeds $0.20$ s, so selectivity passes at this curve point.

Engineering Comment

This single point is not enough. Coordination should also be checked at lower arcing currents, higher bolted currents and device tolerance bands.

Plausibility Check

The upstream device is delayed by about a quarter second, so it has room to let the downstream breaker clear first.

Exercise 7: Inverse-Time Coordination at Two Fault Currents

Two curve points are read from a relay study:

Fault current	Downstream time	Upstream time
$2.0$ kA	$0.74$ s	$1.05$ s
$8.0$ kA	$0.16$ s	$0.30$ s

The required margins are $0.25$ s at $2.0$ kA and $0.12$ s at $8.0$ kA. Check both points.

Solution

Low-current margin:

M_1=1.05-0.74=0.31\ \text{s}

High-current margin:

M_2=0.30-0.16=0.14\ \text{s}

Both margins pass:

0.31>0.25,\qquad 0.14>0.12

Engineering Comment

Checking two points catches more risk than a single curve read. The high-current region often has less time margin.

Plausibility Check

Both devices trip faster at higher current, and the margin shrinks, which is typical for inverse-time behavior.

Exercise 8: CT Saturation Screen During Through Fault

A CT has accuracy-limit current:

I_{AL}=18\ \text{kA primary}

A through fault is:

I_{TF}=16.5\ \text{kA}

The relay-security rule requires:

\dfrac{I_{AL}}{I_{TF}}\ge 1.10

Check the CT margin.

Solution

Ratio:

R=\dfrac{18}{16.5}=1.091

The required ratio is $1.10$ , so the screen fails narrowly.

Engineering Comment

CT saturation can make a through fault look like an internal fault or distort overcurrent timing. Burden, remanence and X/R ratio should be reviewed.

Plausibility Check

The accuracy-limit current is only slightly above the through fault, so a borderline failure is plausible.

Exercise 9: Differential Restraint Trip Check

A transformer differential relay computes:

I_{op}=0.42\ \text{p.u.},\qquad I_{res}=1.80\ \text{p.u.}

The relay trips when:

I_{op}>0.30+0.25I_{res}

Check the trip decision.

Solution

Trip threshold:

I_{th}=0.30+0.25(1.80)=0.75\ \text{p.u.}

Since:

0.42<0.75

the relay should restrain in this simplified screen.

Engineering Comment

Differential release evidence should include CT polarity, ratios, vector compensation, tap position, inrush restraint and saturation review.

Plausibility Check

High restraint current raises the threshold, so a moderate operate current should not trip.

Exercise 10: Zone-Selective Interlocking Timing

A downstream feeder breaker clears in:

t_f=80\ \text{ms}

The upstream main breaker waits:

t_m=320\ \text{ms}

when it receives a ZSI restraint signal. Required coordination margin is:

150\ \text{ms}

Check the restrained margin.

Solution

Margin:

M=t_m-t_f=320-80=240\ \text{ms}

The restrained ZSI margin passes.

Engineering Comment

ZSI also has a failure mode. If the restraint signal is missing, the upstream main may trip fast and defeat selectivity.

Plausibility Check

The upstream delay is four times the downstream clearing time, so a large margin is expected.

Exercise 11: ZSI Signal Arrival Gate

The upstream main breaker makes its fast-trip decision at:

20\ \text{ms}

after fault detection. The downstream restraint signal arrives after:

8\ \text{ms}

The communication and input margin requirement is:

5\ \text{ms}

Check whether the restraint arrives in time.

Solution

Arrival margin:

M=20-8=12\ \text{ms}

The required margin is $5$ ms, so the signal timing passes.

Engineering Comment

Signal timing is only valid for the installed wiring, trip unit model, input configuration and tested source mode. It should be commissioned, not assumed.

Plausibility Check

An $8$ ms arrival before a $20$ ms decision point leaves a clear timing margin.

Exercise 12: Arc-Reduction Maintenance Pickup

An arc-reduction maintenance setting has instantaneous pickup:

I_{inst}=12.0\ \text{kA}

The low arcing-current case is:

I_{low}=13.8\ \text{kA}

The rule requires at least:

10\%

margin above pickup. Check the setting.

Solution

Ratio:

R=\dfrac{13.8}{12.0}=1.15

Margin above pickup:

M=15\%

The setting passes the simplified arc-reduction pickup gate.

Engineering Comment

Maintenance settings reduce arc energy only when they are enabled, labelled, procedurally controlled and restored correctly after the task.

Plausibility Check

The low arcing current is $1.8$ kA above pickup, which is $15\%$ of $12$ kA.

Exercise 13: Backup Clearing Limit

A downstream breaker is expected to clear a fault in:

0.12\ \text{s}

If it fails, the upstream backup clears in:

0.62\ \text{s}

The equipment backup-clearing limit is:

0.75\ \text{s}

Check backup acceptability.

Solution

Backup margin:

M=0.75-0.62=0.13\ \text{s}

The backup clearing time passes the simplified limit.

Engineering Comment

Backup protection should be slow enough for selectivity but fast enough for equipment and arc-energy limits. Both constraints must be visible.

Plausibility Check

The backup time is substantially slower than the downstream time but still below the limit.

Exercise 14: Fuse Damage from Repeated Fast Shots

A recloser fast shot clears in:

t_f=0.09\ \text{s}

The fuse minimum-melt time at the lateral fault current is:

t_m=0.12\ \text{s}

Assume thermal memory factor $0.78$ remains for the second fast shot. Use:

D=\dfrac{t_f}{t_m}+\alpha\dfrac{t_f}{t_m}

Check whether two fast shots stay below damage index $1.0$ .

Solution

Single-shot fraction:

\dfrac{t_f}{t_m}=\dfrac{0.09}{0.12}=0.75

Two-shot damage index:

D=0.75+0.78(0.75)=1.335

The two-fast-shot sequence fails the simplified fuse-heating screen.

Engineering Comment

Fuse-saving coordination is a sequence problem. Repeated fast shots may partially melt the fuse even if the first shot clears before the minimum-melt time.

Plausibility Check

The first shot already uses $75\%$ of the minimum-melt time, so adding a second shot with memory should exceed $1.0$ .

Exercise 15: Recloser Delayed-Shot Selectivity

For a permanent lateral fault, fuse total-clearing time is:

t_{fuse}=0.210\ \text{s}

The recloser delayed shot trips in:

t_r=0.360\ \text{s}

Required selectivity margin is:

0.120\ \text{s}

Check coordination.

Solution

Margin:

M=t_r-t_{fuse}=0.360-0.210=0.150\ \text{s}

The delayed shot passes the selectivity requirement.

Engineering Comment

The delayed shot should let the downstream fuse clear a permanent lateral fault while the first fast shot may save the fuse for temporary faults.

Plausibility Check

The margin is $150$ ms, which exceeds the $120$ ms rule by $30$ ms.

Exercise 16: Maintenance Mode Restoration Gate

A breaker has maintenance mode enabled for:

45\ \text{min}

during energized work. The local procedure requires restoration and verification within:

15\ \text{min}

after work ends. The log shows restoration after:

22\ \text{min}

Check procedure compliance.

Solution

Restoration delay margin:

M=15-22=-7\ \text{min}

The restoration gate fails.

Engineering Comment

Leaving maintenance mode enabled can reduce selectivity or change trip behavior for normal service. Operating-mode evidence belongs in the protection release file.

Plausibility Check

Restoration occurred later than the allowed $15$ min, so the negative margin is expected.

Exercise 17: Setting-File Mismatch Rate

A commissioning audit checks:

N=58

relays. It finds $4$ relays where the installed setting file revision does not match the approved coordination study. Calculate mismatch percentage and decide whether a $0\%$ mismatch release rule is met.

Solution

Mismatch percentage:

P=\dfrac{4}{58}=0.0690=6.9\%

Matched relays:

N_m=58-4=54

The $0\%$ mismatch release rule is not met.

Engineering Comment

Relay setting files are executable engineering decisions. A mismatch can invalidate pickup, selectivity, arc-flash labels and backup timing.

Plausibility Check

Four mismatches among about sixty relays is a mid-single-digit percentage, so $6.9\%$ is plausible.

Exercise 18: Coordination Release Gate

A protection release review assigns five weighted gates:

Gate	Weight	Result
pickup and sensitivity	$0.20$	$0.95$
CT ratio and saturation evidence	$0.20$	$0.89$
downstream-upstream selectivity	$0.25$	$0.94$
backup clearing and ZSI tests	$0.20$	$0.92$
setting-file and label revision	$0.15$	$0.97$

The release threshold is:

S\ge 0.93

and CT evidence may not be below $0.90$ . Calculate the score and decision.

Solution

Weighted score:

\begin{aligned} S&=0.20(0.95)+0.20(0.89)+0.25(0.94)+0.20(0.92)+0.15(0.97)\\ &=0.190+0.178+0.235+0.184+0.1455\\ &=0.9325 \end{aligned}

The weighted score is:

93.25\%

The score passes, but CT evidence fails the $0.90$ floor:

0.89<0.90

Release is held until CT evidence is corrected.

Engineering Comment

Coordination depends on current measurement. A good curve margin is weak if CT saturation, ratio or wiring evidence is incomplete.

Plausibility Check

The total score barely passes while one critical floor fails, so the hold decision follows the stated rule.

Validation Package Checklist

Pickup settings are checked against load, inrush, minimum fault, arcing current and weak-source operation.
CT ratios, secondary scaling, burden, polarity and saturation are documented for the installed devices.
Selectivity margins are checked at more than one current and include tolerances where needed.
ZSI, differential and recloser-fuse schemes are tested as sequences, not only as curve points.
Maintenance settings have enable, label, restoration and verification controls.
Relay files, labels, one-line diagrams and commissioning evidence all match the same approved revision.

Common Release Mistakes

Selecting pickup from maximum load while ignoring minimum fault current.
Converting CT ratios correctly but not verifying CT wiring, burden or saturation.
Claiming selectivity from one time-current curve point.
Treating ZSI as a software checkbox instead of a tested wiring and timing dependency.
Using a fast arc-reduction setting without proving low arcing-current pickup.
Using multiple fast recloser shots while ignoring fuse thermal memory.
Releasing settings before installed relay files match the approved study.

REF