Protection Coordination and Time-Current Characteristic Analysis per IEEE 242

Published: June 2026
Technical Level: Advanced Category: Protection and Coordination

Abstract

Protective-device coordination ensures that, for any fault, the device nearest the fault operates to clear it while every upstream device restrains, isolating the smallest possible portion of the system and preserving service to the remainder. This selectivity is achieved by setting the time-current characteristics of the protective devices so that they are separated by an adequate coordination time interval throughout the range of fault currents, and the methodology for doing so is established in IEEE 242, the Buff Book. This paper develops the analysis: the inverse-time characteristic that relates a relay's operating time to the fault current, the coordination time interval that must separate adjacent devices, the construction and interpretation of the time-current characteristic plot, and the treatment of transformer inrush and damage limits that constrains the settings. The objective is to give the engineer the basis for setting a coordinated protection scheme on a radial distribution system.

1. The Coordination Objective

A protective device exists to detect a fault and to interrupt the current feeding it, and on a system with devices in series — a main breaker, feeder breakers, branch breakers, and the fuses or relays of individual loads — the devices must be coordinated so that a fault is cleared by the device immediately upstream of it while the devices further upstream hold. When coordination is achieved, a fault on a branch circuit trips only that branch's protective device, leaving the rest of the system in service; when coordination fails, the fault trips an upstream device as well, interrupting service to loads that the fault never reached. The economic and operational consequence of miscoordination is the unnecessary loss of service to healthy portions of the system, and the purpose of a coordination study is to set the protective devices so that selectivity is maintained for the full range of faults the system can experience.

2. The Inverse-Time Characteristic

The coordination of overcurrent devices rests on the inverse-time characteristic, by which a protective relay operates faster as the fault current increases. This characteristic allows a single device to discriminate between a small overload, which it clears slowly if at all, and a severe fault, which it clears rapidly, and it provides the time separation by which adjacent devices are coordinated. The operating time of an inverse-time overcurrent relay follows a standard curve defined by the relay's time-dial setting and the multiple of pickup current:

$t = TDS \left[ \frac{A}{M^p - 1} + B \right]$

Where:

$t$ is the relay operating time in seconds.

$TDS$ is the time-dial setting, which scales the operating time.

$M$ is the multiple of pickup current, equal to the fault current divided by the pickup setting.

$A$ , $B$ , $p$ are constants defining the shape of the standard curve.

The constants $A$ , $B$ , and $p$ define the standard curve shapes — moderately inverse, very inverse, and extremely inverse — each of which provides a different rate of change of operating time with current, suited to coordinating against different downstream characteristics. The time-dial setting shifts the whole curve in time, and it is the principal lever the engineer adjusts to position one device's characteristic above another's by the required margin. The pickup setting determines the current at which the device begins to time out, and it is set above the maximum load current the device must carry and below the minimum fault current it must detect.

2.1 Worked Example: Coordinating Two Relays

Consider two inverse-time overcurrent relays in series on a radial feeder, both set to the IEEE Very Inverse curve ( $A = 19.61$ , $B = 0.491$ , $p = 2.0$ ), with a bolted fault of 2000 A at the downstream bus that both relays detect. The downstream relay has a pickup of 100 A and a time-dial setting of $TDS = 2.0$ , so its multiple of pickup is $M = 2000/100 = 20$ and its operating time is:

$t_{dn} = 2.0 \left[ \frac{19.61}{20^2 - 1} + 0.491 \right] = 2.0 \left[ 0.0491 + 0.491 \right] = 1.080 \ \text{s}$

The upstream relay has a higher pickup of 300 A, so at the same 2000 A fault it sees $M = 2000/300 = 6.67$ . To maintain a coordination time interval of 0.30 s, its operating time must be at least $t_{dn} + CTI = 1.080 + 0.30 = 1.380$ s. Solving the inverse-time equation for the required time-dial setting:

$TDS_{up} = \frac{1.380}{\dfrac{19.61}{6.67^2 - 1} + 0.491} = \frac{1.380}{0.9424} = 1.46$

Where the symbols are as defined above. Setting the upstream relay to $TDS = 1.46$ yields an operating time of 1.380 s at the 2000 A fault, exactly 0.30 s slower than the downstream relay, so the downstream device clears first and the upstream device serves as backup. The example shows why the time-dial is the engineer's principal lever: the curve shape is fixed by the standard constants, and coordination is achieved by scaling the upstream curve in time until the margin is satisfied at the fault current the two devices share.

3. The Coordination Time Interval

Two devices in series are coordinated when their time-current characteristics are separated, throughout the range of fault currents they both see, by a coordination time interval adequate to ensure that the downstream device clears the fault before the upstream device begins to operate. This interval must account for the operating time of the downstream device, the interrupting time of its breaker, the overtravel of an electromechanical upstream relay, and a margin for the tolerances and errors in the devices and the study. IEEE 242 establishes the coordination time intervals appropriate to the types of devices being coordinated, with the interval for coordinating two relays differing from that for coordinating a relay against a downstream fuse or static device because the contributing factors differ.

The coordination time interval is the criterion against which the time-current characteristic plot is judged. At every fault current that two adjacent devices both experience, the upstream device's operating time must exceed the downstream device's total clearing time by at least the coordination time interval. Where this margin is maintained across the full range, the devices are coordinated; where the characteristics approach more closely than the interval, or cross, the coordination fails at the currents where the margin is inadequate, and the settings must be adjusted. The engineer adjusts principally the time-dial settings to open the margins, constrained by the requirement that the clearing times remain short enough to protect equipment and personnel.

4. The Time-Current Characteristic Plot

The coordination study is conducted on the time-current characteristic plot, a logarithmic graph on which the operating-time-versus-current characteristic of every device in a coordination path is drawn on common axes. On this plot, a properly coordinated set of devices appears as a family of curves that step upward and to the right from the load toward the source, each device's characteristic lying above the next downstream device's by the coordination time interval, so that for any fault current the lowest curve at that current belongs to the device that should clear the fault. The plot makes coordination and its failures visually evident: curves that maintain their separation are coordinated, while curves that pinch together or cross reveal the currents at which selectivity is lost.

The plot also displays the constraints within which the device characteristics must lie. The damage curves of the equipment being protected — the transformer, the cable, the motor — are drawn on the same axes, and the protective characteristic must lie below the damage curve so that the device operates before the equipment is harmed. The maximum load current and the available fault current bound the range over which coordination must be achieved. Reading the plot, the engineer confirms that each device protects its equipment, coordinates with its neighbors, and operates within the bounds set by load and fault current, and adjusts the settings until all of these conditions are satisfied simultaneously.

The coordinated family of curves is illustrated in Figure 1, which shows the time-current characteristics of a downstream feeder breaker and an upstream main breaker plotted on common logarithmic axes against the transformer damage curve.

Time-current coordination plot. The horizontal axis is current in amperes (log scale) and the vertical axis is operating time in seconds (log scale). The downstream device characteristic lies below and to the left of the upstream device.

Figure 1. Time-current coordination plot. The horizontal axis is current in amperes (log scale) and the vertical axis is operating time in seconds (log scale). The downstream device characteristic lies below and to the left of the upstream device characteristic, separated by the coordination time interval across the full fault-current range, while both lie below the transformer damage curve and to the right of the inrush point. The engineer should observe that selectivity is preserved wherever the curves maintain their vertical separation, and is lost at any current where they pinch together.

5. Transformer Inrush and Damage Constraints

The coordination of the protection on a circuit supplying a transformer is constrained by two transformer-specific characteristics. The transformer's magnetizing inrush — the transient current drawn when the transformer is energized, which can reach many times its rated current for a fraction of a second — must not cause the protective device to operate, so the device's characteristic must lie above the inrush point on the time-current plot. At the same time, the device must protect the transformer against faults, so its characteristic must lie below the transformer's damage curve, which defines the combinations of current and time the transformer can withstand without damage. The protective characteristic must therefore thread between the inrush point below and the damage curve above, a constraint that narrows the available settings and that must be reconciled with the coordination margins to the adjacent devices.

These transformer constraints frequently govern the coordination of the devices around a transformer, and the standard inrush and damage characteristics defined in the relevant IEEE standards provide the points and curves the engineer plots. Where the constraints cannot all be satisfied with a single device characteristic — where, for instance, coordinating above the inrush forces the characteristic above the damage curve at some current — the engineer must reconsider the device selection or accept a documented compromise, and the coordination study makes the conflict explicit so that it can be resolved deliberately.

6. Conclusion

The most consequential point is that coordination is verified by the coordination time interval held across the full fault-current range, not by a single curve overlay at the maximum fault. The CTI that protects selectivity is the margin that survives at the minimum credible fault current, where time-current curves crowd together; an interval that looks ample at the bolted maximum can vanish at the arcing minimum, which is the condition a thorough study must check explicitly.

The most common implementation failure is reading coordination off the curves by eye at one current and declaring selectivity, without computing the CTI at the specific currents where adjacent devices approach each other — the points that decide whether the downstream device clears first or both operate together.

The engineer should next carry a worked CTI calculation through a representative device pair, from the fault current at the coordination point through each device's operating time to the resulting interval, because that computed margin — not the visual separation of the curves — is the quantity that certifies the coordination.

References

[1] IEEE Standard 242-2001, IEEE Recommended Practice for Protection and Coordination of Industrial and Commercial Power Systems (Buff Book), IEEE, 2001.

[2] IEEE Standard C37.112-2018, IEEE Standard for Inverse-Time Characteristics Equations for Overcurrent Relays, IEEE, 2018.

[3] IEEE Standard C57.12.00-2015, IEEE Standard for General Requirements for Liquid-Immersed Distribution, Power, and Regulating Transformers, IEEE, 2015.

[4] IEEE Standard 399-1997, IEEE Recommended Practice for Industrial and Commercial Power Systems Analysis (Brown Book), IEEE, 1997.

[5] NFPA 70-2023, National Electrical Code, National Fire Protection Association, 2023.

[6] J. L. Blackburn and T. J. Domin, Protective Relaying: Principles and Applications, 4th ed., CRC Press, 2014.