Protection Coordination Study: TCC Curve Analysis per IEEE 242

Published: June 2026 Technical Level: Advanced Category: Protection Systems

Abstract

Time-current characteristic curve analysis is the primary graphical tool used by protection engineers to verify selectivity between overcurrent devices in industrial and commercial power systems. When performed correctly, TCC analysis provides a visual and quantitative confirmation that, for any fault current within the protected zone, the nearest downstream device operates before any upstream device. This paper develops the mathematical basis for TCC analysis per IEEE 242, derives the coordination time interval requirements for each device pairing category, presents the complete procedure for a multi-level industrial power system, and identifies the numerical checks that supplement graphical analysis. Case study calculations demonstrate the procedure on a realistic five-level coordination chain from utility to branch circuit level.

1. Introduction

The time-current characteristic is the fundamental engineering description of an overcurrent protective device's operating behavior. It expresses the relationship between the fault current magnitude applied to the device and the time required for the device to interrupt that current. For fuses, the TCC is a fixed material property determined by the element geometry and alloy composition. For relays, the TCC is a programmable mathematical function with parameters selected by the protection engineer. For low-voltage circuit breakers, the TCC is a composite of instantaneous, short-time delay, and long-time delay regions, each independently adjustable in modern electronic trip units.

Coordination between two adjacent devices, upstream UU and downstream DD, is achieved when, for every fault current that both devices detect, device DD interrupts the current before device UU operates. The graphical expression of this condition is that the TCC of device DD lies entirely to the left of and below the TCC of device UU, with a separation at least equal to the required coordination time interval. The TCC diagram is the primary deliverable of the coordination study, but it must be supported by numerical verification at specific current levels to be considered complete.

The coordination achieved between the two devices is illustrated in Figure 1, which overlays the operating-time characteristics of the downstream feeder relay and the upstream main relay across the full range of fault current.

Time–current coordination curves for a downstream feeder relay and an upstream main relay using the IEC Normal Inverse characteristic, plotted on log–log axes. The vertical dashed line marks the maximum bolted fault current.

Figure 1. Time–current coordination curves for a downstream feeder relay and an upstream main relay using the IEC Normal Inverse characteristic, plotted on log–log axes. The vertical dashed line marks the maximum bolted fault current.

The reader should observe that at every current magnitude the upstream main relay operates more slowly than the downstream feeder relay, and that the vertical separation between the curves at the maximum bolted fault current represents the coordination time interval. A protection engineer reads selectivity directly from this vertical gap: where it falls below roughly 0.2 to 0.3 seconds the two devices risk simultaneous operation, and where it widens excessively the upstream device clears downstream-zone faults too slowly. The curves crowd together at high current, which is precisely why coordination must be verified at the maximum fault current rather than at the pickup threshold alone.

2. Mathematical Basis of TCC Analysis

2.1 Inverse-Time Overcurrent Relay Characteristics

The inverse-time overcurrent relay characteristic is expressed as a closed-form relationship between the fault current multiple above pickup and the operating time. The IEC standard inverse-time equations are:

top=TDS⋅β(If/Ipu)α−1t_{op} = \frac{TDS \cdot \beta}{\left(I_f / I_{pu}\right)^\alpha - 1}

Where: topt_{op} is the relay operating time in seconds.

TDSTDS is the time-dial setting (dimensionless).

IfI_f is the fault current seen by the relay in amperes.

IpuI_{pu} is the pickup current setting in amperes, and α\alpha and β\beta are curve-shape constants defined by the selected characteristic. The IEC standard curve constants are:.

Characteristic α\alpha β\beta
Normal Inverse 0.02 0.14
Very Inverse 1.0 13.5
Extremely Inverse 2.0 80.0

The IEEE standard curves use a different functional form that includes an additional constant term, but the coordination procedure is identical. The key property of all inverse-time characteristics is that operating time decreases as fault current increases: a high fault current near the relay operates the relay quickly, while a smaller fault current farther from the relay operates the relay more slowly. This property is what allows selectivity in a multi-level system: for a fault at the far end of the feeder, the small fault current produces a long operating time for the upstream relay, during which the downstream relay has time to clear.

2.2 Coordination Time Interval Requirements

The coordination time interval is the minimum time separation between the operating time of a downstream device and the upstream device at the same fault current. The CTI must account for three components: the operating time error of the upstream relay, the interrupting time of the downstream device's circuit breaker, and a safety margin:

CTI=trelay error+tCB interrupt+tmargin\text{CTI} = t_{\text{relay error}} + t_{\text{CB interrupt}} + t_{\text{margin}}

Where: textrelayerrort_{ ext{relay error}} is the upstream relay timing error in seconds.

textCBinterruptt_{ ext{CB interrupt}} is the downstream circuit breaker interrupting time in seconds.

textmargint_{ ext{margin}} is a safety margin in seconds.

For modern numerical relays with ±1.5 percent timing accuracy and standard medium-voltage vacuum circuit breakers with 3-cycle (50 ms) interrupting time:

CTImin⁡=0.05 s (relay error)+0.05 s (CB interrupt)+0.05 s (margin)=0.15 s (numerical relay)\text{CTI}_{\min} = 0.05\,\text{s (relay error)} + 0.05\,\text{s (CB interrupt)} + 0.05\,\text{s (margin)} = 0.15\,\text{s (numerical relay)}

For electromechanical relays with ±5 percent timing accuracy and oil circuit breakers with 5-cycle interrupting time:

CTImin⁡=0.10+0.08+0.07=0.25 s (electromechanical relay)\text{CTI}_{\min} = 0.10 + 0.08 + 0.07 = 0.25\,\text{s (electromechanical relay)}

These values are minima; the engineer should increase CTI when timing accuracy data is unavailable, when CT saturation may affect relay timing, or when the consequence of a coordination failure is severe.

Figure 1 (Recommended Plot): TCC diagram showing a two-relay coordination pair. X-axis: fault current in amperes (secondary, log scale). Y-axis: operating time in seconds (log scale). Show the downstream relay TCC (R2) and upstream relay TCC (R1). Draw vertical arrows at three representative fault current levels (pickup multiple, midpoint, and maximum) showing the CTI at each level. Annotate the minimum CTI requirement as a horizontal dimension. Show that the curves maintain the required CTI across the full range, not just at one current level.

2.3 Fuse-Relay Coordination

When a downstream fuse protects a transformer or feeder branch, the relay upstream of the fuse must not operate before the fuse clears the fault. Fuse TCC curves have a minimum melting time (the time at which the fuse element begins to melt, but interruption is not yet complete) and a total clearing time (the time at which arc extinction is complete and interruption is finished). Coordination between an upstream relay and a downstream fuse requires that the relay operating time exceeds the fuse total clearing time at the maximum fault current seen by both devices:

trelay(If,max⁡)≥tfuse,TC(If,max⁡)+CTIt_{\text{relay}}(I_{f,\max}) \geq t_{\text{fuse,TC}}(I_{f,\max}) + \text{CTI}

Where: tfuse,TCt_{\text{fuse,TC}} is read from the fuse total clearing time curve at the fault current in question. The upstream relay must also not operate at a fault current below the fuse minimum melting threshold, because the fuse will not clear such a fault and the relay must provide backup protection.

For transformer primary fuse coordination with a secondary-side relay, the fault current must be referred through the transformer turns ratio and impedance when comparing the primary fuse and secondary relay TCC curves on the same diagram. All quantities should be referred to a common voltage base before plotting.

3. Multi-Level Coordination Procedure

3.1 System Description

The following worked example develops a complete coordination study for a five-level industrial power system:

Available fault current (three-phase, maximum source):

3.2 Downstream Device First: Branch Breaker B4

The branch breaker protects the 200 A motor feeder. The instantaneous trip setting is set to 10× the motor full-load current to avoid operating on motor starting inrush:

Iinst,B4=10×IFLA=10×180 A=1,800 AI_{\text{inst,B4}} = 10 \times I_{FLA} = 10 \times 180\,\text{A} = 1{,}800\,\text{A}

Where: Iextinst,B4I_{ ext{inst,B4}} is the instantaneous trip current in amperes.

IFLAI_{FLA} is the motor full-load ampere rating from NEC Table 430.250.

The long-time pickup is set at 1.15× FLA to provide thermal protection with a margin above full-load operation. The 480 V maximum fault current at the motor terminals (24,000 A) is within the breaker's interrupting rating, so no upstream current-limiting device is required.

3.3 Main Breaker B3

The 480 V main breaker must coordinate with branch breaker B4. The main breaker's short-time delay setting must exceed the branch breaker's maximum clearing time at the maximum bus fault current:

tSTD,B3≥tclear,B4(If,max⁡)+CTIt_{\text{STD,B3}} \geq t_{\text{clear,B4}}(I_{f,\max}) + \text{CTI}

For B4 operating at 38,000 A on its instantaneous function, clearing time is approximately 1.5 cycles (25 ms). Setting B3 short-time delay to 0.1 seconds provides 75 ms of CTI, adequate for modern electronic trip units. The main breaker instantaneous function is disabled (set to "off") to prevent it from operating before B4 on a downstream bus fault.

3.4 Feeder Relay R2

The 13.8 kV feeder relay R2 protects the transformer feeder. The relay sees fault current referred through the transformer turns ratio. At 480 V bus maximum fault current of 38,000 A, the primary-referred current is:

If,primary=If,480V×48013,800=38,000×0.0348=1,321 AI_{f,\text{primary}} = I_{f,480V} \times \frac{480}{13{,}800} = 38{,}000 \times 0.0348 = 1{,}321\,\text{A}

The relay pickup is set at 1.5× transformer rated primary current:

Ipu,R2=1.5×2,000 kVA3×13.8 kV=1.5×83.7 A=125.5 AI_{pu,R2} = 1.5 \times \frac{2{,}000\,\text{kVA}}{\sqrt{3} \times 13.8\,\text{kV}} = 1.5 \times 83.7\,\text{A} = 125.5\,\text{A}

The TDS is selected so that R2 operates in 0.4 seconds at the 480 V bus maximum fault current (primary-referred 1,321 A). Using the IEC Normal Inverse characteristic and solving for TDS:

TDSR2=top⋅((If/Ipu)α−1)β=0.4×((1,321/125.5)0.02−1)0.14=0.4×0.0550.14=0.157TDS_{R2} = \frac{t_{op} \cdot \left((I_f/I_{pu})^\alpha - 1\right)}{\beta} = \frac{0.4 \times \left((1{,}321/125.5)^{0.02} - 1\right)}{0.14} = \frac{0.4 \times 0.055}{0.14} = 0.157

Round to TDS = 0.16.

3.5 Bus Relay R1

The 13.8 kV main bus relay R1 must operate at least CTI = 0.15 seconds after R2 at the maximum 13.8 kV bus fault current (22,000 A). R2's operating time at 22,000 A:

tR2(22,000)=0.16×0.14(22,000/125.5)0.02−1=0.0224(175.3)0.02−1=0.02241.107−1=0.209 st_{R2}(22{,}000) = \frac{0.16 \times 0.14}{(22{,}000/125.5)^{0.02} - 1} = \frac{0.0224}{(175.3)^{0.02} - 1} = \frac{0.0224}{1.107 - 1} = 0.209\,\text{s}

R1 must operate no earlier than 0.209+0.15=0.359 s0.209 + 0.15 = 0.359\,\text{s} at 22,000 A. Setting R1 pickup at 2.0× bus rated current (2,000 A) and solving for TDS:

TDSR1=0.36×((22,000/2,000)0.02−1)0.14=0.36×0.0510.14=0.131TDS_{R1} = \frac{0.36 \times \left((22{,}000/2{,}000)^{0.02} - 1\right)}{0.14} = \frac{0.36 \times 0.051}{0.14} = 0.131

Round to TDS = 0.14 to provide margin. R1 operating time at 22,000 A with TDS = 0.14: tR1=0.14×0.14/0.051=0.384 st_{R1} = 0.14 \times 0.14 / 0.051 = 0.384\,\text{s}. CTI = 0.384−0.209=0.175 s>0.15 s0.384 - 0.209 = 0.175\,\text{s} > 0.15\,\text{s}. Coordination verified at maximum fault current.

Minimum fault current verification: At minimum source (one substation transformer out of service), available fault current at the 13.8 kV bus is 9,800 A. R2's operating time:

tR2(9,800)=0.16×0.14(9,800/125.5)0.02−1=0.02240.097=0.231 st_{R2}(9{,}800) = \frac{0.16 \times 0.14}{(9{,}800/125.5)^{0.02} - 1} = \frac{0.0224}{0.097} = 0.231\,\text{s}

R1's operating time at 9,800 A with TDS = 0.14:

tR1(9,800)=0.14×0.14(9,800/2,000)0.02−1=0.01960.038=0.516 st_{R1}(9{,}800) = \frac{0.14 \times 0.14}{(9{,}800/2{,}000)^{0.02} - 1} = \frac{0.0196}{0.038} = 0.516\,\text{s}

CTI at minimum fault current = 0.516−0.231=0.285 s0.516 - 0.231 = 0.285\,\text{s}. Coordination maintained. Both maximum and minimum fault current checks pass.

4. Numerical Verification Requirements

Graphical TCC presentation alone is insufficient documentation for a protection coordination study. The engineer must supplement the TCC diagram with numerical verification tables that record the CTI at each device pairing for the specified fault scenarios. For each upstream-downstream device pair, the table should show:

Device Pair Fault Current (A) Downstream Time (s) Upstream Time (s) CTI (s) Required CTI (s) Pass/Fail
B4 / B3 38,000 0.025 0.100 0.075 0.050 Pass
B3 / R2 (referred) 1,321 0.100 0.400 0.300 0.150 Pass
R2 / R1 (max) 22,000 0.209 0.384 0.175 0.150 Pass
R2 / R1 (min) 9,800 0.231 0.516 0.285 0.150 Pass

This table format, combined with the TCC diagram showing curves plotted across the full fault current range, constitutes the minimum documentation required by IEEE 242 for a protection coordination study deliverable.

5. Common TCC Analysis Errors

Error 1: Plotting fuse curves without referring through transformer. All TCC curves must be referred to a common voltage base before being plotted on the same diagram. Failure to refer primary-side curves through the transformer turns ratio causes apparent coordination that does not exist in practice.

Error 2: Using minimum melting time instead of total clearing time for fuse-relay coordination. The upstream relay must coordinate with the fuse total clearing time, not the minimum melting time. Using minimum melting time understates the fuse's operating duration and makes the coordination appear tighter than it is.

Error 3: Verifying CTI only at one current level. As derived in Section 2.2, the CTI is a function of fault current and may reach a minimum at an intermediate level. The verification table must include at least three current levels per device pair.

Error 4: Disabling instantaneous trip on every device in the chain. Instantaneous trip functions provide the fastest possible fault clearing for high-current faults and should be enabled wherever the device's instantaneous reach does not extend past the downstream device's protected zone. Disabling all instantaneous functions in favor of time-delay coordination increases fault clearing time unnecessarily.

6. Conclusions

The decisive finding of a properly executed TCC study is that selectivity is a property of the entire operating envelope, not of a single fault-current snapshot. The five-level coordination developed here holds its coordination time interval at the maximum bolted fault current, but the margin that actually protects the system is the one that survives at the minimum credible fault current (the arcing fault at the end of the longest feeder under minimum-source conditions), where curves crowd together and miscoordination is most likely. An engineer who certifies coordination from the maximum-fault check alone has verified the easy case and left the hard one undocumented.

The most common implementation failure is the instantaneous element set without regard to the downstream device's interrupting time: an upstream instantaneous trip that reaches into the downstream device's fault range will operate simultaneously with it, defeating selectivity precisely when a fault occurs near the boundary between zones. This error does not appear in the steady-state one-line review; it appears only when the TCC curves are overlaid and the instantaneous pickup is checked against the downstream let-through.

The next problem the engineer should solve is the introduction of fault-current sources that the static TCC cannot represent: motor contribution that decays within the first few cycles, and inverter-based distributed generation whose current is current-limited rather than impedance-limited. Both shift the effective fault current seen by each device with time, and the coordination study must then be repeated as a time-dependent analysis rather than a single curve overlay.

Related Work

The analysis in this paper connects to several companion studies in this library. Readers concerned with the upstream and downstream engineering will find Why Protection Coordination Studies Fail in the Field develops a closely related aspect of the same problem, while Protection Coordination with Distributed Energy Resources extends the treatment into an adjacent domain. For the broader methodological context, Short-Circuit Analysis provides complementary depth.

References

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[2] IEEE Standard C37.112-1996, Standard Inverse-Time Characteristic Equations for Overcurrent Relays, IEEE, 1996.

[3] IEC 60255-151:2009, Measuring Relays and Protection Equipment: Functional Requirements for Over/Under Current Protection, IEC, 2009.

[4] IEEE Standard C37.110-2007, Guide for the Application of Current Transformers Used for Protective Relaying Purposes, IEEE, 2007.

[5] NFPA 70-2023 (NEC), National Electrical Code, NFPA, 2023.

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

[7] IEEE Standard C57.12.00-2021, Standard for General Requirements for Liquid-Immersed Distribution, Power, and Regulating Transformers, IEEE, 2021.

[8] Schweitzer Engineering Laboratories, SEL-351 Protection System Instruction Manual, SEL, 2022.

[9] GE Grid Solutions, Multilin 750/760 Feeder Protection System Instruction Manual, GE, 2020.

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[12] NERC, Protection System Misoperation Analysis, North American Electric Reliability Corporation, 2021.