Protection Coordination TCC

Overview

The Protection Coordination TCC calculator generates Time-Current Characteristic curves for up to 8 protection devices on a single log-log chart. It verifies that adjacent protective devices are properly coordinated — i.e. the downstream device operates faster than the upstream device by a specified time margin.

The calculator provides:

• TCC curve generation — log-log SVG chart with all device curves
• Tolerance bands — ±15% for circuit breakers, ±10% for relays
• Coordination check — automatic verification of time grading between adjacent pairs
• Multiple device types — circuit breakers (IEC/ANSI/IEEE/LSI), fuses, cables, transformers, motors, relays
• Multiple standards — IEC 60255, ANSI, IEEE C37.112 curve families

Input Parameters

Device Types

Circuit Breaker

Supports IEC 60255 (SI, VI, EI, LTI, DT), ANSI (MI, VI, EI, STI, LTI, DT), IEEE C37.112 (U1–U5, DT), and LSI (Long-time/Short-time/Instantaneous) trip units. Tolerance bands at ±15%.

Fuse

Supports gG, gM, aM, and aR fuse types with pre-arcing and total clearing curves. gG and gM use a generic curve that passes inside the IEC 60269-1 gates (rated currents 16–1250 A); aM and aR use an uncited generic shape.

Cable

Adiabatic damage curve: t = (k×S)²/I². Supports Cu and Al conductors with PVC, XLPE, EPR, and MI insulation. Accounts for parallel cables.

Transformer

Through-fault damage curve: t = 1250/M² (per ANSI/IEEE C57.109). Magnetising inrush envelope (8-point standard curve).

Motor

Starting current curve (decaying from LRC to FLA). Thermal damage curve: t = 30/M².

Relay

Same curve families as breakers but with CT ratio conversion from secondary to primary amps. Tolerance bands at ±10%.

Output Results

• TCC Chart — SVG log-log plot with all device curves, tolerance bands, and legend
• Coordination Status — PASS/FAIL for each adjacent device pair
• Minimum Margin — smallest upstream − downstream operating time between adjacent devices, and the current where it occurs
• Device Summary — table of all devices with ratings and settings

Formulas

IEC/ANSI/IEEE Inverse-Time Curve

t = TMS × (A / (M^p - 1) + B)

Where M = I / I_pickup, TMS = Time Multiplier Setting.

IEC 60255 Curves

ANSI Curves

IEEE U-curves (U1–U5)

These are the U.S. relay curves as numbered in SEL relays (SEL-351 / SEL-751 instruction manuals): t = TD × (B + A ÷ (M^p − 1)). U1, U3 and U4 are the IEEE C37.112-2018 Table 1 moderately, very and extremely inverse shapes (the MI/VI/EI rows of the ANSI table above) with the time dial rescaled by about 1/5, so a U-curve TD of 5 is close to a C37.112 TD of 1. U2 (inverse) and U5 (short-time inverse) have no C37.112 counterpart.

Instantaneous Element

Above the instantaneous pickup the operating time is the instantaneous time; below it the inverse-time curve applies. The bands are piecewise by current, as a trip-unit or relay TCC is drawn: the inverse equation is never extrapolated past the instantaneous pickup to a time faster than the instantaneous time.

LSI Circuit Breaker

Electronic trip unit bands per IEC 60947-2 cl. 8.3.3 (overload, short-time-delay and instantaneous releases; UL 489 / IEEE Std 1015 for LSI trip units). Each band governs only its own current range:

Long-time:     t = TD × (6/M)²   (1.05 Ir ≤ I < Ir × ST_pickup)
Short-time:    t = ST_delay      (Ir × ST_pickup ≤ I < Inst_pickup)
Instantaneous: t = Inst_delay    (I ≥ Inst_pickup)

Cable Adiabatic Equation

t = (k × S)² / I²

Where k = conductor constant (Cu/PVC=115, Cu/XLPE=143, Al/PVC=76, Al/XLPE=94), S = CSA in mm².

Fuse Characteristic (gG / gM)

A generic gG pre-arcing curve built from the IEC 60269-1:2006 limits for the rated current I_n (gM: the characteristic current I_ch, which takes the gG gates). Four points are placed mid-window (geometric mean) of each limit, so the curve passes inside every gate:

Between points (log-log straight line):  t_pre = t1 × (t2/t1)^( ln(I/I1) / ln(I2/I1) )
Above point 4 (constant pre-arcing I²t): t_pre = (I²t)0.01 / I²
Below point 1: no operation (the curve starts at 1.414 In)
Total clearing:                          t_total = t_pre + min(0.01 s, (I²t)0.01 / I²)

The total-clearing arcing allowance (half a 50 Hz cycle, reduced where the fuse is current-limiting so that the operating I²t is 2× the pre-arcing I²t) is a generic assumption, not an IEC 60269 value. Worked example, 100 A gG (gates 290 / 580 / 820 / 1450 A, I²t 27–86 kA²s): points (141.4 A, 7200 s), (410.1 A, 7.07 s), (1090.4 A, 0.1 s), (2195.2 A, 0.01 s); pre-arcing 67.4 s at 290 A (gate ≥ 10 s), 1.56 s at 580 A (≤ 5 s), 0.346 s at 820 A (≥ 0.1 s), 0.039 s at 1450 A (≤ 0.1 s); total clearing at 3 kA = 2 × 48 187 / 3000² = 0.0107 s.

aM / aR

Uncited generic shape (not checked against a standard; aR characteristics are manufacturer-specific): t = 10^(3.0 − 5.6 × log10(M)) × 0.8 (pre-arc) / 1.2 (total) below 4 I_n, t = k × In² / I² above (aM k = 15 / 25, aR k = 3 / 5), starting at 1.3 I_n.

Transformer Damage

t = 1250 / M²    where M = I / FLA

Transformer FLA

I_FLA = kVA × 1000 / (√3 × V)

Motor Starting Curve

I(t) = FLA + (LRC - FLA) × (1 - t/t_start)^0.5

Where FLA = full-load amps, LRC = locked rotor current, t_start = starting time.

Motor Thermal Damage

t = 30 / M²    where M = I / FLA

Motor FLA

I_FLA = kW × 1000 / (√3 × V × η × cos φ)

Relay CT Conversion

I_primary = I_pickup(sec) × CT_pri / CT_sec

Note: Relay uses the same IEC/ANSI/IEEE curve formula as breakers.

Worked Examples

The 13 examples below are the validation cases for this calculation. Each one was produced by the calculation engine from the inputs shown, every figure was checked against the independent reference quoted at the end of the example, and the same cases are run against every engine build (see validation scorecard, tool fe_calc_protection; worked examples for every calculation).

Standards & References

• IEC 60255-151 — Measuring relays and protection equipment – Functional requirements for over/under current protection
• IEC 60269-1 — Low-voltage fuses – General requirements (Tables 2, 3 and 7: gG conventional currents, gates and pre-arcing I²t)
• IEC 60947-2 — Low-voltage switchgear and controlgear – Circuit breakers
• IEEE C37.112 — Standard Inverse-Time Characteristic Equations for Overcurrent Relays
• ANSI/IEEE C57.109 — Transformer through-fault current duration guide
• AS/NZS 3000 — Wiring Rules
• AS/NZS 3008.1 — Electrical installations – Selection of cables

Tips & Limitations

• Maximum 8 devices per study
• Coordination check only applies to protection devices (breakers, fuses, relays) — cables, transformers, and motors are treated as protected equipment
• Devices are auto-sorted by pickup current (lowest = most downstream) for coordination grading
• Fuse curves are generic approximations (gG/gM inside the IEC 60269-1 gates, 16–1250 A ratings only) — always verify against manufacturer data
• Tolerance bands assume ±15% for CBs and ±10% for relays — check manufacturer data for specific tolerances
• For LSI breakers, the long-time curve uses a simplified I²t characteristic
• Coordination is checked with exact nominal operating times (fuses: total clearing) at log-spaced test currents (×1.02 apart) from the later curve start up to the current-axis maximum (the maximum fault current), plus that maximum itself and each instantaneous / short-time / fuse breakpoint and the current just below it

Architecture

The component follows the standard calc component architecture:

• calculations.py — Pure Python TCC math (constants, curve generators, coordination check)
• component.py — Schema, calculator class, SVG generator, registration
• equations.py — Report equation builder
• sidebar_form.html — Vue device editor with dynamic device cards

Curve math was ported from protection/tcc-visualiser-complete (2).html (lines 189–232).

Code Paths

calcs/components/c0039_protection_coordination/
├── __init__.py
├── apps.py
├── calculations.py          # Core TCC math
├── component.py             # Schema, calculator, SVG, registration
├── equations.py             # PDF report builder
├── excel_generator.py       # Excel report builder
└── templates/.../sidebar_form.html  # Vue device editor

Testing

pytest calcs/test_c0039_protection_coordination.py -v

Key test scenarios:

• Curve coefficient counts (IEC=5, ANSI=6, IEEE=6)
• IEC SI at M=2, TMS=0.3 ≈ 3.01s
• Cable Cu/PVC 25mm² at 1kA = 8.27s
• Fuse prearc always faster than total; gG pre-arcing curve inside every IEC 60269-1 Table 2/3/7 limit for all 20 ratings
• Tolerance band scaling (±15%, ±10%)
• Coordination PASS/FAIL with known device pairs
• Auto-sort by pickup ascending
• SVG output validation