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Evgenii Konkin
Evgenii Konkin

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The Engineering Math Behind CT Burden: How Secondary Circuit Resistance Squared Affects Protection Accuracy

#ctburden #currenttransformerburden #secondarycircuit #protectionaccuracy

A 5 A secondary current with just 1 Ω of lead resistance imposes 25 VA of burden from resistance alone — enough to saturate many protection-class CTs. This nonlinear relationship is the single most overlooked factor in CT secondary circuit design.

The Formula

The CT burden calculation combines two sources: resistance-based burden from wiring and the connected device burden. The total burden in volt-amperes (VA) is:

burdenResistance = I² × R_total
ctBurden = burdenResistance + deviceBurden
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Where:

  • I = CT secondary current in amperes (typically 1 A or 5 A)
  • R_total = total secondary loop resistance in ohms, including both conductors
  • deviceBurden = sum of burdens from connected meters, relays, and instruments in VA

The resistance term is squared because power dissipated in a resistor follows P = I²R. Doubling the secondary current quadruples the resistive burden. For a 5 A system, the burden is 25 times higher than for a 1 A system at the same resistance.

Worked Example 1

Scenario: A 5 A secondary CT with 200 ft (one-way) of #10 AWG copper wire (0.001 Ω/ft) and a connected relay burden of 0.5 VA.

Step 1: Calculate total loop resistance.

R_total = 0.001 Ω/ft × 2 × 200 ft = 0.4 Ω
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Step 2: Calculate resistance-based burden.

burdenResistance = (5 A)² × 0.4 Ω = 25 × 0.4 = 10 VA
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Step 3: Add device burden.

ctBurden = 10 VA + 0.5 VA = 10.5 VA
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Result: 10.5 VA — classified as HIGH by the Result Intelligence System (RIS). This would likely exceed a typical C100 CT rating, indicating the need for larger conductors or a higher-rated CT.

Worked Example 2

Scenario: A 1 A secondary CT with 50 m (one-way) of 2.5 mm² copper wire (0.007 Ω/m) and a connected meter burden of 0.2 VA.

Step 1: Calculate total loop resistance.

R_total = 0.007 Ω/m × 2 × 50 m = 0.7 Ω
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Step 2: Calculate resistance-based burden.

burdenResistance = (1 A)² × 0.7 Ω = 1 × 0.7 = 0.7 VA
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Step 3: Add device burden.

ctBurden = 0.7 VA + 0.2 VA = 0.9 VA
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Result: 0.9 VA — classified as LOW. This is well within most CT ratings. Note how the 1 A secondary dramatically reduces resistive burden compared to Example 1.

What Engineers Often Miss

First, many engineers use one-way lead length instead of total loop length, underestimating resistance by half. Always double the one-way distance.

Second, resistance-based burden scales with the square of secondary current. A 5 A system is 25 times more sensitive to lead resistance than a 1 A system. When long wiring runs are unavoidable, consider using 1 A secondary CTs.

Third, connected device burden is often omitted from the calculation, especially when multiple devices share the same CT circuit. Always sum all burdens from manufacturers' datasheets.

Try the Calculator

Use the CT Burden Calculator to quickly screen your secondary circuit designs. Enter your lead length or direct resistance, secondary current, and device burden to get an instant result with RIS classification.

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