Determines required Current Transformer (CT) knee-point voltage (Vk), total secondary loop burden resistance (Rct + 2·Rlead + Rrelay), and verifies that protection CTs (Class 5P20, Class PS / PX, or IEEE C-Class) will not saturate under maximum through-fault current and system DC offset X/R.
Governing Formulas & Standards
Standards Basis: IEC 61869-2 (formerly IEC 60044-1) / IEEE Std C37.110
V_k \ge K \cdot I_{sc,sec} \cdot (R_{ct} + 2 R_{lead} + R_{relay}) \quad ; \quad I_{sc,sec} = I_{sc,pri} \times \left(\frac{I_{sec}}{I_{pri}}\right)
Calculates required CT knee-point voltage V_k (V) where K is protection security factor (typically 2.0 for differential/distance protection, or 1 + X/R for transient dimensioning), I_sc,sec is maximum secondary fault current, and R is total loop resistance in ohms.
Worked Engineering Example: Sizing 1200/1 A Class PS CT for Feeder Protection (25 kA Fault Level)
- Secondary Fault Current: I_sc,sec = 25,000 × (1 / 1200) → 20.83 A
- Total Secondary Loop Resistance: R_total = R_ct + 2×R_lead + R_relay = 4.5 + 0.92 + 0.10 → 5.52 Ω
- Required Knee-Point Voltage (Vk): V_k = 2.0 × 20.83 × 5.52 → 229.96 V
Final Solution: Recommended Knee-Point Voltage: Vk ≥ 250 V (at Imag ≤ 30 mA) | Total Loop Burden: 5.52 Ω
Frequently Asked Questions
- What is the knee-point voltage of a Current Transformer?
- The knee-point voltage (Vk) is the point on the excitation curve where a 10% increase in secondary RMS voltage produces a 50% increase in magnetizing current. Above Vk, the CT core enters severe magnetic saturation and distorts secondary current.
- Why are 1 A CTs superior to 5 A CTs for long outdoor switchyard runs?
- Because cable burden scales with the square of secondary current (P = I²R). A 5 A CT produces 25× higher lead resistance voltage drop and burden VA than a 1 A CT over identical 100m cable runs, requiring drastically larger copper cables or impractically massive CT cores.
Interactive calculation engine and real-time CAD solver available online at https://amithvijayan.in/tools/ct-sizing-calculator.