Power System Relaying & Substation Protection, IEEE C37.110 Transient CT Saturation
IEEE C37.110 CT Knee Voltage & X/R Saturation Formula
Calculate Secondary Symmetrical Fault Current (A), Symmetrical Burden Voltage Vs (V), Transient DC-Offset Excitation Demand Vs*(1 + X/R) (V), and % of Knee Voltage Vk.
A C400 relay CT with only 62 V symmetrical burden voltage still saturates violently at 1,178 V when X/R = 18—causing bus differential false trips!
Relay engineers checking **Protective Current Transformers (`CTs`, `IEEE C37.110`)** solely against steady-state **Symmetrical Secondary Voltage `V_{sym} = (I_{fault} / N_{CT}) * Z_b`** (`where N_{CT}` is Turns Ratio e.g. `240` for `1200:5`, and `Z_b = R_{CT} + 2 * R_{lead} + Z_{relay}` Ohm) miss `90%` of real-world CT saturation events! An asymmetrical fault near a generator or substation transformer (`Primary System Inductance-to-Resistance Ratio X / R = 12–30`) injects a uni-directional **Decaying DC Offset** whose core flux integrates `(X / R)` times higher than `60`-Hz AC flux! By the **`IEEE C37.110` Saturation-Free Criterion**, avoiding core clipping altogether requires **Transient Excitation Voltage `V_{tr} = V_{sym} * (1 + X / R) <= V_k`** (`CT Saturation Knee Voltage` V)—otherwise core flux hits `368%` of `V_k` within `1–2` cycles, chopping secondary waveforms and starving `50` instantaneous elements or falsely tripping `87B` bus differential relays on external through-faults!
Verify on a `1200:5` (`N = 240`), `C400`-Class (`V_k = 320` V knee) Substation Feeder CT with Short Digital-Relay Leads—Primary_Symmetrical_Fault `I_f` = 24.0 kA (B2), Turns_Ratio `N_{CT}` = 240 (B3), Total_Secondary_Loop_Burden `Z_b` = 0.18 Ohm (B4), Primary_System `X / R` = 12.0 (B5), and CT_Knee_Point `V_k` = 320.0 V (B6): Secondary Symmetrical Current equals `100.0` A (`20x` `5` A nominal! E2), Symmetrical Burden Voltage looks tiny at `18.0` V (E3), Transient DC-Offset Flux Demand jumps `13x` to **`234.0` V** (E4), staying safely linear at **`73.1%` of `V_k`** (E5)!
| IEEE C37.110 CT Saturation KPI (24 kA Fault, 1200:5 N=240, Vk=320 V) | Formula | Verified Output |
|---|---|---|
| Secondary Symmetrical Fault (A) | (Primary_Fault_kA * 1000) / Turns_Ratio_N | 100.0 A RMS (20x 5 A tap) |
| Symmetrical Burden Voltage Vs (V) | Secondary_Fault_A * Loop_Burden_Zb_Ohm | 18.0 V (62.0 V @ long #12 AWG yard run) |
| Transient DC-Offset Demand Vtr (V) | Symmetrical_Vs_V * (1 + Primary_X_Over_R) | 234.0 V (1,178.0 V >> 320 V knee!) |
| Knee Flux Utilization (%) | (Transient_Demand_Vtr / CT_Knee_Vk_V) * 100 | 73.1% LINEAR (368.1% DEEP SATURATION!) |
IEEE C37.110 (1 + X/R) Transient Dimensioning Factor & Knee-Point Formula
Validate `Primary_Fault I_f` in `[0.5, 100]` kA, `Turns_Ratio N` in `[10, 2,000]`, `Loop_Burden Z_b` in `[0.02, 10.0]` Ohm, `Primary X/R` in `[1, 80]`, and `CT_Knee V_k` in `[20, 2,000]` V!
=LET(if_k, B2, nc_t, B3, zb_o, B4, xr_r, B5, vk_v, B6, is_a, (if_k * 1000) / nc_t, vt_r, (is_a * zb_o) * (1 + xr_r), IF(OR(if_k < 0.5, if_k > 100, nc_t < 10, nc_t > 2000, zb_o < 0.02, zb_o > 10, xr_r < 1, xr_r > 80, vk_v < 20, vk_v > 2000), "Invalid CT Input", ROUND((vt_r / vk_v) * 100, 1)))Long Switchyard Control Cable + Close-In Bus X/R = 18 (`Z_b = 0.62` Ohm) Saturation Check
Run `150` m of `#12 AWG` copper yard leads to the control house (`Z_b` climbs to `B4 = 0.62` Ohm) on a high-`X/R` bus (`B5 = 18`): Steady-state `V_{sym}` E3 (`62.0` V) still looks `5x` below `320` V, YET Transient DC-Offset Demand E4 explodes to **`1,178.0` V** (**`368.1%` of `V_k`** in E5)—proving why utilities specify **`1` A secondary CTs** (`25x` lower `I^2 * R` wire burden!) or step up to a `2000:5` C800 ratio!
=IF(ISTEXT(E5), E5, ROUND(((B2 * 1000) / B3) * B4 * (1 + B5), 1))Try the example
Use the original values or change them to test your understanding.