Synchronous Generator Protection & Commissioning, IEEE C37.102 / ANSI 25 Synchrocheck
IEEE C37.102 Generator Synchrocheck Out-of-Phase Shock
Calculate Phasor Difference Voltage Across Open Breaker dV (pu), Subtransient Synchronizing Surge Current (pu), Synchroscope Beat Period (s), and +/-10-deg Window Dwell Time (s).
Rolled VT secondary leads that close a generator breaker 120° out of phase drive 1.75 pu vector voltage and 7.29x rated current—shearing turbine-generator coupling bolts worse than a 3-phase terminal short!
Before closing a generator breaker onto an infinite utility grid, **ANSI Device `25` Synchrocheck Relays (`IEEE C37.102` / `IEEE C50.13`)** verify `Delta_V <= 0.05` pu, **Slip Frequency `Delta_f = |f_G - f_S| <= 0.067` Hz**, and **Phase Angle `|delta| <= 10°`**! Across Generator Voltage `V_G` (`pu`), Bus Voltage `V_S` (`pu`), and Instantaneous Phase Angle `delta` (`deg`), the law of cosines fixes **Open-Pole Phasor Difference Voltage `Delta_V_{vec} = sqrt(V_G^2 + V_S^2 - 2 * V_G * V_S * cos(delta))`** (`pu`), which drives **Initial Subtransient Stator Shock Current `I_{sync} = Delta_V_{vec} / X_{tot}''`** (`pu` across `X_d'' + X_{GSU} + X_{sys}`)! Meanwhile, Slip Frequency `Delta_f` (`Hz`) sets **Synchroscope `360°` Beat Period `T_{beat} = 1 / Delta_f`** (`s`) and **`+/-10°` (`20°` total) Permissive Dwell Window `t_{win} = (20 / 360) / Delta_f`** (`s`)—if `t_{win}` is shorter than breaker close-coil time (`~50–83` ms), an un-compensated manual close misses `0°` dead-center!
Build this Commissioning Relay Setting Sheet in a shared cloud workbook—Generator_`V_G` = 1.02 pu (B2), Grid_Bus_`V_S` = 1.00 pu (B3), Closing_Angle `delta` = 8.0° (B4), Total_Loop_Subtransient_Reactance `X_{tot}''` = 0.24 pu (B5), and Slip_Frequency `Delta_f` = 0.060 Hz (B6): Phasor Difference `Delta_V_{vec}` equals `0.1423` pu (E2), Initial Synchronizing Surge Current stays gentle at **`0.59` pu** (`<= 3.0` pu IEEE C50.13 fatigue limit! E3), Beat Period equals `16.67` s (E4), and `+/-10°` Window Dwell equals **`0.926` s** (E5)! When protection engineers review commissioning workbooks via `suggester` proposals or the scoped OAuth **Arte Sheets ChatGPT `0.1.0` connector** (currently **`In review` / `Not published`**; `read_range` inspects `<= 200` raw cells/formulas without recalculating and consumes `0` Arte AI credits under the `120`/min account limiter, while `apply_changes` requires Pro + `editor`/`owner` + matching `revision` and routes concurrent edits to `pendingReview`), always verify live recalculated `I_{sync}` inside Arte Sheets before approving relay settings!
| IEEE C37.102 / Device 25 Synchrocheck KPI (VG=1.02 pu, VS=1.00 pu, X''tot=0.24 pu) | Formula | Verified Output |
|---|---|---|
| Vector Voltage Across Breaker (pu) | SQRT(VG^2 + VS^2 - 2*VG*VS*COS(delta_rad)) | 0.1423 pu @ 8° (1.7494 pu @ 120° VT roll!) |
| Subtransient Shock Current (pu) | Vector_Diff_dV_pu / Total_Subtrans_X_pu | 0.59 pu SAFE (7.29 pu SHAFT TWIST!) |
| Synchroscope 360° Beat Period (s) | 1 / Slip_Frequency_df_Hz | 16.67 s/rev (2.86 s/rev racing governor) |
| +/-10° Permissive Window Time (s) | (20 / 360) / Slip_Frequency_df_Hz | 0.926 s ample (0.159 s late-close risk!) |
IEEE C37.102 Law-of-Cosines Synchronizing Shock & Slip-Window Formula
Validate `V_G, V_S` in `[0.80, 1.20]` pu, `Closing_Angle delta` in `[0, 180]`°, `Total X''` in `[0.08, 1.50]` pu, and `Slip_Frequency Delta_f` in `[0.005, 2.00]` Hz!
=LET(vg_p, B2, vs_p, B3, dg_d, B4, xd_p, B5, sf_h, B6, IF(OR(vg_p < 0.8, vg_p > 1.2, vs_p < 0.8, vs_p > 1.2, dg_d < 0, dg_d > 180, xd_p < 0.08, xd_p > 1.5, sf_h < 0.005, sf_h > 2), "Invalid Sync Input", ROUND((20 / 360) / sf_h, 3)))Rolled VT Phase (`delta = 120°`) + Fast `0.35` Hz Slip Catastrophic Mis-Synchronization Check
Swap A-B-C potential-transformer phase wires during commissioning (`delta` = `B4 = 120°`) with fast governor slip (`B6 = 0.35` Hz): Permissive Window E5 shrinks to `0.159` s, Open-Breaker Vector Voltage E2 jumps `12x` to **`1.7494` pu**, and Stator Shock Current E3 explodes to **`7.29` pu**—exceeding GSU winding hoop bracing and shearing turbine coupling keys!
=IF(ISTEXT(E5), E5, LET(dv_p, SQRT((B2 ^ 2) + (B3 ^ 2) - 2 * B2 * B3 * COS((B4 * PI()) / 180)), ROUND(dv_p / B5, 2)))Try the example
Use the original values or change them to test your understanding.