Out-of-Phase Closing Calculator - Synchroscope Training

System Parameters Input

Define system base, impedances, and closure conditions

Voltage Class (kV)

System Base MVA (MVA)

Source 1 Impedance, X₁ (pu on system base)

Source 2 Impedance, X₂ (pu on system base)

Total Impedance, X_total = X₁ + X₂

X/R Ratio (for asymmetry factor)

Bus Voltage, V_bus (kV L-L) Nominal ±10%: 124.2 – 151.8 kV

Incoming Voltage, V_inc (kV L-L) Nominal ±10%: 124.2 – 151.8 kV

Phase Angle at Closure, δ (degrees)

30°

Breaker Closing Time (cycles @ 60 Hz)

Optional Inputs (for mechanical stress calculations)

Generator MVA Rating (MVA) For shaft torque analysis per IEEE C50.13

Transformer MVA Rating (MVA) For winding force & thermal analysis

Results Dashboard

Calculated stresses from out-of-phase closure

Voltage Analysis

V_bus (line-to-line) --

V_incoming (line-to-line) --

Voltage across contacts, V_diff V_diff = √(V₁² + V₂² − 2·V₁·V₂·cosδ) --

V_diff per-unit on system base --

V_diff as % of nominal --

Peak voltage across contacts V_peak = V_diff × √2 --

Current Analysis

Steady-state current, I_ss I_ss = V_diff / (√3 × X_total,Ω) --

Peak asymmetric current, I_peak I_peak = I_ss × √2 × (1 + e^−π/(X/R)) --

Asymmetry multiplier (K_peak) --

Rated system fault current I_fault = S_base / (√3 × V_base × X_total,pu) --

I_peak as multiple of rated --

Energy and Power

Instantaneous 3-phase power P = V_diff² / X_total,Ω --

Energy during closure transient E = P × t_closing --

Equivalent fault MVA S = V_diff,pu² / X_total,pu × S_base --

Equivalent % of bolted 3-phase fault --

Generator Mechanical Stress

Generator rated MVA --

Estimated shaft torque T_pu ≈ V_diff,pu / X_d (typ. X_d=0.3) --

Risk assessment (IEEE C50.13) --

Transformer Stress

Transformer rated MVA --

Per-unit current through transformer I_pu on transformer base --

Winding force ratio (I²) Force ∝ I² --

Thermal stress (I²t) vs rated fault withstand --

Angle Sweep Chart

Key parameters vs. phase angle (0° to 180°)

Voltage across contacts (kV)

Peak transient current (kA)

Transient energy (MJ)

Sync check window (±10°)

Current operating point

Reference Tables

Standard values for design and relay setting verification

Quick Reference — Voltage Across Contacts (Equal Magnitudes)

Phase Angle	V_diff (pu)	V_diff (% nom)	Risk Level
0°	0.000	0.0%	None
5°	0.087	8.7%	Minimal
10°	0.174	17.4%	Low
20°	0.347	34.7%	Moderate
30°	0.518	51.8%	Significant
45°	0.765	76.5%	High
60°	1.000	100.0%	Very High
90°	1.414	141.4%	Severe
120°	1.732	173.2%	Extreme
150°	1.932	193.2%	Catastrophic
180°	2.000	200.0%	Maximum

Typical Sync Check Relay Settings by Application

Application	Angle Window	Voltage Diff	Slip Freq
Generator synchronizing	±10°	≤5%	≤0.067 Hz
Transmission tie line	±20°	≤5%	≤0.05 Hz
Distribution feeder	±15°	≤10%	≤0.1 Hz
Emergency / black start	±30°	≤10%	≤0.1 Hz

Out-of-Phase Closing Engineering Calculator