This simulator models a balanced three-phase Thevenin source feeding a bolted or resistive three-phase fault through a breaker, using an analytic R-L transient solution for each phase. Adjust source voltage, short-circuit strength, X/R ratio, fault resistance, frequency, inception angle and the breaker's contact-separation command, then watch the first cycles of fault current and the current-zero interruption of each pole.
• A real-time 3D model of the Thevenin source, source R/L impedance, three-pole breaker, the three phase conductors (red/teal/violet for A/B/C), the bolted/resistive fault branch and the current-recording point, with home view, focus-selected-part, toggleable enclosure, auto-rotate and expand controls, tappable components with callouts, and numbered labels matching a companion diagram. • Seven live controls: source line-to-line voltage, source short-circuit strength, source X/R ratio, per-phase fault resistance, frequency, phase-A inception angle, and the contact-separation command time. • Play/pause, single-step and larger-step time controls, plus a playback-speed selector from 0.1x to 60x laboratory speed. • Apply three-phase fault and remove fault fixture actions, with a live sequence narrative and per-component status. • Six live metrics: phase A, B and C instantaneous current, prospective symmetrical RMS current, captured absolute peak, and the summed three-phase I²t. • A Three-phase waveforms tab with two charts, the full model equations, and snapshot measurements. • An Experiments tab with four guided scenarios (asymmetric first peak, stronger grid, more persistent offset, added fault resistance), a model-verification bench of independent automated checks, and a timestamped event log with a copyable trial report. • A Learn & assess tab with guided lessons, a knowledge-check quiz and a written scope/reference statement.
Short-circuit strength (MVA) and system voltage together set the source's Thevenin impedance magnitude, which fixes the prospective symmetrical RMS current — the steady AC component the fault would carry indefinitely if there were no decaying transient. But because current in an inductor cannot change instantaneously, the moment a fault is applied, a decaying DC offset appears that forces the total current to start from its actual pre-fault value (zero, in this no-load fixture).
How large that offset is, and therefore how high the very first current peak rises, depends on the phase's inception angle relative to the source impedance angle (set by X/R). A fault started near a natural current zero produces the largest possible offset and can push the first peak well above √2 times the symmetrical RMS value, while a fault started near peak voltage produces little or no offset. Because the three phases are 120° apart, the same event gives each phase a different inception angle and therefore a different offset and first-cycle peak, even though all three share the same symmetrical impedance.
The equations panel shows |Zsource| = VLL²/Ssc, the time constant τ = L/R with impedance angle θ = atan(X/R), and the full analytic current ik(t) = √2·IRMS[sin(ωt + αk − θ) − sin(αk − θ)e^(−t/τ)] for each phase's own inception angle αk = α − k·120°. The thermal integral sums iA² + iB² + iC² over time to give the three-phase I²t shown in the metrics.
The breaker cannot interrupt current at an arbitrary instant — after the contact-separation command, each pole is modeled as clearing independently at its own next current zero, which is why the three poles do not necessarily stop conducting at the same moment. This is a constant-impedance analytic model: it excludes generator subtransient decay, transformer saturation, arc voltage, transient recovery voltage and any certified making/breaking duty rating.
Because current in an inductor cannot change instantaneously, applying a fault forces a decaying DC offset onto the steady-state symmetrical AC current so the total current starts at its actual pre-fault value. When the fault is initiated near a natural current zero, this offset is largest and adds to the AC component, so the very first peak can exceed √2 times the symmetrical RMS current — this is exactly what the asymmetric-first-peak experiment demonstrates.
The decay is governed by the time constant τ = L/R, which is set by the source X/R ratio at the selected frequency. A higher X/R ratio produces a larger time constant, so the DC offset decays more slowly and asymmetrical current persists over more cycles, as shown in the "more persistent offset" experiment with X/R set to 30.
The circuit breaker cannot interrupt current except at a natural current zero. Because the three phases are 120° apart and each has its own inception angle relative to the source impedance angle, their current-zero crossings after the contact-separation command occur at different times, so each pole is modeled as clearing independently at its own next zero.
This is a constant R-L Thevenin source model with zero pre-fault current, a fixed symmetrical impedance and an analytic transient solution per phase. It excludes generator subtransient reactance decay, transformer saturation, arc voltage, transient recovery voltage (TRV), and any certified making or breaking duty rating for the breaker.