gfm_solver v1.0.0 Zero-CDN Browser RK4 + Python State-Space 20 kVA | 230 Vrms | 50 Hz | LCL + TVI + PAW

Grid-Forming (VSG, Droop, dVOC) & Weak-Grid GFL Electromagnetic Workbench

Interactive browser-side 4th-order Runge-Kutta (dt = 250 us) electromagnetic fault & weak-grid simulator coupled with exact Python state-space modal participation, synchronous-dq admittance passivity nu(f), and Generalized Nyquist Z = P + N datasets. (Model-consistency research workbench only, not hardware or grid-code certification.)

Ride-Through Verdict
PASS
Bounded
Peak Bridge |i_1,dq|
--
--
Max Power Angle |delta|
--
--
Frequency Extremum
--
--
GFL Critical Hopf SCR
--
--
dq Passivity min nu(>=25Hz)
--
--
Fault Reactive Q_pcc
--
--
Post-Event Settled P_pcc
--
--

1. Inverter Bridge Current |i_1,dq| (A_pk) vs. 48 A Ceiling

2. Synchronizing Power Angle delta_rel(t) (deg)

3. Weak-Grid Eigenvalue Growth max Re{lambda} vs. SCR

4. Synchronous-dq Admittance Passivity Index nu(f) (S)

Solver-Verified Synchronous-dq Admittance Passivity & Nyquist (SCR = 1.65, P = 15 kW)

Converter Architecture min nu (f >= 25 Hz) Non-Passive Band (>= 25 Hz) Negative Re{Y_qq} Band Stiff-Bus RHP P Nyquist Winding N Closed-Loop Z = P + N

Reproducible Python Solver Benchmark Gallery (main.py)

All 6 publication figures are deterministically generated by python main.py and verified in CI across Python 3.10–3.13 against state-space eigenvalues, SciPy RK45, and Generalized Nyquist invariants.

Figure 1, Small-Signal Modal Participation, dq Admittance Passivity & Generalized Nyquist

Figure 1, Small-Signal Modal Participation, dq Admittance Passivity & Generalized Nyquist

14-state VSG participation matrix P_ki, Qoria F_i = 0.75 passivity restoration (min nu >= 25 Hz = +0.0019 S vs. F_i = 1.00 dip -1.04 S), and exact Z = P + N.

Figure 2, 14-State Electromagnetic FRT (0.15 pu Sag) & -45° Phase-Jump Ride-Through

Figure 2, 14-State Electromagnetic FRT (0.15 pu Sag) & -45° Phase-Jump Ride-Through

Unprotected 160.2 A spike & Hard-Clamp 440.7° windup LOS vs. coordinated TVI + PAW (I_pk = 47.95 A <= 48 A, max delta = 27.5°, zero cycle slips).

Figure 3, Weak-Grid SCR Collapse & Parallel-Line Opening: GFL (SRF-PLL) vs. GFM

Figure 3, Weak-Grid SCR Collapse & Parallel-Line Opening: GFL (SRF-PLL) vs. GFM

GFL Hopf instability at SCR_crit = 2.99 / 1.80 / 1.67 (55/35/10 Hz PLL) and SCR 4.0 -> 1.22 line-trip pole slip vs. Hurwitz GFM VSG & dVOC ride-through.

Figure 4, Comparative GFM Control Triad: Droop (13), VSG (14) & Andronov-Hopf dVOC (12)

Figure 4, Comparative GFM Control Triad: Droop (13), VSG (14) & Andronov-Hopf dVOC (12)

Droop t_90 = 99 ms (18.44 kW), VSG inertial support (21.52 kW, 49.748 Hz nadir), and dVOC exact Bernoulli black-start limit-cycle self-excitation.

Figure 5, 14-State Synchronous-dq LCL Plant & Cascaded Dual-Loop PI Verification

Figure 5, 14-State Synchronous-dq LCL Plant & Cascaded Dual-Loop PI Verification

Cross-timescale agreement against the 4-state Thévenin model plus passive R_d = 1.8 Ohm suppression of the 1049 Hz LCL resonance.

Figure 6, Closed-Loop 4-State VSG Swing & Thévenin AC Grid Baseline (SCR = 6.0)

Figure 6, Closed-Loop 4-State VSG Swing & Thévenin AC Grid Baseline (SCR = 6.0)

20 kVA / 230 Vrms canonical RoCoF & load-step transient: Nadir = 49.748 Hz, Peak P_pcc = 21.60 kW, Final settled P_pcc = 17.90 kW.