Coupled Frequency-Dependent Line Runtime

AIMORA executes one exact accepted L205 complete reciprocal 2n-port scattering realization at a time as a fixed-step phase-domain EMT element. L200 remains the physical Z(f)/Y(f) source and L205 remains the continuous rational-fit and global-passivity owner; the runtime verifies both signatures and never replaces the accepted realization by a constant-parameter, scalar-mode, independent-phase, or visually similar line.

For the continuous state equations $\dot{x}=Ax+Ba$ and $b=Cx+Da$, the default endpoint trapezoidal map uses $\alpha=2/\Delta t$, $A_d=(\alpha I-A)^{-1}(\alpha I+A)$, and $B_d=(\alpha I-A)^{-1}B$. The accepted-boundary recurrence is $x_{k+1}=A_dx_k+B_d(a_{k+1}+a_k)$ and $b_{k+1}=Cx_{k+1}+Da_{k+1}$. A declared prewarp is optional, fixed for the preparation, and must remain below Nyquist; variable-step or DASSL execution is not part of this runtime.

Every sending and receiving terminal current is positive into the line. With positive diagonal reference impedance $R$, voltage, inward current, incident wave, and outgoing wave obey $v=R^{1/2}(a+b)$ and $i=R^{-1/2}(a-b)$. Eliminating $a_{k+1}$ produces one complete reciprocal Norton matrix and one history-current vector in the exact port order. All off-diagonal sending/sending, sending/receiving, receiving/sending, and receiving/receiving terms are stamped; no mutual block may be discarded.

Preparation refuses a stale or failed L205 fit, unstable discrete pole, source band at or above Nyquist, excessive bilinear warping, ill-conditioned state or wave solve, asymmetric companion beyond tolerance, active companion, sampled discrete passivity violation, invalid phase/port/reference order, or nonfinite data. The continuous L205 Hamiltonian certificate remains authoritative; the sampled discrete check confirms the chosen timestep rather than replacing that certificate.

De-energized initialization clears every rational, wave, current, energy, and counter state. Sinusoidal initialization evaluates the exact discrete response at the declared peak-cosine frequency, solves terminal current and incident waves in the same reference basis, and solves $(zI-A_d)x_0=B_d(z+1)a_0$. The first accepted step therefore continues the discrete sinusoid without an artificial state transient.

Stamping is read-only. A trial network solve may be repeated without advancing the line. After one complete accepted nodal solution, AIMORA reconstructs incident and outgoing waves, checks the Norton current against the wave current, checks finite state and the zero-initial-energy passive bound, and then commits all rational and history state exactly once. A failed check leaves the prior accepted state unchanged.

Outputs expose terminal voltages and inward currents, incident and outgoing waves, Norton history currents, terminal power, cumulative supplied energy, maximum KCL residual, state magnitude, accepted time and step count, initialization identity, exact source/response/fit/model/settings/runtime signatures, passivity diagnostics, and explicit unsupported-claim flags. Positive power and energy enter the line.

The typed snapshot binds the complete runtime preparation and mutable accepted state. The line-level snapshot additionally binds the exact sending and receiving node order. Public TOML round-trip retains an integrity signature and refuses unknown schema, malformed data, altered state, stale preparation, changed timestep, or changed terminal nodes. Restoring does not advance time or history, and the next accepted trajectory must match uninterrupted execution exactly.

The public examples coupled_line_runtime_overhead and coupled_line_runtime_cable execute the accepted generic L200/L205 products through sinusoidal initialization, a receiving-end phase fault and clearing, energy/KCL diagnostics, and exact midpoint restart. coupled_line_runtime_mixed_route executes the overhead and cable segments separately and maps the overhead a,b,c receiving junction explicitly into the cable fit's c,a,b sending order. It never forms one length-averaged mixed-route line.

Every public product also executes each exact L205-declared 110 Ω·m soil alternative through the same timestep, discrete initialization, event schedule, terminal maps, outputs, and midpoint snapshot/restart policy. The alternative fit and source identities must match the nominal fit's ordered uncertainty declaration exactly. The resulting runtime_uncertainty.csv reports time-aligned phase-voltage, terminal-current, power, cumulative-energy, and KCL envelopes; the summary records peak bounds and explicitly states that the declared set is incomplete, so unmodelled uncertainty remains unknown.

The nominal and every declared alternative are repeated at 5 µs with identical initialization, event times, phase/port maps, channels, and exact restart. runtime_refinement.csv reports the time-aligned 10/5 µs voltage, current, power, cumulative-energy, and KCL differences. This is public timestep-refinement evidence and does not mislabel either discretization as an external reference.

The catalogue entry is generic_coupled_line_runtime. Each example writes compact waveform, energy/KCL, uncertainty, and refinement CSV files, a runtime report containing nominal and alternative scenarios, one typed nominal snapshot per uniform segment, a summary, and curated voltage and energy SVGs.

The accepted public domain is bounded by the recorded generic source and fit signatures, phase/port/node maps, reference impedances, 1 Hz through 10 kHz public fit band, fixed 10 µs example timestep, declared events, and exact licences. These products do not claim ULM-file compatibility, ATP/PSCAD equivalence, arbitrary imported fits, manufacturer or utility prediction, protected-standard conformance, field-measurement accuracy, variable-step/DASSL behavior, or certification.