Coupled Line Fitting and Passivity

AIMORA prepares one accepted uniform overhead-line or cable segment at a time as a complete reciprocal two-terminal rational response. The preparation consumes the exact L200 phase-domain series-impedance and shunt-admittance matrices, segment length, phase order, positive port reference impedance, and source signature. A changed source signature invalidates the fit.

The public Engine constructs the physical terminal admittance from the multiconductor telegrapher system, maps it to normalized power-wave scattering, tracks modal subspaces, extracts nonnegative delay diagnostics, owns immutable result and interchange types, and continuously recertifies an imported realization. The private production backend fits one stable common pole bank across the complete matrix and applies a complete state-space passivity correction when necessary. Off-diagonal coupling is never removed to simplify fitting.

The released public settings search pole orders 20, 40, 60, and 80 with at most 64 deterministic relocation sweeps and select the first candidate meeting 5% maximum relative spectral error, a 0.92 maximum reciprocal real direct-term singular value, continuous global passivity, and 2% maximum enforcement perturbation in both scattering and physical-admittance domains. The automatic multi-pole solve uses a first-source-row-equivalent low-frequency anchor evaluated at zero frequency; it does not invent an unavailable DC source value. Explicit manufactured poles remain exact and do not receive that automatic constraint.

The deterministic shared-pole fit scales both residue and common-denominator columns, records relocation convergence, condition, and effective rank, and performs a final fixed-pole residue solve. If the unconstrained reciprocal real direct term exceeds the bounded-real limit, AIMORA projects that term to the strict limit and re-solves every residue at the same poles; the complete source-to-fit error still governs acceptance. The continuous Hamiltonian certificate is evaluated after state balancing so that pole ranges spanning several frequency decades do not create a false imaginary-axis crossing.

Global passivity is decided for the complete coupled realization by the continuous bounded-real Hamiltonian test, including zero frequency and the infinite-frequency direct term. The SVG passivity curve is only a sampled explanatory view and cannot replace that certificate. Enforcement uses a positive-conductance linear fractional transformation, then repeats the continuous certificate and reports its effect in both scattering and physical-admittance domains. Excess error or perturbation refuses the result instead of relaxing a tolerance.

The line_fitting_overhead and line_fitting_cable examples each use 81 points from 1 Hz through 10 kHz. The line_fitting_mixed_route example fits its overhead and phase-mapped cable sections separately and retains their ordered signatures; it does not treat a length-weighted route average as one uniform propagation medium. Each example writes an exact fit TOML file, a text report, and compact response, error, and passivity CSV/SVG artifacts. The catalogue entry is generic_coupled_line_fitting_passivity.

These products are frequency-domain preparation only. They do not initialize or execute convolution histories, delay buffers, network stamps, timesteps, switching, faults, checkpoint/restart, or transition-joint behavior. Those belong to the later frequency-dependent line runtime. The products do not claim ATP/PSCAD equivalence, ULM-file compatibility, manufacturer prediction, protected-standard conformance, field-measurement accuracy, or certification.