Selective Harmonic Elimination at N=17 with 16 Simultaneous Eliminations: A Deterministic Result with Independent MATLAB Verification

A single certified solution to the Selective Harmonic Elimination (SHE)problem for a three-phase, two-level voltage source inverter with N = 17switching angles per quarter cycle, simultaneously eliminating sixteennon-triplen harmonics (H5, H7, H11, H13, H17, H19, H23, H25, H29, H31,H35, H37, H41, H43, H47, H49) at modulation index M = 0.81 on an 800 VDC bus. KEY RESULT The reported angle set drives the residual norm of the SHE equationsto 7.71 × 10⁻¹³ — the IEEE 754 double-precision arithmetic floor. Thethree-phase line-to-line THD is 26.4165% (computed with triplenharmonics excluded, as they cancel in the αβ system). The stator-fluxtrajectory in the αβ plane achieves 98.7% circularity, computedanalytically via the Clarke transform. Twenty-three independentcorrectness checks all pass. The solution was produced by the SHE Designer engine (New Leaf ToolsLLC), which performs deterministic enumeration of the certified solutionspace and ranks candidates by user-selected secondary objectives. Forthis operating point, the engine discovered twenty-three certifiedcandidate solutions in 3.7 seconds on a desktop CPU. This depositpresents the candidate selected under the Flux Trajectory Circularitycriterion. INDEPENDENT VERIFICATION The included MATLAB script reproduces every claim in the report fromthe published angles alone, using only the standard SHE Fouriercoefficient equation: b_n = (4·Vdc)/(n·π) · Σ σ_k · cos(n · α_k), k = 1, ..., N No proprietary code is required. The script runs in any base MATLAB orGNU Octave installation, requires no Mathworks add-ons, and completesin under one second. The expected output is "23 / 23 PASSED — ALLCHECKS PASSED." WHAT THIS DEPOSIT IS • A reproducible proof of capability at one operating point • An open, citable reference for the SHE-PWM research community • A timestamped public artifact under CC BY 4.0 • A full hardware-readiness audit including dead-time gaps, DSP timer registers (100 MHz reference clock), quantization survival at 12-bit, and switching-loss comparison vs. conventional 20 kHz PWM WHAT THIS DEPOSIT IS NOT • Not a proof of complete enumeration of the SHE solution space. Twenty-three solutions were discovered by the engine at this operating point; this deposit does not claim that number is exhaustive. • Not a look-up table. One operating point, one elimination set, one topology. • Not a disclosure of the engine. The enumeration method, candidate generation strategy, and ranking algorithms are proprietary to New Leaf Tools LLC. • Not a replacement for electromagnetic simulation or hardware testing in production deployment. The verification covers the mathematical correctness of the ideal stepped switching waveform. CONTENTS 1. Certified solution report (PDF) — full angle set, certification results, hardware audit, αβ flux trajectory, secondary-objective ranking, filter specification, and embedded MATLAB script 2. Standalone MATLAB verification script (.m) 3. README with operating point parameters, verification instructions, and prior-art references 4. CITATION.cff for machine-readable citation APPLICATIONS The capability demonstrated here applies directly to: • UPS inverter modulation stages • Battery energy storage system (BESS) power conversion systems • Grid-tied photovoltaic and wind inverters • STATCOM and active filter modulation • Motor drive inverters with reduced switching loss • Any 800 V DC power-block submodule using two-level VSI topology For multilevel topologies (3-level NPC, 3-level T-type, 5-level CHB,5-level ANPC), the engine produces analogous certified solutions butthose are not the subject of this deposit. INDUSTRIAL LICENSING The engine that produced this result is available for industriallicensing or contract waveform-library generation under NDA. Contactthe author for engagement. PRIOR ART This deposit's contribution is not the underlying SHE-PWM theory,which has a fifty-year history (Patel & Hoft 1973; Sun, Beineke &Grotstollen 1996; Dahidah & Agelidis 2008; Holmes & Lipo 2003). Thecontribution is a concrete, publicly verifiable certified solution atN = 17 with sixteen simultaneous eliminations at machine-precisionresiduals, produced deterministically in seconds and accompanied byan independent verification artifact. CITATION If you reference this result, please cite using the DOI assigned byZenodo to this record. A machine-readable CITATION.cff file is includedin the deposit. CONTACT Craig Ulmer — New Leaf Tools [e-mail]