This work presents a comprehensive framework for analyzing and optimizing grid-tied inverters with a focus on the combined consideration of efficiency and harmonic distortion in their output waveforms. Using dimensional analysis, a physically consistent model for total harmonic distortion is developed, enabling accurate prediction of the optimal switching frequency for pulse-width modulation controllers with a prediction error of only 1.5% compared to full-scale numerical simulations. The study introduces a theoretical upper bound for the combined efficiency and distortion performance, quantifies unavoidable losses arising from filter inductance and magnetic core components, and evaluates five different pulse-width modulation controllers, comparing their efficiency, total harmonic distortion, daily energy delivery, and overall performance scores. Among the controllers tested, the best-performing solution achieves an overall performance score of 0.992 and delivers daily energy savings of 0.160 kWh, corresponding to a 0.97% improvement over the baseline. To address the high computational cost of conventional simulation sweeps, a three-point evaluation protocol is proposed, reducing the number of required simulations from 10,000 to 3, representing a 97% reduction while maintaining less than 1% deviation from full simulation results. The results demonstrate that the framework not only provides accurate, dimensionally consistent predictions of optimal switching frequencies and performance bounds but also enables quantitative assessment of efficiency–distortion trade-offs, practical guidance for controller selection, and substantial reductions in design and computational effort. This approach offers both theoretical insight and practical methodology for the design and optimization of high-performance grid-connected inverters using pulse-width modulation strategies, highlighting achievable gains in energy efficiency, waveform quality, and computational efficiency.