The article introduces a novel 3D model of a yellow hydrogen generation system that utilizes electricity from a photovoltaic carport. Detailed characteristics of all key system components were described, and the monthly energy production from the photovoltaic carport was determined to estimate low-emission hydrogen output. To enhance hydrogen production, a proposal to incorporate a stationary energy storage facility was made. The Metalog probability distribution family was utilized to create a strategic model for low-emission hydrogen generation, offering a solution for companies with low hydrogen demand in the climate and energy transition. The study conducted probabilistic analysis in Poland and Italy to assess the profitability of low-emission hydrogen production from photovoltaic systems, providing insights into monthly energy generation and hydrogen production probabilities. Companies in these countries are participating in a European competition for hydrogen banks, where those offering low-emission hydrogen at competitive prices will secure EU funding.