Herein, I methodically optimize a distributed energy resource in terms of the production, management, utilization, and/or transaction of renewable energies during the deployment process. I deliver a theoretical mathematical model that allows users to visualize three critical output functions of their energy preference, including output power, energy economy, and carbon footprint. The model delivers three eigenstates derived by a power utility matrix (PUM) model. PUM transforms three-input parameters (3i) into three-output functions (3o) through 3i3o-transformation. It is ubiquitous, and its systematic characterization is discussed. Moreover, I discover a mathematical conversion relationship translating energy generation to carbon emissions. Various case-studies demonstrate the optimal energy resource utilization. Furthermore, an energy blockchain approach is employed for microgrid design, development, and carbon reduction. Finally, the authors demonstrate the energy–matter conversion relationship that improves carbon emissions for energy production, reducing the beta factor of carbon emissions to 0.22 kg/kilowatt hour for carbon peak and to zero for carbon neutrality.