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This study presents a novel model and relevant applications for optimal environmental design of distribution networks. The presentation of the concepts is divided into two papers, of which this paper represents Part I. The proposed methodology is based on a trade-off between emission embodied in the circuit and emissions related to operational losses. Hence, the CO2 emission minimisation problem is developed and analysed for a single circuit in terms of continuous optimisation, and is solved in closed form. This leads to establish a continuous optimal environmental capacity for distribution circuits, and allows identification of the key parameters involved in the analysis. Numerical applications for typical low-voltage (LV) cables used in the UK highlight some numerical aspects of the discussed design. Sensitivity analyses are also run in order to test the robustness of the results found, and to estimate how the design characteristics could change in the presence of different generation mixes. The analyses are completed in Part II, illustrating the application of the model to LV radial networks and relevant environmental and economic implications in comparison to alternative design strategies.