City growth goes together with the development of infrastructure, and the power network is one of the most relevant towards economic development. The study of urban infrastructure through the analysis of anthropization coupled with power network growth can produce a tool that supports sustainable infrastructure planning, both economic and environmental. The case study focuses on Ambato, Ecuador, in the period from 1950 to 2019, and assesses quantitatively the changes in the city layout and the evolution of its power network. The data are adjusted to a sigmoid-type objective function through a non-linear least squares problem, that is solved using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. Anthropization data show how the urban area grew during the study period: 37% (1950–1960), 53% (1960–1970), 80% (1970–1980), 35% (1980–1990), 39% (1990–2000), 38% (2000–2010), and 11% (2010–2019), mostly at the expense of agricultural land. The forecast for new power network users by 2050 yields a result of 203,630 total users with a population density of 4850 people/km2. The conclusion is that this type of analysis can help city planners and decision makers further understand city and infrastructure growth dynamics and produce policies that bolster sustainable city growth.