Effects of climate change can already be observed in many regions of the world. The basin of the Paraná River, in South America, has been suffering an important drought since 2019 in the whole region. The extension of the crisis has increased the risks in the flora and fauna, losses in logistics of navigation, besides the problems of urban water cleansing. In this regard, the novel proposal presents a new mathematical model to study the impact of this crisis. Besides the traditional constraints of the literature for hydraulic systems, this paper enhances inventory constraints, connections with electric systems, and other considerations as the head effects in electricity generation. Because several equations related to electricity generation are nonlinear (which the subsequent computational effort impacts), this proposal applies linearization techniques to reduce CPU times. The core is related to hydropower production, and the consequences of the water crisis in the regional markets. The mathematical model analyzes the interrelationships between reservoirs and water flows of the basin. To study the effectiveness of the novel proposal, the reported situation of the basin of the Paraná River is studied by considering two scenarios (normal conditions of the river flow and the conditions related to the drought). Results show that the crisis implies daily net economic losses of about 7 million USD for the operators of the power plants. Other problems (different from the ones related to the energy field) are also mentioned and analyzed.