District heating networks (DHN) are systems offering a substantial solution for the decarbonization of heat production. As these systems involve significant costs, the development of digital tools for their optimization becomes a necessity. In the literature, there is a lack of studies optimizing the sizing of the DHN while considering a dynamic operation of the system with a detailed physics. In this work, we developed a Non-Linear Programming (NLP) optimization used in a case study of a DHN where the pipe sizing and the operation are optimized with a precise modeling of the distribution network. The method of Orthogonal Collocation on Finite Elements (OCFE) was employed to discretize the partial differential equation (PDE) governing the temperature evolution in the pipes. In addition, the pressure drops were modeled using the Darcy–Weisbach equation. Three optimization criteria were used: investment cost of the pipes, operational cost, and the global cost. The optimization provided the pipe diameters that best fit each optimization criterion. Furthermore, several initializations were tested to verify if the obtained optimum was a confidence optimum and if the resolution was robust. Finally, the optimization provided a coherent response to the variation in the cost of heat production.
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