## Dynamic Simulation of a district cooling system using 2D orthogonal Collocation

### SFT 2018

The global air conditioning market has doubled in 10 years and quadrupled in the European market in 3 years. This rise implies a high energy consumption in the summer, linked greenhouse gas emissions that must be reduced. Unlike local or individual production units, distribution networks allow, at city or district level, a better integration of the different primary energy sources, a reduction in the overall impact on the environment and reducing costs. This type of infrastructure, however, requires a heavy initial investment and an appropriate management policy.

Given this, in this article, we present the first stage of a project that aims to develop a methodology for the optimal management of a cooling network, considering the dynamics of the whole system including conversion, storage, and distribution of energy. This step is the development of a mathematical formulation for the dynamic simulation of a simple cold network. The system is composed of a distribution network, a return network and 3 different users (represented as heat exchangers), that are connected to the aforementioned networks as well as to hot fluid pipes in the user sites. The case study aims to understand how the variation in the users' demand influences the flow of chilled water through the distribution and return networks over a 1-hour time horizon. A one-dimensional heat transfer equation is used to describe the temperature dynamics in the pipelines. The resulting algebraic differential system (which includes the mentioned differential equation, mass and energy balances at the mixing and dividing nodes of the network, and the equations of the heat exchanger) is transformed into a set of algebraic equations using the method of orthogonal collocation on finite elements (2D). One of the main advantages of this strategy is that it gives results with very good precision in shorter computation times than other mesh strategies (finite differences, finite volumes) for dynamic systems. This discretization is essential for the implementation of future optimizations.

The problem is solved by using the interior point based solver IPOPT in GAMS (General Algebraic Modeling System). The results obtained show that the proposed model describing the dynamics of the systems, as well as the proposed resolution method, represent a good starting point for future optimization applications, in terms of CPU time and accuracy.