Enhancing District Heating transition through Fast Optimization and Mass flow rate Management

Climate change is an increasingly significant issue, prompting the European Union to set the ambitious goal of achieving zero emissions by 2050. District heating emerges as a critical technology in this effort to reduce greenhouse gas emissions. However, most existing district heating networks operate at high temperatures, a condition suitable for fossil fuels but suboptimal for renewable energy sources. To facilitate the integration of it is essential to reduce operational temperatures. Achieving lower operational temperatures necessitates an increase in mass flow rates. Nonetheless, this adjustment faces several constraints, as network pressures and velocities, which are closely tied to mass flow rates, must not exceed maximum allowable values. Therefore, it is imperative to conduct a study on the maximum permissible mass flow rate to ensure safe and efficient operation. To achieve these results, it is necessary to optimize the pumping stations along the network to find optimal configurations that ensure the desired thermal energy outcomes. This involves fine-tuning the repumping processes to match the desired flow rates and temperatures, thereby maximizing the system's energy-saving performance. To implement these optimizations, a comprehensive model is required. This model utilizes the formulation of the continuity, momentum and energy equation in their 1D formulation for a steady-state period. These concepts have been implemented in a numerical model, specifically adopting a Mixed Integer Quadratically Constraint Program formulation. However, there are certain challenges in this process, such as the non-linearity in the momentum equation, given by the quadratic dependency on the mass flow rate. For complex network, this non-linearity leads to high computational times. To overcome this issue, one can consider linearizing the equation. This leads to a Mixed-Integer Linear Programming MILP formulation. As a first assumption, the constant term is initialized with the values obtained from the solution of the tree-shaped configuration. However, the initial solution is not accurate, so an iterative method is implemented. In this method, the constant term, called auxilliary mass flow rate, is updated using previous values of variable mass flow rate. To enhance the stability of the method, under-relaxation factors are applied, weighting the value of the auxilliary mass flow rate based on previous values of the variable mass flow rate. Initially, simpler optimizations are considered such as the minimization of the maximum pressure, minimization of the maximum velocity and minimization of the total power. These optimizations can lead to different configurations that result in pumping energy savings. To enhance the possibility of increasing the injected mass flow rate, the potential for the injection plants to vary up to a certain limit is also considered. The results of these optimizations demonstrate the effectiveness of the proposed approaches. In fact, performing parametric trials with this last methodology, has been obtained a percentage injection which is 86% higher than the normal utilization. In summary, the comprehensive model developed has demonstrated significant potential in improving energy efficiency. Building on these outcomes, future research can investigate the integration of the network with additional injection nodes to determine the optimal placement. By exploring this possibility, the model can further enhance the efficiency and sustainability of district heating network.