Optimization modeling of district heating networks and calculation by the Newton method

The optimization model of the district heating system for an N-floor building is set up. The mass flow rate and thermal conductance distributions are optimized for prescribed total mass flow rate and prescribed total thermal conductance respectively by the Newton method. Two numerical examples are presented, and the effects of the parameters, such as the heat load, its distribution and the room temperature, on the optimal results are discussed. It is shown that for a three-floor building with two users on each floor, larger heat load requires larger mass flow rate on the corresponding floor when the total mass flow rate is prescribed. Putting the user of larger heat load nearest to the upstream flow reduces the total mass flow rate for fixed total heat load on the floor. For the three-floor building with one user on each floor, larger thermal conductance of the corresponding heat exchanger is required for the room with higher temperature when the total thermal conductance is prescribed. With fixed total heat load of two floors, distributing more heat load to the room with lower temperature reduces the total mass flow rate.