A TWO-PHASE OPTIMIZATION METHOD FOR THE EXPANSION PLANNING OF DISTRICT HEATING SYSTEMS USING DIFFERENT DISCRETIZATION TECHNIQUES

The current high costs of district heating systems set limits regarding the minimum heat demand density required for economic network expansions.Optimized routing with ideal pipe sizing offers a potential for cost reduction.Therefore, this paper introduces a two-phase method for district heating network expansion planning.This method consists of consecutive optimizations, starting with a mixed-integer linear programming followed by a nonlinear optimization.During the mixed-integer linear programming, the district heating system is optimized with continuous diameters, and the nonlinear pressure and temperature dependencies must be linearized.The resulting topology and the continuous diameters are afterward handed over to a nonlinear sparse sequential quadratic programming.During this second phase, the continuous diameters have to be discretized.This study investigates a rational approximation of material properties and a tangent hyperbolic penalization method.Different versions of these methods with varying diameter ranges (two and three available diameters) and penalization directions are studied.The results of this study indicate that methods without changing penalization methods within the same optimization problem provide higher accuracy in the discretization of the pipe's diameter.Moreover, if the accuracy of the discretized diameter should be emphasized during the optimization, penalization methods considering only two diameters should be preferred over penalization methods considering three diameters.Vice-versa, if obtaining the lowest possible diameters is prioritized over the accuracy of the discretization, methods considering three diameters should be preferred.