A spatial decomposition procedure for efficient solution of two-dimensional energy distribution problems

As more and more technologies emerge in the energy sector, there is a possibility that structures of energy systems and networks will move towards a more distributed, decentralised structure, with multiple smaller power plants and energy supplier units providing the energy previously commonly supplied by a large centralised plant. If well planned, these distributed structures are anticipated to increase the efficiency, flexibility and security of energy systems. Many mathematical models have been formulated for aiding the design process and analysis of distributed energy systems such as district heating systems. A search for optimal structures and multi-period operational schemes of district heating networks consisting of supplier, consumer and storage nodes connected via pipelines can be formulated as a mixed-integer linear program and solved using standard algorithms, but as the problem sizes increase, the solution times become too long for practical use. For this reason, a procedure for decomposing such an optimization problem in order to reduce the required computational time is proposed. The procedure is based on dividing the geographical area of the energy system into separate sectors which are treated as nodes in a simplified network. During consecutive iterations, the number of sectors, along with the detail level of the simplified network, is increased. Each iteration reduces the search space of the original problem, thus reducing the time needed for the solution. While reaching global optima cannot be guaranteed, examples are given where the procedure finds better solutions than standard algorithms could find within any reasonable, or even relatively unreasonable, time limits.