A fundamental study on the optimal/near-optimal shape of a network for energy distribution

Usually, a medium such as water and electrical current is transported through an energy distribution network for delivering energy. Driving the medium through the network will lead to power loss. In this paper, a fundamental study was conducted to find out the optimal/near-optimal shape of an energy distribution network for minimising the total power loss under the constraint of the network's total flow volume. A general equation was developed for calculating the total power loss. A parameter was used to classify all media into three types. For Type I and II medium, it was found that a radial shape network was the optimal one. A global search method was proposed to find out the near-optimal shape of the network for Type III medium. A case study was carried out for finding out the optimal/near-optimal shape of the networks for electric current, refrigerant and water in laminar flow, respectively, with a supplier and six users. The power losses to drive these media through the networks with the optimal/near-optimal shape were compared to those through the networks with other shapes. The comparison results indicated the power losses could be reduced when using the optimal/near-optimal networks.