16. Partitioning Approaches for Large-Scale Water Transport Networks

Large-scale systems (LSS), such as WTNs, present control theory with new challenges due to the large size of the plant and of its model. In order to apply decentralized or distributed control approaches to LSS, there is a prior problem to be solved: the system decomposition into subsystems. The importance of this issue has already been reported in the general literature of decentralized control of LSS. The decomposition of the system into subsystems could be carried out during the modelling of the process by identifying subsystems as parts of the system on the basis of physical insight, intuition or experience. But, when a large-scale complex system with many states, inputs and outputs is considered, it may be difficult, even impossible, to obtain partitions by physical reasoning. A more appealing alternative is to develop systematic methods, which can be used to decompose a given system by extracting information from its structure and representing it as a graph. Then, this structural information can be analysed by using methods coming from graph theory. This chapter discusses partitioning approaches towards the development of subsystem decomposition methods for LSS by reviewing automatic decomposition algorithms and techniques based on graph partitioning. The general aim of the discussed methods is to provide decompositions consisting of sets of non-overlapping subgraphs whose number of vertices is as similar as possible and the number of interconnecting edges between them is minimal. The real case study based on the Barcelona WTN in Chap. 2 is used to exemplify the discussed decomposition methodologies.