Abstract
This chapter applies hetero-functional graph theory to an interdependent smart city infrastructure test case called “Trimetrica.” One feature of “Trimetrica” is its significant heterogeneity of function. It integrates a water distribution system, a power grid, and an (electrified) transportation network. The chapter demonstrates the construction of a single system adjacency matrix for such a heterogeneous system. The approach is incremental: each of the models in hetero-functional graph theory is discussed and connected to the other models to construct the system adjacency matrix piece-by-piece. Additionally, the heterogeneity found in the “Trimetrica” test case shows that hetero-functional graph theory overcomes the ontological and modeling constraints found in the multi-layer network literature.
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Notes
- 1.
While reference architectures overcome doubts about how representative a certain instantiated architecture may be, their meta-data may still violate the four ontological properties. The examples provided above indicate the degeneracy of power flow analysis data despite its widespread use.
- 2.
The water pipes are assumed to be loss-less, without any elevation differences. The water system pressure is assumed to be maintained by the water treatment facilities and the water storage facilities, rather than the use of pumps in the pipe lines.
- 3.
The name of multi-operand resource classes uses the following convention: its name is a combination of each of its parent interface classes. The sequence of the combination is: first the transformation resource, then the buffer, and last the transportation resource. For example, M E &B W is a multi-operand resource that inherits from the interface class M EW in the electric power system and B WE in the water distribution system.
- 4.
Figure 5.4 presents 36 possible resource types. In all three systems, the transformation resources, independent buffers, and transportation resources are specialized as four interface classes.
- 5.
Note that the cyber-resources Q SC are discussed in Section 5.5 on Page 37.
- 6.
Note that contrary to set H TC, this set has one resource per edge with a bidirectional capability.
- 7.
Note that Figure 5.12 includes the refined transportation processes rather than differentiating between regular transportation processes and holding processes.
- 8.
Note that the test case has chosen a simplified representation of the “end users,” as a single aggregated cyber-resource. One can also decide to represent each of the end users as a separate cyber-resource. However, the current representation has been chosen to reduce the complexity of the visualizations and maintain intuition.
- 9.
The addition of a single “maintain operand state” transition for each place is absolutely necessary once holding processes of a transformative nature are added to the model. This has been discussed on Page 35.
- 10.
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Schoonenberg, W.C.H., Khayal, I.S., Farid, A.M. (2019). Modeling Interdependent Smart City Infrastructure Systems with HFGT. In: A Hetero-functional Graph Theory for Modeling Interdependent Smart City Infrastructure. Springer, Cham. https://doi.org/10.1007/978-3-319-99301-0_5
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