## Abstract

This work is devoted to the analysis of fluid networks stemming from automated modeling processes in system simulation software. Today’s system modeling software typically offers a wide range of basic physical components (e.g. pumps, pipes), which can be assembled to customized physical networks simply by drag and drop. The governing equations are derived by representing

the network as a linear graph whose edges and nodes correspond to the basic physical components.

Combining the connection structure of the graph with the physical equations of the components, the physical network is modeled as Differential-Algebraic Equations (DAE). Using algebraic graph and DAE theory, the solvability of the mathematical model can be analyzed and translated as conditions on the network structure and properties of its elements. To control these networks or

to connect them to the environment, boundary conditions are present, allowing to incorporate user defined components. In many practical applications, these external components (e.g. controllers) are given by black-box models. Recently the Functional Mock-up Unit (FMU) has been established as a standardized structured interface for those kinds of black-box models, giving the input-output relation as differential state and algebraic output equation. Incorporating these types of black-box components into physical networks may drastically affect its physical validity and solvability. Within this work, a coupled DAE-FMU system is analyzed and conditions on the network structure, its elements and the coupled FMUs are presented, that allow to preserve the physical validity as well as the solvability of the physical network. Keeping a close connection between the topology of the model and the equations of the network, the solvability conditions of the model can be interpreted as easy-to-check graph theoretical conditions on the network and the FMUs, which can significantly

increase the usability of such system simulation processes for fluid networks.

the network as a linear graph whose edges and nodes correspond to the basic physical components.

Combining the connection structure of the graph with the physical equations of the components, the physical network is modeled as Differential-Algebraic Equations (DAE). Using algebraic graph and DAE theory, the solvability of the mathematical model can be analyzed and translated as conditions on the network structure and properties of its elements. To control these networks or

to connect them to the environment, boundary conditions are present, allowing to incorporate user defined components. In many practical applications, these external components (e.g. controllers) are given by black-box models. Recently the Functional Mock-up Unit (FMU) has been established as a standardized structured interface for those kinds of black-box models, giving the input-output relation as differential state and algebraic output equation. Incorporating these types of black-box components into physical networks may drastically affect its physical validity and solvability. Within this work, a coupled DAE-FMU system is analyzed and conditions on the network structure, its elements and the coupled FMUs are presented, that allow to preserve the physical validity as well as the solvability of the physical network. Keeping a close connection between the topology of the model and the equations of the network, the solvability conditions of the model can be interpreted as easy-to-check graph theoretical conditions on the network and the FMUs, which can significantly

increase the usability of such system simulation processes for fluid networks.

Original language | English |
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Publisher | Johann Radon Institute for Computational and Applied Mathematics |

Number of pages | 26 |

Publication status | Published - 2018 |

Externally published | Yes |

### Publication series

Name | RICAM-Report |
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Volume | 38 |