European Numerical Mathematics and
Advanced Applications Conference 2019
30th sep - 4th okt 2019, Egmond aan Zee, The Netherlands
15:45   MS20: Solvers and models for multi-carrier energy networks
Chair: Johan Romate
25 mins
The state-space representation of a heat conducting compressible fluid
Volker Mehrmann, Arbi Moses Badlyan
Abstract: Finite or infinite dimensional dynamical systems often contain terms that can be identified as part of a Hamiltonian system, whereas other terms can be associated to a gradient system. The so-called ’General Equation for the Non-Equilibrium Reversible-Irreversible Coupling’ (GENERIC) is an abstract rate equation that represents the additive combination of a generalized Hamiltonian flow and a gradient flow. In [1] the GENERIC state space model of a heat conducting inviscid compressible fluid, given as open thermodynamic system, is rewritten into a representation that may be considered as dissipative port-Hamiltonian system in descriptor form. In this talk we discuss some of the structural properties of the reformulated state-space model introduced as a system of operator equations in [1, Sec. IV]. We show that this system of operator equations corresponds to an infinite-dimensional non-linear dissipative dynamical system. Furthermore, we demonstrate that it also encodes a weak formulation of the partial differential equations which are known as the mathematical model of the heat conducting inviscid compressible fluid in the framework of classical continuum thermodynamics. References [1] A. Moses Badlyan, B. Maschke, C. Beattie, and V. Mehrmann, Open physical systems: From GENERIC to port-Hamiltonian systems. Proceedings of the 23rd International Symposium on Mathematical Theory of Systems and Networks, July 16 - 20, 2018, Hong Kong, China, pp. 204 - 211.
25 mins
Efficient Numerical Methods for Gas Network Modeling and Simulation
Yue Qiu, Sara Grundel, Martin Stoll, Peter Benner
Abstract: We study the modeling and simulation of gas pipeline networks, with a focus on fast numerical methods for the simulation of transient dynamics. The obtained mathematical model of the underlying network is represented by a nonlinear differential algebraic equation (DAE). With our modeling, we reduce the number of algebraic constraints, which correspond to the second block row in our semi-explicit DAE model, to the order of junction nodes in the network, where a junction node couples at least three pipelines. We can furthermore ensure that the (1,1) block of all system matrices including the Jacobian is block lower triangular by using a specific ordering of the pipes of the network. We then exploit this structure to propose an efficient preconditioner for the fast simulation of the network. We test our numerical methods on benchmark problems of (well-)known gas networks and the numerical results show the efficiency of our methods.
25 mins
Steady-state load flow for multi-carrier energy systems
Anne Markensteijn
Abstract: Steady-state load flow models are an important tool for the design and operation of energy transportation and distribution networks. Conventional load flow models for single-carrier networks, such as a power grid, have been widely studied. In recent years, the interest in multi-carrier energy systems (MES) has increased. These systems consist of different energy carriers, such as electricity, gas, and heat, combined into one energy network. This requires the development of steady-state load flow models and solvers for MES. Different models for multi-carrier networks have been proposed, either using the energy hub concept or using a case specific approach. However, these studies do not consider the effect of coupling single-carrier networks on the steady-state load flow model for a MES. Specifically, the effect of coupling on the solvability and well-posedness of the resulting system of non-linear equations has not been discussed. Furthermore, there is a difference in the physical scale of the variables of interest for each energy carrier, such that scaling might be needed to solve load flow problems in MES. We use a general graph-based model framework to model the steady-state load flow problem for MES, and use Newton’s method to solve the resulting non-linear system of equations. We consider a small and a large example MES consisting of electricity, gas, and heat. Using different boundary conditions in both examples, we discuss the difficulties arising due to the coupling of single-carrier networks into one multi-carrier network.