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
Scaling of the steady-state load flow equations for multi-carrier energy systems
Anne Markensteijn, Johan Romate, Kees Vuik
Abstract: Coupling single-carrier networks (SCNs) into multi-carrier energy systems (MESs) has recently become more important. Steady-state load flow analysis of energy systems leads to a system of nonlinear equations, which is usually solved using the Newton-Raphson method (NR). Due to various physical scales within a SCN, and between different SCNs in a MES, scaling might be needed to solve the nonlinear system. In single-carrier electrical networks, per unit scaling is commonly used. However, in the gas and heat networks, various ways of scaling or no scaling are used. This paper presents a per unit system and matrix scaling for load flow models for a MES consisting of gas, electricity, and heat. The effect of scaling on NR is analyzed. A small example MES is used to demonstrate the two scaling methods. This paper shows that the per unit system and matrix scaling are equivalent, assuming infinite precision. In finite precision, the example shows that the NR iterations are slightly different for the two scaling methods. For this example, both scaling methods show the same convergence behavior of NR in finite precision.