Friedrich-Alexander-Universität Erlangen-Nürnberg
Refine
Year of publication
Keywords
- Bilevel optimization (8)
- Optimal control (7)
- Gas networks (6)
- Uniqueness (6)
- Convergence (5)
- Networks (5)
- Robust optimization (5)
- robust optimization (5)
- Branch-and-cut (4)
- Mixed-Integer Nonlinear Optimization (4)
Optimization and control of large transient gas networks require the fast
simulation of the underlying parametric partial differential algebraic systems. Sur-
rogate modeling techniques based on linearization around specific stationary states,
spatial semi-discretization and model order reduction allow for the set-up of para-
metric reduced order models that can act as basis sample to cover a wide parameter
range by means of matrix interpolations. However, the interpolated models are often
not stable. In this paper, we develop a stability-preserving interpolation method.
This work deals with the model order reduction (MOR) of a nonlinear-
parametric system of partial differential equations (PDEs). Applying a semidis-
cretization in space and replacing the nonlinearities by introducing new state vari-
ables, we set up quadratic-linear differential algebraic systems (QLDAE) and use a
Krylov-subspace MOR. The approach is investigated for gas pipeline modeling
Proceeding from balanced truncation-based parametric reduced order
models (BT-pROM) a matrix interpolation strategy is presented that allows the
cheap evaluation of reduced order models at new parameter sets. The method ex-
tends the framework of model order reduction (MOR) for high-order parameter-
dependent linear time invariant systems in descriptor form by Geuss (2013) by
treating not only permutations and rotations but also distortions of reduced order
basis vectors. The applicability of the interpolation strategy and different variants is
shown on BT-pROMs for gas transport in pipeline-networks
We present a solution algorithm for problems from
steady-state gas transport optimization.
Due to nonlinear and nonconvex physics and engineering models as
well as discrete controllability of active network devices, these
problems lead to difficult nonconvex mixed-integer nonlinear optimization
models.
The proposed method is based on mixed-integer linear techniques using
piecewise linear relaxations of the nonlinearities and a tailored
alternating direction method.
Most other publications in the field of gas transport optimization only consider
pressure and flow as main physical quantities. In this work, we additionally
incorporate heat power supplies and demands as well as a mixing model for
different gas qualities.
We demonstrate the capabilities of our method on Germany's largest
transport networks and hereby present numerical results on the largest
instances that were ever reported in the literature for this problem
class.
In the following paper a combined optimization of a coupled electricity and gas system is presented. For the electricity network a unit commitment problem with optimization of energy and reserves under a power pool, considering all system operational and unit technical constraints is solved. The gas network subproblem is a medium-scale mixed-integer nonconvex and nonlinear programming problem. The coupling constraints between the two networks are nonlinear as well. The resulting mixed-integer nonlinear program is linearized with the extended incremental method and an outer approximation technique. The resulting model is evaluated using the Greek power and gas system comprising fourteen gas-fired units under four different approximation accuracy levels. The results indicate the efficiency of the proposed MIP model and the interplay between computational requirements and accuracy.
We propose a decomposition based method for solving mixed-integer nonlinear optimization problems with “black-box” nonlinearities, where the latter, e.g., may arise due to differential equations or expensive simulation runs. The method alternatingly solves a mixed-integer linear master problem and a separation problem for iteratively refining the mixed-integer linear relaxation of the nonlinear equalities. The latter yield nonconvex feasible sets for the optimization model but we have to restrict ourselves to convex and monotone constraint functions. Under these assumptions, we prove that our algorithm finitely terminates with an approximate feasible global optimal solution of the mixed integer nonlinear problem. Additionally, we show the applicability of our approach for three applications from optimal control with integer variables, from the field of pressurized flows in pipes with elastic walls, and from steady-state gas transport. For the latter we also present promising numerical results of our method applied to real-world instances that particularly show the effectiveness of our method for problems defined on networks.
Finite Time Blow-up of Traveling Wave Solutions for the Flow of Real Gas through Pipeline Networks
(2016)
In the context of gas transportation, analytical solutions are essential
for the understanding of the underlying dynamics described
by a system of partial differential equations. We derive traveling wave
solutions for the 1-d isothermal Euler equations. A non-constant compressibility
factor is used to describe the correlation between density
and pressure. The blow-up of the traveling wave solution in finite time
is proven. We then extend our analysis to networks under appropriate
coupling conditions and derive compatibility conditions to fulfill these
coupling conditions.