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In this article we investigate methods to solve a fundamental task in gas transportation, namely the validation of nomination problem: Given a gas transmission network consisting of passive pipelines and active, controllable elements and given an amount of gas at every entry and exit point of the network, find operational settings for all active elements such that there exists a network state meeting all physical, technical, and legal constraints.
We describe a two-stage approach to solve the resulting complex and numerically difficult feasibility problem. The first phase consists of four distinct algorithms applying linear, and methods for complementarity constraints to compute possible settings for the discrete decisions. The second phase employs a precise continuous programming model of the gas network. Using this setup, we are able to compute high quality solutions to real-world industrial instances that are significantly larger than networks that have appeared in the mathematical programming literature before.
The recently imposed new gas market liberalization rules in Germany lead to a change of business of gas network operators. While previously network operator and gas vendor were united, they were forced to split up into independent companies. The network has to be open to any other gas trader at the same conditions, and free network capacities have to be identified and publicly offered in a non-discriminatory way. We discuss how these changing paradigms lead to new and challenging mathematical optimization problems. This includes the validation of nominations, that asks for the decision if the network’s capacity is sufficient to transport a specific amount of flow, the verification of booked capacities and the detection of available freely allocable capacities, and the topological extension of the network with new pipelines or compressors in order to increase its capacity. In order to solve each of these problems and to provide meaningful results for the practice, a mixture of different mathematical aspects have to be addressed, such as combinatorics, stochasticity, uncertainty, and nonlinearity. Currently, no numerical solver is available that can deal with such blended problems out-of-the-box. The main goal of our research is to develop such a solver, that moreover is able to solve instances of realistic size. In this article, we describe the main ingredients of our prototypical software implementations.
Mobile communication is nowadays taken for granted. Having started primarily as a service for speech communication, data service and mobile Internet access are now driving the evolution of network infrastructure. Operators are facing the challenge to match the demand by continuously expanding and upgrading the network infrastructure. However, the evolution of the customer's demand is uncertain. We introduce a novel (long-term) network planning approach based on multistage stochastic programming, where demand evolution is considered as a stochastic process and the network is extended as to maximize the expected profit. The approach proves capable of designing large-scale realistic UMTS networks with a time-horizon of several years. Our mathematical optimization model, the solution approach, and computational results are presented in this paper.
A Decomposition Approach for Optimal Gas Network Extension with a Finite Set of Demand Scenarios
(2018)
Today's gas markets demand more flexibility from the network
operators which in turn have to invest into their network
infrastructure. As these investments are very cost-intensive and
long-living, network extensions should not only focus on a single
bottleneck scenario, but should increase the flexibility to fulfill
different demand scenarios. In this work, we formulate a model for
the network extension problem for multiple demand scenarios and
propose a scenario decomposition in order to solve the arising
challenging optimization tasks. In fact, each subproblem
consists of a mixed-integer nonlinear optimization problem (MINLP).
Valid bounds on the objective value are derived even
without solving the subproblems to optimality. Furthermore, we
develop heuristics that prove capable of improving the initial
solutions substantially. Results of computational experiments on
realistic network topologies are presented. It turns out that our
method is able to solve these challenging instances to optimality
within a reasonable amount of time.
In 2005 the European Union liberalized the gas market with a disruptive change
and decoupled trading of natural gas from its transport. The gas is now trans-
ported by independent so-called transmissions system operators or TSOs. The
market model established by the European Union views the gas transmission
network as a black box, providing shippers (gas traders and consumers) the
opportunity to transport gas from any entry to any exit. TSOs are required
to offer the maximum possible capacities at each entry and exit such that any
resulting gas flow can be realized by the network. The revenue from selling these
capacities more than one billion Euro in Germany alone, but overestimating the
capacity might compromise the security of supply. Therefore, evaluating the
available transport capacities is extremely important to the TSOs.
This is a report on a large project in mathematical optimization, set out
to develop a new toolset for evaluating gas network capacities. The goals and
the challenges as they occurred in the project are described, as well as the
developments and design decisions taken to meet the requirements.