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This thesis considers the transient gas network control optimization problem for on-shore pipeline-based transmission networks with numerous gas routing options.
As input, the problem is given the network's topology, its initial state, and future demands at the boundaries of the network, which prescribe the gas flow exchange and potentially the pressure values.
The task is to find a set of future control measures for all the active, i.e., controllable, elements in the network that minimizes a combination of different penalty functions.
The problem is examined in the context of a decision support tool for gas network dispatchers.
This results in detailed models featuring a diverse set of constraints, large and challenging real-world instances, and demanding time limit requirements.
All these factors further complicate the problem, which is already difficult to solve in theory due to the inherent combination of non-linear and combinatorial aspects.
Our contributions concern different steps of the process of solving the problem.
Regarding the model formulation, we investigate the validity of two common approximations of the gas flow description in transport pipes: neglecting the inertia term and assuming a friction term that linearly depends on the gas flow and the pressure.
For both, we examine if they can be applied under real-world conditions by evaluating a large amount of historical state data of the network of our project partner, the gas network operator Open Grid Europe.
While we can confirm that it is reasonable to ignore the influence of the inertia term, the friction term linearization leads to significant errors and, as a consequence, cannot be used for describing the general gas flow behavior in transport pipes.
As another topic of this thesis, we introduce the target value concept as a more realistic approach to express control actions of dispatchers regarding regulators and compressor stations.
Here, we derive the mechanisms defined for target values based on the gas flow principles in pipes and develop a mixed-integer programming model capturing their behavior.
The accuracy of this model is demonstrated in comparison to a target-value-based industry-standard simulator.
Furthermore, we present two heuristics for the transient gas network control optimization problem featuring target values that are based on approximative models for the target-value-based control and determine the final decisions in a post-processing step.
To compare the performance of the two heuristics with the approach of directly solving the corresponding model, we evaluate them on a set of artificially created test instances.
Finally, we develop problem-specific algorithms for two variants of the described problem.
One considers the control optimization for a single network station, which represents a local operation site featuring a large number of active elements.
The used transient model is very detailed and includes a sophisticated representation of the compressor stations.
Based on the shortness of the pipes in the station, the corresponding algorithm finds valid solutions by solving a series of stationary model variants as well as a transient rolling horizon approach.
As the second variant, we consider the problem on the entire network but assume an approximative model representing the control capabilities of network stations.
Aside from a new description of the compression capabilities, we introduce an algorithm that uses a combination of sequential mixed-integer programming, two heuristics based on reduced time horizons, and a specialized dynamic branch-and-bound node limit to determine promising values for the binary variables of the model.
Complete solutions for the problem are obtained by fixing the binary values and solving the remaining non-linear program.
Both algorithms are investigated in extensive empirical studies based on real-world instances of the corresponding model variants.