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In this paper, modeling of piston and generic type gas compressors for a globally convergent algorithm for solving stationary gas transport problems is carried out. A theoretical analysis of the simulation stability, its practical implementation and verification of convergence on a realistic gas network have been carried out. The relevance of the paper for the topics of the conference is defined by a significance of gas transport networks as an advanced application of simulation and modeling, including the development of novel mathematical and numerical algorithms and methods.
Solving transport network problems can be complicated by non-linear effects. In the particular case of gas transport networks, the most complex non-linear elements are compressors and their drives. They are described by a system of equations, composed of a piecewise linear ‘free’ model for the control logic and a non-linear ‘advanced’ model for calibrated characteristics of the compressor. For all element equations, certain stability criteria must be fulfilled, providing the absence of folds in associated system mapping. In this paper, we consider a transformation (warping) of a system from the space of calibration parameters to the space of transport variables, satisfying these criteria. The algorithm drastically improves stability of the network solver. Numerous tests on realistic networks show that nearly 100% convergence rate of the solver is achieved with this approach.
The formulation of transport network problems is represented as a translation between two domain specific languages: from a network description language, used by network simulation community, to a problem description language, understood by generic non-linear solvers. A universal algorithm for this translation is developed, an estimation of its computational complexity given, and an efficient application of the algorithm demonstrated on a number of realistic examples. Typically, for a large gas transport network with about 10K elements the translation and solution of non-linear system together require less than 1 sec on the common hardware. The translation procedure incorporates several preprocessing filters, in particular, topological cleaning filters, which accelerate the solution procedure by factor 8.
In this paper, an analysis of the error ellipsoid in the space of solutions of stationary gas transport problems is carried out. For this purpose, a Principal Component Analysis of the solution set has been performed. The presence of unstable directions is shown associated with the marginal fulfillment of the resistivity conditions for the equations of compressors and other control elements in gas networks. Practically, the instabilities occur when multiple compressors or regulators try to control pressures or flows in the same part of the network. Such problems can occur, in particular, when the compressors or regulators reach their working limits. Possible ways of resolving instabilities are considered.
