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The numerical simulation of the flow in the Stage D compressor stage was verified as a result of an experimental study. For verification, the most widespread turbulence models, k-ε and SST, are used in engineering practice. Comparison of the data is performed both by integral characteristics and by the distribution of the total pressure, angles, axial velocity along the step height. As a result of the comparison, it is established that the integral flow parameters and πk have a high accuracy of coincidence with experiment. When comparing the height parameters, the greatest discrepancy is observed in the end regions. Проведена верификация численного моделирования течения в осевой компрессорной ступени Stage D по результатам экспериментального исследования. Для верификации использованы наиболее распространенные в инженерной практике модели турбулентности k-ε и SST. Сравнение данных выполнено как по интегральным характеристикам, так и по распределению полного давления, углов, осевой скорости по высоте ступени. В результате сравнения установлено, что интегральные параметры расхода и πк имеют высокую точность совпадения с экспериментом. При сравнении параметров по высоте наибольшее расхождение наблюдается в торцевых областях.

This paper proposes a new method for partitioning power grids based on the nonlinear Koopman Mode Analysis (KMA). Grid partitioning is the fundamental problem in the controlled islanding strategy. The KMA is a new technique of nonlinear modal decomposition based on properties of the point spectrum of the so-called Koopman operator. The key idea in the proposed method is to determine a set of islanded sub-grids using KMA of data on voltage angle dynamics of every bus. The method is numerically investigated with the IEEE 118-bus test system. It is shown that the proposed method provides partitions on a multiple frequency scale as well as captures the intrinsic structural properties of a grid characterized by spectral graph theory. QC 20140613

To view the electricity supply in our society as just sockets mountedin our walls with a constant voltage output is far from the truth. Inreality, the power system supplying the electricity or the grid, is themost complex man-made dynamical system there is. It demands severecontrol and safety measures to ensure a reliable supply of electric power.Throughout the world, incidents of widespread power grid failures havebeen continuously reported. The state where electricity delivery to customersis terminated by a disturbance is called a blackout. From a stateof seemingly stable operating conditions, the grid can fast derail intoan uncontrollable state due to cascading failures. Transmission linesbecome automatically disconnected due to power flow redirections andparts of the grid become isolated and islands are formed. An islandedsub-grid incapable of maintaining safe operation conditions experiencesa blackout. A widespread blackout is a rare, but an extremely costlyand hazardous event for society.During recent years, many methods to prevent these kinds of eventshave been suggested. Controlled islanding has been a commonly suggestedstrategy to save the entire grid or parts of the grid from a blackout.Controlled islanding is a strategy of emergency control of a powergrid, in which the grid is intentionally split into a set of islanded subgridsfor avoiding an entire collapse. The key point in the strategy is todetermine appropriate separation boundaries, i.e. the set of transmissionlines separating the grid into two or more isolated parts.The power grid exhibits highly nonlinear response in the case oflarge failures. Therefore, this thesis proposes a new controlled islandingmethod for power grids based on the nonlinear Koopman Mode Analysis(KMA). The KMA is a new analyzing technique of nonlinear dynamicsbased on the so-called Koopman operator. Based on sampled data followinga disturbance, KMA is used to identify suitable partitions of thegrid.The KMA-based islanding method is numerically investigated withtwo well-known test systems proposed by the Institute of Electrical andElectronics Engineers (IEEE). By simulations of controlled islanding inthe test system, it is demonstrated that the grid’s response following afault can be improved with the proposed method.The proposed method is compared to a method of partitioning powergrids based on spectral graph theory which captures the structural propertiesof a network. It is shown that the intrinsic structural propertiesof a grid characterized by spectral graph theory are also captured by theKMA. This is shown both by numerical simulations and a theoreticalanalysis.

In this paper possibilities to obtain a satisfactory multigrid convergence when a domain is partitioned into blocks are discussed. First, standard parallel multigrid with alternating line Gauss-Seidel as smoother is investigated for the Euler equations in a partitioned domain. When the domain is partitioned into blocks the smoother updates lines per block. A possibility to regain the single block multigrid convergence for many block splittings for this problem is given. For singular perturbed problems with strongly coupled unknowns in one direction only this method will not be satisfactory. Therefore, the research for nonstandard multigrid methods that are based on point smoothers and are robust is sketched. Another flexible nonstandard multigrid method, called MG-S, is introduced. Because the method is equivalent with standard multigrid with a lower dimensional multigrid smoother the behaviour of the method is quite clear. Finally, the nonstandard multigrid method is tested for two-dimensional model equations, the rotated anisotropic diffusion equation and the convection diffusion equation.