In this paper the functional modeling (FM) method developed for efficient solution of simulation, planning and control problems in large power systems and interconnections is presented. In the first part of the paper outline of the FM method is given. According to the FM method a power system is represented by hierarchical model, consisting of systems of equations of subsystems (lower level) and system of equations of higher level, in which only boundary variables of subsystems are present. Next part of the paper is devoted to description of hierarchical algorithms for solution of power flow , optimization and stability analysis problems of power systems, based on the FM method. It is shown in the last part of the paper how general structure of the FM algorithms and principles of the FM method are used to form the basis, on which construction and functioning of distributed control system assuring optimal operation control in large integrated electrical power systems is founded.
The stability of bilinear systems is investigated using spectral techniques such as selective modal analysis. Predictive models of bilinear systems based on inductive knowledge extracted by big data mining techniques are applied with associative search of statistical patterns. A method and an algorithm for the elementwise solution of the generalized matrix Lyapunov equation are developed for discrete bilinear systems. The method is based on calculating the sequence of values of a fixed element of the solution matrix, which depends on the product of the eigenvalues of the dynamics matrix of the linear part and the elements of the nonlinearity matrixes. A sufficient condition for the convergence of all sequences is obtained, which is also a BIBO (bounded input bounded output) systems stability condition for the bilinear system.
The paper offers an approach to the investigation of the dynamics of nonlinear non-stationary processes with the focus on the risk of dynamic system stability loss. The risk is assessed on the basis of the accumulated knowledge about power supply system operation. New methods for power supply modes analysis are developed and applied as follows: linear discrete point knowledge-based models are developed for nonlinear non-stationary objects; wavelet analysis is used for non-stationary processes; stability loss risks are analyzed through the investigation of spectral decompositions of Gramians of these linear predictive models. Case studies are included.
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