Study For Algorithm Of Real-time Digital Simulation

To make Runge-Kutta(RK) formulae as research object, the algorithms of real-time digital simulation are studied in this paper.First, based on analysis of stability and error for the common explicit RK formulae, the problem concerned with the stability region of real-time RK formulae is converted into the one of restricted optimization for max,and the condition for maximum stability region of real-time fourth-order RK formulae is found. Then, at the basis of the relation of truncation error and related coefficients,a real-time RK4 formula with maximum stability region and minimum truncation error is deduced. Ulteriorly, a fifth-grade third-order formulae is gotten. These formulaes constitute a pair of RK formulae to estimate error. Finally, the pair is developed to the continuous RK formulae so as to be applied better in non-real-time and step-change simulation.Also, a real-time simulation algorithm with discontinuities is discussed. To use the fourth-order real-time continuous RK formula for forecasting discontinuous points and to deal averagely discontinuous regions, subsection combining algorithm for real-time discontinuous treatment is proposed. In the subsection regions containing discontinuous points a new weighting method is applied, while in the others not containing discontinuous points real-time RK formulae with different order are used, therefore real-time simulation can carried out without changing step-size.In the end, a digital simulation algorithm of delay real-time systems is discussed. The pair of fourth-order continuous RK formulae with a maximum stability region is applied to the digital simulation of delay real-time systems. In every integration step, the values of state vector at correlative output nodes, which should be used for successive simulation, are calculated and stored. By this means, the problem that needed output-nodes are not tallied with count-nodes is solved effectively.