Abstract
The dynamics of power systems is often analyzed using real-time simulators. The basic requirements of these simulators are the speed of obtaining the results and their accuracy. Known algorithms (backward Euler or trapezoidal rule) used in real-time simulations force the integration time step to be reduced to obtain the appropriate accuracy, which extends the time of obtaining the results. The acceleration of obtaining the results is achieved by using parallel calculations. The paper presents an algorithm for mathematical modeling of the dynamics of linear electrical systems, which works stably with a relatively large integration time step and with accuracy much better than other algorithms widely described in the literature. The algorithm takes into account the possibility of using parallel calculations. The proposed algorithm combines the advantages of known methods used in the analysis of electrical circuits, such as nodal analysis, multi-terminal electrical component theory, and transient states analysis methods. However, the main advantage over other algorithms is the use of the method based on average voltages in the integration step (AVIS method). The attention was focused on the presentation of the scientifically acceptable general principle offered to mathematical modeling of dynamics of linear electrical systems with parallel computations. However, the evidence of its effective application in the analysis of the dynamics of electric power and electromechanical systems was indicated in the works carried out by the team of authors from the Institute of Electrical Engineering UTP University of Science and Technology in Bydgoszcz (Poland).
Highlights
Accepted: 7 May 2021Mathematical models of complex electric power and electromechanical systems for transients simulation can be derived directly on the basis of mathematical descriptions of physical phenomena occurring in the elements of these systems or on the basis of equivalent diagrams containing the fundamental elements of electrical circuits, including: resistors, inductors, capacitors, and sources
The original contributions of the author of this paper were the method of determining the areas of application of the proposed integration method, in which it has an advantage over other methods and the theory of mathematical modeling of dynamics of linear electrical systems using parallel calculations
The organization of the article is as follows: (1) we present in detail the derivation and physical basis of the mathematical models of individual structural elements and the mathematical model of the generalized electrical system; (2) we present the method of separating the fragments of the mathematical model of the generalized electrical system into computational threads that can be implemented in parallel; and (3) we present, on a relatively simple example, the application of the mathematical modeling method proposed in this paper
Summary
Mathematical models of complex electric power and electromechanical systems for transients simulation can be derived directly on the basis of mathematical descriptions of physical phenomena occurring in the elements of these systems or on the basis of equivalent diagrams containing the fundamental (ideal) elements of electrical circuits, including: resistors, inductors, capacitors, and sources. The goal of this paper was the presentation of the scientifically acceptable general method for the mathematical modeling of the dynamics of linear electrical systems using parallel calculations. The original contributions of the author of this paper were the method of determining the areas of application of the proposed integration method, in which it has an advantage over other methods and the theory of mathematical modeling of dynamics of linear electrical systems using parallel calculations. A detailed description of the implementation of the proposed mathematical modeling method of electrical systems, due to its specificity (PC, DSP, FPGA, GPU), is beyond the scope of this paper
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