Method of average voltages in integration step: theory and application
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ORIGINAL PAPER
Method of average voltages in integration step: theory and application O. Plakhtyna1,2 · A. Kutsyk1,2 · A. Lozynskyy2 Received: 23 December 2019 / Accepted: 10 June 2020 © The Author(s) 2020
Abstract A numerical one-step method of average voltage values in integration step, which allows to algebraize the differential equations for electric circuits of electromechanical systems with semiconductor converters, was described in the paper. The method is proposed for the creation of digital power circuit real-time models of electrical systems in hybrid models that combine digital and physical components. Digital models in hybrid systems must continuously function over a long time period in conjunction with physical objects. The indicated method provides stability of mathematical models, and is also effective in the sense of the amount of calculations. The article describes the application of the method of average voltage values in the integration step to create a hybrid model of power generation system for a ship’s power plant with diesel generator. The digital component of the hybrid model, in this case, is power conversion system that includes a synchronous generator driven by a diesel engine, while the physical part is real excitation controller of generator with automatic voltage regulator. The research results obtained on the hybrid model and their comparison with the results of the physical experiment at the laboratory plant are presented. Keywords Numerical integration · Electric circuit · Power system · Real-time model
1 Introduction Systems containing electric circuits are described by differential and algebraic equations, which are usually nonlinear. Their solution requires the application of numerical methods that carry out the algebraization of differential equations in integration step. The algebraization of equations for electric circuits by explicit methods is obviously complicated by the error of calculating currents, as a result of which, after multiple calculations, there is a deviation from the first Kirchhoff’s law. The algebraization of these equations by implicit methods is complicated by the error of calculating voltages, as a result of which, after multiple calculations, there is a deviation from the second Kirchhoff’s law. These deviations lead to instability of mathematical models, especially those that are used in conjunction with real objects, and in which
* A. Kutsyk [email protected] 1
University of Science and Technology UTP, Bydgoszcz, Poland
Lviv Polytechnic National University, Lviv, Ukraine
2
the integration step is very small, and the calculation time is very long. Authors faced this problem, during the development of hybrid models. Such problems are mentioned in [1–10]. In particular, it is noted that most of the electrotechnical objects are stiff systems [1], for which the use of explicit methods is not feasible, since it may cause numerical instability [2, 3, 6, 7]. Reducing the step of numerical integration for stiff systems, if explicit metho
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