Michał Radzik

The steady state response of a synchronous machine to the torque with angle dependent pulsating component is of great practical importance for the piston drive. Determining such a response is not easy due to the necessity of solving the system of nonlinear differential equations. This paper describes an algorithm that allows directly determining the steady states of a synchronous machine driven by an internal combustion engine (e.g. diesel engine). To create such an algorithm, the harmonic balance method and the iterative Newton–Raphson procedure are used. This approach allows obtaining steady-state solutions directly in the frequency domain. Exemplary calculations are performed for synchronous generators derived from the four-stroke internal combustion engine.

The main aim of this paper is to identify relationships for direct determination in the time domain of periodic steady-state solutions for differential equations. A new discrete operator of differentiating has been defined. As a result, a set of algebraic equations has been written. Based on this, an algorithm for nonlinear differential equations has been proposed. Numerical tests have been carried out both for a new discrete operator and for steady-state analysis in a simple electromechanical converter.

This paper presents an algorithm that uses the harmonic balance method for finding the steady-state solution in the moment of excited synchronous machine with periodic mechanical component of the alternating depending on the angle of rotation of the rotor. The problem is complicated because the presence of periodic component leads to problems of nonlinear. This procedure allows the direct determination of the Fourier spectra of the most important volumes describing the synchronous machine. Sample calculations were performed for a synchronous motor operating in the state of synchronism and fixed mechanical load torque varying periodicaly at a specifed course.