Steady-state analysis of DC converter using Galerkin's method. Issue 6 (19th September 2019)

• Record Type: Journal Article
• Authors: Korotyeyev, Igor
• Is Part Of: Compel. Volume 38:Issue 6(2019)
• Page Start: 2057
• Page End: 2069
• Publication Date: 2019-09-19
• Subjects: Circuit analysis -- DC–DC converters -- Galerkin method -- Partial differential equations -- Differential equation extension -- Generalised state-space averaging method; Electrical engineering -- Data Processing -- Periodicals; Electrical engineering -- Mathematics -- Periodicals; Electrical engineering -- Periodicals; Electronics -- Data Processing -- Periodicals; Electronics -- Mathematics -- Periodicals; 621.3
• DOI: 10.1108/COMPEL-02-2019-0062
• Languages: English
• ISSNs: 0332-1649

Abstract

Abstract : Purpose: The purpose of this paper is to present the Galerkin method for analysis of steady-state processes in periodically time-varying circuits. Design/methodology/approach: A converter circuit working on a time-varying load is often controlled by different signals. In the case of incommensurable frequencies, one can find a steady-state process only via calculation of a transient process. As the obtained results will not be periodical, one must repeat this procedure to calculate the steady-state process on a different time interval. The proposed methodology is based on the expansion of ordinary differential equations with one time variable into a domain of two independent variables of time. In this case, the steady-state process will be periodical. This process is calculated by the use of the Galerkin method with bases and weight functions in the form of the double Fourier series. Findings: Expansion of differential equations and use of the Galerkin method enable discovery of the steady-state processes in converter circuits. Steady-state processes in the circuits of buck and boost converters are calculated and results are compared with numerical and generalized state-space averaging methods. Originality/value: The Galerkin method is used to find a steady-state process in a converter circuit with a time-varying load. Processes in such a load depend on two incommensurable signals. The state-space averaging method is generalized for extended differential equations. A balance of active power for extended equations is shown.