## Abstract

Purpose: The paper aims to emphasise how switched systems can be analysed with elementary techniques which require only undergraduate-level linear algebra and differential equations. It is also emphasised how math software can become useful for simplifying analytic complications. Design/methodology/approach: The time domain voltage balance methodology is used for stability analysis. As for deriving formulas for the asymptotic average of both capacitor voltage and inductor current, a new simple analytic method is introduced. Findings: It was shown analytically that the time average of capacitor voltage converges to half of the source voltage. A formula for the time average of the current of the inductor is also computed. As a by-product, it was discovered that the period of the current is half of the switching period. Numerical simulations are obtained to illustrate the accuracy of the results. Research limitations/implications: Higher dimensional generalisations could become a bit complicated, as stability analysis of higher dimensional exponential matrices is not so easy to handle. On the other hand, the new discovery on the period of the current is more likely to give new insights into handling higher dimensional systems. Practical implications: Analytical formulas are exact, and it helps in accurately modelling flying capacitor converts (FCCs) in practice. Originality/value: FCC is well studied in engineering society. However, not much is done in obtaining closed form solutions using analysis. Also, math software is much used in computation of numerical results and obtaining simulations. In this paper, one more important aspect of math software is emphasised, namely, use symbolic and numeric computing environment Maple in analysis.

Original language | English |
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Pages (from-to) | 1244-1257 |

Number of pages | 14 |

Journal | COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering |

Volume | 37 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 1 2018 |

## Keywords

- Flying capacitor converter
- Linear ODE
- Periodic solutions
- Piecewise constant coefficients

## ASJC Scopus subject areas

- Computer Science Applications
- Computational Theory and Mathematics
- Electrical and Electronic Engineering
- Applied Mathematics