Obtaining the most exact Jacobian of the time modelling of power electronics structures for gradient-based optimisations

Abstract

PurposeThe paper aims to deal with the exact computation of the Jacobian of a time criteria from a numerical simulation of power electronics structures, for the sizing by gradient-based optimization algorithm.Design/methodology/approachRunge Kutta 44 is used to solve the state equations. The generic approach combines numerical and symbolic approaches. The modelling of the static converter is based on ideal switches.FindingsThe paper extends the state equations to derivate any state variable according a sizing parameter. The integral expressions used for some sizing performances (e.g. average or RMS values) mix symbolic and numerical approaches. Choices are made for the derivatives of the extrema of which the search is not a continuous process. The use of an object-oriented implementation allows to have generic formulation of some design performances.Research limitations/implicationsThe paper aims to propose and to test formulations of sizing criteria and their gradients; so, the modelling of the study case is carried out manually. Due to generic modelling approach used for the power electronics, the model is not completely continuous. So, the derivatives according some parameters (e.g. switch controls) must be carried out by finite differences. However, as the global behaviour is continuous, it is not critical.Practical implicationsThe proposed formulations can be easily applied on simple static converter applications. For applications with large state equations, it should be possible to use the basic model of switches used in simulation tools of power electronics. The solving process and the sizing criteria formulation (with their derivatives) are generic and can be instantiate for any study.Originality/valueThe approach proposes formulations giving a numerical sizing dynamic model with a Jacobian computed, if possible, by an exact derivation useful for optimization studies. The approach gives fast simulation and fast computation of the derivatives by combining numerical and analytical approaches.