ESTC 2014 Template

In this work, we present an automatized, computationally efficient and stable compact modeling technique for a large-scale multiport model of MEMS based piezoelectric energy harvester. The method includes structure preserving model order reduction based on Krylov subspaces. We further demonstrate a cosimulation between the reduced harvester model and the power circuitry. Introduction MEMS (micro-electro-mechanical-systems) based piezoelectric energy harvesters (see Fig. 1) play the role of power suppliers for the self-contained systems, such as monitoring sensors. The operational principle of such devices is based on the conversion of the ambient vibration energy to electrical domain by exploiting a piezoelectric effect [1]. Fig. 1: Schematic design of a piezoelectric energy harvester [1]. The efficiency of the energy transformation highly depends both on the harvester design and on a power circuitry connected to it. To get a maximum output, one needs to perform the system level simulation that is the co-simulation of these two parts. At the system level, piezoelectric harvester can be represented as a block with input and output ports. As it is shown in Fig. 2, the model, which is used in this work, has three input ports (one mechanical named displ and two electrical named el1_in, el2_in) and five output ports (three mechanical named centr, north, south and two electrical named el1_out, el2_out). Fig. 2: System level representation of energy harvester model. There are several ways to describe the relation between input and output ports. Usage of lumped elements, being one of the most popular and simple among others methods, can lead however to oversimplifying of piezoelectric model. Multi-physical models, generated directly from spatial discretization of the governing partial differential equation via e. g. , finite elements (FE), are more accurate and hence, more realistic. The FE discretization of the harvester model, leads to a large-scale second order linear ordinary differential equation system (1): ,