Estimation of non-linear continuous time models for the heat exchange dynamics of building integrated photovoltaic modules

Abstract

This paper focuses on a method for linear or non-linear continuous time modelling of physical systems using discrete time data. This approach facilitates a more appropriate modelling of more realistic non-linear systems. Particularly concerning advanced building components, convective and radiative heat interchanges are non-linear effects and represent significant contributions in a variety of components such as photovoltaic integrated façades or roofs and those using these effects as passive cooling strategies, etc. Since models are approximations of the physical system and data is encumbered with measurement errors it is also argued that it is important to consider stochastic models. More specifically this paper advocates for using continuous–discrete stochastic state space models in the form of non-linear partially observed stochastic differential equations (SDE’s)—with measurement noise for modelling dynamic systems in continuous time using discrete time data. First of all the proposed method provides a method for modelling non-linear systems with partially observed states. The approach allows parameters to be estimated from experimental data in a prediction error (PE) setting, which gives less biased and more reproducible results in the presence of significant process noise than the more commonly used output error (OE) setting. To facilitate the use of continuous–discrete stochastic state space models, a PE estimation scheme that features maximum likelihood (ML) and maximum a posteriori (MAP) estimation is presented along with a software implementation. As a case study, the modelling of the thermal characteristics of a building integrated PV component is considered. The EC-JRC Ispra has made experimental data available. Both linear and non-linear models are identified. It is shown that a description of the non-linear heat transfer is essential. The resulting model is a non-linear first order stochastic differential equation for the heat transfer of the PV component.