Application of the Filippov Method for the Stability Analysis of a Photovoltaic System

Abstract

This paper describes bifurcation phenomena of a photovoltaic system. The studied photovoltaic (PV) system includes a solar panel, a boost converter, a maximum power point tracking (MPPT) controller and a storage device. Computer simulations are performed to capture the effects of variation of some chosen parameters on the qualitative behavior of the system. The impact of the maximum power point (MPP) current and voltage variations due to luminosity changes is determinate, as well as the load variation. The stability of the system is analyzed using the state transition matrix over one switching cycle (the monodromy matrix) including the state transition matrices during each switching (the saltation matrices). This investigation is important to predict nonlinear phenomena and for the components dimensioning for a proper functioning

Application of the Filippov Method to PV‐fed DC‐DC converters modeled as hybrid‐DAEs

“…The reason these assumptions are not valid is because the system is modeled as a set of DAEs. It is a nonlinear system and cannot be described by (27). The algebraic constraint can cause the perturbation to shrink or grow over time.…”

“…In Reference 27, an MPPT controlled boost converter fed by a PV‐panel is studied. In all the articles discussed in this literature survey, the temperature and solar irradiance is fixed when studying the effect of other parameters on the nonlinear dynamics of the system or the solar irradiance is the bifurcation parameter with all other parameters fixed.…”

“…In all the articles discussed in this literature survey, the temperature and solar irradiance is fixed when studying the effect of other parameters on the nonlinear dynamics of the system or the solar irradiance is the bifurcation parameter with all other parameters fixed. However, in Reference 27, the authors calculate the maximum power point for each value of solar irradiance and fix v in at the MPP. For this reason, the results of Reference 27 are for a specific converter, at a specific temperature, and operating under specific conditions.…”

“…However, in Reference 27, the authors calculate the maximum power point for each value of solar irradiance and fix v in at the MPP. For this reason, the results of Reference 27 are for a specific converter, at a specific temperature, and operating under specific conditions. The algorithm presented in this article is generalized and can be applied to any DC‐DC converter with a PV source with any operating conditions.…”

The Salted Kalman Filter: Kalman filtering on hybrid dynamical systems

“…68) The plastic, frictionless impact reset map into mode S follows (68) but with e = 0 (and written with M † S for mode S, though M † S = M † n since J S = J n ):…”