Nonlinear Dynamics and Bifurcation Analysis of a Boost Converter for Battery Charging in Photovoltaic Applications

Abstract

Photovoltaic (PV) systems with a battery back-up form an integral part of distributed generation systems and therefore have recently attracted a lot of interest. In this paper, we consider a system of charging a battery from a PV panel through a current mode controlled boost dc-dc converter. We analyze its complete nonlinear/nonsmooth dynamics, using a piecewise model of the converter and realistic nonlinear v–i characteristics of the PV panel. Through this study, it is revealed that system design without taking into account the nonsmooth dynamics of the converter combined with the nonlinear v–i characteristics of the PV panel can lead to unpredictable responses of the overall system with high current ripple and other undesirable phenomena. This analysis can lead to better designed converters that can operate under a wide variation of the solar irradiation and the battery's state of charge. We show that the v–i characteristics of the PV panel combined with the battery's output voltage variation can increase or decrease the converter's robustness, both under peak current mode control and average current mode control. We justify the observation in terms of the change in the discrete-time map caused by the nonlinear v–i characteristics of the PV panel. The theoretical results are validated experimentally.

Modeling and Stability Analysis of a Single-Phase Two-Stage Grid-Connected Photovoltaic System

“…Therefore, λ 10,11 is only associated with the angular frequency of power grid and has no influence on the stability of the system. Actually, λ 1,2 and λ 8,9 are different when T i1 varies. However, the slight differences are disregarded in this paper.…”

“…When K p2 decreases, λ 6,7 moves towards right in the s-plane. For λ 8,9 , the most sensitive parameters is T i3 . The increase in T i3 leads to λ 8,9 moving towards right in the s-plane.…”

“…For λ 8,9 , the most sensitive parameters is T i3 . The increase in T i3 leads to λ 8,9 moving towards right in the s-plane. λ 10,11 are insensitive to all these parameters listed in Table 3.…”

“…In some studies on stability analysis of PV systems, the PV array is replaced by a constant voltage source [5,6] or a constant current source [7]. These methods neglect the nonlinear characteristics of the PV array and may cause deviation between the theoretical analysis and the behavior of the real system [8]. Some studies take into account this characteristic of the PV array by using the v-i curve calculated from numerical techniques with the aid of a computer [8,9].…”

“…These methods neglect the nonlinear characteristics of the PV array and may cause deviation between the theoretical analysis and the behavior of the real system [8]. Some studies take into account this characteristic of the PV array by using the v-i curve calculated from numerical techniques with the aid of a computer [8,9]. However, specific parameters of the PV array such as shunt resistance and series resistance are necessary for implementing the calculation.…”