Analysis of Nonlinear Dynamics of a Quadratic Boost Converter Used for Maximum Power Point Tracking in a Grid-Interlinked PV System

Abstract

In this paper, the nonlinear dynamics of a PV-fed high-voltage-gain single-switch quadratic boost converter loaded by a grid-interlinked DC-AC inverter is explored in its parameter space. The control of the input port of the converter is designed using a resistive control approach ensuring stability at the slow time-scale. However, time-domain simulations, performed on a full-order circuit-level switched model implemented in PSIM© software, show that at relatively high irradiance levels, the system may exhibit undesired subharmonic instabilities at the fast time-scale. A model of the system is derived, and a closed-form expression is used for locating the subharmonic instability boundary in terms of parameters of different nature. The theoretical results are in remarkable agreement with the numerical simulations and experimental measurements using a laboratory prototype. The modeling method proposed and the results obtained can help in guiding the design of power conditioning converters for solar PV systems, as well as other similar structures for energy conversion systems.

Multiple-Loop Control Design for a Single-Stage PV-Fed Grid-Tied Differential Boost Inverter

“…The nonlinear v − i characteristic equation of a PV module can be found in many references in the literature. The PV generators have a nonlinear characteristic changing with the temperature Θ and irradiation S. For constant or slowly varying temperature and irradiance levels, the v − i equation of the PV model can be approximated by the following linear Norton equivalent model [31]:…”

“…A PI regulator is used to control the PV voltage to its desired reference value. The design of the PV DC-link voltage controller was performed analytically based on the reduced-order model (31). Using this expression, the parameters of this controller have been selected to provide a settling time of one grid voltage cycle.…”

Analysis of Subharmonic Oscillation and Slope Compensation for a Differential Boost Inverter

“…Floquet theory has been widely used in the analysis of stability of dynamical systems [53] in general and switching converters in particular [38][39][40]. For DC-DC converters, the stability dynamics at the fast switching cycle can be accurately predicted by analyzing the stability of the fixed points of the Poincaré map of the system using its Jacobian matrix or using Floquet theory combined with Filippov method which leads to the same results as the Poincaré map [38].…”

“…For DC-DC converters, the stability dynamics at the fast switching cycle can be accurately predicted by analyzing the stability of the fixed points of the Poincaré map of the system using its Jacobian matrix or using Floquet theory combined with Filippov method which leads to the same results as the Poincaré map [38]. The main tool for studying the stability of periodic orbits using Floquet theory is the principal fundamental matrix or the monodromy matrix M. This matrix plays a key role in the accurate stability analysis of switching systems [38][39][40]53]. The monodromy matrix is such that the dynamics in the vicinity of a quasi-static periodic orbit can be expressed as followŝ…”

“…Therefore, understanding these nonlinear phenomena, their analysis, prediction and control have increasingly become of great concern of many researchers all over the world [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The major part of the analytical results on subharmonic oscillation in power electronics converters has been achieved for DC-DC converters [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. DC-AC inverters are more difficult to deal with, since their dynamics is governed by two vastly different frequencies, namely the high switching frequency and the low frequency of the output voltage reference sinewave.…”