Bifurcations and Chaos in a Photovoltaic Plant

Abstract

This paper presents a comprehensive approach to analyze the dynamics of a photovoltaic system by using a discrete-time modeling approach. The proposed structure consists of a photovoltaic array, a two-cell DC–DC buck converter and a load connected in cascade through a DC bus. The research efforts focus on the modeling process and stability analysis, which leads to an implementation with a comprehensive description validated through simulation results. The research efforts focus on the numeric simulation improvements and dynamic investigation of the photovoltaic system under digital controls. The chaotic behaviors that appear in the photovoltaic plant are then studied. The aim of the last part is to detail the stability study using numerical simulation.

PI-Type Controllers and Σ–Δ Modulation for Saturated DC-DC Buck Power Converters

“…By substituting the inductor current dynamics Ldi/dt (see equation (22)) into the expression (23) and considering thaṫ d 2 = 0, the following second-order linear equation is obtained:…”

“…In [21], the authors introduced a method to avoid duty cycle saturation during the startup in the bidirectional buck/boost converters. The combination of a photovoltaic plant with a two-cell buck converter with input saturation was analyzed in [22]. In [23], the maximum power from a photovoltaic array is obtained, taking into account input constraints of a boost DC-DC converter.…”

Nonlinear Dynamics and Stability Analysis of a Three-Cell Flying Capacitor DC-DC Converter

“…Namely, the validity of (39) is first demonstrated before obtaining the approximate expression of the monodromy matrix. Figure 8 shows the evolution of the voltage and the current coordinates of x(0) as function of the feedback gain κ i for two different values of the current reference i ref using the exact expression (9) and the approximate one (39). A remarkable agreement can be clearly observed which demonstrates that for design-purposes, the approximate expression (39) can be used without having to use the state exact transition matrices whose computation could be very time consuming in a repetitive simulation process.…”

“…With the approximated vector x(0) given in (39) and the simplified expressions of the state transition and the saltation matrices, the expressions of the monodromy matrix evaluated at the previous limit cycle can be explicitly expressed as follows Table 3 shows a comparative analysis of the results from the exact and the approximate monodromy matrix. This table shows the limit cycle represented by their initial values x(0), the corresponding Floquet multiplies, the exact and the approximate monodromy matrix M and the stability of limit cycles.…”

“…A discrete-time digital predictive control for a three-level flying capacitor buck converter with voltage balancing is presented in [38]. Discrete-time PWM control has been applied to a two-cell DC-DC converters [29][30][31][32]39]. This procedure can be adapted to any multi-cell converter with a generic number of cells [40].…”