Stability Study and Nonlinear Analysis of DC-DC Power Converters with Constant Power Loads at the Fast Timescale

Rapidly growing distributed renewable networks make an increasing demand on various types of power converters to feed different loads. Power converters with constant power load are one typical configuration that can degrade the stability of the power conversion system due to the negative impedance characteristic. This paper presents a nonlinear analysis method using the developed complete-cycle solution matrix method by transforming the original linear time-variant system into a summation of segmented linear time-invariant systems. Thus, the stability of the nonlinear system can be studied using a series of the corresponding state transition matrix and saltation matrix. As this derived matrix contains all the comprehensive information relating to the system’s stability, the influence of the constant power load to system’s fast-timescale stability in both continuous conduction mode and the discontinuous conduction mode can be fully investigated and analyzed. The phenomena of fast-timescale instability around switching frequency for power converters with a constant power load are observed and investigated numerically. Finally, experimental results have proven the analysis and verified the effectiveness of the developed method

Modeling, Control and Characterization of Aircraft Electric Power Systems

A study model of advanced aircraft electric power system (AAEPS) corresponding to B767 Aircraft is developed in the PSIM9 software environment. The performance characteristics of the system under consideration for large sharing of non-linear loads are studied. A comprehensive mathematical model describing system dynamics is derived where the GSSA technique is applied for reduced-order system approximation. The transient and steady-state performance of the hybrid PEM-FC/battery APU integrated to the aircraft electric network is analyzed while different loading scenarios are taken into account. In addition, dynamic bifurcation analysis is employed to characterize the systems stability performance under multi-parameters condition. Also, the power quality of the system is assessed under various loading configurations, and the effect of installing active/passive power filters (APF/PPF) on power quality of the system is investigated for a wide range of operating frequencies

Simulation, bifurcation, and stability analysis of a SEPIC converter controlled with ZAD

This article presents some results of SEPIC converter dynamics when controlled by a center pulse width modulator controller (CPWM). The duty cycle is calculated using the ZAD (Zero Average Dynamics) technique. Results obtained using this technique show a great variety of non-linear phenomena such as bifurcations and chaos, as parameters associated with the switching surface. These phenomena have been studied in the present paper in numerical form. Simulations were done in MATLAB

Two-parameter bifurcation analysis of the buck converter

This paper is concerned with the analysis of two-parameter bifurcation phenomena in the buck power converter. It is shown that the complex dynamics of the converter can be unfolded by considering higher codimension bifurcation points in two-parameter space. Specifically, standard smooth bifurcations are shown to merge with discontinuity-induced bifurcation (DIB) curves, giving rise to intricate bifurcation scenarios. The analytical results are compared with those obtained numerically, showing excellent agreement between the analytical predictions and the numerical observations. The existence of these two-parameter bifurcation phenomena involving DIBs and smooth bifurcations, predicted in [P. Kowalczyk et al., Internat. J. Bifur. Chaos Appl. Sci. Engrg., 16 (2006), pp. 601–629; A. Colombo and F. Dercole, SIAM J. Appl. Dyn. Syst., submitted], is confirmed in this important class of systems.Postprint (published version

Non-linear behavior of a Z-source DC/DC converter based on dual-loop control

As a new topology, Z-source converter can be potentially applied in emerging energy power fields. In contrast to traditional converters, Z-source converter under dual-loop control exhibits particularity, but this property has been rarely investigated. In this study, the bifurcation and chaos phenomena are investigated in the Z-source converter under dual-loop control. A dynamic model with a shoot-through state of the Z-source converter is initially derived. The stability of fixed points is then investigated. The parameter region of a steady-state operation is subsequently schemed. The evolution and mechanism of bifurcations and chaos are also analyzed in detail. Results show that the system is intermittently stable at relatively low Vref, as Vref gradually increases, the system enters a bifurcation state and then exhibits chaos

On the dynamic behavior of the current in the condenser of a boost converter controlled with ZAD

In this paper, an analytical and numerical study is conducted on the dynamics of the current in the condenser of a boost converter controlled with ZAD, using a pulse PWM to the symmetric center. A stability analysis of periodic 1T-orbits was made by the analytical calculation of the eigenvalues of the Jacobian matrix of the dynamic system, where the presence of flip and Neimar–Sacker-type bifurcations was determined. The presence of chaos, which is controlled by ZAD and FPIC techniques, is shown from the analysis of Lyapunov exponents

PID controller using rapid control prototyping techniques

To analyze the performance of the PID controller in a buck type converter implemented in real time. We begin by designing a continuous controller using the analytical method for calculating PIDs. Pulse width modulation is then used and bifurcation diagrams analyzed to reveal some problems of switching and sampling time. The model converter is then implemented with a PID controller in dSPACE. The experimental results provide detailed requirements of sampling frequency and switching speed, and show the performance of the PID controller. Converters are used in power generation solar systems and conmuted power sources for feed telecommunication devices, smart grids, and other applications

Dynamical analysis of an interleaved single inductor TITO switching regulator

We study the dynamical behavior of a single inductor two inputs two outputs (SITITO) power electronics DC-DC converter under a current mode control in a PWM interleaved scheme. This system is able to regulate two, generally one positive and one negative, voltages (outputs). The regulation of the outputs is carried out by the modulation of two time intervals within a switching cycle. The value of the regulated voltages is related to both duty cycles (inputs). The stability of the whole nonlinear system is therefore studied without any decoupling. Under certain operating conditions, the dynamical behavior of the system can be modeled by a piecewise linear (PWL)map, which is used to investigate the stability in the parameter space and to detect possible subharmonic oscillations and chaotic behavior. These results are confirmed by numerical one dimensional and two-dimensional bifurcation diagrams and some experimental measurements from a laboratory prototype.Peer ReviewedPostprint (published version

Stability analysis and control of DC-DC converters using nonlinear methodologies

PhD ThesisSwitched mode DC-DC converters exhibit a variety of complex behaviours in power electronics systems, such as sudden changes in operating region, bifurcation and chaotic operation. These unexpected random-like behaviours lead the converter to function outside of the normal periodic operation, increasing the potential to generate electromagnetic interference degrading conversion efficiency and in the worst-case scenario a loss of control leading to catastrophic failure. The rapidly growing market for switched mode power DC-DC converters demands more functionality at lower cost. In order to achieve this, DC-DC converters must operate reliably at all load conditions including boundary conditions. Over the last decade researchers have focused on these boundary conditions as well as nonlinear phenomena in power switching converters, leading to different theoretical and analytical approaches. However, the most interesting results are based on abstract mathematical forms, which cannot be directly applied to the design of practical systems for industrial applications. In this thesis, an analytic methodology for DC-DC converters is used to fully determine the inherent nonlinear dynamics. System stability can be indicated by the derived Monodromy matrix which includes comprehensive information concerning converter parameters and the control loop. This methodology can be applied in further stability analysis, such as of the influence of parasitic parameters or the effect of constant power load, and can furthermore be extended to interleaved operating converters to study the interaction effect of switching operations. From this analysis, advanced control algorithms are also developed to guarantee the satisfactory performance of the converter, avoiding nonlinear behaviours such as fast- and slowscale bifurcations. The numerical and analytical results validate the theoretical analysis, and experimental results with an interleaved boost converter verify the effectiveness of the proposed approach.Engineering and Physical Sciences Research Council (EPSRC), China Scholarship Council (CSC), and school of Electrical and Electronic Engineerin

Nonlinear behavior analysis of Z-source DC/DC converter based on current control

Z-source converter as a kind of power converter will be responsible for the energy transmission and load switching and other important functions, the paper focuses on the nonlinear characteristic analysis of Z-source DC/DC converter, in the continuous conduction mode (CCM), take the Z-source converter with peak current control as the research object, establish stroboscopic mapping model for analyzing its bifurcation and chaos characteristic based on system accurate modeling. According to numerical simulation and analysis, estimate parameter range in which Z-source occur bifurcation and chaos under different design. Considering the change of reference current, input voltage and load impedance, the experiment results prove that Z-source converter stroboscopic mapping model is correct for analyzing its nonlinear behavior, which provides a theoretical basis for optimal design and control