Mohammed M. Al-Hindawi

Nonlinear dynamics and bifurcation analysis of a boost converter for battery charging in photovoltaic applications

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 batterys state of charge. We show that the v–i characteristics of the PV panel combined with the batterys output voltage variation can increase or decrease the converters 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.

An Adaptive Quadrature Signal Generation-Based Single-Phase Phase-Locked Loop for Grid-Connected Applications

The quadrature signal generation-based phase-locked loops (QSG-PLLs) are highly popular for synchronization purposes in single-phase systems. The main difference among these PLLs often lies in the technique they use for creating the fictitious quadrature signal. One of the most popular QSG approaches is delaying the original single-phase signal by a quarter of a cycle. The PLL with such QSG technique is often called the transfer delay-based PLL (TD-PLL). The TD-PLL benefits from a simple structure, rather fast dynamic response, and a good detection accuracy when the grid frequency is at its nominal value, but it suffers from a phase offset error and double-frequency oscillatory error in the estimated quantities in the presence of frequency drifts. In this paper, a simple yet effective approach to remove the aforementioned errors of the TD-PLL is proposed. The resultant PLL structure is called the adaptive TD-PLL (ATD-PLL). The stability of the ATD-PLL is evaluated by the derivation of its small-signal model. Parameter design guidelines are also presented. Finally, the effectiveness of the ATD-PLL is confirmed using numerical results.

Analysis of Discontinuity Induced Bifurcations in a Dual Input DC-DC Converter

DC-DC power converters with multiple inputs and a single output are used in numerous applications where multiple sources, e.g. two or more renewable energy sources and/or a battery, feed a single load. In this work, a classical boost converter topology with two input branches connected to two different sources is chosen, with each branch independently being controlled by a separate peak current mode controller. We demonstrate for the first time that even though this converter is similar to other well known topologies that have been studied before, it exhibits many complex nonlinear behaviors that are not found in any other standard PWM controlled power converter. The system undergoes period incrementing cascade as a parameter is varied, with discontinuous hard transitions between consecutive periodicities. We show that the system can be described by a discontinuous map, which explains the observed bifurcation phenomena. The results have been experimentally validated.

Dynamical analysis of single-inductor dual-output DC-DC converters

In this paper, a single-inductor single-input boost-type dual-output dc-dc converter is studied. Peak current-mode control is used for the main switch whereas the output switch is controlled by voltage-mode controller. To regulate both the output voltages proportional-integral compensator is introduced. In the state-space the five-dimensional system is divided into four subsystems by four switching surfaces. Due to the large number of subsystems, Filippovs method is used to obtain the stable operating region in the design parameter space. Coexisting attractors, period-doubling and Neimark-Sacker bifurcations are identified as the major causes of the possible instabilities. Detailed studies of the possible bifurcation scenarios (smooth as well as nonsmooth) have been done by detecting the stable as well as unstable orbits and by calculating their eigenvalues.

Control-oriented design guidelines to extend the stability margin of switching converters

Power electronic systems exhibit different types of fast- and slow-scale instabilities which limit the stable operating range of the parameters. It has been shown that the stability of complex power electronic systems can be fruitfully investigated using the Filippov method, where the stability of the system is given by the eigenvalues of the monodromy matrix, which is a combination of the state transition matrices through each subsystem and those across the switching events, called saltation matrix. In this paper we show that the components of the saltation matrix can be used to change the stability status of the system, and propose three specific techniques, which can be used individually or together to extend the range of stability significantly. The performance of these techniques are shown using line and load disturbances.

A Family of Gradient Descent Grid Frequency Estimators for the SOGI Filter

This paper applies the adaptive gradient descent method to the second-order generalized integrator (SOGI) filter in order to find an online estimation algorithm for the grid frequency, which leads to the proposal of three possible estimators. One of them is identical to the frequency-locked loop algorithm reported in the literature, which proves that it should be understood as a gradient descent estimation algorithm and not as a “frequency locked loop.” The proposed gradient descent estimators are simple and suitable to be implemented into a digital processor with small computational burden. However, due to the SOGI characteristics, the estimators show to be especially sensitive to subharmonic and dc-offset voltage distortion. These problems are removed adopting a cascaded double SOGI approach, which strongly increases the rejection capability to harmonics and enhances the response to voltage sags. Simulation and experimental results are provided to validate the proposed contribution.

A novel nonlinear modulation technique for stabilizing DC-DC switching converters

In this paper a novel modulation technique is proposed to eliminate instabilities such as subharmonic and chaotic oscillations in dc-dc switching converters. This modulation technique injects a stabilizing signal which is generated internally from its own state variables so that the system is free from the problems due to externally injected signal, such as frequency mismatch, phase shift, etc. Stability analysis of the system is carried out using Floquet theory taking into account its switching nature. Our results show that the system has larger stable region in the parameter space compared to the conventional modulation techniques. Numerical simulations illustrate the performance of the proposed technique under line and load disturbances.

Dynamical behaviors of interconnected converters in intermediate bus architecture

In this paper, a typical intermediate bus architecture is modeled from circuit theory and nonlinear dynamics point of view. In the studied system a regulated DC-DC buck converter in the first level supplies two parallel connected regulated buck converters in the second level through an intermediate bus. The loads connected to the second level converters are resistive. The complexity of the system is due to the interaction of the output voltage of the first converter with the downstream converters. Unlike the earlier studies where averaged or simplified reduced-order model were used only for two cascaded converters, we have done our study using the exact switching model of the DC-DC converters. This paper shows different mechanisms of instability when the parallel converters are fed through another converters instead of constant voltage. This knowledge will help in designing more reliable intermediate bus architecture for different application under different operating conditions.

Analysis of an AC-DC Full-controlled Converter Supplying Separately Excited DC Motor Parallel with Series DC Motor Loads@@@تحليل مقوم محكوم ( كامل التحكم ) يغذي محركاً منفصل الإثارة على التوازي مع محرك مستمر

Controlled rectifiers are widely used as a source of DC motors power supply. It is important to study motor characteristics when fed from such converters. Early work has studied single motor characteristics when fed from a converter. This paper is concerned with the study of an AC-DC full-controlled converter supplying separ- ately excited DC motor parallel with series DC motor loads. Continu- ous and discontinuous converter currents are considered. The critical firing angle is deduced. The margin firing angle that separates motor operation from generator operation of the separately excited machine is investigated. The performance characteristics have been derived and studied for each of: constant firing angle, constant torque of the separately excited motor and constant horsepower of the series motor. Waveforms for each load current and converter current are investigat- ed for different modes of operation.