This paper investigates the impact of bifurcations on the performance of power electronic circuits. We focus on circuits that include energy-harvesting devices, which exhibit a maximum power point (MPP). In particular, a DC–DC converter with a photovoltaic (PV) module is considered a representative example of such systems to evaluate the relationship between the circuit performance indices (such as power conversion and maximum power point tracking (MPPT) efficiency) and the bifurcation phenomena observed in the system. First, experimental results are reported that evaluate circuit characteristics and performance under MPPT control. Then, a novel mathematical PV model is presented and fully defined using experimentally measured parameters; this model does not necessitate the use of root-finding algorithms. Next, this model is integrated with the switched nonlinear model of a DC–DC converter subject to peak current mode control (PCMC), and a stability analysis of the periodic orbits is performed. Finally, the relationship between circuit performance and observed bifurcation phenomena is investigated and discussed. This research demonstrates the occurrence of both period-doubling and Neimark–Sacker bifurcations in the system considered here, and these features are shown in a two-parameter bifurcation diagram.

A switched-inductor (SL) multi-cell boost converter is analyzed in this paper for a high-voltage gain application, stepping up a dc voltage from 36 V to 380 V in the first stage of a photovoltaic (PV) conversion chain. A fast maximum power point tracker (MPPT), processing the system input voltage, is used to extract the maximum power from the PV generator regardless of atmospheric conditions. A single sliding-mode control (SMC) loop forces the PV generator voltage to follow the maximum power point (MPP) voltage provided by a Perturb and Observe (P&O) algorithm. The sliding-mode analysis uses the equivalent control approach to demonstrate that the linearized ideal sliding dynamics are unconditionally stable. Theoretical predictions are corroborated by simulations and experimental measurements of the system under step-type changes in input irradiance and output load. The MPPT performance is experimentally evaluated against two classical approaches applied to a canonical boost converter: a current-based SMC and a voltage-based PWM. Both approaches track the MPP current and voltage, respectively, as given by the P&O algorithm. The proposed system outperforms the two classical systems, showing a better tracking accuracy.

Over the decades, bifurcation theory has emerged as a significant area of research, providing deep insights into the complex dynamics of systems across multiple disciplines. Moreover, it serves as a foundation for devising effective control methodologies aimed at avoiding or delaying undesirable dynamical transitions. This paper deals with both local and global dynamics of a bidirectional dc-dc boost converter supplying a constant power load (CPL) with a stabilizing resistor inserted in series with the main inductor. Numerical simulations performed on the averaged model of the system show interesting bifurcation phenomena explaining its local and global dynamical behavior. In particular, it is shown that in some parametric region, the system has two coexisting equilibria, one of them being a saddle and the other one an anti-saddle. The latter can be stable or unstable. An unstable limit cycle also coexists with the stable anti-saddle equilibrium. This limit cycle disappears through a homoclinic bifurcation. Moreover, a parameter space reduction is carried out by choosing suitable bifurcation parameters, and the normal form of the Bogdanov-Takens bifurcation is obtained hence mathematically demonstrating its existence. Finally, the analytical and simulation results on the switched model are partially validated by experimental measurements from a laboratory prototype.

This paper presents a comprehensive investigation into the analysis, design, and fixed frequency digital control of a three-phase four-wire (3P4W) ac-dc rectifier followed by a CLLC resonant converter, targeting 11 kW battery charging applications. First, the 3P4W front-end rectifier is characterized under steady-state and dynamic conditions, emphasizing on achieving a near-unity power factor, input-current harmonic mitigation, and neutral-point voltage stabilization in both bal¬anced and unbalanced loading scenarios. Second, the CLL- Cresonant converter is designed and analyzed to achieve zero-voltage and zero-current switching (ZVZCS) in both charging and discharging modes to minimize switching losses in wide load ranges. Fixed-frequency operation is maintained through phase-shift modulation for the constant-current/constant-voltage (CC-CV) charging protocol, ensuring robust performance despite wide variations in battery voltage and load current. Fixed-frequency control simplifies electro-magnetic interference (EMI) filtering and facilitates predictable timing. The simulation results show power factor exceeding 0.99 and a total harmonic distortion below 5%.

This paper demonstrates the design and analysis of a novel Virtual Impedance based Lyapunov Controller for DC-DC boost converter fed Permanent Magnet Direct Current (PMDC) drive. The motor drive acts as Constant Power Load (CPL) destabilizing the system in open loop condition. The non-minimum phase nature of boost converter restricts the use of conventional Voltage Mode Control (VMC) method due to slowed dynamics. Two Loop Control provides an active damping to stabilize the system in closed loop. On the other hand, the Virtual Impedance (VI) Control provides active damping to the system in a more effective way with advantages of wide duty-ratio operation, improved transient performance and efficiency. In case of Lyapunov Controller (LC), an improved supply and load disturbance rejection is achieved. The proposed controller offers excellent dynamics and control of dc-link voltage and speed of motor. It also offers way better transient performance and is insensitive to large-signal perturbations. The comparison for conventional Two Loop Control, Virtual Impedance Control, Lyapunov Controller and the proposed controller has been carried out. The theoretical analysis is validated by simulation results.

In this paper, the steady-state performances of a piecewise quadratic auto-tuned slope compensation technique proposed recently to eliminate subharmonic oscillations in dc-dc switching converters are evaluated. With this technique, a self-generated compensating signal is used resulting in a naturally full duty cycle stability domain by appropriately self-adapting the amplitude of the generated signal both in transient and in steady-state regimes. The circuit corresponding to the proposed technique can be implemented using standard analog devices. A boost converter under current mode control is used to validate the theoretical results both by numerical simulations and by experiments showing that the technique efficiently eliminate subharmonic oscillation and is robust against parameter variations such as load current and inductor value.

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.

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.

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.

This paper presents a new approach for small-signal analysis of all types of dc-dc converters with any number of topological modes within a switching cycle. So far, sampled-data modeling and sensitivity analysis are mostly used for such a purpose. In both cases, the switching conditions implicitly appear in the small-signal matrices which increases the complexity of the computation for the system with a larger number of topological modes. Here, we propose an alternative approach based on Filippov's method, which studies the effects of each switching separately. It uses a shooting method with an event detector to locate a periodic steady-state, and, when the Newton-Raphson search process of the shooting method converges, it also gives the Jacobian matrix. The algorithm can be easily implemented in a software program as an analytical tool which is expected to be useful for fast and accurate frequency-domain analysis (by small-signal transfer functions) to facilitate controller design. Moreover, since it uses the Filippov's method, this algorithm can also predict the slow- and fast-timescale instabilities.

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, Filippov's 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.

The complex behavior of load resonant converters is investigated by using a newly developed stability analysis tool. In this paper we specifically consider the series-parallel load resonant converter with L-C output filter, controlled by the frequency modulation technique. The close loop variable frequency control consists of a feedback loop and a PI controller with voltage controlled oscillator (VCO). The VCO is used to convert the error in output voltage into a change of frequency to control the voltage in close loop system. Two converter designs are considered with different combinations of L-C output filter. With the variation of the proportional gain, Neimark-Sacker and symmetry-breaking bifurcations are observed.

This paper reports the occurrence of symmetry-breaking bifurcation in the series-parallel load-resonant dc-dc converter with L-C output filter. The constant frequency phase shift modulation technique is employed with proportional- integral controller in the output voltage regulation. It is shown that the dynamics are not only related to the resonant components but are also heavily dependent on the output filter design. The first instability can be caused by smooth and nonsmooth symmetry breaking bifurcations. Stable as well as unstable periodic orbits are identified by a newly developed algorithm based on fundamental solution matrix. As a significant result of this paper, it is shown that the symmetry-breaking can be caused by a grazing event.

The paper demonstrates, both numerically and experimentally, the quasiperiodic and subharmonic operation in a load resonant DC-DC converter. The output voltage of the converter is controlled by a closed loop, applying constant-frequency pulse width modulation. The complexity of the system is contributed by fact that the state space is five-dimensional, with four switching surfaces dividing it into 9 subsystems. A method is developed to perform the stability analysis and to investigate the bifurcation sequences following the first instability in such a complex switching system.