A study of a DC–DC boost converter fed by a photovoltaic (PV) generator and supplying a constant voltage load is presented. The input port of the converter is controlled using fixed frequency pulse width modulation (PWM) based on the loss-free resistor (LFR) concept whose parameter is selected with the aim to force the PV generator to work at its maximum power point. Under this control strategy, it is shown that the system can exhibit complex nonlinear behaviors for certain ranges of parameter values. First, using the nonlinear models of the converter and the PV source, the dynamics of the system are explored in terms of some of its parameters such as the proportional gain of the controller and the output DC bus voltage. To present a comprehensive approach to the overall system behavior under parameter changes, a series of bifurcation diagrams are computed from the circuit-level switched model and from a simplified model both implemented in PSIM© software showing a remarkable agreement. These diagrams show that the first instability that takes place in the system period-1 orbit when a primary parameter is varied is a smooth period-doubling bifurcation and that the nonlinearity of the PV generator is irrelevant for predicting this phenomenon. Different bifurcation scenarios can take place for the resulting period-2 subharmonic regime depending on a secondary bifurcation parameter. The boundary between the desired period-1 orbit and subharmonic oscillation resulting from period-doubling in the parameter space is obtained by calculating the eigenvalues of the monodromy matrix of the simplified model. The results from this model have been validated with time-domain numerical simulation using the circuit-level switched model and also experimentally from a laboratory prototype. This study can help in selecting the parameter values of the circuit in order to delimit the region of period-1 operation of the converter which is of practical interest in PV systems.
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.
This paper focuses on the control design of a differential boost inverter when used in single-stage grid-tied PV systems. The inverter performs both Maximum Power Point Tracking (MPPT) at the DC side and Power Factor Correction at the AC side. At first, the state-space time-domain averaged model of the inverter is derived and the small signal frequency domain model is obtained using a quasi-static approximation in which the inverter is treated as a DC–DC converter with a slowly varying output voltage. Then, the controllers are designed using a three-loop strategy in which the inverter inductor currents loop is used for suitable compensation, the DC Photovoltaic (PV) voltage loop is used for MPPT and the output grid current loop is used for Power Factor Correction (PFC) and active power control. The selection of the control parameters is based on a compromise among suitable system performances such as settling time of the input PV voltage, the sampling period of the MPPT, total harmonic distortion of the output grid current, power factor as well as suppression of subharmonic oscillation for all the range of the operating duty cycle. The resulting design ensures that the oscillations of the voltage, current and power at the DC side and the grid current at the AC side are effectively controlled. The validity of the proposed control design is verified by numerical simulations performed on the switched model of the system demonstrating its robustness and fast response under irradiance variations and MPPT perturbations despite the nonlinearity and complexity of the system.
Summary Two main methods for controlling switching converters exist in the literature. The direct one is the voltage mode control, which suffers from some disadvantages such as slow response to load variations and an input voltage‐dependent total loop gain. The current mode control can overcome these problems but at the expense of extra cost and more complex control design. V1 concept is a new promising control technique for designing voltage mode control of buck‐type converters with an optimal response similar to current mode control. In this paper, the dynamics and the stability of buck converters under V1 control are studied. In particular, subharmonic oscillation limits in the parameter space are addressed. First, a closed‐loop state‐space model is derived and then used to formulate an analytical matrix‐form expression for predicting the stability limit of the system. Using this expression, multi‐parametric stability boundaries are obtained. It is shown that the equivalent series inductance of the output capacitor can narrow the stability region. It is also demonstrated that the integral action in the feedback loop of a V1‐controlled buck converter has a negligible effect on the subharmonic oscillation boundary. The theoretical analysis is validated through numerical simulation of the circuit‐level switched model of the system. Copyright © 2017 John Wiley & Sons, Ltd.
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