Robust continuous-time model predictive control of a grid-tied photovoltaic system

Power converters are an important part of renewable energy conversion systems. When the photovoltaic (PV) system is connected to the grid, it is confidently expected that it delivers the required active power to the grid at the AC system frequency, while regulating the reactive power at a desired level depending on whether the system operates under normal or voltage sag conditions, but the question is how it knows which frequency to operate at, or how it is able to extract the specified amount of power from the PV panel depending on whether the PV generator works under maximum or reduced power. The PV energy conversion systems use power electronic converters to efficiently control the power exchange between the PV panel and the grid. A look at the literature reveals that there are several topologies that have been developed to ensure sustainable, reliable, and efficient use of PV energy-based power generation. The most popular one consists of interconnecting a DC-DC converter to a DC-AC converter via a DC-link capacitor. This topology allows one-way energy flow and is generally placed between the PV panel and the grid. The DC-DC converter allows extracting the desired power from the PV panel, while the inverter has the role of controlling the DC-link voltage and the reactive power injected into the AC system in order to comply with the grid requirement. It is important to emphasize that the regulation of the DC-link voltage is equivalent to controlling the active power delivered to the grid. The use of power converters with controlled switching devices reveals the need for designing an appropriate controller to guarantee good transient and steady-state performances. This chapter deals with the design methodology of a robust continuous-time model predictive control (CTMPC) for the DC-DC and the DC-AC converters, used in a grid-tied PV system. This control technique is now being considered for power converters thanks to the drastic advances in power electronics and processors capabilities. The control design is based on minimizing a quadratic cost function pertaining to the difference between the output and its set point. To do so, the cost function is approximated using Taylor series expansion in order to obtain a closed-form solution even though the system model is represented by a nonlinear model. The form of the controller is closely related to feedback linearization technique, but the gains are specified by solving an optimization problem. The resulting controller can also be considered as high-gain feedback control. The major drawback of this type of controller is that the steady-state error cannot be completely eliminated under model uncertainty and unknown disturbances because of the limited prediction accuracy. To alleviate this lack of robustness, a disturbance observer is designed to improve the prediction accuracy under both matched and unmatched disturbances. More specifically, the CTMPC approach uses the disturbance estimation to compensate for its effect, which allows the control to achieve zero steady-state error. Another advantage of the disturbance observer is its ability to recover the transient performance of the CTMPC technique, particularly when the observer is relatively fast enough. In this chapter, it is shown how to design the controller and the disturbance observer based on either linear or nonlinear model as well as how to choose the parameters of the composite controller with the consideration of the performance specifications and the practical limitations. The simulation results are also given at end of each section to provide the reader with an understanding of how to test the composite controller.