Multiple-input multiple-output modeling and robust control design for stand-alone photovoltaic systems

This study focuses on a novel Multiple-Input Multiple-Output (MIMO) mathematical modelling and control design to enhance the effectiveness of a common stand-alone photovoltaic (PV) system with constant DC voltage output. Standard approaches in the literature, for the design of such controllers, are typically based on single-input single-output (SISO) methods. As a result they suffer numerous unpredicted characteristics in case they are exposed to particular irradiation, temperature and load variations. Such unanticipated behaviour is a consequence of the effect of environmental conditions on power generation such that they change on a daily base and they cannot be managed which behaves like a disturbance to the system. It is additionally troublesome that it is difficult and may be insufficient to employ traditional linearization techniques to model the system and construct the controller since the system contains substantial nonlinearities attributable to DC/DC switching converters operated by means of pulse width modulation (PWM). This is remedied by using a modeling approach based on identifying a MIMO Hammerstein-Wiener (HW) nonlinear plant. The model represent the whole system consisting of the PV panels, DC/DC converters, electric battery and DC load. Moreover, an innovative extension to the method is considered by constraining the input/output nonlinearities to be invertible and derive the appropriate conditions. This allows for a strategy where the inverse functions are utilized to carry out controller design on the linear portion of the HW model and later map it to the full nonlinear HW system. With the help of this technique H∞ loop shaping and LQG servo MIMO robust controllers are designed. Performance of these robust MIMO controllers are compared with PI and PI/LQG hybrid SISO controllers under different irradiation/temperature and load conditions. Results regarding performance and robustness of output voltage regulation, as well as sensitivity to uncertainties in system parameters are discussed. Assessing the system effectiveness unveils the fact that newly designed H∞ loop shaping MIMO control system is able to provide more stable output voltage to the load against changing atmospheric and load combinations while assuring the maximum power point tracking of the PV panels. It is also more robust than SISO controllers and LQG servo MIMO controller against disturbances and system uncertainties.