Lyapunov Stability Analysis for a Boost Converter with Coupled PV Panel

Power converters have been widely used to provide regulated energy through an appropriate approach to a control law. Although it is known that these systems are controllable in a switched manner, stabilization criteria in interconnected systems (converters with other dynamic elements) have not been sufficiently explored. In this work, the stability of a system made up of a power converter and a photovoltaic panel is analyzed. In order to carry out the conjunction of both systems, the transformation of the switched model of the converter to an averaged expression is considered. The mathematical expression of a photovoltaic cell is based on the Shockley equation. An equation that describes the complete operation of the panel is described through the addition of the dependent element of the Shockley equation (diode) in conjunction with resistive elements to define both output voltages and currents. Since this equation is not dynamic, it is not possible to couple it to the converter differential equations system. The panel dynamics are included through decoupling by charging an output capacitor. Once we have a system of three coupled differential equations, the system is analyzed by searching for a Lyapunov function. The conditions/constraints of the Lyapunov function are verified to define the stabilization of the system in some sense. The interaction of the equations system is simulated and the present dynamics are graphed.