Multivariable Control of Solar Battery Power by Extremum Seeking: Starting from Linear Analysis

Abstract

In this study, we tried to combine maximum power point trackers (MPPT) and «Extremum Seeking» in a single multi-parameter extremum seekeng system for orienting solar panels and draw attention to the problem of a deeper study of nonlinear adaptive control using appropriate methods for their analysis. MPPT controller becomes one of the extremum seeking loops, and as a result, the maximum power is achieved not only by searching for the optimal voltage value, but also due to the optimal angular position of the solar panel in Euclidean space, because the photocurrent depends on the angle of inclination of the Sun’s rays to the surface. The task of tuning extremum seeking loops becomes more analytically difficult, which is associated with nonlinear and multiply connected properties. This requires starting the solution from a simpler “linear” level. We applied the approach associated with the passage of modulating oscillations with a given frequency and amplitude through an open-loop system. This approach, which is generalized in this work at least for extremum seeking of the solar panels power, should be used for approximate calculations if there are no strict requirements for convergence and energy loss for the search. Research design is as follows: parametric identification of the current-voltage and volt-watt curves; obtaining the transfer function by the semi-automated sparse matrix method; reducing the order of the transfer function of coordinate electric drives by introducing a scaling factor. To the most important theoretical result, we attribute the property of the generalized amplitude of the solar panel power oscillations with multi-parameter control to be a combination of input modulating oscillations superimposed on the signals of the control integrators. Having revealed the relationship of their properties, it becomes possible to eliminate non-linearity from the system and operate only with the analytical relationship of the input modulating oscillations and the generalized oscillation of the controlled parameter. We attribute the prediction of the effect to one of the most interesting physical results, in which, for the same amplitude of modulating oscillations, the amplitudes of the photocurrent oscillations and the power of the solar panel at different angular positions will be generally different.