# State Space Analysis of a Solar Power Array Taking a Higher Degree Of Non-Linearity into Account

#### DOI NO:

https://doi.org/10.26782/jmcms.2014.07.00003

#### Keywords:

solar array power system ,non linear state variable model, forcing function,laplace transform,time response,

#### Abstract

This paper develops a mathematical technique for the solution of a non linear state variable model of a solar array power system powering a non linear load. The significance of the technique lies in the fact that experimental complexities can be avoided to reach a desired conclusion regarding the design of the controller associated with a solar power array system. An iterative method has been used in which the initiating assumption has been made to consider the system to depend entirely upon its initial values at the instant t = 0 and taking the forcing function to be zero at that instant. In the next step we use the solution at t = 0 and plug it into the equation iteratively while having a non zero value of the forcing equation during the second iteration. The non linearity lies in the fact that the forcing function is a function of the state variable itself. We have applied the Maclaurin series to find the laplace transform of certain mathematical functions containing a singularity at the zero time instant. The time response is obtained and then it is plotted by using MATLAB and various graphs have been obtained.

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