Abstract:
This study develops a mathematical technique for the solution of a non-linear state variable model of a solar array power system. 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 array power 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 zero time instant and taking the forcing function to be zero. In the next step of the analysis the obtained time response of the state variable again has been used iteratively to reach the final solution with the forcing function considered. The non-linearity appearing in the state variable formulation is due to the fact that the forcing function is a function of the state variable itself. In the intermediate stage of analysis Maclaurin Series has been applied to find the Laplace Transform of certain mathematical function containing singularity at zero time instant. The time response expression resulting from the analysis has been used to obtain various plots. The results of simulation in MATLAB establish the fact that there is a difference in the energy stored between the inductor and capacitor. This difference is attributed to the natural resistance value associated with the inductor coil and the fictitious resistance (responsible for power loss) associated with the capacitor and any incremental resistance in the controller circuit.
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