Abstract. In order to improve the utilization rate and cost of photovoltaic panels, MPPT control strategy is needed to make the PV array get the maximum power output because of the change of environmental conditions. Perturbation and Observation method is one of the most widely used MPPT algorithms in the traditional maximum power tracking algorithm, which is simple and easy to implement. However, the traditional fixed-length perturbation and observation method is easy to oscillate near the maximum power point when the step size is large. Although the tracking accuracy is small when the step size is small, the tracking time is long and the tracking efficiency is not achieved. This paper presents an improved method of variable step size.
We are concerned with the following system of third-order three-point boundary value problems: ( ) + ( , V( )) = 0, ∈ (0, 1), V ( ) + ( , ( )) = 0, ∈ (0, 1), (0) = (0) = 0, (1) = ( ), V(0) = V (0) = 0, and V (1) = V( ), where 0 < < 1 and 0 < < 1/ . By imposing some suitable conditions on and , we obtain the existence of at least one positive solution to the above system. The main tool used is the theory of the fixed-point index.
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