An improved Fractional MPPT Method by Using a Small Circle Approximation of the P–V Characteristic Curve

Abstract

This paper presents an analytical solution to the maximum power point tracking (MPPT) problem for photovoltaic (PV) applications in the form of an improved fractional method. The proposal makes use of a mathematical function that describes the relationship between power and voltage in a PV module in a neighborhood including the maximum power point (MPP). The function is generated by using only three points of the P–V curve. Next, by using geometrical relationships, an analytical value for the MPP can be obtained. The advantage of the proposed technique is that it provides an explicit mathematical expression for calculation of the voltage at the maximum power point (vMPP) with high accuracy. Even more, complex calculations, manufacturer data, the measurements of short circuit current (iSC) and open-circuit voltage (vOC) are not required, making the proposal less invasive than other solutions. The proposed method is validated using the P–V curve of one PV module. Experimental work demonstrates the speed in the calculation of vMPP and the feasibility of the proposed solution. In addition, this MPPT proposal requires only the typical and available measurements, namely, PV voltage and current. Consequently, the proposed method could be implemented in most PV applications.

Amoralism in the Hanfeizi

“…The goal was to enact laws that provide "a safety net against the arbitrariness of the decisions taken by the people in power and capable of providing an equal status to all members of society." 65 From this perspective, the ruler's depersonalization is clearly aimed at a higher purpose than mere political deceit (as proponents of the strong view claim). Romain Graziani likewise argues that Han Fei's primary concern was to establish a system that could "absorb shocks caused by unruly individuals, whatever their position in the system;" he took great care to "protect the state and the work of the bureaucrats against the folly, stupidity, or ignorance of a bad sovereign."…”