Fractional Area (FA) Theory: A New Transformative Paradigm for PV Energy System Optimization, Comprehensive Review, In-depth Multi-Solar-Technology Analysis, and Long-Term Performance Insights

In this paper, a new Fractional Area (FA) theory is proposed to photovoltaic (PV) systems. Based on this theory, an ultra-fast maximum power point tracking (UFMPPT) technique is presented. The underlying principle is to restrict the maximum power point (MPP) to a narrow-bounded fraction on the P-V curve. This reduces the maximum power point tracking problem to a local tracking problem. To implement this technique, an intelligent sensor-less model based on voltage, current, and resistance parameters only is created to estimate the voltage at the maximum power point without the use of any irradiance and temperature sensors. This model is created using 558 randomly distributed points on the irradiance-temperature diagram and tested on three different commercial PV modules: monocrystalline (SM55), polycrystalline (KC200GT), and thin film (ST40). The results revealed that the FA is found to be very small in all realistic operating cases, typically below 0.07 in more than 100 climatic cases. This proves the high localization capability of the introduced framework. To verify the long-term reliability of the technique, it is also tested on 20 years of modeled aging. While the modules undergo significant deterioration, as indicated by voltage accuracy loss ranging from 18.14% to 29.13% and optimum power loss from 40.62% to 61.25%, the FA distortion is limited to a maximum deviation of only 0.0524. As a further extension of the reduced search, the UFMPPT method is able to attain fast, stable, and low-overhead tracking with the adoption of the two-stage method consisting of rapid pre-acceleration and impedance refinement. Overall, the study demonstrates that the FA framework provides a simple, scalable, and robust pathway for sensorless and ultra-fast PV optimization.