Transient Differentiation Maximum Power Point Tracker (Td-MPPT) for Optimized Tracking under Very Fast-Changing Irradiance: A Theoretical Approach for Mobile PV Applications  
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P&O has been widely employed due to its relatively simple structure, reasonably good performance, easy implementation on low-cost digital controllers, and no dependence on previous information about the system or environmental measurements [3]. Nonetheless, this algorithm suffers from two main drawbacks, as pointed out in [6; 7]. First, the operating point oscillates around MPP, reducing overall efficiency, as it needs to keep perturbing a fixed increment (8) to track MPP. Second, it can becomes confused and tracks in the wrong direction during fast irradiance changes in an issue commonly referred to in the MPPT literature as drift [8]. A modification of P&O that addresses these two issues while maintaining its advantages could improve the efficiency of current systems without requiring significant hardware changes. To reduce the issue of oscillations around MPP during steady irradiance, dynamic perturbation sizes have been proposed [9; 10; 11; 12; 13]. These algorithms use the ratio between power change observed and perturbation size (\(\Delta\text{p}/\delta\)) to establish the next perturbation size. Since the PV curve abruptly decreases around MPP, the perturbations introduced by MPPT are reduced as the system moves closer to MPP. However, this solution might exhibit some disadvantages under rapidly varying irradiance conditions, as significant variations on perturbation size may occur. In [14], constraining the increment size to a reasonable range by introducing a logarithmic function is proposed. This modification keeps the perturbation size small even if the ratio, \(\Delta\text{p}/\delta\), grows. Nevertheless, even if the oscillation is reduced, the loss of tracking direction is not addressed. Several modifications to the P&O algorithm have been proposed to solve the drift issue [15; 16; 17; 18; 19; 20; 21]. The use of boundary conditions combined with dynamic perturbation sizes has been suggested to prevent the system from drifting away too far from the MPP by [15; 16]. Although this reduces efficiency losses, the system still drifts in between the MPP and the boundary condition. In [17], a method to detect irradiance changes using fractional short circuit current (FSCC) while reducing the perturbation size is presented. In [18], a modified P&O for drift avoidance adds a current condition to the traditional P&O when it is more prone to fail. The proposed algorithm consists of three stages. First, the short circuit current is measured, and MPP is calculated as a fraction of it. Second, a regular P&O searches the MPP starting at the operating point estimated in the first stage. In the final stage, at each iteration of P&O, the module current is compared with FSCC. If a change over a certain threshold is detected, the system returns to the first stage. The use of a smaller perturbation size reduced steady-state oscillations. The algorithm showed better tracking during irradiance changes than traditional P&O. Although [17; 18] reduced steady-state oscillations, an inherent loss of power occurs in the operation of FSCC. Adding extra samples associated with a combination of perturbations has been proposed in [19] to isolate the effects in power caused by irradiance (or temperature) fluctuations from the overall power change observed after MPPT perturbation. MPPT then considers this additional information to make a better decision on the next perturbation direction.