# A Novel Variable Step Size Incremental Conductance Method with an Adaptive Scaling Factor
## 1 Introduction  
Solar power is clean, safe, and pollution-free. Furthermore, no rotating parts are required during the assembly and operation of solar generation systems (SGS). Consequently, solar power is among the most valuable of green energy resources. Because of their ease of installation, SGSs are widely accepted and popular in remote areas [1]. However, SGSs have high construction costs, and their power output is affected by solar irradiance and panel temperature. Hence, many researchers have examined methods to maximize the available output power of SGSs, and have presented a number of maximum power point tracking (MPPT) methods. Traditional MPPT techniques (e.g., hill-climbing, perturbation, and observation (P&O), and incremental conductance (INC) are algorithms that are easy to implement and widely applied [2]. However, for such methods, the main problem lies in the tradeoff of the perturbation step in the MPPT process, because the appropriateness of the perturbation step size has a considerable impact on the transient response dynamics and steady-state oscillation. A small perturbation step leads to slow transient response, while a large perturbation step aggravates steady-state oscillation. To address the above-mentioned problem, researchers have presented several novel MPPT algorithms, which can be applied to a rapidly-changing environment and provide good transient response dynamics and low steady-state oscillation [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. Specifically, these new MPPT algorithms include variable step size (VSS) techniques that adopt several fixed steps, defined by operating points [3; 4], adaptive VSS algorithms [5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15], methods that estimate MPP locations by mathematical models [16], and advanced algorithms that calculate maximum power point (MPP) by fuzzycontrollers [17], extremum seeking control [18], and sliding mode control [19]. Among these algorithms, attention has been given to the adaptive VSS algorithms because they enable the simple calculation and are easy to be realized and integrated with common P&O or INC algorithms. For the adaptive VSS algorithms, the perturbation step is determined based on the following: (1) slope of power to voltage (dP/d\(V\)) [5; 7; 10; 11; 12; 15]; (2) derivative of power to duty cycle (dP/d\(D\)) [6]; (3) tangent of power to current (dP/d\(I\)) [8]; (4) gradient of current to duty cycle (dJ/d\(D\)) [9]; (5) derivative of power to the difference between voltage and current (dP/(d\(V\)-d\(I\))) [13]; (6) power variation (dP) [14]. In the adaptive VSS algorithms, the above variables must be multiplied by a scaling factor to determine the required perturbation step. However, the performance of the adaptive VSS algorithm is essentially decided by the scaling factor. Manual adjusting of this parameter is slow and tedious, and a particular selection of the constant scaling factor only achieves optimal performance in a certain irradiance level. That is, if the same scaling factor is used under all irradiance levels, system performance is optimal only under one specific condition but is relatively worse (including oscillation or slow dynamics) under other conditions. Hence, adjusting the scaling factor automatically by (k - k2*P) has been proposed to solve these problems [12]; however, this method requires that the two constant values (k1 and k2) be determined, and it is impossible to ensure that the two values are optimal. Alternatively, selecting two different scaling factor values according to the irradiance level range (i.e., high irradiance and low irradiance) may offer a solution [14]. Nonetheless, system performance cannot be optimized under other irradiance levels. Partial shading is another major issue in SGS where the shade of objects in the environment, such as clouds, trees, and buildings causes multiple peaks in the power versus voltage curve of the solar panel.