## 3 Maximum Power Point Tracking Algorithms
### The Cuckoo Search Optimizer (CSO)  
The CSO constitutes a nature-inspired approach drawing inspiration from the reproductive strategies observed in certain cuckoo species, particularly those employing brood parasitism tactics. Brood parasitism involves the practice of depositing eggs in the nests of other birds. The methodology of CSO is governed by the following principles [20; 21]:  
* The cuckoo introduces eggs sequentially, placing one egg at a time in a nest chosen at random. * Nests containing superior-quality eggs are retained and may be passed on to subsequent generations. * To enhance the chances of the hatchlings receiving more nourishment, the cuckoo may eliminate some of the host bird's eggs. * Upon detecting an unfamiliar egg, the host bird faces a decision point. It may either eliminate the cuckoo's eggs or abandon the nest entirely, opting to construct a new one elsewhere, with a probability denoted as Pa. The utilization of the CSO for tracking the global peak in PV power systems involves a series of well-defined steps. In this study, the CSO is employed for simulation purposes, following the outlined procedure:  
Step 1: The parameters of CSO for searching the GPP are initially established, with a focus on defining the converter duty ratio (\(D_{i}\), where \(i\) = 1, 2... n) and the Levy multiplication factor (\(L_{m}\)) as the selected parameters. Step 2: The duty ratios (\(D_{i}\)) are sequentially applied to the converter, and the corresponding power is computed. The GPP and duty ratio are retained as the current best sample. The new \(D\) samples are generated using the Levy flight, using the following:  
\[D_{i}^{k+1}=D_{i}^{k}+L_{m}\left(\frac{u}{|v|^{\frac{1}{D}}}\right)\left(D_{ best}^{k}-D_{i}^{k}\right) \tag{1}\]  
In this process, \(\beta\) is set to 1.5, while \(L_{m}\) represents the Levy scaling factor. The variables \(u\) and \(v\) are randomly drawn from a normal distribution. Step 3: The updated duty ratios are applied to the boost converter, and the corresponding power output is recorded. The duty ratio that yields the highest power is designated as the new optimal candidate. Furthermore, a fraction of samples is randomly discarded based on a probability factor (Pa), mimicking the natural behavior of a host bird detecting and eliminating foreign eggs. New random samples are then introduced to replace the discarded ones, and their power outputs are evaluated. The most effective candidate is selected by comparing the recorded power values. Step 4: Once the stopping condition is met, the CSO algorithm concludes, identifying the optimal duty cycle as the final output corresponding to the global peak power (GPP). These steps outline the systematic application of the CSO for GPP tracking in PV energy systems, encompassing the parameter definition, sample generation, power measurement, and termination criteria. The approach integrates the unique characteristics of the CSO, such as Levy flights and random sample replacement, to effectively track the GPP in PV systems under dynamic circumstances. The pseudo code of CSO for tracking the GPP in PV systems is illustrated in Table 3. On the other hand, Figure 3 shows a flowchart that outlines the CSO-based MPPT process for a PV system, starting with the initialization of duty cycles and parameters. Duty cycles are iteratively updated using the Levy flight equation, and power outputs are evaluated to identify the GPP. The algorithm ensures efficient global search, reduced oscillations, and adaptability to dynamic conditions. After completing iterations, the best duty ratio corresponding to maximum power is output.