## 4 Proposed Hybrid (InC-DFO) Technique for PV Energy Systems  
For the sake of making a new strong technique, the authors of this paper merge the powerful characteristics of InC with variable step size and DFO algorithm known as (InC-DFO) technique based on their features in a meta-heuristic context. The proposed InC-DFO technique is a computational technique that has the advantages of both algorithms. These two techniques are sequentially executed to enhance the effectiveness of the optimization problem. The output of the InC technique with variable step size calculates the initialization of the DFO technique. However, the InC-DFO technique is applied for all weather conditions like UI, partial, and complex partial conditions for PV energy systems. InC-DFO algorithm is used in two stages, in the first stage, the InC technique with variable step size is used because it performs efficiently under UI values and their less convergence and settling time but this technique is trapped on LM and results in power loss. However, practically it is not possible to achieve constant MPP so there is still some oscillation present around MPP. Thus, a satisfying compromise has to be made among the oscillations and the dynamics for MPPT with fixed step size in the conventional InC technique. The smaller step size can decrease the oscillations around the MPP with decelerating dynamics. On the other side, a larger step size gives the speedy tracking of MPP but it may results in steady-state unavoidable oscillations. For solving these challenges, the InC algorithm is used with variable step size is given as follows:  
\[dk=d(k-1)\pm N*\left|\frac{dev\times P}{dev\times V-dev\times I}\right| \tag{17}\]  
where \(d(k-1)\) and \(dk\) are the boost converter duty cycle at previous instant \((k-1)\) and at instant \(k\). N represents the scaling factor to adjust the step size. Whereas \(dev\times P\), \(dev\times V\) and \(dev\times I\) are the output power, voltage and current of PV array respectively. It can be written as follow:  
\[devP(k) =P(k)-P(k-1) \tag{18}\] \[devV(k) =V(k)-V(k-1)\] (19) \[devI(k) =I(k)-I(k-1) \tag{20}\]  
The location of the DF's in global MPP searching of PV systems is the duty ratio at which dc to dc boost converter runs. It is a one-dimensional issue. The PV array's power output is the goal function to be optimized, and the DA is employed to maximize this power. The following procedures are followed to implement the DF algorithm in the second stage for global MPP tracking. * Step 1: The DF's are dispersed with a one search space within \(d_{min}\) and \(d_{max}\) that are the search space in contexts of duty cycle. The values of \(d_{min}\) and \(d_{max}\)in this article are selected to be and 2% & 98%, correspondingly. The population's value of the step \(P_{i}\) is initialized. * Step 2: PV power of the DF's at each position (duty ratio) is calculated. The food supply and opponent positions are modified as a result of this. * Step 3: Modified the's', 'a', 'c', 'f', and 'e' values. * Step 4: The Equations \(S_{i}=-\sum_{(k=1)}^{N}(P-P_{k})\) and \(E_{i}=P_{Enomy}+P\) are used to compute 'S', 'A', 'C', 'F', and 'E' for each individual. * Step 5: The radius of the neighborhood has been modified. * Step 6: The DF's positions are changed with the help of equation \(P_{i}=P_{i}+\Delta P_{i}\). If this equation produces a location outside of the \(d_{min}\) and \(d_{max}\) bounds, the flies are placed on the other side of the boundary. * Step 7: Exit the algorithm if the termination criteria are satisfied. * Step 8: If the perceived power changes, relaunch the tracking. Any individual's neighborhood radius is expanded in this application, and the weights 'f', 'c', 'a','s', and 'e' are lowered in accordance with the iteration calculation. This helps the swarm accomplish effective exploration in its early generations. The DF's are more impacted by each other in subsequent rounds as the algorithm approaches convergence. It would also ensure precise convergence and keep the DF's out of local maxima.