## 3 Proposed Converter Topology
### Optimization Method  
It is a better regulator for plants; the plant is a DC-DC converter with several state variables that must be regulated. It sees the plant as a limited collection of linear programming. The optimal method of the HGBC-PVS system is shown in Figure 4. The system consists of adaptive incremental conductance-predicted results and a optimization block. Based on the conductance value, the gain of the system is increased. The prediction is used to speed up the computation process. The optimization module reduces the voltage drop in the converter circuit. The updating algorithm of the HGBC-PVS system is designed and shown in Figure 5. The initial population is analyzed, and the parameter values are initialized. The parameter-updating model is computed, and the fitness module for mean squared error is used. The fitness evaluation function is used to analyze and find better results using optimum parameters under the process of selection, crossover, and mutation. The final optimized solution is used for further analysis, and each model depicts a stage of transition. MPC determines the forecast of each switching cycle, and then the computational complexity undergoes the minimizing procedure, and the state with the least error is created and implemented in the plant. Figure 3: Graphical view of the mathematical function \(\Delta V\). The DC-DC converter is the recommended plant in a photovoltaic and it has two-state variables, owing to the continuous current operation. Three screens are necessary to forecast the future amount of PV power, which would raise the network's cost and capacity. One voltmeter is removed due to this technology, which lowers the system cost while maintaining performance. The final stage in MPC management is to optimize all potential future situations and choose the best value with the least error. The cost function is used to optimize and is expressed in Equation (14)  
\[f^{\kappa=[0,1]}=\|i_{0}-i_{PV}\| \tag{14}\]  
Figure 4: Optimization method of the HGBC-PVS system. Figure 5: Updating algorithm of HGBC-PVS system. The optimization process, like selection, crossover, and mutation processes, is given in the above flowchart. Correspondingly, the cost function and standard current are denoted by f and \(i_{0}\). The proposed control method generates the reference current \(i_{0}\). The PV current is denoted \(i_{PV}\). The scaling factor is denoted \(\propto\). The diagram shows that the algorithm merely senses the PV energy and voltage. It then uses a proposed control technique to build the reference signal in peak power performance. The MPC method starts to control the converter to keep it in sync with the current. The preceding section states that the voltage watcher ignores the battery voltage sensor. The perturbation step size represented as \(Z\) is set to a constant value to create a constant step length MPPT, or it could be configured to be adaptive using Equation (15). \[Z=\beta\times\left|\frac{\Delta i}{\Delta E}\right|\times\frac{1}{D+1} \tag{15}\]  
where \(\Delta E\) is the change in the present and prior amount of the reference signal, \(\Delta i\) is the differential between the present and prior value of a PV power supply, and \(\beta\) is a scale parameter. A graphical model of the mathematical function \(Z\) is shown in Figure 6. The system uses current deviation, deviation in the duty cycle, the original duty cycle, and the scaling factor \(\beta\) to produce the final result \(Z\). In this way, the power is optimized in the proposed HGBC-PVS system. The HGBC-PVS system is designed in this section for photovoltaic systems with power optimization. The voltage drop and current variations at the output are reduced by the HGBC-PVS system. In the remaining part, the HGBC-PVS system's simulation results are examined and evaluated. Figure 3 represents that, while varying the duty cycle, the changing voltage occurs in the output terminal in the same way. Figure 6 represents how the overall output is obtained.