# Power Quality Enhancement in a Grid-Integrated Photovoltaic System Using Hybrid Techniques
## 6 Proposed Method
### Grey Wolf Optimization  
In order to overcome this obstacle (MPP), the grey wolf optimization (GWO) method is proposed in order to track the global maximum power point and to maximize the energy extraction of the PV system. During improper irradiation, the P-V curve is categorized by  
Figure 4: Flowchart of the proposed BPSO–GWO method. multiple peaks with various local peaks (LPs) and one global peak (GP). It is noteworthy that when the wolves find the MPP, their correlated coefficient vectors become nearly equal to zero. In the proposed method, an attempt was made to combine GWO with duty-cycle control; i.e., at the MPP, the duty cycle is sustained at a constant value, which in turn reduces the steady-state oscillations that exist in conventional MPPT techniques, and lastly, the power loss due to oscillation is reduced, resulting in higher system efficiency. To implement the GWO-based MPPT, the duty cycle D is defined as a grey wolf. GWO is generally inspired by the leadership and hunting behavior of the grey wolves. The grey wolves are categorized into four levels based on the social dominance hierarchy, namely, alpha wolf (\(\alpha\)), beta wolf (\(\beta\)), delta wolf (\(\delta\)), and omega wolf (\(\omega\)). Generally, the GWO depends on the following assumptions: (1) \(\alpha\), \(\beta\), and \(\delta\) denote the optimum, second optimum, and third optimum solutions, respectively. (2) The remaining level is supposed to be the omega wolf (\(\omega\)). (3) The three wolves' alpha, beta, and delta are considered the optimum solutions with better information about the potential location of prey. The information about prey is known by the three wolves, in that the alpha wolf knows much better than the remaining two wolves. (4) The omega wolf follows the three best wolves. The global best position (\(gbest\)) from the AHCS is considered a location vector of prey [20]. The process of GWO is given as follows:  
1. Encircling prey Equation (13) defines the encircling behavior of grey wolves. \[Y^{t+1}=Y^{t}_{p}-B^{t}\times\left|D^{t}\times Y^{t}_{p}-Y^{t}\right|\] (13) where the prey's location vector is represented as \(Y^{t}_{p}\), the coefficient vectors are \(B^{t}\) and \(D^{t}\), and the grey wolf's position vector is \(Y^{t}\). Equations (14) and (15) are represented as the coefficient vector of \(B^{t}\) and \(D^{t}\), respectively. \[B^{t}=2b^{t}rand_{1}-b^{t}\] (14) \[D^{t}=2 rand_{2}\] (15) where the exploration rate is specified as \(b^{t}\), and \(rand_{1}\) and \(rand_{2}\) represent the random vectors among 0 and 1. The exploration rate is linearly minimized from 2 to 0 over the number of iterations. The exploration rate is specified in Equation (16). \[b^{t}_{j}=2-\frac{2t}{N_{max}}\] (16) where \(N_{max}\) specifies the maximum number of iterations. 2. Hunting The hunting process of grey wolves is handled by the alpha wolf. Sometimes, the remaining beta and delta wolves contribute as guides during the hunting period. However, it is very difficult to obtain the prey location in a search space. The three wolves, alpha, beta, and delta, have better information about the potential location of prey. These prey locations are used to process the hunting behavior of grey wolves. Equations (17)-(19) are used to stimulate the hunting process of the GWO. \[Y_{1}=Y^{t}_{\alpha}-B^{t}_{1}\times\left|D^{t}_{1}\times Y^{t}_{\alpha}-Y^{t}\right|\] (17) \[Y_{2}=Y^{t}_{\beta}-B^{t}_{2}\times\left|D^{t}_{2}\times Y^{t}_{ \beta}-Y^{t}\right|\] (18) \[Y_{3}=Y^{t}_{\delta}-B^{t}_{3}\times\left|D^{t}_{3}\times Y^{t}_{ \delta}-Y^{t}\right|\] (19)where \(Y_{\alpha}^{t},\ Y_{\beta}^{t}\), and \(Y_{\delta}^{t}\) are the positions of the alpha, beta, and delta wolves, respectively. The average states of the positions obtained from the alpha, beta, and delta wolves are given in Equation (20). The average position provides the optimum position of the grey wolf. \[Y^{t+1}=\frac{Y_{1}+Y_{2}+Y_{3}}{3} \tag{20}\]  
For the GWO, the convergence factor is linearly dropped from 2 to 0 through the iteration count.