## 3 Control Strategies
### Learning-Based Incremental Conductance (LINC) Technique  
The performance of the PV and WT is developed at the maximum power point by employing a suitable MPPT technique. The block diagram of the controlling strategy of MPPT in PV and WT system is represented in Figure 3. The MPPT controller allows us to optimize and maximize the power produced by both PV and WT systems. The modeling of PV, WT, and BESS with the selection of controlling parameters are presented in Appendix A.1-A.3. The duty cycle \((D)\) for the DBC is calculated as:  
\[D=1-\frac{V_{R}}{V_{dcR}} \tag{1}\]  
where, \(V_{R}\) is the reference voltage, \(V_{dcR}\) is the reference DC link voltage. The comparator compares the sawtooth signal and \(D\). The output of the comparator is capable of generating gating pulses for the DBC. The selection of DC-Link capacitor based on DBC calculation is presented in Appendices A.1 and A.5. The reference DC link voltage is computed as:  
\[V_{dcR}=\sqrt{3}\times\theta\times V_{A} \tag{2}\]  
where, \(V_{A}\) is the supply voltage amplitude and \(\theta\) is loss component. The '\(V_{A}\)' is expressed as:  
\[V_{A}=\sqrt{\frac{2}{3}\Big{(}v_{a}^{2}+v_{b}^{2}+v_{c}^{2}\Big{)}} \tag{3}\]  
The voltages \(v_{a},v_{b},v_{c}\) are expressed as the product of in-phase unit-templates and \(V_{A}\). The DC link error voltage \((e_{dc})\) is given as:  
\[e_{dc}=V_{dcR}-V_{dc} \tag{4}\]  
\(V_{dc}\), \(V_{dcR}\) are, respectively, the dc link and reference dc-link voltage. The \(e_{dc}\) is provided to the PI, which supplies the DC loss component value \((\tau_{dc})\) as:  
\[\tau_{dc}(n+1)=\kappa_{P1}\times e_{dc}(n)+\kappa_{P1}\times\int_{0}^{t}e_{dc} (n)dn \tag{5}\]  
Figure 3: Block diagram of maximum power point tracking (MPPT) controller in photovoltaic (PV) and wind turbine (WT) system. Here, \(\kappa_{P1}\) and \(\kappa_{I1}\) are, respectively, the proportional and integral gains of the PI controller. The controlling structure of the LINC technique with the duty cycle and PIC is shown in Figure 4. The working strategy of the LINC technique is provided in Figure 5.  
The working procedure of the LINC technique is distributed in two parts. In one part, it deals with steady-state conditions, and in another stage, it deals with dynamic conditions. For detecting or assuming the circumstances, an envelope is formed with band limits in every iteration. The band limits are given as:  
\[Bu=\left(100+\left(\left(\frac{V_{\infty}}{1-d_{\text{base}}}\right)-V_{ \infty}\right)\times\frac{100}{V_{mpp}}\right)\times\frac{1}{100} \tag{6}\]  
\[D=1-\frac{V_{R}}{V_{dcR}} \tag{1}\]0  
where, \(Bu\) and \(Bl\), respectively, are upper and lower bands of the envelope and \(d_{\text{base}}\) is the base step size. \[D=1-\frac{V_{R}}{V_{dcR}} \tag{1}\]1 \[D=1-\frac{V_{R}}{V_{dcR}} \tag{1}\]2  
During dynamic state, change in step size is given as:  
\[\left|\frac{p-p1}{p1}\times 100\right|\Rightarrow\left. \begin{array}{l l l} if\ <=10&\rightarrow\ dn=d_{\text{base}}/2\\ if\ else\ <=50&\rightarrow\ dn=d_{\text{base}}\\ else&\rightarrow\ dn=2\times d_{\text{base}}\end{array} \right\} \tag{9}\]  
In the steady-state condition, variable '\(vl\)' is considered as store addition of the first three conjugative duty cycles, and variable '\(vl\)' is considered as the latter conjugative duty cycles. Figure 4: The control scheme for the learning-based incremental conductance (LINC) technique in grid-tied PV and WT system. Figure 5: Block diagram of the learning-based incremental conductance (LINC) technique. Therefore, \(dn\) is given as:  
\[ \begin{array}{ll}if\ |ul-vl|&=dn1\ \Rightarrow\ n=0,\ dn=dn1/2\\ &else\ \Rightarrow\ n=ul,\ dn=dn1\end{array} \right\} \tag{10}\]  
Finally, analyze the logics of optimal \(D\) computation and is provided as:  
\[\begin{array}{ll}if\ dv=0,\ \left\{\begin{array}{cc}if\ \ \ \ \ \ \ \ \ \ \ \ \ \ \  
The transformation of three-phase load currents \(i_{La}\), \(i_{Lb}\), and \(i_{Lc}\) in the rotating \(dq\) frame are presented in Equation (12). \[\left[ \begin{array}{c}i_{d}\\ i_{q}\\ i_{0}\end{array}