## 8 Voltage Analysis  
Figure 7 depicts the voltage profile determined for analysing the maximum load energy scenario, while Figure 8 depicts the voltage profile for minimum load capacity. The system operates under single-phase loading leading to unbalanced loads, thereby warranting a voltage profile analysis. In both situations, the voltage profile adheres to the appropriate operating standards. Nevertheless, as highlighted in Figure 7, when demand is at its maximum level, low voltage grid (220 V) buses 2 and 3 witness a noteworthy drop in voltage. Voltage profile quality is specified using indicators depicted in Figures 7 and 8. Equations (24) and (25) specify the calculation for average voltage deviation for the system.  
\[\textit{Voltage Average Deviation}=\frac{1}{\textit{{n}}}\times\sum_{n=1}^{n}| \mathcal{V}_{d^{i}}-\mathcal{V}_{i}| \tag{24}\]  
where: \(\mathcal{V}_{d^{i}}\) is the desired voltage, and \(\mathcal{V}_{i}\) is the bus voltage, and n is the buses number.  
The maximum voltage deviation magnitude is represented by [33]:  
\[\textit{Maximum Voltage Deviation}=\max_{1\leq i\leq n}[\mathcal{V}_{\textit{d},i}- \mathcal{V}_{i}] \tag{25}\]  
Using Figure 7, it can be seen that, under a peak demand situation, the maximum average voltage deviation for the system is up to 0.048 per unit. Nevertheless, this system is determined to have a maximum voltage deviation of 0.072 on bus 3 (first, second, and third stage values are 0.087, 0.05, and 0.08, respectively). Figure 8 depicts that, under a minimum load situation, the voltage profile for all buses is positive. The computation of the average of maximum deviations and system voltage deviations is quite low, thereby highlighting that the system is operating under appropriate conditions. The analysis and computation for this scenario were performed concerning the reactive power compensation scheme to address maximum demand situation that could potentially affect minimum demand setting with respect to its voltage profile.  
In the case study, the fictitious w-domain was used to numerically check the precision and frequency response of the system PR controller with a fictional w-plane. W-domain is a technique that allows structures to be evaluated in a z-domain near the s-domain by frequency charts. All advantages in the frequency domain are regarded as true for the mapping of the z plane into the w plane, except for high frequency. The w-transformation is given by the z-plane to the w-plane transformation.  
\[\varkappa=\frac{\frac{\textit{w}\times\mathcal{G}_{a}}{2}+1}{-\frac{\textit{ w}\times\mathcal{G}_{a}}{2}+1} \tag{26}\]  
\[\textit{v}=\frac{2}{\mathcal{G}_{a}}\tan\frac{\textit{w}\times\mathcal{F}_{a} }{2} \tag{27}\]  
The PR controller's resonant filter, described by \(\mathcal{R}_{r}(\varkappa)\), is first analysed. The built resonant filter is therefore mapped to the w-plane.  
\[\mathcal{H}_{r}(\omega)=\mathcal{H}_{r}(\varkappa)\big{|}_{x=\frac{\textit{ w}\times\mathcal{G}_{a}+1}{-\frac{\textit{w}\times\mathcal{G}_{a}+1}{2}}} \tag{28}\]  
\[\textit{magnitude}\left(\textit{v}\right)=20\log\big{|}\mathcal{H}_{r}( \omega))\big{|} \tag{29}\]  
\[\textit{Phase}\left(\textit{v}\right)=\textit{argument}\left|\mathcal{H}_{r}( \omega)\right| \tag{30}\]  
Figure 8: Minimum demand voltage.