# Voltage Optimization in PV-Rich Distribution Networks--A Review
## 4 Voltage Optimization in PV-Rich Distribution Networks--Formulation and Solution Methods
### Test Network Models  
To validate the efficiency of different solution methods for the voltage optimization problem, the authors use test network models that can be divided into a standard test model and a test model based on real-life examples. The most common test network models used in literature represent IEEE test network models which, depending on the number of buses, can be IEEE-13 bus, IEEE-15 bus, IEEE-33 bus, IEEE-34 bus, IEEE-37 bus, IEEE-69 bus, IEEE-123 bus, and IEEE-8500 bus. Almost all have radial topology. According to the processed problem, some authors modify standard test models. For instance, the standard test model [70] is modified according to balance. Real-life-based models represent urban residential feeders located in the US, China, Italy, Egypt, Australia, Ireland, and the UK. Unbalanced networks are mostly low voltage and belong to real-life models. In Table 7, test network models, their voltage level, and balance are summarized. According to the reviewed literature, more authors utilize standard test network models IEEE-33 bus, IEEE-69 bus, and IEEE-123 bus node due to their flexibility and robustness. One possible problem that can appear is the OPF application for unbalanced DNs. For instance, the authors in [72] reduce an unbalanced system to a balanced assuming that voltage magnitudes between phases are analogous and phase angles on nodes are not drastic. Therefore, an unbalance between phases is low, and almost balanced. For more, see [72].  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Advantages** & **Shortcomings** \\ \hline Analytical methods & - & well-developed methods & - \\ (simplex method, SLP, SQP, ADMM, & - & fast computational performance of \\ gradient projection method, IPM) & linear methods and IPMs & - \\ Computational intelligence methods & - & do not depend on mathematical formulation & - \\ methods, artificial intelligence methods, FL) & - & convergence is easier to set up compared to analytical methods & - \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of analytical and computational intelligence methods.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reference** & **Test Network Model** & **Voltage Level** & **Balanced/Unbalanced** \\ \hline
[32,79,80] & IEEE–34 bus & MV–24.9 kV and 4.16 kV & Balanced \\
[70] & IEEE–34 bus modified according & MV–24.9 kV and 4.16 kV & Unbalanced \\  & to balance & MV–24.9 kV and 4.16 kV & Unbalanced \\
[55,63,67,81,82,85,89,90] & IEEE–33 bus & MV–12.66 kV & Balanced \\
[63] & Real–266 bus, Shenzen, China & MV–20 kV & Balanced \\
[53,64,83,88,113] & IEEE-123 bus & MV–4.16 kV & Unbalanced \\
[70,72] & IEEE–123 bus modified according & MV–4.16 kV & Balanced \\  & to balance & MV–12.47 kV and LV–120/240 V & Balanced \\
[65] & Real distribution feeder–187 bus & MV–12.47 kV and LV–120/240 V & Balanced \\
[38,75] & Perth Solar City–101 bus & LV–415/240 V & Unbalanced \\
[66] & Tala City, Egypt–37 bus & MV–11 kV & Balanced \\
[67,76,78,81] & IEEE–69 bus & MV–12.66 kV & Balanced \\
[32,57] & IEEE–13 bus & MV–4.16 kV & Balanced \\
[70] & IEEE–13 bus & MV–4.16 kV & Unbalanced \\ \hline \hline \end{tabular}
\end{table}
Table 7: Overview of test network models.