## 2 Literature Overview
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Test System**} & \multirow{2}{*}{**Reference**} & \multicolumn{2}{c}{**Variable Load/Variable**} & \multirow{2}{*}{**Nonlinearity in Bus**} \\  & & & **Harmonic Level** & \\ \hline \multirow{2}{*}{IEEE 5} & [16] & No & 1 bus \\ \cline{2-4}  & [20] & No & 2 bus \\ \hline IEEE 16 & [34] & No & 5 bus \\ \hline IEEE 17 & [22] & No & 8 bus \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Test network overview. _Applied Optimization Objective Functions with Constraints in APF Allocation_  
The optimal allocation of APFs can generally be described through two different approaches to the optimization problem, as the authors in [12] presented. The first category of approach to the optimization problem aims to minimize harmonic voltage distortions in the entire network while meeting the limits of filter currents as well as Individual Harmonic Voltage Distortion (\(\mathit{IHD_{\text{V}}}\)) and Voltage Total Harmonic Distortion (\(\mathit{THD_{\text{V}}}\)) on all buses of the observed network. The second approach focuses on minimizing the injected currents of APFs while simultaneously ensuring that the standard harmonic levels and filter current limits are met. The optimization problem of active filter placement involves defining an objective function and constraints. Minimizing the effective current values of the source and optimally placing the APFs in the tested network are the most common objectives for APFs. The currents of the APFs are determined using a control algorithm to compensate for all harmonics in the line current at the bus where the APF is connected. Minimizing the number and size of APFs provides a proper Total Harmonic Distortion (\(\mathit{THD}\)) level \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Test System** & **Reference** & \begin{tabular}{c} **Variable Load/Variable** \\ **Harmonic Level** \\ \end{tabular} & **Nonlinearity in Bus** \\ \hline \multirow{8}{*}{IEEE 18} & [35] & No & 3 bus \\ \cline{2-4}  & [36] & Two cases & 5 bus \\ \cline{2-4}  & [36] & Three test cases & 3 NLL *1 \\ \cline{2-4}  & [37] & Three test cases & 5 + 2 NLL *1 \\ \cline{2-4}  & [38] & Three test cases & 6 bus \\ \cline{2-4}  & [17] & No & 3 bus \\ \cline{2-4}  & [39] & No & 3 bus \\ \hline \multirow{4}{*}{IEEE 33} & [11] & Three test cases & max 5 bus \\ \cline{2-4}  & [40] & No & 5 bus with PV \\ \cline{2-4}  & [39] & No & 3 bus \\ \hline \multirow{4}{*}{IEEE 69} & [32] & YES & 8 bus (ends of RDS *2) \\ \cline{2-4}  & [34] & No & 19 bus \\ \cline{2-4}  & RDS 5 & [16] & No & 3 NLL *1 \\ \cline{2-4}  & RDS 13 & [18] & No & 6 bus \\ \hline \multirow{4}{*}{RDS 17} & [12] & Yes (three cases) & 7 bus \\ \cline{2-4}  & [41] & No & 7 bus \\ \cline{2-4}  & [42] & Three cases & 3 type of NLL *1 \\ \cline{2-4}  & RDS 20 & [15] & No & 4 bus \\ \cline{2-4}  & RDS 33 & [20] & No & 4 bus (ends of RDS *2) \\ \hline \multirow{4}{*}{Lab. setup 7. Buses} & [43] & No & 3 NLL *1 \\ \cline{2-4}  & [44,45] & No & not specified \\ \cline{2-4}  & [23] & \
\begin{tabular}{c} Percentage increase in the \\ share of RES *3 \\ \end{tabular} &
\begin{tabular}{c} different types—34\% of \\ the load \\ \end{tabular} \\ \hline \multirow{2}{*}{Ski station } & [4] & No & 20 bus \\ \cline{2-4}  & Mine & [33] & No & different types of NLL *1 \\ \hline \multicolumn{4}{l}{3-phase 415 V AC} \\ \multicolumn{4}{l}{system} & [46] & Yes (six test cases) & different types of NLL *1 \\ \hline \hline \end{tabular}  
* NLL—nonlinear load. *2 RDS—radial distribution system. *3 RES—renewable energy sources.  
\end{table} 
Table 1: _Cont._considering the limits prescribed by the standards and loss reduction caused by harmonics and economic indicators improvement [9]. The expression given in (1) presents the most commonly used objective function, which is defined as the sum of the effective current values of all APFs installed in the test network [4; 11; 13; 20; 22; 28; 38; 41; 47].