# Optimal Design and Control of MMC STATCOM for Improving Power Quality Indicators
## 5 Problem Formulation  
Usually, in electric power systems, shunt compensating devices are used for voltage and reactive power control. A MATLAB model for the system under study is shown in Figure 9. The parameters of each component in the system are summarized in Table 2. The system under study compromises the utilization of the MMC STATCOM, which is increasingly used in modern electric networks. The proposed MMC STATCOM is based on full-bridge MMC to form 22 modules per phase power converter. The STATCOM can produce or take reactive power from the grid. The transfer of both types of reactive power is obtained via phase reactance. The proposed MMC generates a three-phase voltage, which has the same phase as that of the grid voltage at the point of coupling. When the amplitude of the voltage generated from the MMC is lower than the grid voltage amplitude, the STATCOM performs like inductance and absorbs reactive power from the grid utility. When the amplitude of the MMC voltage is higher than that of the bus of common coupling, the STATCOM works like a capacitor and reactive power will be inj \begin{table}
\begin{tabular}{c|c|c|c} \hline STATCOM power capacity & 12 MVA & Transformer T1 & 120 kV/34.5 kV \\ \hline RMS line to line voltage at PCC & 34.5 kV & Transformer T2 & 34.5 kV/600 V \\ \hline Number of MMC in each phase & 22 modules & Load 1 & 2 MW \\ \hline Total stored energy in all & 30 kV/MVA & & \\ submodule capacitors & & & \\ \hline DC link voltage & 1600 & Load 2 & 30 MW \& 3 MVAr \\ \hline Line frequency & 50 Hz & Transformer X/R ratio & 18 \\ \hline Carrier frequency & 300 Hz & Load 3 & 5 MW \& 1 MVAr \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters of the studied network. Figure 9: A model of the power system under study. control circuit of the MMC is shown in Figure 9(a). The controller of the high voltage side includes a phase-locked loop (PLL), transformation and measurement blocks, DC-bus voltage regulator and current regulator. Meanwhile, the controller of the low voltage side includes individual and phase balancing controllers of the DC-bus voltage, which are responsible for generating the control signals for producing the pulses applied to the gates of the transistors. Moreover, the optimized controller for phase balancing based on the HHO or ASO optimization techniques is shown in Figure 9(b), and the optimized controller of DC voltage based on the HHO or ASO optimization techniques is shown in Figure 9(c). Figure 10: The controller of the MMC converter: (**a**) Simulink configuration; (**b**) An optimized controller for phase balancing based on the Harris hawk’s optimization (HHO) or Atom search optimization (ASO) optimization techniques; (**c**) An optimized controller of DC voltage based on the HHO or ASO optimization techniques. As discussed in Section 2, the impact of the second component harmonic voltage of the module capacitor on the MMC impedance behavior is expressed. Optimal determination of the value of the module capacitor results in an improvement in the second component of harmonic in the voltage of the module capacitor. Moreover, by reducing the capacitance value, in increase in the second component of harmonic voltage will be observed. Furthermore, it is easy to find that with an increase in the magnitude of the module capacitor voltage second harmonics, an effective increase is observed in the magnitude of the impedance response at low frequencies, but there is no change noticed in positive-sequence. Starting from the introduced explanation, the optimal determination of the module capacitor can be addressed as the design of the impedance of the MMC. However, if a stable performance of the STATCOM is desired, the proposed design should give the minimum demands for energy storage and filtering ripples arising in the capacitance voltage, which shape the constraints of controlling module capacitance to produce an optimal impedance response.