# Research Needs for Realization of Zero-Carbon Power Grids with Selected Case Studies
## 3 Selected Case Studies and Numerical Results
### HVDC Applications and Optimal Control
#### 3.1.2 Voltage Stability  
The intermittent nature of wind power also renders it difficult to control offshore grid voltages. In general, OWFs supply power via long feeders with low X/R ratios at medium voltage (MV) levels, leading to considerable deviations in offshore grid voltages as the wind power fluctuates. To address this issue, grid codes have been established that require OWFs to engage in real-time regulation of offshore grid voltages under normal operating conditions.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Frequency Deviations**} & \multicolumn{2}{c}{**Case 1**} & \multicolumn{2}{c}{**Case 2**} & \multicolumn{2}{c}{**Case 3**} \\ \cline{3-8}  & **Individual** & **Total** & **Individual** & **Total** & **Individual** & **Total** \\ \hline Figure 4 (left) & \(\mid\Delta f_{i}\mid_{max}\) [Hz] & 1.08 & 3.16 & 2.22 & 4.44 & 0.86 & 4.04 \\  & \(\mid\Delta f_{r}\mid_{max}\) [Hz] & 1.08 & 2.22 & 2.22 & 3.18 & 4.04 \\ Figure 4 (right) & \(\Delta f_{irrms}\) [Hz] & 0.25 & 0.44 & 0.44 & 0.10 & 1.03 & 1.13 \\  & \(\Delta f_{rrms}\) [Hz] & 0.28 & 0.53 & 0.80 & 1.24 & 1.03 & 1.13 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparisons of the results for the step and continuous response tests.  
Figure 4: Responses to (**left**) step and (**right**) continuous variations in the inverter-side and rectifier-side loads and in the OWF power generation when the LQG strategy (Case 1) and conventional PI-based strategies (Cases 2 and 3) are applied: (**a**) inverter-side frequency \(f_{i}\), (**b**) rectifier-side frequency \(f_{r}\), (**c**) DC-link voltage \(V_{dc}\), and (**d**) DC current \(I_{dc}\).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**HVDC Control Strategies in Figure 4**} & \multicolumn{2}{c}{**DC-Link Voltage**} & \multicolumn{2}{c}{**Control Target Grids**} & \multicolumn{2}{c}{**Secondary Frequency Control**} \\ \hline Proposed & Case 1 & time-varying & both-side grids & LQG \\ Conventional & Case 2 & time-varying & both-side grids & PI \\ Case 3 & fixed & inverter-side grid & PI \\ \hline \hline \end{tabular}
\end{table}
Table 3: Features of the proposed and conventional strategies.  
Following the codes, HVDC systems and OWFs can be optimally coordinated to improve real-time voltage stability, as in the case of FR discussed in Section 3.1.1. For example, in [57], the optimal coordination of a VSC-HVDC system and OWFs was achieved using an MPC algorithm to maintain the terminal voltages of the OWFs within an acceptable range. In [58], MPC-based coordination was achieved in a distributed manner. Moreover, Figure 2b shows an optimal real-time strategy for secondary voltage control (SVC) of HVDC-linked OWFs, with consideration of the communication time delays between the central and local controllers [59]. The optimal coordination between the HVDC system and OWFs reduced voltage fluctuations at the PCC, POC, and the terminals of OWFs in the offshore grid. Using a dynamic model of HVDC-linked OWFs, an LQG regulator was designed to generate continuous reference signals ensuring optimal SVC and thus improve robustness against increased communication time delays. Figure 2b also shows the integration of a centralized LQG controller with the local controllers of the HVDC system and OWFs. As depicted in Figure 5, the optimal SVC strategy effectively suppressed voltage deviations in an offshore grid and ensured voltage stability in the offshore grid, even when relatively large time delays occurred. The performance was better than those of conventional no-SVC and PI- and MPC-based SVC strategies, as described in Tables 5 and 6.