## 7 Black Start Capabilities through HVDC
### Frequency Support through MMC-VSC Overload  
While electric grids continue to include more and more asynchronous generation-like photovoltaic energy, system operators have to take into account that this poses a reduction in overall inertia, a phenomenon that increases the complexity of frequency control. In [30], a method is proposed for providing the grid with additional frequency support in case of emergencies through the use of Modular-Multilevel-Converter Voltage-Source Converters available in HVDC terminals, while keeping semiconductors within operational limits.  
This method consists of allowing momentary overload capability to VSCs for acting outside their rated P/Q conditions through controlled circulating currents, allowing this  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Paper** & **Problem** & **Solution** & **Results** \\ \hline \multirow{8}{*}{[11]} & In decentralized and independent & A method based on a coordinated \\  & control wind power and energy & control strategy of multi-energy \\  & storage systems, the high variability & storage supporting blackstart based \\  & generated by charging and & on dynamic power distribution \\  & discharging of energy storage & divided into two layers is proposed to \\  & produces an unbalanced system & deal with the disorder of charging \\  & power which leads to the failure of & and discharge of energy storage. \\  & Renewable energy cannot provide & In order to deal with the low and \\  & inertia response or frequency & method of wind farm with an energy \\
[13] & response as traditional synchronous & storage system for \\  & generators; at lower inertia situations, & frequency regulation. \\  & the frequency changes faster. & HVDC connected offshore wind \\  & The black start capability on & power plants (OWPPs) provide fast \\  & conventional power plans is & and environmentally friendly \\  & characterized by long start-up times & solutions for power \\  & due to their slow dynamics. & system restoration. \\  & Traditional case studies have been & The dynamic changes related to AC \\  & widely applied to two terminal & In this sense, multi-terminal direct \\
[63] & hybrid systems which are used in a & current systems facing the dynamic \\  & black start power provided by a & changes in a feasibility and \\  & single healthy AC grid. & effectiveness manner. \\  & The faster recovery and & A phase-locked loop (PLL) control \\
[64] & controllability of black start capability & scheme based on intelligent adaptable \\  & during fault and maintenance. & control to effectively achieve real \\  & The classical VSC-HVDC controller is & Power control is proposed. \\
[65] & load-dependent and has to be & A robust controller design that \\  & adjusted according to each & increases the robustness until \\  & adjusted according to each & operation conditions experience \\  & operation condition. & continuous variations. \\ \hline \hline \end{tabular}
\end{table}
Table 2: Cont.  
capability to be used as a primary frequency response during unplanned events. Two alternatives are explored for this method:  
1. Frequency-power droop controller, in which the converters' support is proportional to the frequency deviation, given by \[P=K\Delta f(t)=K(f_{0}-f(t))\] (2) where: \(P\) = Power response \(K\) = Gain \(\Delta f(t)\) = Frequency deviation \(f_{0}\) = Nominal frequency \(f(t)\)= Measured frequency
2. Maximum power release controller, in which the converter provides the maximum support available, expressed as follows: \[P=P_{\max}-P_{rated}=0.275P_{rated}\] (3) where: \(P\) = Power response \(P_{\max}\) = Maximum power support available \(P_{rated}\) = Rated power output