## 4 Adaptive DC Voltage Droop Control at VSC Terminal  
When the system experiences frequent power fluctuations, each converter station takes on the task of smoothing out power fluctuations, allocating power margins according to a pre-set slope curve so that the overall power of the system is stabilized. In traditional DC voltage droop control, which generally uses the fixed droop coefficient. The DC voltage linearly decreases with the increase in output current or power. If the droop coefficient is too large, a small voltage change will lead to a large power fluctuation so that when the system is disturbed, the converter station with a small power margin will be easily overloaded. If the droop coefficient is too small, the system's ability to control the voltage will be relatively weakened; that is to say, too large or too small droop coefficients can affect the stable operation of the entire system. In the traditional voltage droop control, the power margin and operating conditions of each converter station are not adequately considered, which may result in the transmission power of the converter station exceeding the rated value, thus leading to system instability. In contrast, adopting an adaptive droop control strategy allows the droop coefficient to adapt to changes in DC power and voltage. The core of this strategy is to adjust the droop coefficient as the available power margin of each converter station changes, thus reasonably allocating unbalanced power. This approach maximizes the utilization of individual power margins, enhances the rapidity of power adjustment for converter stations, and maintains the stable operation of the multi-terminal system. Assuming there are \(N\) converter stations in the system using DC voltage droop control, let \(\Delta U_{\text{dc}}=U_{\text{dc}}-U_{\text{dcref}}\) be the DC voltage deviation and \(\Delta P=P-P_{\text{ref}}\) be the system DC imbalance power, where \(P\) and \(P_{\text{ref}}\) are the actual and reference values of DC power, and \(U_{\text{dc}}\) and \(U_{\text{dc}}\) and \(U_{\text{dc}}\) are the actual and reference values of DC voltage. \(K\) represents the droop coefficient. \(\Delta P_{\text{n}}\) and \(K_{i}\) are the DC power deviation and droop coefficient of the nth converter station, and \(K\) determines the distribution of unbalanced power among the converter stations in the system, satisfying the following:  
\[\Delta P_{n}=\frac{K_{n}\Delta P}{\sum\limits_{i=1}^{N}K_{i}}. \tag{19}\]  
The voltage threshold for adjusting the droop coefficient \(K\) is set to \(U_{\text{dm}}\) to limit the frequent power fluctuations of the converter stations. When \(\Delta U_{\text{dc}}>U_{\text{dm}}>0\), if the system's DC voltage level is high, the converter station needs to reduce active power. Based on the above equation, the initial droop coefficient \(K_{\text{H}}\) can be defined when the DC voltage is high:  
\[K_{H}=\frac{P_{ref}}{\Delta U_{\text{dcmax}}}. \tag{20}\]  
When \(\Delta U_{\text{dc}}<U_{\text{dm}}<0\), if the system's DC voltage level is low, the active power of the converter station should increase. Based on the power margin of the converter station, define the initial droop coefficient \(K_{\text{L}}\) when the DC voltage is low:  
\[K_{L}=\frac{P_{\text{max}}-P_{ref}}{\Delta U_{\text{dcmax}}}. \tag{21}\]  
To sum up, the adaptive droop coefficient can be defined as follows:  
\[ \begin{array}{l}K^{*}=\left\{\begin{array}{ll}\alpha\frac{P_{1}}{\Delta U _{\text{dcmax}}}+K_{H}\Big{/}_{3},&\Delta U_{\text{dc}}>U_{\text{dm}}\\ 0\hskip 28.452756 pt,&-U_{\text{dm}}\leq\Delta U_{\text{dc}}\leq U_{\text{dm}} \\ \alpha\frac{P_{\text{max}}-P_{1}}{\Delta U_{\text{dcmax}}}+K_{L}\Big{/}_{3},& \Delta U_{\text{dc}}{<}-U_{\text{dm}}\end{array}\right.,\end{array}  \tag{22}\]  
where \(\alpha\) is the weight coefficient, which varies according to the parabolic function, \(m\) is a constant, and \(\alpha\) ranges from (0, 2/3).