# Impacts of MT-HVDC Systems on Enhancing the Power Transmission Capability
## 3 Power Transfer Capability Evaluation
### Security Regions  
Transmission capability can also be assessed through the security regions [37]. Security regions determination is a graphical method to indicate safe re-dispatch of power between different zones/areas. This is important in online applications as it provides visualization to the power system operator as to how power transfer can be altered, preserving the system integrity. [PERSON] et.al. presented a methodology to develop security regions, known as nomogram [39]. Although authors have discussed only static security aspects but the presented technique can be extended for dynamic security analysis.  
Typically to construct security regions (nomogram), three generation groups (Group-1, Group-2 and Group-3) are considered. Group-3 (G\({}_{\text{p}}\)\({}^{3}\)) acts as slack bus and power is transferred between other two groups. As a result, a three-dimensional graph is obtained, whose security boundaries constitute power generation in each group. Voltage security analysis is done using nomogram in [40], offer provision to use for security assessment to PSO's.  
Figure 2 shows a security nomogram, relating the power produced by two generation groups: Group-1 (G\({}_{\text{p}}\)\({}^{1}\)) and Group-2 (G\({}_{\text{p}}\)\({}^{2}\)). The group G\({}_{\text{p}}\)\({}^{3}\) is not in the nomogram of Figure 2 as the nomogram is just an orthogonal projection onto one of the generation planes, e.g., (G\({}_{\text{p}}\)\({}^{1}\)\(\times\) G\({}_{\text{p}}\)\({}^{2}\)). However, it is emphasized that two additional nomograms (G\({}_{\text{p}}\)\({}^{2}\)\(\times\) G\({}_{\text{p}}\)\({}^{3}\)) and (G\({}_{\text{p}}\)\({}^{3}\)\(\times\) G\({}_{\text{p}}\)\({}^{1}\)) can be plotted and would be analogous to the one demonstrated in Figure 2.  
Re-dispatch directions are defined using initial operating point and the angle \(\alpha\). Angle \(\alpha\) establish the direction, as shown in Figure 2, and determine the proportion of power to be re-dispatched in each group. Once defined, the re-dispatch direction (\(\alpha\)), total re-dispatched power (\(\Delta R\)), and power changes in \({G_{p}}^{1}\) (\(\Delta\)\({G_{p}}^{1}\)) and \({G_{p}}^{2}\) (\(\Delta\)\({G_{p}}^{2}\)) are obtained as in (2):  
\[\left\{\begin{array}{l}\Delta G_{p}^{1}=\Delta R\times\cos\alpha\\ \Delta G_{p}^{2}=\Delta R\times\sin\alpha\end{array}\right. \tag{2}\]  
and \(\alpha\) can be determined from (3) [39]:  
\[\alpha=\alpha_{0}+j\frac{360}{N_{D}} \tag{3}\]  
where \(\alpha_{0}\) is the initial angle and \(\mathrm{N_{D}}\) represents the number of directions; \(j\) = 0, 1, 2, 3...... \(\mathrm{N_{D}}\). While change in power (\(\Delta P_{i}\)) from each generator \(i\) within each group can be:  
\[\Delta P_{i}=\Delta G_{p}^{1,2}\times\frac{P_{i}}{\sum\limits_{i=1}^{N_{G}}P_ {i}} \tag{4}\]  
where \(Pi\) represents prior output power of generator \(i\) while \(N_{G}\) shows number of generators within selected group. \(\Delta P_{i}\) can be positive or negative based on the direction of re-dispatched power.  
During the construction of nomogram, power balance is needed and provided by the slack bus, \({G_{p}}^{3}\), while the system load is kept constant. For instance, considering the operating point in the 1 st quadrant, where generations from both groups \({G_{p}}^{1}\) and \({G_{p}}^{2}\) are increasing and thus \({G_{p}}^{3}\) would have to reduce its power for system security.  
System security is evaluated for each power change step, for both dynamic and static securities. If any security standard is violated, a step back in re-dispatch is realized via binary search until a safe limit is reached. However, sometimes the power limit is enforced by the generation capability of one specific group as shown in Figure 2 with squares (boxes). The accuracy of the security boundary increased with the number of directions (\(\mathrm{N_{D}}\)).