# Development of A Loss Minimization Based Operation Strategy for Embedded BTB VSC HVDC
## 3 Determination of Embedded HVDC Operation Point
### System Total-Loss Minimization (STLM) Control
#### 3.1.3 Line Overload  
The active/reactive power control of HVDC also affects the power flow of nearby lines. In this paper, we restrict the operation of BTB VSC HVDC so that overloads do not occur on other lines in the steady state. \[\underline{F_{line,l}}\leq F_{line,l}\leq\overline{F_{line,l}} \tag{5}\]  
in which  
\(\underline{F_{line,l}}\), \(\overline{F_{line,l}}\) is the minimum/maximum power flow on line \(l\); and  
\(\overline{F_{line,l}}\) is power flow on line \(l\). The change of the BTB VSC HVDC operating point has a significant effect on some lines, but not all lines. Monitoring the overload of all the lines depending on the system conditions is a burden of communication. Therefore, it is necessary not to observe all the lines, but to find lines that are sensitive to the operation of the HVDC. At this time, the bus lines to be observed are chosen using the PTDF described in [27; 28; 29]. PTDF is an index of line sensitivity based on the DC power flow model, and it is easy to analyze system reconfiguration and installation of DC facilities. When the power to the specific bus changes, it is possible to determine the sensitivity of the lines by indicating the influence of the power flow change on the lines. The PTDF is expressed as shown in Equation (6). \[\varphi_{m}^{l}=\frac{\Delta F_{l}}{\Delta P_{m}} \tag{6}\]  
in which  
\(\varphi_{m}^{l}\) is the PTDF of line \(l\) with respect to bus \(m\);  
\(\Delta F_{l}\) is the amount of the power flow change in line \(l\); and  
\(\Delta P_{m}\) is the amount of the power change injected for bus \(m\). The \(AC\) line sensitivity caused by HVDC can be represented by the PTDF values at both ends and capacity of the HVDC as shown in Figure 3. For the HVDC operation, PTDF values at both ends of the HVDC are similar for the \(AC\) lines where the power change is not large (low sensitivity); and in the opposite case, the difference between the PTDF values is large, and the result of Equation (7) is large too. Equation (7) is obtained by multiplying the difference of the PTDF values at the end of the HVDC for any \(AC\) line by the capacity of the HVDC, and it predicts the maximum value that can be reached in the \(AC\) line when the operation of the HVDC is maximized. The obtained value can be compared with the reference value of each line to decide whether to consider the \(AC\) line in the monitoring line or not. The reference value is obtained by weighting the capacity of each line as shown in Equation (8). In Equation (8), \(W\) affects the number of monitoring lines. The larger the \(W\) value, the smaller the number of monitoring lines, and the smaller the value of \(W\), the larger the number of monitoringlines. Therefore, even when the \(W\) value is large, the branches determined as the monitoring line can be regarded as a line that is highly influenced by the HVDC operation. On the contrary, when \(W\) is controlled to a lower value, relatively less sensitive lines are considered as monitoring branches, so that it is possible to operate the system in detail, but it can be a heavy burden for HVDC operators. The system operator should carefully determine the \(W\) value according to the purpose and convenience. \[M_{normal}^{l}=2\cdot P_{cap},\left(\varphi_{rec}^{l}-\varphi_{inv}^{l}\right), \tag{7}\]  
\[M_{ref}^{l}=S_{MVA}^{l}\times W, \tag{8}\]  
\[if\;\;M_{normal}^{l}\;\geq\;M_{ref}^{l}\;:\;\text{Choose line l as monitoring line}, \tag{9}\]  
\(\Delta F_{line,l}\) is the power flow change of line \(l\) by HVDC control  
\(M_{normal}^{l}\) is the maximum variation of line \(l\);  
\(M_{ref}^{l}\) is the reference value of line \(l\);  
\(P_{cap}\) is the active power capacity of the HVDC;  
\(\varphi_{rec}^{l}\) is the PTDF of line \(l\) with respect to the rectifier end;  
\(\varphi_{inv}^{l}\) is the PTDF of line \(l\) with respect to the inverter end;  
\(S_{MVA}^{l}\) is the capacity of line \(l\); and  
\(W\) is a weighting factor. The monitoring lines determined using the PTDF should consider both normal and contingency conditions.