# Decision Optimization for Power Grid Operating Conditions with High- and Low-Voltage Parallel Loops
## 5 Case Study
### Actual AC/DC Interconnected Power System  
In many modern power systems with intensive load, the AC power system and DC transmission systems are usually operating together and interacting in a complicated way. An actual AC/DC interconnected power system is shown in Figure 5. With the development of 1000 kV transmission systems, 1000 kV/500 kV parallel loops would emerge, which can be recognized in Figure 5. \begin{table}
\begin{tabular}{c c c c} \hline
**No.** & **Candidate Opening Scheme** & \(\xi\) & \(P\) \\ \hline
1 & Partition 1, Partition 2, Partition 3 & 0.5775 & 0.5304 \\
2 & Partition 1, Partition 2 + Partition 3 & 0.5327 & 0.5102 \\
3 & Partition 1 + Partition 2, Partition 3 & 0.5101 & 0.4854 \\
4 & Partition 1 + Partition 3, Partition 2 & 0.5091 & 0.4603 \\
5 & Open line 2–25, line 14–15 and line 3–18 & 0.4566 & 0.4517 \\
6 & Open line 1–2, line 3–4, line 14–15 and line 16–17 & 0.4891 & 0.4633 \\ \hline \end{tabular}
\end{table} 
Table 2: Filtering Index and Priority Index of Candidate Schemes. Figure 4: Basic partitions of New England 39-bus system. Substation QCT, CLT, LYT, ZZT and HZT are 1000 kV substations, which are also hub substations in this power grid network. The number of hub substations decides the number of basic partitions. Thus, the power grid network can be divided into five basic partitions at most. During the line switching process, the edge betweenness of each branch is dynamically calculated until all of the five basic partitions are separated. Because of the huge amount of branches, it is not appropriate to list the edge betweenness of all of the branches at each line switching round. The switched-off branches and their edge betweenness are shown in Table 3.  
In this AC/DC interconnected power system, there are three inverter stations: QDC, NDC and LDC. It should be noted that the inverter stations QDC and LDC are hierarchically interconnected to the receiving-end power grid [28,29]. Thus, each of them is equivalent to two inverter stations (One is in 1000 kV power grid and another is in 500 kV power grid), respectively. The MISCR calculation results are shown in Table 4. QDC-L and LDC-L are equivalent inverter stations in a 500 kV power grid. QDC-H and LDC-H are equivalent inverter stations in a 1000 kV power grid. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Partition Times** & **Switched-Off Line** & **Edge Betweenness** \\ \hline
1 & BZ-ZC & 5.6125 \\
2 & TY-TS & 6.3311 \\
3 & LZ-LQ & 9.2143 \\
4 & YN-MZ & 7.4017 \\
5 & ZC-GZ & 8.1541 \\
6 & RZ-LY & 10.3012 \\
7 & SG-GQ & 4.2884 \\
8 & SG-YC & 3.1251 \\
9 & JN-ZB & 5.3021 \\
10 & ZXP-YM & 1.2185 \\
11 & ZXP-XT & 1.8547 \\
12 & JX-ZZ & 2.5622 \\
13 & ZZ-YM & 1.0221 \\
14 & LZ-YN & 0.9836 \\
15 & YH-LL & 1.3647 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Computation Results of Edge Betweenness. Figure 5: Actual AC/DC interconnected power system. The basic partitions of this actual power system are shown in Figure 6. After six branches are switched off, the power system is divided into two partitions. And three partitions would emerge with nine branches switched off. Then, there are four partitions with twelve switched-off branches and five partitions with fifteen switched-off branches. These five partitions are basic partitions and can be combined to generate different opening schemes. According to Combinatorics and the neighboring relationships among basic partitions, 46 different opening schemes can be generated. It is not necessary to have all of these opening schemes evaluated by the comprehensive evaluation model and fuzzy evaluation algorithm, which usually costs a lot of computation time. Thus, the generated opening schemes should be filtered first using the filtering index defined in (11) in Section 3 The weighted factors of filtering index are assigned as \(\lambda_{1}\) = 0.5, \(\lambda_{2}\) = 0.5. Four generated opening schemes (No. 1-4) with the largest filtering index as well as two experiential opening schemes (No.