**5. Simulation Analysis**

#### *5.1. Parameter Design*

The CEPRI36V7 power grid model in the power system analysis comprehensive program (PSASP) was used for simulation analysis to verify the effectiveness of the proposed BESS configuration strategy. The parameters of the CEPRI36V7 model are referred to in reference [35]. The topology of the CEPRI36V7 model is shown in Figure 2. The parameters of the CEPRI36V7 model are referred to in reference [35]. The node parameters, generator parameters, and branch parameters of the CEPRI36V7 model are shown in Tables 1–3, respectively.

**Figure 2.** The power grid structure of CEPRI36V7.




**Table 2.** The generator parameters of the CEPRI36V7 model.

**Table 3.** The branch parameters of the CEPRI36V7 model.


The capacity of the CEPRI36V7 power grid is 2600 MW, and nodes 33 to 34 are DC transmission lines, with a DC transmission capacity of 2 × 200 MW; DC power flows from 33 nodes to 34 nodes, and nodes 10, 15, and 17 in the system are the central nodes of three-winding transformers T1, T2, and T3.

This article uses lithium BESS. The maximum rated power and capacity of the total installed BESS are 800 MW and 1600 MW. h respectively, and the cost coefficients are 1500 yuan/kW and 2000 yuan/kWh. The charge and discharge rate of BESS is 0.5 C.

#### *5.2. Sensitive Line Identification*

The simplified structure of the power grid is shown in Figure 3. The red line represents the DC bipolar locking fault line. The blue line and black line represent the non-shortest path AC line. The green line represents the shortest path AC line. The converter station of node 33 has a DC bipolar locking fault, and the Dijkstra algorithm is used to obtain the shortest path composed of node 33 and node 34, namely: 33, 31, 30, 19, 14, 15, 12, 27, 28, 13, 17, 16, 29, and 34, a total of 13 AC lines. The power change curve of the AC line is shown in Figures 4 and 5 after the converter station of node 33 has a dual-machine locking fault at 5 s.

**Figure 3.** The simplified grid structure of CEPRI36V7.

**Figure 4.** Change curve of AC line after DC blocking.

**Figure 5.** Power change curve of the shortest path line after DC blocking.

It can be seen from Figure 4 that the power variation of lines L19-14 and L14-15 is the largest, with a power variation greater than 2 p.u., and the power variation of other lines is less than 1.3 p.u. It can be seen from Figure 5 that the power variation of the AC line on the shortest path is greater than 1.5 p.u. It can be seen that after the DC bipolar locking fault, the power flow is mainly in the shortest path composed of node 33 and node 34.

The improved power flow exceeding risk index of each line on the shortest path is shown in Table 4 after the bipolar locking fault occurs at the converter station of node 33 at 5 s. From Table 4, it can be seen that the absolute value of the improved power flow exceeding risk index of lines L30-31, L19-30, L14-19, L15-14, L15-12, L17-13, L17-16, and L16-29 is less than 0.5, so the above AC lines are sensitive and vulnerable. Since node 15 and node 17 are the central nodes of the three-winding transformer, and BESS is configured at the sending end of the AC line, the candidate nodes for BESS are 31, 19, 14, and 16.

**Table 4.** The improved power flow exceeding risk index of the shortest path.


#### *5.3. Optimization Configuration Results of Single BESS*

To verify that the BESS is configured in the sensitive and vulnerable line, the BESS to improve the improved power flow exceeding risk index is the best. Firstly, the PSO algorithm is used to obtain a set of Pareto solutions of the BESS configuration capacity and location, as shown in Table 5.



From Table 5, there are two sets for the BESS configuration at node 16. There are two sets for the BESS configuration at node 16. The annual investment cost of BESS is 226.44 million yuan and 321.15 million yuan. Similarly, the BESS configuration also obtains the optimal solution at 31 nodes; the annual investment cost of BESS is 226.44 million yuan and 443.47 million yuan. Therefore, we obtained the lowest annual investment costs in Pareto solutions in Table 2.

To verify that the PSO algorithm has obtained the optimal solution, the iterative convergence curve comparison between PSO and GA (Genetic algorithm) is shown in Figure 6. According to the iterative convergence curve of Figure 6, it can conclude that the PSO has fewer convergence times, more effectively avoid local convergence, and has better stability than the GA. We know that the PSO algorithm can obtain the optimal solution.

**Figure 6.** The iterative convergence curve. (**a**) Iterative convergence curve of energy storage annual investment cost. (**b**) Iterative convergence curve of the sum of improved power flow exceeding the risk index.

Then, the following three scenarios are compared and analyzed: (1) the BESS is configured in a node in the sensitive and vulnerable line, and 31 nodes are selected in this paper; (2) the BESS is configured in the nodes in the shortest path except for the sensitive and vulnerable lines. This paper selects 27 nodes; (3) 21 nodes are selected for other nodes with BESS configured outside the shortest path. Under the three conditions, each node is connected to 541.15 MW of BESS, and the improved power flow exceeding risk index of sensitive and vulnerable AC lines is shown in Tables 6–8.


**Table 6.** The improved power flow exceeding risk index of the AC line with vulnerability after node 31 is connected to BESS.

**Table 7.** The improved power flow exceeding risk index of the AC line with vulnerability after node 27 is connected to BESS.


**Table 8.** The improved power flow exceeding risk index of the AC line with vulnerability after node 21 is connected to BESS.


It can be seen from Tables 6–8 that after the BESS is arranged at the 31 nodes of the sensitive and vulnerable line, the risk index of tidal current out-of-limit of lines L31-30, 19-14, L14-15 and L17-16 exceeds 0.5, and only the risk index of tidal current out-of-limit of lines L15-12 and L16-29 is lower than 0.5; After the BESS is arranged at 27 nodes, only the improve power flow exceeding risk index of line L17-16 exceeds 0.5, and the improve power flow exceeding risk index of other lines does not exceed 0.5; After the BESS is configured at node 21, the improve power flow exceeding risk index of lines 19-14 and L14-15 exceeds 0.5, and the improve power flow exceeding risk index of other lines does not exceed 0.5; It can be seen that the BESS configuration on the sensitive and vulnerable lines has greatly improved the safe operation ability of AC lines.

It can be seen from Figures 7–9 that after the BESS is incorporated into 31 nodes, it is helpful to suppress the oscillation of line power, and the change of line power is lower than 1.5 p.u; after the BESS is incorporated into 27 nodes, the oscillation of line power is increased, and the power variation of some lines is greater than 1.5 p.u; after the BESS is connected to 21 nodes, the power of AC lines on the shortest path changes irregularly, and the power of some lines increases gradually after 17 s, greatly reducing the system stability. It can be seen that only when the BESS is connected to the sensitive and vulnerable lines that the safe and stable operation capacity of the AC lines can be effectively improved.

**Figure 7.** The shortest path power change curve after BESS is connected to node 31.

**Figure 8.** Shortest path power change curve after BESS access node 27.

**Figure 9.** The shortest path power change curve after BESS is connected to node 21.

#### *5.4. Optimization Configuration Results of Multi-BESS*

When the system configures two and three BESS, a set of Pareto solutions is shown in Table 9. The improved power flow exceeding risk index of sensitive and vulnerable AC lines after configurations two and three BESS is shown in Tables 10 and 11. The shortest path power change curve after BESS is shown in Figures 10 and 11.


#### **Table 9.** The multi-BESS configuration capacity and location.

**Table 10.** The improved power flow exceeding risk index of sensitive and vulnerable AC lines after the configuration of two BESS.


**Table 11.** The improved power flow exceeding risk index of sensitive and vulnerable AC lines after configuration three BESS.


It can be seen from Table 6 that when two and three BESS are configured on sensitive lines, the total power of the BESS is the same, and the annual investment cost and the sum of improved power flow exceeding risk index are also the same. Moreover, the sum of the power of 19 nodes and 31 nodes, when three BESS are configured on sensitive lines, is equal to the sum power of configured two BESS. It can be seen from Tables 7 and 8 that the improved power flow exceeding risk index for sensitive and vulnerable AC lines is greater than 0.5, and when three BESS are configured, the impact on the improved power flow exceeding risk index is relatively small. It can be seen from Figures 9 and 10 that when two and three BESS are configured for sensitive lines, the power variation of the line is much lower than configuring one BESS for sensitive lines. And suppressing power oscillation is greatly improved. We know that configuring BESS for multiple nodes eliminating the impact of DC power transfer on AC lines is better than the BESS configured for a single node. Configuring BESS for multiple nodes to improve the safe and stable operation ability of AC lines is better than the BESS configured for a single node. Secondly, when the configured BESS quantity is greater than 2, it has a small impact on the sum of improved power flow exceeding risk index and annual investment cost.

**Figure 10.** Shortest path power change curve after configuring 2 BESS.

**Figure 11.** Shortest path power change curve after configuring 3 BESS.
