In order to verify the effectiveness of the proposed scheme, the IEEE 39-bus system was used for analysis. It represents a 345 kV equivalent power network in New England of the United States. The system topology is shown in
Figure 4. In the simulation process, the wind turbine in the wind farm adopts the constant power factor model, and its power factor is 0.95. Meanwhile, it assumes that the wind speed remains unchanged during the fault and recovery process, and the main research is to study the influence of wind power location-allocation on the power system coherence when the grid fault occurs.
4.1. The Influence of Location-allocation of Wind Power
In order to illustrate the influence of wind power on the generator shrinkage admittance matrix, node 10 and node 18 are taken as the integrated locations with 300 MW wind power, and the shrinkage admittance difference is shown in
Figure 5.
In
Figure 5, the horizontal axis represents the generator label, and the vertical axis represents the difference between the shrinkage admittance matrix after and before the integration of wind power. Compared with the above figures, it is found that there is a more obvious hollow in
Figure 5a, while in
Figure 5b, the hollow is even. It mainly lies in that bus 10 is directly connected with bus 32, corresponding to generator 32, thus the integrated wind power has a greater impact on the admittance value of the generator node after shrinkage. However, bus 18 is far away from all generators, so there is no very prominent hollow. Correspondingly, when the integrated capacity of wind power changes, the hollow degree also changes accordingly. According to this analysis, it is effective to consider the influence of the location-allocation of wind power on the electrical connection of the system.
Furthermore, take node 1 as the integrated location, and take 0.6 MW as the step, then get the curves of different integrated capacity and fitness values. The change of node correlation model values under different integrated capacity are shown in
Figure 6.
It can be seen from
Figure 6 that when the integrated capacity of wind power is gradually increased in the same location, the model fitness value does not show a correlation change, which is mainly because, after the integration of wind power, what changes is the overall power flow of the system. When the coherency of a certain area is enhanced due to the change of power flow, it may weaken the coherency of other original coherency areas at the same time. It further shows that this problem is a nonlinear complex problem, so it is reasonable to adopt the improved intelligent optimization algorithm to solve it.
4.2. Slow Coherence Clustering and Fault Simulation
In order to elaborate the calculation process of the slow coherence theory, the IEEE 39-bus system was taken as an example to analyze. There are 10 generators in the grid, corresponding to 10 kinds of electromechanical oscillation modes. After the characteristic calculation, the calculation results of eigenvalues were arranged from small to large, as shown in
Table 1.
According to the maximum difference method, there is
r = 6, then the system can be divided into 6 groups (including zero mode). According to the eigenvalues, the corresponding eigenvectors are selected to construct the modal matrix, and then the slow coherence correlation matrix
S can be calculated by Gaussian elimination. The clustering results are shown in
Table 2.
After the above steps, the slow coherence correlation matrix and node distribution information can be obtained, and the fitness value can be calculated according to the node correlation model. According to this calculation process, assuming that at most 10 nodes can integrate wind power, and the capacity of each node is not limited (but the total capacity should be less than the active output of the balance generator in the initial grid), the bi-level planning model is solved to obtain the appropriate location-allocation scheme of wind power. The upper model uses Monte Carlo sampling algorithm and the sample capacity is 1000. In the lower model, PSO, GA, and improved PSO are used to determine the integrated capacity of each location. The population number is 200 and the number of iterations is 400.
Figure 7 shows the comparison of fitness curves before and after capacity optimization under different integrated location schemes. Each point on the
x-axis represents a location scheme, the
y-axis represents the fitness value, the blue curve is the fitness result with optimized capacity, and the black curve is the fitness result with random capacity. It can be seen that different location schemes have different coherence effects, but after capacity optimization, the coherence effects can be improved. Therefore, in the actual process, even if the integrated locations of wind power have been determined according to the actual geographical location, only the wind power capacity of each integrated location needs to be adjusted, which can also achieve a better optimization effect to ensure the splitting section appearing in the no-coherence area as much as possible.
In order to verify the superiority of the improved PSO algorithm, take the same sample number and iteration times for each optimization algorithm. The calculation results and iterative convergence curve are shown in
Table 3 and
Figure 8.
Comparing the data in
Table 3, it reveals that the three algorithms can effectively improve the value of the objective function in the initial grid structure. Meanwhile, in
Figure 8, the
x-axis represents the number of iterations, the
y-axis represents the optimal fitness value. It can be seen that although the difference between the final optimization results of the improved algorithm and the traditional algorithms is not obvious, the improved algorithm needs less iterations to converge. As shown in
Figure 8, the improved PSO algorithm needs 120 iterations to achieve convergence; nevertheless, the iterations of PSO and GA are 145 and 208, respectively. Therefore, the improved PSO algorithm has a better effect on solving this problem.
Table 4 gives the suggestions for the location-allocation scheme of wind power under the proposed optimization strategy. In order to verify the effectiveness of the scheme, PSS/E is used to simulate N-1 faults and analyze the coherency of nodes in the coherency group before and after the integration of wind power.
Figure 9 shows the comparison diagram of node phase angle curves under three kinds of N-1 faults: (1) three-phase short-circuit fault occurs in line 7–8 at 1.0 s, and the fault is removed at 1.5 s; (2) three-phase short-circuit fault occurs in line 10–11 at 1.0 s, and the fault is removed at 1.7 s; (3) three-phase short-circuit fault occurs in line 25–37 at 1.0 s, and the fault is removed at 1.7 s. In
Figure 9, the
x-axis represents the fault simulation time and the
y-axis represents the voltage phase angle of the system node. It can be found that, after optimization, the number of clustering groups is less, and the oscillation deviation of nodes belonging to the same clustering group is reduced, which indicates that the coherency is enhanced.
Further, all the N-1 faults are simulated to find all the splitting lines and calculate the decision space of high-probability splitting. The calculation results are listed as
Table 5.
According to the data comparison in
Table 5, the reduction of the splitting section and the decision space of the splitting section with high probability, as well the increase of average splitting frequency of splitting lines with high probability, indicate that the splitting section will fall in a certain range more likely when a fault occurs.
Figure 10 clearly compares the change of splitting range. The gray area represents the decision space of splitting with high probability. It can be seen that adding certain capacity of wind power in specified locations can effectively concentrate the splitting range in a small area, which is convenient for splitting control.