## 4 Numerical Results
Table 2 shows the optimal regulating cost under different wind generation uncertainty scenarios and load levels, which suggests that for a given uncertainty degree of the wind power generation, the regulating reserve cost will increase slightly due to the slightly increase in the load level. In contrast, for a given load level, the regulating reserve cost will increase significantly with the increase of uncertainty degree, due to the large increase in the uncertainty degree of the wind power generation. This implies that the large uncertainty degree requires more regulating reserve to guarantee the power balance, which is represented by the Equations (13), (21) and (22). Therefore, the regulating reserve cost will increase. More concretely, Figure 3 depicts the optimal energy and reserve costs under different  
Meanwhile, Table 3 compares the spinning reserves in each zone with/without consideration of the zonal reserve placement, and the results suggest that the dispatch model obtains a better distributed result of the spinning reserve in each generator in the consideration of the zonal reserve placement. In particular, without considering the zonal reserve placement, some zones may have few spinning reserves cleared in generator, which is far below the minimum requirements of the zonal reserve from offline analysis. This will significantly affect the reliability of the system under the N-1 contingency in the zone, where the transmission bottlenecks inhibit the deliverability of the reserve. Finally, the computational time of four different solution strategies to deal with N-1 transmission line contingencies in the co-optimization model is shown in Table 4. As shown in the above model, the security/contingency constrained approach is based on the DC (direct current) power flow, and the computational tractability has been guaranteed by introducing the Equations (15)-(17). Therefore, all the constraints and the objective function of the model are linear, resulting in a very efficient computational behavior. \"A-L\" represents the robust joint dispatch modeling N-1 contingencies of all transmission lines simultaneously in the optimization model. \"N-L\" is the robust joint dispatch without the consideration of N-1 contingency constraints of transmission lines and generators. \"C-L\" is the robust joint dispatch only taking the vital N-1 contingency constraints for transmission lines into account. \"I-L\" refers to the active set method to sequentially add the N-1 contingency constraints into the model and solve the model iteratively. Obviously, the A-L method, taking into account all the transmission lines in the robust optimization model, can fully address the security of transmission lines without any violation, but it requires more computational burden and challenges the real-time electricity markets, especially for large-scale power systems. Although N-L needs about 0.1716 s, which is much slower than other three strategies, this method cannot guarantee the transmission security. For instance, the transmission lines {#44, #51, #54, #76, #79,  
Figure 3: Total costs of energy and reserve under different uncertainty degrees. (**a**) Uncertainty degree 0.0; (**b**) uncertainty degree 0.1; (**c**) uncertainty degree 0.2.