## 4 Numerical Results
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Wind Power Uncertainty**} & \multirow{2}{*}{**0**} & \multirow{2}{*}{**0.05**} & \multirow{2}{*}{**0.10**} & \multirow{2}{*}{**0.15**} & \multirow{2}{*}{**0.20**} & \multirow{2}{*}{**0.25**} & \multirow{2}{*}{**0.30**} \\ \multicolumn{2}{c}{**Spinning Reserve**} & & & & & & & & \\ \hline \multirow{3}{*}{With consideration} & I & 358.58 & 360.35 & 349.70 & 339.06 & 328.41 & 377.76 & 307.11 \\  & II & 134.20 & 134.20 & 134.20 & 134.20 & 134.20 & 134.20 & 134.20 \\  & III & 312.42 & 310.65 & 321.30 & 331.94 & 324.59 & 353.24 & 363.89 \\ \hline \multirow{3}{*}{Without consideration of zonal reserve (MW)} & I & 420.00 & 420.00 & 420.00 & 420.00 & 420.00 & 415.03 & 397.00 \\  & II & 0.00 & 7.39 & 14.77 & 22.16 & 29.54 & 36.93 & 44.32 \\ \cline{1-1}  & III & 385.20 & 377.81 & 370.43 & 363.00 & 355.65 & 353.24 & 363.89 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Spinning reserves in each zone with/without consideration of zonal reserve. #84, #88, #90, #105, and #106] will violate the transmission line limit. Meanwhile, C-L method only considers vital N-1 contingency constraints, which need 0.8418s. However, this method still cannot fully guarantee the feasibility in real-time power markets, transmission lines [#76, #79, #84, #88, #90] can still be violated under other contingencies. When employing the active set method to formulate the N-1 contingency constraints and solving the model iteratively, the computational time is about 3.2926 s. Compared to the C-L robust joint dispatch, the proposed I-L method sacrifices only little time but the transmission security can be fully guaranteed as the A-L method. Moreover, compared to the A-L method considering all the N-1 contingencies of transmission lines, the computational time using the iterative solution can be significantly improved while leading to the same solution. This work was supported in part by National Key Research and Development Program of China (2016 YFB0901904), in part by the Science and Technology Project of SGCC-Research on Grid Dispatching and Transaction Mode for Global Energy Interconnection, in part by China Postdoctoral Science Foundation (2015M580847), in part by Natural Science Basis Research Plan in Shaanxi Province of China (2016Q5015) and in part by the project of State Key Laboratory of Electrical Insulation and Power Equipment in Xi'an Jiaotong University (EIPE17205, EIPE16301). [PERSON] wrote the paper, [PERSON] and [PERSON] designed and performed the experiments; [PERSON] and [PERSON] analyzed the data; [PERSON] revised the paper and contributed analysis tools. The authors declare that there is no conflict of interests regarding the publication of this paper. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Methods** & **N-L** & **C-L** & **I-L** & **A-L** \\ \hline Time (s) & 0.1716 & 0.8418 & 3.2926 & 43.3617 \\ Violated & \#44, \#51, \#54, \#76, \#79, \#84, \#88, & \#76, \#79, \#84, \#88, \#90 & - & - \\ Transmission Lines & \#90,\#105, \#106 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Computational time of four treatments of N-1 line contingency (s) and the transmission line number (which are violated N-1 contingency constraints in “C-L” robust joint dispatch). The robust joint dispatch modeling N-1 contingencies of all transmission lines simultaneously in the optimization model (A-L); the robust joint dispatch without the consideration of N-1 contingency constraints of transmission lines and generators (N-L); the robust joint dispatch only taking the vital N-1 contingency constraints for transmission lines into account (C-L); the active set method to sequentially add the N-1 contingency constraints into the model and solve the model iteratively (I-L).