## Case Study  
The performance of the proposed day-ahead risk averse stochastic unit commitment (RA-SUC) model with transmission reserves is tested on a modified IEEE 57-bus system, with 6 wind farms located at buses 30, 31, 32, 33, 36 and 40. The wind power output and the forecast data are obtained from State Grid Electric Power Research Institute [37] database in Nantong grid of total 365 days of the year 2017, each with 100 MW nominal capacity. The forecast uncertainty is assumed to be conditional to the day-ahead point forecast and follow a beta distribution characterized by the correlation coefficient matrix. The load data and other parameters of the network are taken from [38] and remain unchanged. To observe more number of incidents of congestion and verify the effectiveness of the proposed method in alleviating the congestion, all the line capacities are lowered to half of their nominal ratings. Other parameters in the model are given as VOLL = 2000 $/MWh, VOWC = 50 $/MWh, \(\gamma_{D}=\gamma_{W}=5\%\). The study is implemented in MATLAB 2014b (MathWorks, Natick, MA, USA) and ILOG CPLEX 12.6 (IBM, Armonk, NY, USA, 2015) with its default settings [39] on a personal computer (PC) with Intel Core i5 3.0 GHz and 3 GB RAM. Four different cases are carried out to illustrate the impact of wind power penetration \(P_{W}\) and congestion conservativeness factor \(\alpha_{I}\) (Case 1: \(P_{W}=1\), \(\alpha_{I}=0.2\); Case 2: \(P_{W}=1\), \(\alpha_{I}=0.45\); Case 3: \(P_{W}=1.5\), \(\alpha_{I}=0.2\); Case 4: \(P_{W}=1.5\), \(\alpha_{I}=0.45\)) on the operation outcomes. The utility value of \(P_{W}\) corresponds to the original wind power data and the value of 1.5 denotes that the wind power input is multiplied by 1.5 of the original data. Table 1 lists the key expected economic indices obtained from RA-SUC and conventional UC (C-UC) with and without considering the wind power correlation. It is observed that the average operation cost by adopting RA-SUC is relatively lower than that of its counterpart C-UC for all four cases. In terms of wind utilization and load serve ratio, there is a slight increase in RA-SUC compared to C-UC as a result of the reduction of wind curtailment and load shedding. The ratios are close to the utility for case 2 and 4, where there is a tighter acceptable risk of transmission congestion since \(\alpha_{I}\) is larger. The proposed method also results in less required spinning reserves in real-time operation, thus improving the operational reliability of the system. Moreover, comparing the results on both sides of the table shows that the total cost and reserve requirements are intensified when accounting for wind power correlation. This observation is justified owing to the fact that when no correlation is considered, it is likely that the variations of wind power compensate for each other, leading to a smaller risk of transmission congestion. In addition to the experiment results for the four specific scenarios in Table 1, Figures 3 and 4 compare the total operation cost and congestion hours of the proposed RA-SUC with C-UC under various \(\alpha\) values for a range of wind power levels from 1 to 1.8. The black solid line corresponds to C-UC, whereas the other three dash-dot curves, which are well below the black one, corresponding to the proposed RA-SUC with three different \(\alpha\) values (\(\alpha\) = 0.2, 0.25 and 0.3). The significant reduction of operation cost and congestion hours under each wind power level confirms the effectiveness and robustness of the proposed method in enhancing the economic benefits and operation reliability. It is noted that assigning a larger \(\alpha\) would increase the occurrence of congestion events as well as the total cost at high wind power levels. Specifically, in Figure 3, the operation cost decreases before it starts increasing at a certain wind power level (\(P_{W}=1.2\) or 1.3), regardless of whether the RA-SUC is used.