## 4 Numerical Results  
In this section, the IEEE-118 bus test system with 6 wind farms is formulated, including 91 load buses, 54 generators and 186 transmission lines. The information of each generator and the information of load demand are available from MATPOWER 5.1 [28]. The entire system is geographically divided into three zones as shown in Figure 2. There are nine AGC units in the system assigned to three zones, respectively. The AGC units at bus #6, #12 and #15 are assigned to Zone I; those at bus #34, #36 and #40 are assigned to Zone II; and the units at bus #70, #72 and #73 are assigned to Zone III. The 11 zonal interconnection lines are highlighted in Figure 2. The regulating reserve system  
Figure 1: Flow-chart of the optimization model. requirement is determined by offline study and denoted as \(D_{A}^{s}\) and \(D_{R}^{s}\), as shown in Table 1. It is assumed that the wind farms are installed at bus #4, #8, #18, #44, #66 and #69. The basic predicted output value is denoted as vector \(\mathbf{w}=[80;100;120;160;120;140]\)\(\mathbf{MW}\) and the ratio of the predicted error to the basic predicted output value is denoted as the uncertainty degree \(\alpha\), which reflects the level of wind power generation uncertainty. A large \(\alpha\) implies that the wind power output has large uncertainty. In addition, the proposed method is performed using MATLAB2015a, CPLEX 12.5 and MATPOWER on a personal computer with Intel(r)Core(tm) i7 Processor 6500U (2.5 GHz) and 4 GB RAM. Note that the purpose of the deployment of the regulating reserve in this paper is to balance the forecasted error of wind power generation outputs; we hereby assume that the forecasted load data is relatively accurate. As explained in [29], the requirement of the reserve can be determined by a certain ratio of the load demand. According to the empirical data and off-line calculation results from MISO [17], the system regulating reserve minimum requirement is assumed as 1% of the basic total load plus wind power uncertainties. Moreover, the system spinning reserve minimum requirement is assumed as 8% of the total load (denoted as \(D_{R1}^{s}\)). At the same time, the system spinning reserve minimum requirement should be above the maximum installed capacity among all the generators (denoted as \(D_{R2}^{s}\)). The zonal spinning reserve minimum requirement is procured by the practical power system operation experience and offline simulation results. In addition, considering that after N-1 contingency occurs, transmission line congestion may lead to the cleared reserve being unable to deploy, the zonal spinning reserve minimum requirement is assumed to be 10% of this zonal load demand. The concrete calculation results are listed in Table 1. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Minimum Requirements of Regulating and**} & \multicolumn{2}{c}{**Minimum Requirements of Zonal Regulating and**} \\ \multicolumn{2}{c}{**Spinning Reserve**} & \multicolumn{2}{c}{**Spinning Reserve**} \\ \hline \(D_{A}^{s}\) & \(D_{R1}^{s}\) & \(D_{R2}^{s}\) & **Zone I** & **Zone II** & **Zone III** \\ \hline
42.42 & 339.36 & 805.2 & 96.3 & 134.2 & 193.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System/zonal regulating and spinning reserve minimum requirements (MW). Regulating reserve system requirement (\(D_{A}^{s}\)); system spinning reserve minimum requirement (\(D_{R1}^{s}\)); maximum installed capacity among all the generators (\(D_{R2}^{s}\)). Figure 2: Graph of the IEEE-118 bus system. Furthermore, the analysis on the feasibility and economy of solved solutions from the proposed optimization model is studied in Figure 3 and Table 2. By setting different parameters of load levels (1.0, 1.05, 1.10, 1.15, 1.20 and 1.25 times of the rated load under normal condition) and wind power uncertainty degrees (0.0, 0.1 and 0.2), the proposed optimization model can be solved accordingly by the CPLEX optimizers (IBM, New York, NY, United States).