# Online Static Security Assessment of Power Systems Based on Lasso Algorithm
## 5 Case Studies
### IEEE 14-Bus System
#### 5.1.2 Base Load Condition  
Under the condition of \(N\)\(-\)1 contingencies in the normal load conditions of the IEEE 14-bus system, the values of security index \(PI_{c}\) are computed by using the NRLF analysis results and predicted by adopting the MSA-Lasso, ANN, and SVM algorithms. One of the ANN algorithms, the back-propagation (BP) neural network, is employed in this paper, and it is a relatively commonly used ANN algorithm [9]. The parameter settings of each algorithm are listed in Table 4, and the comparison of times for contingency screening and ranking by adopting these methods are listed in Table 5. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Parameter** & **Value** \\ \hline \multirow{2}{*}{MSA-Lasso} & Penalty parameter & 1 \\  & Number of shrinkage & \\  & tuning parameters & \\ \hline \multirow{4}{*}{ANN} & Hidden layer nodes & 5 \\  & Epochs & 100 \\  & Learning rate & 0.1 \\  & Goal & 0.001 \\ \hline \multirow{2}{*}{SVM} & Penalty parameter & 1000 \\  & Kernel parameter & 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameter settings of the three algorithms. MSA-Lasso: multi-step adaptive Lasso; ANN: artificial neural network; SVM: support vector machine. Figure 4: Single line diagram of the IEEE 14-bus system. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **NRLF** & **MSA-Lasso** & **ANN** & **SVM** \\ \hline Time (s) & 0.2529 & 0.0783 & 0.1052 & 0.0927 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of computation times of a 14-bus system. NRLF: Newton–Raphson load flow. It can be obviously seen that the time of the proposed module is faster than the others. So, the proposal is more available for online applications. The tested controlled variables are listed in Table 6, with the considerations of adjustable transformer taps and reactive power compensation capacitor banks. The detailed comparisons of \(PI_{c}\) are listed in Table 7, and the relative errors are listed in Table 8, with each branch exiting from operation. In addition, the ANN and SVM algorithms are employed for contrast, and the results are also listed in the tables. From the above two tables, it can be seen that the values of \(PI_{c}\) obtained by algorithm prediction are basically close to those obtained by direct calculation. Compared with ANN and SVM, the MSA-Lasso algorithm has the advantage for predicting the security indices \(PI_{c}\), because the maximum relative error of MSA-Lasso is the smallest among the three algorithms. For a better presentation, the relative errors are shown in Figure 5. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable** & **Value (p.u.)** & **Variable** & **Value (p.u.)** \\ \hline \(P_{C_{1}}\) & 2.3597 & \(U_{5}\) & 1.0075 \\ \(P_{G_{2}}\) & 0.3753 & \(U_{6}\) & 1.0076 \\ \(P_{G_{3}}\) & 0 & \(U_{7}\) & 0.9607 \\ \(P_{G_{4}}\) & 0 & \(U_{8}\) & 1.0047 \\ \(P_{G_{5}}\) & 0 & \(U_{9}\) & 0.9510 \\ \(Q_{G_{1}}\) & \(-0.0165\) & \(U_{10}\) & 0.9528 \\ \(Q_{G_{2}}\) & 0.3743 & \(U_{11}\) & 0.9760 \\ \(Q_{G_{3}}\) & 0.0206 & \(U_{12}\) & 0.9886 \\ \(Q_{G_{4}}\) & 0.4733 & \(U_{13}\) & 0.9805 \\ \(Q_{G_{5}}\) & 0.2509 & \(U_{14}\) & 0.9441 \\ \(U_{1}\) & 1.0500 & \(T_{1}\) & 0.17 \\ \(U_{2}\) & 1.0266 & \(T_{2}\) & 1.075 \\ \(U_{3}\) & 0.9689 & \(T_{3}\) & 1.025 \\ \(U_{4}\) & 0.9993 & \(Q_{C_{1}}\) & 1.025 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Tested controlled variables of the IEEE 14-bus system. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Outage Line** & **NRLF** & **MSA-Lasso Prediction** & **ANN Prediction** & **SVM Prediction** \\ \hline L 1(1–2) & 0.6467 & 0.6485 & 0.6430 & 0.6392 \\ L 2(1–5) & 0.4065 & 0.4069 & 0.4090 & 0.4046 \\ L 3(2–3) & 0.4184 & 0.4171 & 0.4188 & 0.4163 \\ L 4(2–4) & 0.4798 & 0.4808 & 0.4842 & 0.4843 \\ L 5(2–5) & 0.3506 & 0.3515 & 0.3481 & 0.3519 \\ L 6(3–4) & 0.14 As shown in Figure 5, the MSA-Lasso algorithm has a narrow error range of initiation in the three algorithms, which means that the MSA-Lasso algorithm is more stable and accurate than the others.