# Comparative Technical-Economical Analysis of Transient Stability Improvements in a Power System
## 3 IEEE 9 Bus System Description  
IEEE 9-bus system is a widely used test system template for a variety of steady-state and dynamic simulation studies by researchers and engineers to simulate new algorithms, especially power system stability studies [7; 10; 11]. The limited number of nodes of this test system is indeed useful to fully analyze and compare the effects of different parameters, such as the faulty line or the node where FACTS can be installed. In addition, the electrical and mechanical relationships between the different decisions and effects become clear. The system consists of three loads, three transformers, and three generators interconnected by a network of nine buses. In this paper, a modified version of the IEEE 9-bus system, shown in Figure 1, is simulated using PowerWorld Simulator software for transient stability studies. The base power for the system is 100 MVA according to the work of [12], while the base power values of the generators are given in Table 1. The length of the lines is determined starting from the typical parameters for the 230 kV transmission lines in the work of [13], equating to the p.u. values for the reactance of the lines in the work of [7; 12]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Gen.** & **1** & **2** & **3** \\ \hline _Base MVA_ & 247.5 & 192 & 128 \\ _Exciter_ & IEEET1 & IEEET1 & IEEET1 \\ _Governor_ & IESGO & IEESGO & IEESGO \\ _Stabilizer_ & PSS2A & PSS2A & PSS2A \\ \hline \hline \end{tabular}
\end{table} 
Table 1: MVA base and model types of generators in IEEE 9 bus system. Figure 1: Improved IEEE 9 bus system. In addition, the system in Figure 1 is modified by a parallel line between buses 5 and 7 and a FACTS device at bus 8. These choices are justified by sensitivity analyses shown later in this section. In the base case, whose load flow analysis results are shown in Figure 1, the two systems are disconnected. The transient stability analysis of the test network is performed by simulating a three-phase short circuit. In this context, the system engineering solutions to improve the transient stability of the network are analyzed and compared. In order to perform the transient stability analysis, the dynamic models of each component must be adequately implemented. The models used to implement the synchronous generators of the IEEE 9-bus system are summarized in Table 1, where all parameters are set to default values. The frequency response of the load is not considered because, as can be seen in the work of [14], the most commonly used load model for static and dynamic studies is the constant power load model. Moreover, as reported in the work of [15], the effect of the exponential load model, where only the voltage term of the model is considered while the frequency term is neglected, depends on its parameters. This type of study requires a deep analysis of the load model, which is beyond the scope of this paper. This choice is in line with other similar studies [7; 10; 11]. In this way, the results reported in this work can be compared with those published in the literature. For this case study, the transient stability analysis is divided into the following steps:  
* Initialize the system with the load flow analysis;
* At 1 s, a three-phase symmetrical short-circuit fault is applied to a transmission line;
* The duration of the fault, FCT (fault clearing time), is 0.35 s;
* The duration of the simulation is 10 s;
* The simulation time step is 5 ms.  
To analyze the effect of the short circuit on the rotor angle stability, a sensitivity analysis of the fault location is performed by applying the fault in each line of the system. In addition, to determine the best bus location for the improving solutions, a sensitivity analysis is performed for the device location by connecting the device to each load bus of the system. For simplicity, Table 2a shows the results of these sensitivity analyses obtained without the contribution of the improvement device and on the other hand with STATCOM.