# Synchronous Generator Stability Characterization for Gas Power Plants Using Load Rejection Tests
## 4 Fitting Simulations  
After obtaining the registers, simulations are necessary to obtain the GAST, SEXS and GENSAL model parameters. These models were fitted manually using Simulink(r), with a global simulation scenario that linked all the models together, as shown in Figure 1.  
From the no-load voltage variation tests, some of the parameters of the AVR are fitted, and, analogously, from the no-load frequency variation tests, some speed governor parameters are fitted in a first iteration (the real responses can be observed from diagrams (a) and (b) of Figures 8-10). Afterwards, the rest of the parameters are fitted from the load rejection test.  
In terms of simulation setup, the simulation time is set to the same time as the real responses obtained above. Once reaching the steady-state simulation, the variations in voltage and frequency references are performed with the same amplitude as in the real cases. As the tests were carried out with no load and with test rejection, an ideal grid was supposed in terminals of the main CB, so, once it is opened, the grid has no influence in the simulation. It is only required to set the initial conditions previously to the SG disconnection.  
After several iterations, we obtained the parameters shown in Table 5, which produced the transient behaviors shown in Figures 11-13 for Plants 1, 2 and 3, respectively. As can be observed, the AVR and speed governor single fitting was performed with good accuracy. However, the load rejection test transients were only well fitted for the first oscillation. The transfer functions of real governors and AVRs are more complex than the computer models such as the governor model (GAST) and the automatic voltage regulator model (SEXS). Rather, the simplified models capture the essential behavior of synchronous generators in the case of transient operation. They neglect some of the finer details of the regulators, such as the change in setpoint, in order to have the generator ready to be synchronized again to the power system.  
In order to achieve more accurate solutions, heuristic fitting algorithms should be implemented in the iterative processes of GAST and SEXS models, such as genetic [27; 28] or evolutionary algorithms [29]. They would be good candidates for this application, as the computation time is not a critical variable in the characterization process and they avoid the effect of local minimum solutions.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Plant 1** & **Plant 2** & **Plant 3** & **Units** \\ \hline \(T_{A}\) & 5 & 2 & 4 & [s] \\ \(T_{B}\) & 12 & 6 & 8 & [s] \\ \(K\) & 100 & 120 & 80 & [pu] \\ \(T_{E}\) & 0.08 & 0.03 & 0.05 & [s] \\ \(E_{MIN}\) & \(-4.53\) & \(-4.20\) & \(-4.33\) & [pu] \\ \(E_{MAX}\) & 5.64 & 5.10 & 5.30 & [pu] \\ \(R\) & 0.05 & 0.56 & 0.58 & [pu] \\ \(T_{1}\) & 0.40 & 0.22 & 1.40 & [s] \\ \(T_{2}\) & 0.15 & 0.14 & 0.70 & [s] \\ \(T_{3}\) & 3.0 & 3.2 & 2.7 & [s] \\ \(A_{T}\) & 0.9 & 0.9 & 0.9 & [pu] \\ \(K_{T}\) & 2 & 2 & 2 & [pu] \\ \(V_{max}\) & 0.8 & 0.8 & 0.9 & [pu] \\ \(V_{min}\) & 0 & 0 & 0 & [pu] \\ \(D_{turb}\) & 0.32 & 0.50 & 0.50 & [pu] \\ \hline \hline \end{tabular}
\end{table}
Table 5: Gas power plants simulation parameters.