## 2 Gas Turbine
### Gas Turbine Model
#### 2.2.1 Physical Model
The equations and connection of the diagram are based on the isentropic efficiency equations together with the power balance in the physical model [56]. This model is applied to represent both the dynamic and physical models as in [37] for the overall airflow study to cool down the turbine blades. The IEEE model and [PERSON]'s model are commonly compared in power system stability since both models are derived from the nominal conditions provided by the manufacturers. However, the IEEE model equations are relatively complicated and require high computational time, especially for a large system. A later extension of [PERSON]'s model, aero-derivative, is introduced for the smaller machine ratings in the network connection. The model is derived from the jet engines for two-shaft gas turbines and utilized for better efficiency in part-load operation. As shown in Figure 9, the format of the block diagram is similar to [PERSON]'s model. However, the model is split into two sections; control functions and turbine dynamics. Apart from that, one additional speed signal is introduced, making it two signals instead of one signaling into the low-value selector. First is the speed of the engine (High Power Turbine), which determines the speed of the compressor, and the second signal is the speed of the low power turbine of the generator. From the figure, the turbine characteristics \(f_{1}-f_{4}\) follow [PERSON]'s model equation, which is also easily extracted from the operating curves. The extracted parameters include exhaust temperature versus fuel flow, the electrical power versus fuel flow and various other parameters. However, the ultimate model parameters are still obtained through a trial and error approach until the simulated responses are perfectly matched to the actual gas turbine responses. Figure 7.1 IEEE Gas turbine model for stability studies [55]. As the utilization of the gas turbine is increased, and higher efficiency in the operation is desirable, the combined cycle power plant is introduced in later studies. However, numerous trips from the combined-cycle generating plants are observed by CIGRE Task-force, which leads to further investigation into the error. From the analysis, the improper modeling of governor response and exclusion of thermal unit influence in the network are the principal reasons for the trips. Thus, the CIGRE model is introduced as illustrated in Figure 10 for gas and steam turbines in combined-cycle power plants [58]. As with the proposed [PERSON]'s model, three control loops are fed into the low-value selector: speed/load governor, temperature, and acceleration control loop. However, the main differences are the governor transfer function substitution to the additional control loop for MW and the torque calculation represented by the second-order transfer function. The exhaust temperature is not explicitly calculated, but provided via the \(F(x)\) function, as shown in the figure. Thus, no derivations are involved in this model. However, the operating curves must determine the constant parameters, and the trial and error approach is still employed. Hence, the model is still prone to error and is time-consuming. Most of the mentioned models in the previous section are insufficient for evaluating the gas turbine's frequency dependency. Hence, a frequency-dependent model is introduced to clarify the effects of shaft speed and ambient temperature on the power output. Changes in frequency are equivalent to the change in shaft speed, and the airflow fluctuation directly affects the maximum power output. Thus, the phenomenon is studied from the model as shown in Figure 11 for the overall block diagram. The control scheme for the model follows [PERSON]'s model with additional thermodynamic equations to represent the dynamic behavior of the gas turbine. Unlike [PERSON]'s model, where the main calculations are the output power and exhaust temperature, this model includes the compressor pressure ratio in addition to the available outputs.