## 2 Gas Turbine
### Gas Turbine Model
#### 2.2.2 Black-Box Model  
Few works are reported utilizing the black-box model in gas turbine modeling. Nevertheless, two studies are reported by [PERSON] in [60] using Artificial Neural Network and  
Figure 11: Frequency-dependent model for gas turbine operation [59].  
Figure 10: CIGRE model for combine-cycle gas turbine operation [58].  
Non-linear Autoregressive Exogenous (NARX). The NARX structure, as in Figure 12, is applied to model the gas turbine operation. The output signals are compared with the mathematical signals, and the black box and the mathematical model performance are almost identical. However, this area is not favorable since the gas turbine is a complex system, and the black-box method cannot represent the operational dynamics.  
[PERSON]'s model is widely adopted due to the capability to imitate an actual gas turbine operation from the functional derivation of the operating curves [55; 61]. It has various applications in the dynamic study and is extensively used in present works. It offers a stable model for gas turbine modification in temperature control and stability, load frequency control [59; 62] and PID control [57]. In [63], an integration of Bayesian and Dempster-Shafer theory into [PERSON]'s model serves as a performance monitoring tool for gas turbines. The well-known model also extended into a fault characterization study during frequency excursion. Thus, [PERSON]'s model is widely applied in dynamic studies. Hence, [PERSON]'s model is suitable to be used to represent DLE gas turbine operation. Moreover, [PERSON]'s model only consists of two unknown parameters, which are easily derived compared to other methods as summarized in Table 2. Furthermore, the detail of dynamic models for gas turbine stability study is depicted in Figure 13.  
Figure 12: A schematic of NARX structure for gas turbine model [60].  
Figure 13: Gas turbine dynamic models for system stability.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Gas Turbine** & **Rowen’s Model** & **IEEE Model** & **Aerodeivative Model** & **CIGRE Model** & **Frequency Dependant** \\  & **Component Design** & & & & & \\ \hline
**Derivation** & Dynamic and physical & & & & & \\  & thermodynamic & Simplified mathematical & & & Derived from jet engines & Additional outer loop for & Frequency dependency on \\
**Base** & properties and laws & representation & thermodynamic equations & and Rowen’s model & MW control. & gas turbine \\ \hline  & 1. Pressure loss is & & & & & \\  & negligible. & & & & & \\  & 2. Comressor and turbine & 1. For simple cycle, & & & & \\  & are irreversible. & single-shift. & & & & \\  & 3. Process 2-3 and 4-1 is & & generator drive only & & & \\  & isobaric. & 2. Constant speed is & & & & \\  & 4. Process 1-2 and 3-4 is & & maintained at 95\%–10\% & & & \\  & isentropic. & 3. Operates are ambient & & & & \\  & 5. Turbine efficiency is & 150C and 101.325 kPa & & & & \\  & 6. Combustore efficiency & & & & \\  & is assumed to be 1. & & & & \\ \hline
**Main** & 2 main equations with & 3 main equations with & 4 main equations with & 6 main equations with & All transfer functions. & 9 main equations with \\
**Equation** & 8 unknowns parameters. & 2 unknowns parameters. & more than 10 unknowns & more than 10 unknowns & more than 10 unknown & more than 10 \\ \hline
**Application** & Components modelling & Open cycle, close cycle, & Overall airflow to cool & & & \\  & (ducting, compressors, & combined cycle & down the & & \\  & combustors and air blades) & gas turbine operation & turbine blades & & & \\ \hline
**References** & [47, 48, 49, 50] & [37, 54, 56, 61, 62] & [55] & [57] & [58] & [59] \\ \hline \end{tabular}
\end{table}
Table 2: Summary of gas turbine models.