## 2 Overview of the System and Its Modeling
### Model of the Diesel Engine Driven Power Plant  
The speed governor and torque output model shown in Figure 2 is used for diesel engine-driven power plants DG1 and DG2, respectively. Several types of diesel engine and governor models have been presented; however, an uncomplicated model is adopted in this study [17; 18]. The speed governor regulates the power of the diesel engine so as to keep its speed at a preset reference speed. In the case of an FS-SG generator, it is essentially controlled by a governor free mode with droop characteristics. In the case of ASG, the speed governor should control the varying speed to return it back to the preset reference more precisely; therefore, PID controller is used. The range of torque output of the diesel engine is limited, in general, between 50% and 100%, which is a typical range from the point of view of fuel cost and the lifetime of the diesel engine. Moreover, in consideration of mechanical stress reduction of the engine, the rate of change of the torque output also needs to be limited to \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Plant**} & \multirow{2}{*}{**Generator Type**} & \multicolumn{5}{c}{**Rated Capacity (MVA)**} & \multicolumn{2}{c}{**Rated Voltage (kV)**} & \multicolumn{2}{c}{**Inertia**} \\ \cline{3-8}  & & **Case 1** & **Case 2** & **Case 3** & **Case 4** & **Voltage (kV)** & **Constant H (s) \({}^{1}\)** \\ \hline DG1 & FS-SG & 5 & 7.5 & 5 & 2.5 & & \\ \hline DG2 & FS-SG & 5 & - & - & - & 3.3 & 2 \\ \cline{2-8}  & ASG & - & 2.5 & 5 & 7.5 & & \\ \hline \multicolumn{8}{c}{**Wind Power Station** (Permanent Magnet Synchronous Generator)} \\ \hline  & Rated Capacity (MVA) & & & 0.5 & & \\ \hline  & Rated voltage (kV) & & & 0.69 (1.0 at the connection point of the power system) & & \\ \hline  & Inertia constant H (s) \({}^{1}\) & & & 3 & \\ \hline  & \multicolumn{5}{c}{**Loads** (Common to Load A and B)} \\ \hline  & Capacity (MVA) & & & 3.75 & \\ \hline  & Power Factor & & 1.0 & & \\ \hline \hline \end{tabular} \({}^{1}\) Including prime mover.  
\end{table} 
Table 1: Parameters of power plant and loads. Figure 1: Model of small-scale power system. 90%/minute, for example. Parameters of the model are expressed in Table 2, and machine parameters of the conventional FS-SG are expressed in Table 3.  
In addition to the governor free control, the outputs of DG1 and DG2 are also regulated by load frequency control (LFC), which maintains a balance between the power demand and consumption over more than several minutes. The LFC configuration is shown in Figure 3. Output commands for LFC are distributed to DG1 and DG2 in accordance with a ratio of power rating of each generator. Figure 4 shows the model of automatic voltage regulator installed in FS-SG. Figure 5 shows a fundamental structure of the adjustable speed generator (ASG), which consists of a doubly-fed \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **FS-SG (DG1 and 2)** & **ASG (DG2)** \\ \hline Time constant of the Transducer \(T_{DC}\) (s) & 0.1 & 0.1 \\ Gain of the Transducer \(G_{DG}\) (s) & 20 & 20 \\ Proportional gain \(K_{P}\) & 0.1 & 0.01 \\ Integral gain \(K_{l}\) & 0.0 & 0.0002 \\ Differential gain \(K_{D}\) & 0.0 & 0.1 \\ Time constant of the pilot serve \(T_{PDG}\) (s) & 1.0 & 1.0 \\ Time constant of the diesel fuel delay \(T_{dDC}\) (s) & 0.5 & 0.5 \\ Speed reference \(\omega_{\textit{nf}}\) (pu) & 1.0 & 1.044 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the diesel governors. Figure 3: Model of a load frequency control (LFC). \begin{table}
\begin{tabular}{c c} \hline \hline Resistance of Stator Winding & 0.0025 pu \\ Leakage reactance of stator winding & 0.14 pu \\ Resistance of field winding & 0.0004 pu \\ Leakage reactance of field winding & 0.2 pu \\ \(D\)-axis synchronous reactance & 1.66 pu \\ \(Q\)-axis synchronous reactance & 0.91 pu \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Electrical parameters of the fixed speed synchronous generator (FS-SG).