# Analysis of Synchronous Generators' Local Mode Eigenvalues in Modern Power Systems
## 5 Experimental Analysis of the Laboratory-Size Synchronous Generator  
Confirmation of the correctness of numerical calculations and the obtained conclusions was, unfortunately, not possible on synchronous generators in power plants. Therefore, we performed a series of tests to measure the frequencies and damping of local oscillations throughout the entire operating range on a laboratory-size synchronous generator. A salient pole synchronous generator with the nominal power \(P_{\rm n}=12\) kW was used for the experiments. The manufacturer's data are shown in Table 7.  
\(P_{\rm n}\) denotes the rated active power. \(U_{\rm n}\), \(I_{\rm n}\), \(U_{\rm Fn}\), and \(I_{\rm Fn}\) are the rated stator and excitation winding voltages and currents. The\(f_{\rm n}\) and \(n_{\rm n}\) are rated frequency and mechanical speed, respectively. To determine the synchronous generator's parameters, the standardized steady-state, transient, and frequency response tests were used [24; 25]. The obtained parameters are shown in Table 8.  
For a nominal operating point, the calculated linearization coefficients are given in Table 9. \begin{table}
\begin{tabular}{c c c c c} \hline  & \(\sigma_{\rm min}\) & \(\sigma_{\rm max}\) & \(\omega_{\rm min}\) (\(s^{-1}\)) & \(\omega_{\rm max}\) (\(s^{-1}\)) \\ \hline hydro-generators & \(-0.2156\) & \(0.2804\) & \(2.9230\) & \(10.8261\) \\ \hline turbo-generators & \(-0.6421\) & \(0.3247\) & \(3.6418\) & \(10.5310\) \\ \hline \end{tabular}
\end{table} 
Table 5: The boundaries of real and imaginary parts of local mode eigenvalues of hydro and turbo synchronous generators with AVR systems of different nominal powers in the range \(P=0.0\) pu to \(P=1.2\) pu and from \(Q=0.0\) pu to \(Q=1.2\) pu. \begin{table}
\begin{tabular}{c c c c} \hline \(P_{\rm n}=12\) [kW] & \(U_{\rm n}=400\) [V] & \(I_{\rm n}=21.7\) [A] & \(\cos\,\varphi_{\rm n}=0.8\) \\ \hline \(U_{\rm Fn}=400\) [V] & \(I_{\rm Fn}=21.7\) [A] & \(f_{\rm n}=50\) [Hz] & \(n_{\rm n}=1500\) [\(\min^{-1}\)] \\ \hline \end{tabular}
\end{table} 
Table 7: Manufacturer’s data of the tested synchronous generator. \begin{table}
\begin{tabular}{c c c c c} \hline \(L_{\rm d}=2.11\) [pu] & \(L_{\rm q}=1.45\) [pu] & \(L_{\rm d}\)\({}^{\prime}=0.25\) [pu] & \(L_{\rm d}\)\({}^{\prime\prime}=0.18\) [pu] \\ \hline \(l_{\rm d}=0.15\) [pu] & \(l_{\rm q}=0.15\) [pu] & \(R_{\rm e}=0.003\) [pu] & \(L_{\rm e}=0.03\) [pu] \\ \hline \(R_{\rm s}=0.05\) [pu] & \(R_{\rm F}=0.015\) [pu] & \(H=0.19\) [pu] & \(D=1\) [pu] \\ \hline \(R_{\rm D}=0.262\) [pu] & \(R_{\rm Q}=1.08\) [pu] & \(T^{\prime}_{\rm d0}=0.5\) [s] & \(\omega_{\rm s}=2\pi 50\) [\(s^{-1}\)] \\ \hline \end{tabular}
\end{table} 
Table 8: Synchronous generator’s data obtained with tests. The testing system for the determination of the parameters and for experiments is shown in Figure 20. For the rotor voltage generation, the solid-state power amplifier was used as the excitation system. The induction machine with frequency converter was implemented to produce mechanical torque. The data acquisition system Dewetron was used for recording of time responses. A dSpace R&D controller board was used for control of the power amplifier and frequency converter. Data processing was done using MathWorks/MATLAB. From the experiments and simulations, it is evident that the 7 th-order NLM of a synchronous generator describes well the responses of the laboratory synchronous generator to the changes in both inputs in the entire operating range. Agreement in the first amplitude, the frequency, and the damping of the transient response is very high. It also turned out that for small deviations from the observed operating point, simplified linearized H-P model allows sufficiently accurate dynamic and static calculations. A detailed comparison of the laboratory model experimental results with the NLM and H-P model simulation  
Figure 20: Laboratory experimental system. results is shown in [8]. The main conclusion in [8] was that the H-P model was entirely appropriate for the analysis of the local oscillations.