## 2 Unbalanced Load Effect on Operation of a Low-Power Synchronous Machine
To increase the inertia on one shaft of the synchronous generator and the DC machine, we installed a flywheel with a moment of inertia of 0.009 N\(\cdot\)m\(\cdot\)s\({}^{2}\). Figure 5: Schematic (**a**) and photo (**b**) of the experimental setup: SS—RPM sensor; T—turbine; SM—synchronous machine; FW—field winding; VT—voltage transformer; CB—circuit breaker. The generator in the simulation served resistive and inductive loads. The unbalance was created by increasing the load in phase A; the loads in the other phases were reduced by an appropriate amount to maintain full loading. Regulation of generator speed and voltage was carried out on the basis of digital PID controllers, the block diagrams of which are shown in Figure 6.  
Experimental data obtained with the physical model of the turbogenerator, presented in Tables 3 and 4 and Figure 7, confirmed the results of the computer-aided simulation detailed above. As a result of these studies, we found that when the generator served an unbalanced load, the stator winding had higher current and voltage harmonics, and the third harmonic had the greatest amplitude. This is explained by the fact that in the presence of an unbalanced load, a current of double frequency (100 Hz) is induced in the rotor winding, which in turn excites the magnetic field of the rotor, which rotates in the forward direction at a double frequency with respect to the rotor. This field is superimposed on the fundamental frequency magnetic field, which leads to the formation of a magnetic field of the rotor rotating in the forward direction at three times the frequency of the stator. Thus, the generated field will induce a current of triple frequency (150 Hz) in the stator winding. Figure 6: Flow charts of Simulink models of the ARE (**a**) and ARS (**b**) of the experimental setup. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline \multirow{2}{*}{**Harmonic No. **} & \multicolumn{4}{c}{**Voltage Harmonic Distortion**} & \multicolumn{4}{c}{**Current Harmonic Distortion**} \\ \cline{2-7}  & \(\mathbf{k_{l\mathbf{l}(n)A}\%}\) **\%** & \(\mathbf{k_{l\mathbf{l}(n)B}\%}\) **\%** & \(\mathbf{k_{l\mathbf{l}(  
Figure 7: Generator load flow as a function of the current unbalance ratio \(k_{2I}\). (**(a)**—\(k_{U}\)=\(f\) (\(k_{2I}\)),\(k_{2U}\)=\(f\) (\(k_{2I}\)); (b)**—\(f\) (\(k_{2I}\)); (c)**—\(U\)=\(f\) (\(k_{2I}\))). Due to the fact that the generator was loaded at about one third of its rated power, the maximum phase current difference slightly exceeded the allowable 12% only at the value of \(k_{2I}\) equal to 40%. It should also be noted that the effective value of the excitation current of the generator serving an unbalanced load remained practically unchanged. The relationships shown in Figure 7 differ slightly from the nearly linear ones obtained by computer-aided simulation. The differences are due to a number of assumptions made in the simulation, as well as measurement errors. This is especially true for current measurements in the presence of harmonic distortions. The results of computer-aided and physical modeling revealed the following:  
1. When the synchronous generator served an unbalanced load, there was a noticeable negative sequence current, which may exceed the maximum allowable value with respect to overheating. The generator began to emit higher harmonics into the network, which led to extra heating. In the experiments carried out on computer and physical models, the difference between the currents of the stator phases slightly exceeded the maximum permissible value and amounted to 12.5% for the computer model and 12.9% for the physical one. 2. The average excitation current of a generator serving an unbalanced load was practically unchanged, but there was a 100 Hz current in the field winding whose amplitude increased linearly as the load unbalance increased. Therefore, the excitation current and the generator load should be limited. 3.