## 4 Joint Effect of Unbalanced and Non-Linear Loads on Operation of a Low-Power Synchronous Generator  
To assess the levels of unbalance and harmonic distortion in 6, 10, and 35 kV networks, fed from traction substations (TS), we modeled a section of a standard power RPSS, the circuit of which is shown in Figure 12. The modeling was carried out based on the Fazonord software package developed at Irkutsk State Transport University [23]. A flow chart of the computational model is shown in Figure 13. We studied three freight trains weighing 5000 tons moving in the odd direction. The train schedule is shown in Figure 14, and the current profile of the train is shown in Figure 15.  
Figure 16: Negative sequence unbalance ratios at 6 kV busbars of the TS. \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{3}{c}{**Phase**} \\ \cline{2-3}  & **A** & **B** & **C** \\ \hline Mean value & 6.04 & 9.69 & 4.58 \\ \hline Maximum value & 28.68 & 31.68 & 21.27 \\ \hline Minimum value & 0.07 & 0.96 & 0.11 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results of calculating total harmonic distortions at 6 kV buses of TS2. Figure 17: Total harmonic distortion at 6 kV buses of TS2. The obtained results allow us to conclude that even a limited movement induced significant levels of unbalance, and harmonic distortions were observed at 6 kV buses of the simulated RPSS. The mean values of the total harmonic distortion were within 4.5...10%, and the maximum value of the unbalance ratio in the negative sequence reached 3.7...6.5%. Thus, the relevance of the problems related to the study of load flows of low-power generators under increased unbalance and harmonic distortions was further confirmed. The flow chart of the investigated simulation model that was implemented using the MATLAB Simulink and SimPowerSystems packages is shown in Figure 19. The turbogenerator served an active and inductive load of 2 + \(j\)0.6 MWA. The rectifier load was consistently increased to increase the deviation from the sine waveform. At the same time the main balanced load was reduced so that the total load of the generator remained unchanged. The unbalanced currents and voltages were introduced by increasing the linear load between phases \(a\) and \(b\). At the same time, the load between phases \(b\), \(c\) and \(c\), \(a\) was reduced to maintain the total power. Figure 19: Flow chart of a computer model of the turbogenerator serving an unbalanced and non-linear load. Figure 18: Waveforms of phase voltages at 6 kV busbars of TS2. It should also be noted that with increasing unbalance and deviation of current and voltage waveform from the sine waveform, the amplitude of the mechanical vibrations of the generator rotor at 100 and 300 Hz increased, which can cause excessive runout during operation and accelerated wear of the generator. The increase in the difference of currents in the generator phases led to an increase in the coefficient \(k_{2l}\), which was accompanied by an increase in the level of voltage unbalance at the generator terminals, as well as the appearance of harmonic distortions (Figure 22). These facts of RPSSs should be taken into account when introducing DG units since failure to do that can lead to the accelerated wear and tear of electrical equipment. Results of our study also indicated that when the generator served unbalanced and non-linear loads with a total power of \(2.4+j1.45\) MV-A (which corresponded to 90% turbo-generator load), the amplitude of the forced oscillations of the electrical and mechanical parameters reached the limiting values, which led to a significant increase in equipment wear, the improper operation of the microprocessor-driven ARE and ARS, and, consequently, a decrease in the stability margin. For example, when an additional load was connected, the system lost its stability (Figure 23).