## 1 Introduction  
In order to improve the flexibility and resilience of electric power systems (EPS), a transition is underway from the construction of large power units to the large-scale adoption of distributed generation (DG) facilities installed near power consumers [1; 2; 3]. This approach is also applicable to railroad power supply systems (RPSSs). The use of DG units in RPSSs will make it possible to cut the costs of power supply of railway transport infrastructure facilities, increase the reliability of power supply, and improve the power quality [4; 5; 6], including in areas of power supply to non-traction loads. However, certain features unique to load flows of RPSSs that are related to the markedly variable nature of traction loads, the presence of unbalance and harmonic distortions, complicate the operating conditions of synchronous machines of DG units. In the presence of an unbalanced load, the stator windings of a synchronous machine have negative sequence currents flowing through them, resulting in a magnetic flux that rotates relative to the rotor at double angular velocity. This flux induces double frequency currents in the rotor winding, resulting in additional losses. Moreover, an electromagnetic torque pulsing at double frequency is created, which causes additional vibrations as well as harmonic distortions of stator and rotor voltages and currents. Therefore, there is a need to limit the capacity of the generator and the duration of its operation under reduced power quality. Even a slight increase in current unbalance requires a significant reduction in the generator's full-load runtime. The appearance of harmonic distortions [7; 8] leads to a decrease in the power factor, which can cause the rotor current to increase as a result of the action of the automatic regulator of excitation. In general, the occurrence of higher harmonics in the stator windings of a synchronous machine is the subject of many studies, for example, [9; 10; 11; 12; 13; 14]. From the analysis of the reviewed works it follows that the generation of higher harmonics in stator voltages depends on the type of its winding [10; 11], the shape of the cores [12] and the degree of their saturation, and the availability of damper windings [13], as well as on the excitation current control system of the generator [14]. Studies of load flows of generators under a reduced power quality, the results of which were reported in papers [15; 16; 17; 18], allowed the significant expansion of the scope of the use of asynchronous and unbalanced load flows in practical applications. The general principle governing the application of generators under such conditions, formulated in [16] and consisting in limiting the continuous load of the synchronous generator when there is an unbalance and harmonic distortion, still holds valid today. Methods for assessing the effect of load unbalance with a non-sine waveform of current were based on the fact that the effect of the negative-synchronous field and the fields of higher-harmonic current of the stator lead to the same effect, i.e., extra heating of the active parts of the generator. These conclusions are confirmed by a study carried out in [19] on the calculation of the permissible load of a synchronous generator with different shares of power consumers with a non-linear current-voltage characteristic. In [20], a method is proposed to reduce the influence of higher-current harmonics on the operation mode of synchronous hydrogenerators, and the permissible generated power of a synchronous hydrogenerator when operating on a non-sinusoidal load is determined. In such modes, it is mandatory to use thermal protection of the synchronous generator, taking into account the harmonic distortion of the stator and rotor currents. For example, in [21], a new model of thermal protection of the rotor of a synchronous generator is presented, taking into account the simultaneous occurrence of rotor overload due to the excitation current and rotor overload due to the negative sequence current.