In this work, the real-time mathematical models of electromechanical power systems with semiconductor converters based on the author’s method of the average voltages in the integration step are described. As well as the theoretical basics of the method, the algebraization algorithm of differential equations on a time quantum is described. This time quantum in the hybrid model is synchronized with the time quanta of signal samples of the physical part of the model. In the hybrid model, only algebraic equations of electromechanical power systems are present. Software and technical applications of the hybrid models of energy-generating blocks for selected thermal and nuclear power plants are described. In the process curve courses obtained and projected in this paper, the author’s hybrid models are illustrated. In the existing models, the nonlinearity of the electric machines and the semiconductor converters are taken into account. The numerical stability of the method of average voltages in integration step—in the sense of the resistance to computer calculation disturbances—is proven.

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The analyses of the influence of spatial harmonics on the electromagnetic torque of the multi-phase induction machine and reducing this influence are important tasks to ensure the high efficiency of the induction machine. Designing the machine to consider the influence of spatial harmonics is essential to ensure the desired mechanical and energy characteristics. In the case of the sinusoidal winding supply of the induction machine, the magnetomotive force has high spatial harmonics, which are caused by the machine-winding design. The interaction between the 5th, 7th, 11th and 13th spatial harmonics of the winding function and the first time-harmonic of the winding supply causes the appearance of the 6th and 12th harmonics in the electromagnetic torque of the machine. A prototype of the symmetrical six-phase induction machine and the experimental study for the influence of spatial harmonics on the harmonic content of the stator currents in different machine modes are given in this paper. The mathematical model of the six-phase induction machine has been developed using the average voltages in integration step method. The introduction of the harmonic components into the magnetization inductance in the mathematical model of the six-phase induction machine for taking into account the spatial harmonics of the machine-winding function is proposed in this paper. The adequacy of the mathematical model was confirmed by comparing the simulation and experimental results. The harmonic content of the electromagnetic torque, which is caused by spatial harmonic influence, is analyzed.

In this paper, testing and diagnosis methods for the static excitation systems of power plant synchronous generators using Hardware-In-the-Loop technology are described. These methods allow a physical excitation system to be connected to a real-time model of a power plant unit. A feature of a static excitation system is the presence of generator self-excitation—that is, when the input voltages of the excitation system are defined by a synchronous generator. These voltages are determining by the digital model, which creates additional difficulties with combining a digital model with a real excitation system. Various ways to solve this problem are described in this article; in particular, we focus on the option in which the gate-impulses of a thyristor converter are applied to the digital model by a real static excitation system. The real-time models are based on the method of average voltages in the integration step. This method is effective for providing numerical stability for the models of power schemes and their functioning in real time mode over a long period. A synchronization method for the calculation time of the model with real time is described. The adequacy of the described method is proved by the results of the static excitation system of synchronous generators testing in operating and fault modes.

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