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In the context of the ever-increasing complexity of modern power systems, optimizing consumers' performance to improve electrical energy quality becomes paramount. This article thoroughly examines the power transfer effects in the context of distorting and non-symmetrical regimes in three-phase, four-wire power systems, focusing on heavily nonlinear and unbalanced consumer influence across the grid. Particular emphasis is placed on the impact of these regimes on the parasitic active and reactive powers affecting linear and balanced consumers due to distorting and unbalanced ones. An essential aspect of this analysis is including the neutral conductor in the experimental circuit, enhancing relevance and a more profound understanding of consumer interactions in modern networks. Quantitative aspects of the phenomena involved are assessed from the perspective offered by SCPT (introduced by Andrei Ţugulea), allowing us to identify the source of non-symmetry and residual powers through comprehensive power balance equations for the active and reactive powers.

The present study proposes a feedforward angle droop strategy based on a discrete-time mathematical model for operation dispatchable distributed generation (DG) units connected directly or through voltage source converters (VSC) to the microgrid. These units should supply their local and common loads. Droop coefficients should be increased to improve power division between different DG units. Also, a time delay in systems' state variables and controller input is a disruptive parameter for the control system's performance. These two parameters have negative effects on network stability. To ensure the stability of the closed-loop system, a predictive sliding mode controller can be used based on discrete-time systems. However, this strategy cannot reduce the chattering phenomenon. This paper discusses the effect of time delay and increases in droop angle coefficients on the whole system and how these impacts can be eliminated. So, a combination of integral sliding mode controller (ISMC), composite nonlinear feedback (CNF), and sliding mode learning control (SMC), which is called hybrid SMC, is used with an angle droop controller.

This paper brings in the spotlight the theory of catastrophes and its application for the analysis of the equilibrium positions of dynamic electrical systems. A study model was adopted in the case of a DC electric motor with series excitation operating in transient regime. From the perspective of the theory of catastrophes, starting from the operating equations of the direct current electric motor with series excitation, the functions that describe its behavior in the phase-space and in the control-space were obtained and then the equilibrium points of the chosen model were determined. Also, for a clearer understanding of the results obtained, the evolution of this behavior in the phase-space and in the control-space was highlighted graphically, using the MATLAB software.

The Hănțilă method has proven its effectiveness in solving non-linear three-phase circuits. It is the only effective method for analyzing non-linear three-phase circuits containing machines with different sequence reactances. Since solving a system of equations is unnecessary, the computational effort is reduced, and a large number of harmonics can be considered. The convergence of the method is certain - demonstrated mathematically and allows the use of overrelaxation. To develop the method, we analyze the efficiency of computing a dynamic overrelaxation factor for accelerating the computational algorithm.