Relevance. At present time many technological processes in oil and gas industry sector apply the high-performance three-phase equipments with power electronic converters such as variable-frequency AC drives or uninterruptible power supplies which are nonlinear loads and can cause various problems in distribution systems, including voltage and current unbalance, resonances phenomena, resistance current losses in the neutral wire, overheating of motors and transformers etc. In order to improve the electromagnetic compatibility of different power consumers in the industrial power supply systems the passive capacitor compensators for reactive power correction are usually used, that are ineffective in case of nonlinear loads. Furthermore this equipment generates the reactive power even if any loads are absent and do not meet modern requirements in area of power conditioning. To avoid the impact of the above-mentioned drawbacks on normal operation conditions of three-phase systems the development of novel technical approaches to power circuit design, methods for analyzing electrical power processes and control strategies for power filtering are needed that provide the desired power quality in the low voltage and medium voltage distribution grids regardless of the load electrical circuits. The aim of the research is a comprehensive analysis of existing approaches to electromagnetic compatibility improvement of the three-phase loads in the distribution AC system and description of the main restrictions of power compensators under normal operation conditions for industrial applications in mineral resources sector; the control design for enhancing an operational stability of active power filters under time-varying parameter disturbances as well as variations of load behaviors or distribution system configuration. Objects: AC electrical power supply systems with power electronics converters and load units in which there are distortions in the instantaneous sinusoidal waveforms of grid three-phase variables; passive and active power filters for high-frequency harmonic correction. Methods: non-commutative algebra of quaternion; four-dimensional hyper-complex space representation; methods of spectral analysis and Fourier series decomposition. Results: the brief survey of different approaches and techniques to the power quality enhancing in the AC electrical power supply systems of mineral resources industrial sector and control strategy of active power filters that will provide balanced or/and sinusoidal grid currents in the three-phase systems with the zero or leading/lagging phase shift relative to the corresponding voltage.