Electrical Engineering and Power Engineering

Improving approaches to the linearization of magnetic properties of electromechanical converter cores for numerical calculations

2026-01-20T11:07:45+02:00

Purpose. Improving the mathematical model for the linearization of magnetic properties of stator and rotor electrical steel based on the piecewise linear approximation of the magnetization curve, which will significantly reduce the number of nonlinear equations and substantially decrease the computational time for 2D and 3D circuit-field models of an asynchronous electromechanical converter while maintaining the accuracy of numerical calculations.

Methodology. Analytical methods for electromagnetic field calculation, the finite element method, analytical methods for electrical and magnetic circuit calculation, and piecewise linear approximation methods are utilized.

Findings. Mathematical models for linearizing the magnetization curve of stator and rotor electrical steel has been improved for both spatial 3D and plane-parallel 2D geometric models of the active part of AC electromechanical converters. An approach has been implemented to partition the general 2D geometric model of the stator and rotor core into n-elementary planes, applying a linear magnetization curve function at µ_r = const. Based on the 2D field modeling results of an electromechanical converters prototype in idle mode, compared to modeling results considering the full magnetization curve across the entire computational domain, the armature current residual does not exceed 2.654%. This allowed for a 4.89-fold reduction in the numerical calculation time for the 2D transient problem formulation using Comsol Multiphysics software.

Originality. The method for linearizing the magnetic properties of stator and rotor electrical steel in electromechanical converters has been improved, allowing for the application of a constant relative permeability value (µ_r =const.) to specific areas of the stator and rotor core computational domain while maintaining a sufficient level of numerical calculation accuracy.

Practical value. The proposed methodology for the linearization of the magnetization curve of stator and rotor electrical steel for spatial 3D and plane-parallel 2D geometric models of the active part of AC electromechanical converters can be applied to various types of electrical machines.

Features of the synthesis of reduced state monitoring devices for dc electric actuators with modal control

2026-01-08T21:57:06+02:00

Purpose. The purpose of the study is the development and justification of a methodology for the synthesis of reduced state monitoring devices for DC electric drives with modal control, as well as the analysis of their impact on the dynamic properties, stability and quality indicators of transient processes of electromechanical systems.

Methodology. The work uses methods of automatic control theory and state space theory, in particular methods of modal synthesis and pole placement. To build a reduced observation device, analytical methods of linear algebra and matrix analysis were used. The study of the dynamic properties of the electromechanical system was performed using methods of mathematical modeling and simulation experiment in the MATLAB software environment. The quality of transient processes was assessed based on the analysis of time characteristics and stability indicators of the control system.

Findings. Mathematical models of full and reduced state observation devices in the state space are developed and an algorithm for synthesis of a reduced observer is proposed, which provides recovery of only unmeasured state variables of the electric drive. It is shown that the choice of the speed of the reduced observation device, which exceeds the speed of the control object, guarantees the convergence of estimates and the correct operation of the modal control system. Using the example of second- and fourth-order electric drives, the possibility of recovering the integral component of the PI controller and the load moment without using additional sensors is proven. The simulation results show that in low-order systems, the use of a reduced observer can lead to a slight increase in overshoot and the duration of transients, while in higher-order systems its impact on dynamic indicators is minimal.

Originality. The paper first substantiates the use of typical normalized equations of modular optimum for the synthesis of reduced observation devices in DC electric drive systems with modal control, and also establishes the dependence of the influence of a reduced observer on the dynamics of the system on its order.

Practical value. The results obtained can be used in the design of control systems for electric drives with limited sensor capabilities, allowing to reduce the structural and hardware complexity of the system, increase its reliability, and simplify practical implementation without significantly degrading control quality indicators.

Analysis of the specific weight and size indicators of a high-speed permanent magnet synchronous motor

2026-01-22T22:42:04+02:00

Purpose. Determination of the dependence of specific power and specific volume on the calculated power and design dimensions for the formation of criteria for assessing the efficiency of weight and dimensions of a high-speed synchronous motor with permanent magnets and an external rotor.

Methodology. Classical methods of electromagnetic calculation of the main dimensions of synchronous motors with magnetoelectric excitation.

Findings. According to the results of calculations of weight and dimensions of high-speed synchronous motors with permanent magnets, performed by the classical method, the weight and volume of active materials were determined: magnetic core, permanent magnets and stator winding copper. For the calculation, the power range from 250 W to 15 kW at 10,000 rpm was adopted, which corresponds to the most frequently used motors in terms of power in various industries and applications. The nonlinear nature of the change in specific parameters of synchronous motors with permanent magnets was established. It was determined that the maximum specific power (about 80 kW/kg) is achieved in the range of 7–9 kW, after which this indicator decreases due to thermal limitations and an increase in the mass of structural elements. The optimal power range according to the specific volume criterion, with a cylindrical design of the prototype with an external rotor, is 1.5–4.5 kW. The results of the research show that with increasing power, the mass balance changes: the relative proportion of copper in the stator winding increases, while the proportion of the magnetic core decreases. This is due to the need to minimize electrical losses to maintain high efficiency and restrictions on heat dissipation.

Originality. The dependence of the specific characteristics of high-speed indicators of synchronous motors with permanent magnets with an external rotor on their geometric parameters and the level of use of active materials was systematized, which allowed identifying the zones of the highest efficiency of the design at a constant rotation speed.

Practical value. The proposed approach provides engineering criteria for a well-founded choice of topology and basic dimensions of high-speed engines at the early design stages, ensuring the achievement of the best weight-to-size characteristics.

Mathematical model of recovery of the reduced magnetic moment of a point dipole for identification of ferromagnetic objects

2025-10-01T18:33:35+03:00

Purpose of the work. The purpose of the work is to develop and study a mathematical model for restoring the reduced magnetic moment of a point dipole based on the integral characteristics of the magnetic field, which allows to ensure the correct solution of the inverse problem of magnetometry in conditions of limited a priori information and real noise interference.

Research methods. The work uses mathematical modeling, analytical methods of inverse magnetometry, integral transformations and a numerical experiment to assess the accuracy of restoring the magnetic moment components. To construct the calculated dependencies, the field discretization on a rectangular grid of measuring points and algorithms for minimizing the reconstruction error were used.

Results. A generalized model of the relationship between the measured components of magnetic induction and the components of the magnetic moment vector of the dipole was constructed. A mathematical algorithm for calculating the reduced moment based on the sums of the integral characteristics of the field in the coordinate directions was proposed. A study was conducted for different sizes of the measurement grid, which confirmed the efficiency of the method and showed that the reconstruction error decreases with an increase in the number of measurement points. The results obtained indicate the possibility of reliable identification of the object from a limited set of magnetic field data.

Scientific novelty. A method for restoring the reduced magnetic moment is proposed, which is based not on local field values, but on integral characteristics, which provides increased noise resistance and reduces the influence of medium inhomogeneities. The effectiveness of using the discrete-integral approach in inverse magnetometry problems is shown.

Practical value. The developed model can be used in systems for detecting and classifying ferromagnetic objects in underwater, underground and terrestrial environments, in particular in tasks of non-destructive testing, technical diagnostics and search and rescue operations. The proposed approach allows the implementation of small-sized measuring systems with reduced requirements for the accuracy of sensor positioning.

Determination of the optimal slip value for minimizing electrical losses in an induction motor

2026-02-15T14:59:22+02:00

Purpose. The aim of the work is to conduct theoretical research and develop a methodology for determining the optimal operating slip value to minimize electrical losses under varying load conditions on the induction motor rotor shaft.

Methodology. The research was conducted using the fundamentals of mathematical modeling theory for a generalized AC electrical machine, classical optimization methods, the basics of automated control theory, loss minimization techniques in induction motor drives, and methods for the interpolation and approximation of calculated data.

Findings. A methodology has been developed for determining the optimal operating slip value to minimize electrical losses under varying rotor shaft load conditions in a quasi-steady-state mode of induction motor operation. A universal objective function for minimizing electrical losses in the induction motor as a function of slip frequency has been obtained. In the process of solving the optimization problem using classical single-variable optimization methods, an expression for the optimal slip frequency was derived, as well as the relationships between current magnitudes and the parameters of the induction motor stator and rotor winding phases. These were obtained based on the conventional mathematical description of a generalized AC electrical machine for its steady-state operation. The effectiveness of the proposed methodology has been proven using the example of an AIR225M2 induction motor with a power rating of 55 kW, for which the electrical loss dependence in a quasi-steady-state mode under a static load of M_c = 0.5M_nom was obtained. It was established that the optimal slip value for this induction motor is s = 0.038.

Originality. For induction motors of various power ratings, a universal objective function has been derived to minimize electrical losses as a function of slip frequency. This function enables the determination of a performance characteristic representing the dependence of the maximum attainable efficiency on the load torque on the shaft for induction motors of any power range.

Practical value. The research findings can be implemented in induction motor drive systems equipped with rotor speed sensors to enable automated self-regulation of the motor speed. This ensures the rotor operates at the optimal slip value across the entire load range of the driven mechanism.

Automatic control system for data center cooling hydraulic modules

2026-02-24T10:03:13+02:00

Purpose of the work. Development and research of an automatic control system for a data center cooling hydromodule based on the Siemens S7-1200 industrial controller with the implementation of the digital twin concept in the MATLAB / Simulink environment to ensure precise stabilization of temperature regimes under variable thermal load.

Research methods. Mathematical modeling based on differential equations, simulation modeling, and classical methods of automatic control theory.

Results. A complex mathematical model of the hydromodule has been developed that adequately reproduces the nonlinear thermophysical interactions between the primary and secondary cooling circuits. An integrated control architecture has been created, in which a real microprocessor controller controls a virtualized object within the simulation model's circuit. Numerical modeling indicates that the developed system supports target microclimate indicators with high precision and zero static error. The analysis of transient processes confirmed the aperiodic nature of regulation during extreme thermal power disturbances.

Scientific novelty. The methodology for designing intelligent systems for the automatic control of heat engineering facilities based on the Digital Twin concept, with direct integration of a real industrial controller into a virtual control loop, has been further developed. For the data center cooling hydromodule, an architecture has been proposed in which the Siemens S7-1200 operates in hardware-software communication mode with a simulation model implemented in the MATLAB/Simulink environment, providing two-way data exchange via the ISO-on-TCP protocol in real time. Methods for predictive analysis of energy efficiency in cooling systems have been further developed by moving the regulator-tuning stage into a virtual environment, with hardware verification of the algorithms. It has been shown that the proposed system provides an aperiodic nature of transient processes and zero static error during thermal power disturbances.

Practical value. A toolkit has been created to enable safe, cost-effective adjustment of automation systems for data center cooling hydromodules without risking damage to expensive equipment. The proposed system allows: to ensure stabilization of the secondary circuit temperature with an error not exceeding 5%; to achieve aperiodic regulation with a time constant T = 20 s; to increase energy efficiency and reliability of pumping equipment; to reduce costs for commissioning and adjustment due to preliminary testing of algorithms in a digital twin. The developed solutions can be integrated into automated control systems of large data centers and scaled for multi-module configurations by synthesizing load redistribution algorithms across several cold sources.

Investigation of electricity costs during energy flow optimization in a microgrid with distributed energy sources under conditions of unstable generation

2025-11-28T15:25:14+02:00

Purpose. Development of an optimal control procedure for a microgrid with alternative energy sources, external power supply, and a diesel generator unit

Methodology. In the course of the study, methods of formulating linear optimization problems and corresponding linear programming techniques were used, as well as simulation modeling methods within a visual programming environment.

Findings. The study investigates the control processes of a hybrid microgrid that includes a solar power plant, a wind energy installation, a battery storage unit, a diesel generator, and an external power grid. Using a developed model in the MATLAB/Simulink environment, the energy flows and the operation of the microgrid subsystems were analyzed under four operating modes with varying electrical power flows. Linear programming methods were applied to optimize the energy balance, enabling the minimization of electricity costs while maintaining power balance and ensuring voltage stability within standard limits. The obtained results demonstrate the effectiveness of combining renewable energy sources, battery storage, and diesel generation for optimal microgrid control by balancing the battery storage unit’s state of charge and confirm the feasibility of applying optimization algorithms for managing energy operating modes.

Originality. An objective function is proposed for solving the optimization problem of minimizing financial costs for electrical energy in a microgrid power system. The objective function accounts for the variable cost of electricity during power exchange with the external grid, constraints on the state of charge and discharge of the battery energy storage system, prioritization of renewable energy sources, as well as the economic feasibility of engaging a diesel generator unit depending on the current energy balance and economic conditions.

Practical value. The obtained results using the energy balance optimization algorithm can be applied to the design of energy management systems and optimal control of microgrids with combined low- and medium-power energy sources.

Research on ensuring annual energy consumption of a residential building with a photoelectric plant

2026-03-09T11:44:27+02:00

Purpose. To assess the capability of rooftop photovoltaic power plant (PVPP) to supply the operation of engineering systems in multi-apartment residential buildings and to determine a set of engineering and technical measures that ensure the effective integration of rooftop photovoltaic power plants in order to achieve regulatory energy-efficiency indicators and minimize climate impact.

Methodology. Calculation and analytical methods were applied to determine the energy consumption of residential buildings, along with a methodology for calculating electrical loads of multi-apartment buildings to evaluate changes in electricity demand under different configurations of building climate systems. Scenario analysis and energy modeling were used to assess the interaction between heating technologies, operating conditions, and renewable energy generation.

Findings. Rooftop photovoltaic systems equipped with modern photovoltaic modules and inverter equipment and installed on typical five-storey multi-apartment residential buildings are capable of covering the annual electricity demand of building climate systems, which corresponds to the requirements for achieving operational climate neutrality. Comprehensive modeling was carried out to analyze the interaction between building climate system configurations, energy sources, heating system temperature regimes, and actual outdoor temperature conditions on the achievable level of energy efficiency in typical residential buildings. The modeling of rooftop photovoltaic system operation and the comparison of expected electricity generation with the electricity demand of thermally modernized buildings equipped with heat-pump-based climate systems demonstrated the feasibility of balancing annual energy consumption with on-site renewable generation. It was found that comprehensive thermal modernization of typical five-storey buildings combined with the transition to electric heating using heat pumps as the primary heat source enables the electricity demand of building climate systems to be supplied by rooftop photovoltaic systems.

Originality. The study substantiates a set of energy-efficient measures, including the integration of rooftop photovoltaic systems, that allow achieving operational climate neutrality indicators for typical five-storey multi-apartment residential buildings. It is shown that the transition to heat-pump-based electric heating can reduce electricity consumption by 1,8-2,0 times under actual average outdoor temperature conditions compared with conventional electric heating systems. Furthermore, the implementation of low-temperature heating regimes reduces electricity consumption by 2,8-3,2 times compared with direct electric heating and enables achieving operational climate neutrality for building climate systems.

Practical value. The results can be applied in the development of renovation projects for existing multi-apartment residential buildings, in new residential construction, and in the design of electric heating systems that utilize electricity generated by rooftop photovoltaic systems. The proposed solutions contribute to the objectives of the Energy Strategy of Ukraine until 2035, strengthen national energy security, and support the implementation of international commitments on reducing primary energy consumption and greenhouse gas emissions.