Damir Žarko

University of Zagreb Faculty of Electrical Engineering and Computing · Department of Electric Machines Drives and Automation

Dear colleagues, I invite you to contribute a paper to the special issue entitled "Design and Production Process Optimization for High Performance and Energy Efficiency in Electrical Machines" of the open access journal "Energies" from Switzerland (impact factor 3.252) For more information on the special issue: https://www.mdpi.com/journal/energie...

In this paper, an algorithm for calculating the asymmetric current distribution in parallel-connected high-voltage winding sections of a transformer during a short-circuit test caused by an asymmetric magnetic field is described. This calculation is essential in multi-winding transformers, such as traction transformers and rectifier transformers, w...

This study describes a method for calculation of transformer short circuit voltage using conformal mappings, which map the transformer longitudinal and transverse cross-section geometry to a unit disk where an analytical solution for magnetic flux density is obtained and then transformed back to the original domain. The short-circuit voltage is cal...

In the distribution transformers design oval windings are used due to economic advantages. On the other hand, such windings are more susceptible to radial forces in a short circuit. A diamond dotted paper with an epoxy coating is used in order to increase the stiffness of the winding. Despite that, winding failure may occur during the short circuit...

This paper analyzes an engineering problem of adjusting the rated current of a synchronous reluctance motor to match the rated current of a commercially available inverter. This situation may occur when a synchronous reluctance motor is optimally designed for maximum torque per ampere (MTPA) operation using standard IEC stator frames for induction...

This paper presents a simple model for the calculation of core losses in permanent magnet machines based on the total flux linkage of the stator winding. In reality, the total core losses will vary as a function of permanent magnet field and the combination of d-q current components even in the case when different d-q currents produce the same amou...

This paper proposes the novel scalable model of synchronous permanent magnet and synchronous reluctance machines which combines ultra-fast scaling laws with saturated flux-linkage and loss model. The scalable model is used for fast and accurate calculation of efficiency/loss maps and can also be used for drive cycle analysis including calculation o...

This paper presents an iterative method based on conformal mapping and magnetic equivalent circuits for on-load analysis of saturated surface permanent magnet machines with integer slot and fractional slot windings. Magnetic saturation is taken into account by defining additional point wires in the stator slots and interpolar region between the mag...

In this paper an analytical approach for calculation of mechanical strength of oval windings in distribution transformers is presented. The calculation is given for radial forces resulting from interaction of the axial component of leakage flux density and the current in the windings. The analysis is focused on the inner foil winding subjected to r...

This paper presents a complete solution for constrained control of a permanent magnet synchronous machine. It utilizes field-oriented control with proportional-integral current controllers tuned to obtain a fast transient response and zero steady-state error. To ensure constraint satisfaction in the steady state, a novel field-weakening algorithm w...

This paper presents a method for reducing computational time in constrained single objective optimization problems related to permanent magnet motors modeled using computationally intensive finite element method. The method is based on Differential Evolution algorithm. The principal approach is to interrupt the evaluation of inequality constraints...

In this paper, an improved analytical model accounting for thermal effects in the electromagnetic field solution as well as efficiency map calculation of an outer rotor surface permanent magnet (SPM) machine is described. The study refers in particular to an in-wheel motor designed for automotive electric powertrain. This high torque and low speed...

Air gap field solution for an outer rotor permanent magnet (PM) machine is derived based on numerical Schwarz–Christoffel (SC) transformation of a single slot geometry and analytical solution of a point wire field in the rectangular canonical domain. This approach takes into account geometrical distortions of PM edges and field evaluation points lo...

In this paper, six different modelling methods for permanent magnet (PM) electric machines are compared in terms of their computational complexity and accuracy. The methods are based primarily on conformal mapping, mode matching, and harmonic modelling. In the case of conformal mapping, slotted air gap of a complex machine geometry is transformed t...

This paper presents a control method for constrained control of a permanent magnet synchronous machine. The control system utilizes field oriented PI current control tuned using linear control theory to obtain good steady-state performance and a fast transient response. However, the linear control theory does not consider constraints, violation of...

In this article, a novel method for the determination of spatial vectors of multi-phase windings is proposed. The proposed method is applied to squirrel-cage induction motors and it allows for the calculation of the rotor currents space vectors with any slot number (even and odd), that cannot be determined by classical expressions. On the basis of...

This paper presents a comprehensive approach to design of series of permanent magnet assisted synchronous reluctance motors using combined analytical and finite element calculations. A global optimisation metaheuristic algorithm (differential evolution) is utilised in order to achieve optimal design in terms of maximum torque per volume with numero...

Scaling laws are used when the size of a certain machine design with known performance needs to be adjusted for a new application with known requirements, or when a machine design is geometrically scaled and one needs to determine its performance. Scaling laws derived in this study allow one to quickly and accurately recalculate parameters of a geo...

The paper presents a method for calculating the back electromotive force and cogging torque waveforms of surface permanent-magnet motors using a model based on conformal mapping and magnetic equivalent circuits. The model takes into account the saturation of the iron core and its variation due to rotor movement. Because of the shorter execution tim...

This paper describes a method for calculation of the no-load saturation curve for wound field synchronous machines based on magnetic equivalent circuits and conformal mapping. The method uses conformal mapping to calculate reluctances of the magnetically active parts of the machine which are then used in magnetic equivalent circuit for the calculat...

This paper presents an overview of methodology for usage of mathematical optimization procedures e.g. optimization algorithms to achieve optimal design of an electrical machine. A special care must be taken in order to handle parameter definition, boundary constraints, constraint functions, model feasibility and computationally expensive calculatio...

This paper defines the scaling laws for synchronous permanent magnet machines which include three separate procedures: rewinding, axial scaling, radial scaling. The derivation of scaling relations is based on the requirement that the magnetic fields in the scaled model should be the exact images of the fields in the referent model. The exact equati...

This paper presents a new formulation for minimization of copper and iron losses in interior permanent magnet for the purpose of minimum loss control. Motor losses are formulated based on electromagnetic torque to total torque ratio resulting in simplified expression of minimal loss condition which can be easily solved online. The flux-weakening me...

This paper presents a finite-element (FE) method approach to calculation of the common-mode choke (CMC) impedance over a wide frequency range. The proposed method involves a 3-D electrostatic FE calculation of each turn-to-turn and turn-to-core capacitance, and their usage as electric circuit lumped parameters in the 3-D time-harmonic magnetic FE c...

This paper introduces a method for determination of equivalent linear electromagnetic parameters (constant complex permeability and electrical conductivity) of nonlinear magnetic steel, which can be used in a time-harmonic finite-element simulation to yield the same losses in the volume of that material as the measured ones. The conductivity and th...

A simplified model of transformer hysteresis curve utilized for calculation of core losses is presented. It incorporates eddy current losses and hysteresis losses into the same hysteresis curve thus simplifying a set of equations used for solving the magnetic circuit. The parameters of the hysteresis curve model are determined by evolutionary optim...

Onboard traction transformers are used for power supply of railway electric vehicles from the catenary system, such as high-speed trains, electric multiple units (EMUs) and electric locomotives, on 50, 60 and 16 2/3 Hz AC networks. Multi-system locomotives and trains, besides AC networks, operate on DC networks (1,5 or 3 kV) as well. In that case t...

This paper presents summarized electromagnetic and thermal design of interior permanent magnet motor for a low-floor tram TMK 2200. Motor geometry is optimized for maximum torque density using differential evolution algorithm. The influences of winding configuration on power losses and thermal transients in the motor during one driving cycle of the...

The selection of a three phase synchronous generator most suitable to be used as a power supply for testing of single-phase and threephase power transformers is described in the paper. The emphasis is on the analysis of the armature winding connection and sizing of the damper winding due to unsymmetrical load of a generator in the temperature rise...

This paper presents a general approach to the optimized design of a series of interior permanent magnet motors with the same lamination cross section. A concept of a referent and particular design has been introduced and analytical expressions which relate the principal machine parameters for the referent and particular machine have been derived. T...

The paper presents an optimized design of a low mass brushless DC (BLDC) permanent magnet motor for propulsion of an ultra light aircraft. The optimization has been carried out using Differential Evolution algorithm implemented in Matlab combined with SPEED and MotorCAD software packages for electromagnetic and thermal modeling of the BLDC motor us...

This paper presents an analytical model of a common-mode choke suitable for accurate calculation of the choke impedance over a wide frequency range. The model consists of lumped parameters (resistances, inductances, and capacitances) related to individual turns of the coils wound on the core. It takes into account the mutual interactions between th...

In this paper, the unbalanced magnetic forces which act upon the rotor of a salient-pole synchronous generator due to eccentric motion of the rotor shaft in the presence of magnetic field in no-load and loaded condition are calculated using the finite-element method. The displacement of the rotor is modeled using the actual shaft orbit measured on...

The unbalanced magnetic forces which act upon the rotor of a salient-pole synchronous generator due to eccentric motion of the rotor shaft in the presence of magnetic field originating from the field current in no-load operation have been calculated using finite-element method. The displacement of the rotor has been modeled using the actual shaft o...

In the article measured and calculated electromagnetic field in the surrounding of power transformer are compared. The goal of this research is to examine a possibility of making a computer model which will be able to serve as a substitute to the real measurement. In the computer model made for this paper, various objects in the close surroundings...

The main design features and the results of tests carried out on a prototype of a 750 kW interior permanent-magnet (IPM) motor for ship propulsion are presented. The principal reasons for choosing an IPM motor design over other available types of permanent-magnet (PM) motors for ship propulsion have been discussed in detail. The test results indica...

In this paper, we apply an original numerical Schwarz-Christoffel (SC) transformation to analyze magnetic field originating from permanent magnets and the armature winding currents in a slotted air gap of an inset permanent-magnet synchronous motor. We obtained the solution of the SC integral numerically using Matlab SC Toolbox. We used this field...

We present an analytical method for the calculation of electromagnetic torque in surface permanent-magnet (PM) motors. Our method uses conformal mapping to calculate the electromagnetic torque by integrating the Maxwell stress tensor inside the air gap. It uses the radial and tangential components of the flux density in the slotted air-gap produced...

This paper deals with the analytical and numerical analysis of the flux density distribution in the slotted air gap of permanent magnet motors with surface mounted tangentially magnetized permanent magnets. Two methods for magnetostatic field calculations are developed. The first one is an analytical method in which the effect of stator slots is ta...

An analytical model is presented, which uses two-dimensional field theory in polar coordinates to determine the flux density distribution, cogging torque, back EMF and electromagnetic torque in the slotted air gap of permanent-magnet motors with surface mounted magnet bars which are magnetized in shifting direction. The magnet arc to pole pitch rat...

The presented study compares measured and calculated electromagnetic field in the surroundings of a large power transformer with the aim to avoid the necessity of measuring the field on subsequent units and use a computer model instead. The influences of various objects located in the vicinity of the transformer during measurement are also analyzed...

In this paper we apply analytical and numerical conformal mapping (CM) to analyze magnetic field originating from permanent magnets and armature winding currents in a slotted air-gap of a surface mounted radial permanent-magnet synchronous motor (SPM) with taking into account the effect of arbitrarily curved motor surfaces. One of the conformal map...

The realization of different load torque characteristics in the laboratory for the purpose of teaching electric drives is presented. The torque characteristics with linear and quadratic dependence on speed are achieved by mechanically coupling the induction motor with a DC generator connected to a resistor. By controlling the excitation current of...

In this paper the application of motors in plants at risk of explosive atmospheres, and the special requirements of such applications from the standpoint of explosion protection are considered. The application of motors with type of protection increased safety, marked as ldquoEEx erdquo, with and without associated safety systems, are analyzed for...

The aim of this study was to compare the short-circuit forces in the U-type and I-type low voltage winding of a large power transformer. The comparison of forces calculated using 2D Rabinpsilas method and 3D finite element method is conducted. The influence of the winding helix pitch on the winding forces calculated using 3D finite element method i...

An analytical model is presented, which uses two-dimensional field theory in polar coordinates to determine the flux density distribution, cogging torque, back EMF and electromagnetic torque in the slotted air gap of permanent magnet motors with surface mounted magnet bars which are magnetized in shifting direction. The effect of stator slots is in...

We present an analytical method for the calculation of cogging torque in surface permanent-magnet (PM) motors. The cogging torque is calculated by integrating the Maxwell stress tensor inside the air gap. The principle of complex relative air-gap permeance derived from conformal transformation of the slot geometry is used to take into account the e...

This work presents a general magnetically nonlinear three-phase dynamic model of permanent magnet machine. The model is composed of elementary phase windings. The voltage balance in each individual phase winding is given as a function of back-emf and magnetic couplings among individual phase windings that depend on magnetic conditions in the machin...

The paper presents a method for determination of nonlinear B-H characteristics of materials used for construction of stator and rotor core of a synchronous generator. The B-H characteristics are determined by evolutionary optimization coupled with 2D finite-element (FE) computation. The objective function is to minimize the difference between the m...

This paper focuses on the specific selection of electrical motors for electrical drives (ED) in areas endangered by explosive atmospheres (hazardous areas), from the aspect of mandatory application of ATEX Directives, and the risk assessment associated with this. The paper primarily analyzes the selection of an electrical motor depending on the req...

The complexity of the permanent magnet (PM) machine structure makes the optimal design of the PM machine always a difficult task. The multiple objectives of an optimal design make most classic optimization algorithms inapplicable, due to the nonlinearity and some discontinous variables. In this paper, two interior permanent magnet (IPM) machine des...

A procedure for improving the design of a servo motor by means of finite-element method (FEM), optimization using differential evolution (DE) and cost analysis is presented. A comparative analysis has been carried out for four different motor designs taking into account the motor performance and the cost of the investment for manufacturing of the r...

We present an analytical method for calculation of no-load magnetic field distribution in the slotted air gap of a surface permanent-magnet (PM) motor with radial or parallel magnetization. The method introduces the notion of complex relative air-gap permeance, calculated from the conformal transformation of the slot geometry, to take into account...

A method for calculation of parameters of an interior permanent magnet (IPM) motor at any operating point using 2-D finite element method is presented. This approach is suited to be used in the design stage where it is necessary to determine the motor parameters, namely inductances, which are simultaneously a function on motor dimensions and termin...

An analytical technique that can be effectively used for the calculation of the end-winding leakage inductance of a turbogenerator has been presented. It is based on a three-dimensional geometric model of the end-winding region in which each coil is modeled as a set of serially connected straight filaments. The calculation of the mutual inductance...

A multiobjective optimization procedure for the design of interior PM motors based on differential evolution algorithm is presented. A comparative analysis has been carried out for the optimized 5 kW, 50 kW and 200 kW IPM motors with two and three layers of cavities in the rotor to show design trade-offs between goals to minimize the motor volume w...

High-temperature superconducting (HTS) material in bulk form is used to design a linear synchronous motor for an electromagnetic aircraft launch system. The motor is designed without an iron core. Stator coils are placed in the air while the permanent magnets used in conventional design of linear permanent magnet synchronous motors are replaced by...

Two basic linear motor designs suitable for an electromagnetic aircraft launch system (EMALS) have been presented in the paper. The motors have been designed with an emphasis on easy assembly and replacement even at the cost of slightly reduced performances. Both, linear permanent magnet synchronous motor (LPMSM) and linear induction motor (LIM) ar...

The paper describes a computation of basic electromagnetic parameters of a turbogenerator using 2D finite element method with completely automated preprocessing. The results obtained by 2D method are compared to the ones obtained by classical (analytical) method and to the measured values from tests carried out on a 194 MVA turbogenerator manufactu...

An optimization based method for determining magnetically nonlinear iron core characteristics of transformers is proposed. The method requires a magnetically nonlinear dynamic model of the transformer as well as voltages and currents measured during the switch-on of unloaded transformer. The magnetically nonlinear iron core characteristic is in the...

In this paper a linear switched reluctance gener-ator used in a direct drive wave energy converter is considered for modeling and model-based opti-mal control. Linear switched reluctance generators (LSRGs) are highly nonlinear electromechanical converters which must be adequately controlled in order to achieve a satisfactory energy conversion effic...

The computation of steady-state, transient and subtransient reactances by using both, magnetostatic and time-harmonic simulations is presented. The variation of steady-state reactances under various operating conditions was analysed considering the saturation effect. The saturation under transient and subtransient regimes was considered by magnetos...

The realization of different load torque characteristics in the laboratory for the purpose of teaching electric drives is presented. The torque characteristics with linear and quadratic dependence on speed are achieved by mechanically coupling the induction motor with a DC generator connected to a resistor. By controlling the excitation current of...

This report describes four low-cost alternative power converters for processing the power developed by a doubly fed wound-rotor induction generator for wind energy conversion systems.

We present a solution to torque ripple minimization in switched reluctance motors (SRM) based on set invariance theory. We start from a piecewise affine approximation(PWA) of the overall torque characteristics over rotor angle - phase currents space and derive a PWA motor model. Within it we also take into account finite bandwidth of the phase curr...

During the full load operation of the bulb type generator in HPP Dubrava in Croatia the problem of power oscillations occurs. It is particularly emphasized on one of the two generators where the oscillation is observable on the instruments in the command room. The frequency of power oscillation is 2,083 Hz which is the same as the rotor speed frequ...

In this paper we apply analytical and numerical conformal mapping (CM) to analyze magnetic field originating from permanent magnets and armature winding currents in a slotted air-gap of a surface mounted radial permanent-magnet synchronous motor (SPM) with taking into account the effect of arbitrarily curved motor surfaces. One of the conformal map...

In the paper an overview of achievements known in the world in the area of construction and application of various electric generator systems for wind turbines is given. Using the available literature and other technical data a comparison is made between the following commonly used types of generator: induction, synchronous with classical excitatio...