Benchmarks are crucial in electrical machine research to establish reference points for evaluating performance improvements. Identifying key characteristics becomes challenging when there is no data available and measurement techniques are expensive or destructive. Solving the inverse problem to determine material properties, such as in a drone brushless DC motor (BLDC), is ill-posed when only system-level measurements are available, and deterministic methods risk converging to local solutions without indication of uniqueness. This paper proposes a probabilistic approach using Bayesian inference (BI) supported by neural network surrogate models trained on finite element simulation data, to infer the material properties of the permanent magnets, stator, and rotor core non-destructively. The framework demonstrates that BI is applicable to solve this class of inverse problem, delivering parameter estimates with credible intervals, correctly identifying magnet remanence and stator saturation flux density, while revealing the limitations of the arctangent BH model under mixed operating conditions.

This paper proposes a novel post-processing-based control strategy for the flux-weakening operation of variable flux reluctance machines. The proposed method achieves a high-efficiency operation at elevated speeds by determining the optimal values for both d- and q-axis currents together with the dc-field current. A 5 kW variable flux reluctance machine, which develops a continuous maximum torque of 16 Nm at a base speed of 3000 rpm, is modeled using a nonlinear magnetodynamic finite element method model. The nonlinear magnetic characteristics of the laminated rotor and stator steels are simulated in transient to calculate the torque production, back-EMF voltage, and efficiency in relation to the excitation parameters. The proposed control algorithm applies the scattered data interpolation in the post-process to obtain possible combinations of the excitation currents for a specific torque reference. An efficiency map for the analyzed variable flux reluctance machine has been generated at a rotor speed of 5000 rpm, taking both copper and iron losses into account. The findings demonstrate that the proposed control strategy ensures an efficiency exceeding 85% during the flux-weakening operation by manipulating the controllable dc-field current, thereby enabling high-efficiency performance beyond the base speed.

This research proposes a novel current reference selection algorithm based on the most critical performance constraints to achieve improved control of a variable flux reluctance machine (VFRM). The proposed strategy defines the VFRM’s torque ripple, efficiency, and power factor, which are the inherent technological challenges in the torque and efficiency profile of this machine class, as a cost function and aims to select the field and armature current combination that satisfies the torque requirement while minimizing the cost function. These cost function components of the VFRM are initially determined using a transient finite element model (FEM), and the machine representation in the electromagnetic domain is then built using regression based on the generated dataset. The paper includes the details of the representation of the machine parameters, such as the design of experiments for dataset generation and comparison of different regression analyses. Finally, the proposed current reference selection algorithm is compared with the conventional strategies, and its performance and limitations within the entire drive operation range are evaluated.

This paper presents an extended design methodology for variable flux reluctance machines to investigate their potential for heavy-duty vehicle applications. The proposed strategy considers both constant-torque and flux-weakening operations in the design stage to maximize the efficiency, torque density, and power factor and to minimize the torque ripple. The nonlinear magnetostatic finite element analysis is coupled with the single-valued curve of the laminated soft-magnetic rotor and stator for the constant-torque region, while the nonlinear magnetodynamic model, including the classical eddy current and excess fields in the laminated steel, is utilized for the maximum speed operation. A 3-ton fully electric tractor is selected as the benchmark for the feasibility study, where the maximum continuous torque is 200 Nm at a nominal speed of 1600 rpm. It is demonstrated that the optimal high-torque variable flux reluctance machine achieves a torque density of 20 Nm/L and a power factor above 0.7 in both constant-torque and flux-weakening regions. Torque ripple is 10% during continuous operation, with efficiency reaching 90% at the nominal speed and 95% in flux weakening due to reduced copper loss by adjusting the dc-field excitation. Additionally, the optimal design is capable of sustaining 400 Nm overload for up to 65 seconds before reaching the 100 degrees C winding temperature limit.

This paper suggests a maximum-torque-per-watt (MTPW) control approach for a variable flux reluctance machine (VFRM), considering factors like the machine's magnetic saturation and cross-coupling between field and armature windings, which are both located in the stator. The VFRM's torque production, which can be highly affected by saturation, relies on the cross-coupling between field and armature windings, and on the varying field and armature currents. The operating points on the torque-speed locus are determined by different combinations of these currents. The paper presents a strategy to obtain the optimum combination of reference field and armature currents based on a saturation-dependent VFRM model with a focus on minimizing the total copper loss, as it is the most dominant loss component for all operating regions of the VFRM. The proposed method is evaluated in both constant-torque and field-weakening operation regions, by employing both saturation-dependent and saturation-independent VFRM model. It is concluded that the adoption of the saturation-dependent model becomes highly critical in the constant-torque region, whereas the effect of saturation becomes insignificant in field-weakening operation.

This paper proposes a method to include the anisotropic hysteresis characteristics of soft-magnetic laminated steels in the magnetic equivalent circuit (MEC) modeling. The loop-based MEC formulation is improved to handle the nonlinearity of the anisotropic magnetic hysteresis, including the dynamic classical eddy-current and excess fields. The developed MEC model is coupled with both the single-valued $B$ - $H$ curve (SVC) in magnetostatic and the dynamic vector hysteresis model (VHM) in transient analysis. Results with a single elementary MEC element show that an alternating magnetic field in a single direction with a peak value smaller than 300 A/m causes a discrepancy of more than 10% between the magnetic flux densities calculated by the VHM and SVC at 50 and 200 Hz excitation frequencies. Moreover, the proposed modeling technique is verified experimentally using the laminated transformer core of TEAM problem 32. The induced voltage calculated by the MEC model with the VHM demonstrates a good agreement with the measurements, while the MEC model with the SVC calculates inaccurate voltage waveforms. Lastly, the total iron loss dissipated in the transformer's iron core is investigated to verify the proposed technique under different excitation levels and frequencies up to 500 Hz. It is observed that the proposed MEC model with the vector hysteresis characteristics of laminated steels is able to calculate the iron loss accurately, while the conventional single-valued curve method fails to estimate the iron loss.

Nonlinear modeling of soft-magnetic laminated steels is critical for electromagnetic devices operating under magnetic saturation. Although it is possible to introduce the single-valued saturation curve of the soft-magnetic material in the 2-D modeling utilizing an iterative nonlinear solver, the modeling of dynamic magnetic field intensity components, i.e. eddy current and excess fields, requires solving the diffusion equation in 3-D. This article proposes a novel 2-D nonlinear finite element analysis coupled with the dynamic field components using the weak formulation. The proposed technique is applied to a variable flux reluctance machine to develop 100 Nm electromagnetic torque for heavy-duty applications. It is observed that the local flux density discrepancy between the proposed magnetodynamic and conventional magnetostatic models reaches 0.5 T, which causes a 51% discrepancy in the iron loss calculation.

This article presents an extended magnetodynamic finite element modeling technique for 2-D time-dependent electromechanical problems with soft-magnetic laminated steels. The proposed modeling technique includes magnetic vector hysteresis, eddy-current, and excess field components in the system of equations instead of obtaining them in the post-processing. A transient finite element solver is coupled with the Jiles-Atherton vector hysteresis model, while the dynamic components, i.e. eddy current and excess field, are modeled in a weak formulation. The proposed method is experimentally verified using a laminated transformer core similar to TEAM problem 32. It is demonstrated that the proposed magnetodynamic model with vector hysteresis characteristics calculates the flux linkage and iron loss more accurately than magnetostatic and magnetodynamic models coupled with the single-valued magnetization curve. The proposed method estimates the iron loss with a discrepancy of less than 15% up to an excitation frequency of 1500 Hz when it is compared to the transformer core measurements. Later, the experimentally verified magnetodynamic model is employed to model a 48 V, 5 kW variable flux reluctance machine with 16 Nm peak torque under various excitation levels. The machine is tested in laboratory conditions utilizing a field-oriented control algorithm in motor mode at 1000 rpm rotor speed. The average percentage error of the magnetodynamic model with vector hysteresis characteristics is found to be 14% compared to the iron loss measurements while the magnetodynamic and magnetostatic models coupled with the single-valued curve exhibit 25% and 45% average percentage errors, respectively.

This paper proposes a new multi-objective optimization approach to investigate the feasibility of 12/10 variable flux reluctance machines for heavy-duty applications requiring a high-torque generation. Eight parameters describing the geometry of the variable flux reluctance machine are optimized by the tournament selection-based genetic algorithm aiming at the minimum torque ripple, maximum torque density, and efficiency. A 2-D magnetostatic finite element method model is coupled with the nonlinear single-valued magnetization curve of the soft-magnetic material to calculate the objective function. Boundaries of the optimization variables are determined by scaling an existing design. Two constraints are introduced for the winding temperature and developed torque to reduce the number of optimization variables. The torque constraint, 500 Nm, is achieved by selecting a suitable stack length while the constraint of 100 °C maximum winding temperature is satisfied by the applied current density, which a 3-D analytical steady-state thermal model calculates. The magnetic vector hysteresis property of the soft-magnetic material is investigated at the end of the optimization to improve the estimation of torque and efficiency. The optimal variable flux reluctance machine exhibits 20.4 Nm/L torque density, 5.2% torque ripple, and 92.8% efficiency at the base speed of 1200 rpm.

This article presents the magnetostatic analysis of a 12/10 variable flux reluctance machine where the nonlinear magnetic characteristics of the soft-magnetic material are modeled using two different techniques: the single-valued magnetization curve and Jiles-Atherton vector hysteresis modeling. The root mean square and the peak local errors in the magnetic flux density calculated by the single-valued curve are found to be 0.23 T and 0.5 T, respectively. Moreover, the calculated torque under magnetic saturation with a single-valued curve exhibits over 5% error when compared to the Jiles-Atherton model, as it only models uni-directional material characteristics. Lastly, the modeled hysteresis loss of the applied two techniques is compared. The discrepancy between the two models is found to be 25% in magnetic saturation and reaches 48% for large dc-to ac-field excitation ratios in the linear region.

This paper proposes a method to include the anisotropic magnetic hysteresis property of the soft-magnetic material in the magnetic equivalent circuit (MEC) modeling. The loop-based MEC formulation is improved to handle the non-linearity of the anisotropic magnetic hysteresis. Single MEC element of NO27 electrical steel is modeled in 2-D under both rotating and alternating magnetic fields to achieve an accurate iron loss estimation for different excitation frequencies. The developed model is coupled with both the single-valued BH curve (SVC) and the hysteresis BH loop (HL) of the non-linear magnetic material. The magnetic flux density is calculated as the output of the model and used for the comparison of both magnetic saturation calculations. The results show that an alternating magnetic field in a single direction with a peak value smaller than 300 A/m causes a discrepancy of more than 10% between HL and SVC, where the knee point of the SVC is located at 200 A/m. Although the SVC approximation gives realistic results under the deep magnetic saturation, it is not capable of estimating the iron loss accurately. The proposed model with the HL calculates the core loss density as 4 and 28 W/kg for 1000 A/m peak value with 50 and 200 Hz alternating magnetic field excitation, respectively.

The analysis of the velocity skin effect (VSE) in electromagnetic launchers (EMLs) requires a 3-D transient finite element method, unlike magnetic skin and proximity effects. However, VSE is dominant at high speeds, and this creates convergence problems when moving or deformed mesh physics is used in a transient FEM in the 3-D analysis. Commercial finite element software cannot solve the electromagnetic aspects of such a high-speed application with a transient solver in 3-D. Although 2-D approximations can be used, such an approximation overestimates VSE resistance due to geometry simplifications. In this study, we proposed a novel quasi-transient 3-D FEM model where the air-armature region's conductivity is varied to emulate the high-speed motion of the armature. Results showed that the 2-D approximation overestimates the VSE resistance by almost 40%. The proposed VSE model has been included in the EML model, and simulation results are compared for experimental results with different EMLs, EMFY-1, and EMFY-2 and showed good agreement.

This article presents the convergence analysis of the fixed-point method (FPM) to model the nonlinear magnetic characteristics of a 2-D magnetostatic problem. In this study, FPM is used as the iterative nonlinear solver of the hybrid analytical modeling (HAM) technique for the accurate computation of the magnetic field distribution. The benchmark consists of a stator with excitation windings, an air gap, and a slotless mover. The relative errors between two successive iterations are calculated using different error estimators: the attraction force on the mover, the Fourier coefficients defined in the air gap, the magnetic flux density, and the magnetic scalar potential distributions. The effect of the number of mesh elements and harmonics on the accuracy and computational cost of the model is investigated for different levels of magnetic saturation. It is observed that the maximum rate of change in the relative difference of attraction force during the iterations is found to be 0.52 under the magnetic saturation. In addition, the absolute error of the attraction force between the developed hybrid model with FPM and the finite element method (FEM) is achieved to be 0.18%, while HAM has approximately three times less number of degrees-of-freedom when compared to FEM.

This article presents a method for the computation of the incremental inductances in a 12/10 variable flux reluctance machine (VFRM) using the hybrid analytical modeling coupled with a fixed-point nonlinear solver. The variation of incremental and apparent inductance with respect to the dc-field excitation is investigated for both zero and non-zero ac-field excitations. The results show that the difference between both inductance values is not negligible after 25 A/mm 2 dc-current density for the investigated benchmark without the ac field. Moreover, when a non-zero ac field is introduced in addition to the dc-field, the apparent inductance becomes misleading not only under magnetic saturation but also under low excitation in the linear region of the saturation curve. The results obtained with the proposed nonlinear hybrid model are compared with the finite element method in terms of magnetic flux density distribution and incremental inductance value. The root-mean-square discrepancy of magnetic flux density distribution is found to be 37.6 mT. Furthermore, the discrepancy between incremental inductance results of the proposed method and the finite element model is calculated as 1.43%, while the proposed approach requires less post-processing and necessitates ten times less number of degrees-of-freedom.

This article presents a comprehensive comparative study between two nonlinear solvers for the hybrid analytical modeling (HAM) formulation. The Newton-Raphson method (NRM) and the fixed-point method (FPM) are compared in terms of their convergence rate, computational time, and accuracy. A new HAM formulation using the loop-based magnetic equivalent circuit (MEC) instead of the node-based one is proposed to improve the convergence and condition number. The loop-based formulation is coupled with both NRM and FPM nonlinear solvers to perform the magnetostatic analysis of a 12/10 variable flux reluctance machine (VFRM) under local magnetic saturation. It is shown that both methods can achieve convergence for various saturation levels, mesh, and harmonic refinements. However, FPM exhibits a 0.4 larger convergence rate than NRM. It is also observed that the accuracy of NRM decreases under deep magnetic saturation, and the number of required iterations of NRM increases with the model refinement. However, FPM is able to converge for all analyzed refinements with less than six iterations.

Although electromagnetic launchers (EMLs) are superior to classical gun-powder-based launchers, they have to withstand extreme electrical and mechanical conditions. Therefore, the optimal design and precise simulations of these devices are crucial. In this article, a new simulation strategy for EMLs is proposed in order to achieve high accuracy and reduced complexity. The inductance and electromotive force (EMF) variations in the transient, which have a considerable influence on the launch process, are modeled using the finite element method (FEM) coupled with electrical circuit simulation. The proposed method has a good agreement with the experimental results of two EMLs (EMFY-1 and EMFY-2), which have 25- and 50-mm square bores and 3-m-length launchers. The study showed that the hybrid model with transient inductance and EMF calculations showed a good agreement with experiments that have 625 kJ-3.241-MJ input energies.

The utilization of external field windings in electromagnetic launchers provides an additional electromagnetic field between the rails of an electromagnetic launcher which increases the Lorentz force acting on the armature in the acceleration direction. However, additional magnetic field created by the conventional copper windings are very limited due to their low maximum current carrying capability. Therefore, using high temperature superconductors (HTS) with a current carrying capability up to 100 A/mm 2 for the external coils can be used to increase the magnetic field density between rails. This paper presents an optimization study for the design of two external coils with rectangular tape YBCO superconducting wire. The HTS coils are proposed to increase the efficiency of a 3 meter long launcher with 25 mm x 20 mm rectangular bore caliber. The optimization parameters are selected as the magnitude of the DC coil current, the coil position, the number of turns of the coil, and the number of coil layers. Also, the objective function of the optimization is the electromagnetic force acting on the armature, which is dependent of the rail current and B field on the armature. During the operation of the launcher and the external coils, it is critical to prevent quenching of the HTS coils due to the perpendicular and tangential magnetic field on the coils, temperature and current density of the coils. In order to estimate the quench and calculate the objective function, finite element analysis (FEA) is used in 2D. Real coded genetic algorithm (RCGA) is also used as optimization method. The results of the optimization study shows that HTS coil augmentation is feasible for small caliber railguns. The HTS coil position is limited by cryogenic chamber and rail containment dimensions. The maximum coil current is determined by the self field due to cancellation B field generated by the rails and the coils. For 500 kA rail current the force acting on the armature increases from 55 kN to 70 kN with and increase rate of 26%, a muzzle velocity increase from 1650 m/s to 1900 m/s with an increase rate of 12% and a muzzle energy increase from 160 kJ to 210 kJ with and increase rate of 25% when external HTS coil augmentation is used.

Inductive and capacitive types are the most common pulsed power supply (PPS) topologies. In this paper, the comparison of inductive XRAM generator and capacitor-based (C-based) generator topologies is discussed for the excitation of an electromagnetic launcher (EML). In addition, the effect of capacitance or inductance of the storage element on the load current and laucher efficiency is investigated. The circuit simulation results of these PPS topologies are presented, each of which having 200 kJ PPS energy. The EML used in the study has 0.1 kg total mass of projectile, 3 m long rail. Although the energy density of the XRAM generators is larger than C-based PPSs, the design of an XRAM generator is more challenging than C-based PPS due to the large voltage drop of its opening switches. Moreover, the efficiency of the total system is highly dependent on the design of the storage element. For the XRAM generator, the efficiency is limited by the capability of the opening switches. In this study, using RC snubber circuit, the voltage stress on the GTO (gate turn-off) thyristor opening switches of the XRAM generator is decreased to 2 kV peak voltage, which is available in the market.

Increasing renewable energy integration to grid requires inertial support to improve frequency stability of the power system. Inertial support of renewable energy systems requires hardware verification in order to test practical limitations and absence of dynamical grid simulators makes verification studies more challenging. In this study, a test rig which is composed of a DC motor, an AC synchronous generator and an external flywheel, is developed in order to provide a platform in which dynamic properties of an actual power plant can be simulated in the laboratory conditions. A 4 kVA power plant simulator with a field exciter and a speed governor is developed with 1kVA buck converters. The frequency response of the test bench is controlled in parallel with the computer simulations in Digsilent Powerfactory environment. The developed test rig is a low cost and simple solution aimed for experimental studies regarding inertial support of renewable energy systems or power system frequency studies.

Barrel and pulsed power supply modules are two crucial parts of an electromagnetic launcher (EML), in terms of overall efficiency. One of the most important features of the barrel side is the armature geometry. In this paper, the shape of the armature of an EML with 10-MJ current pulse generator, 1000-kA peak current, and 4.5-ms excitation time is optimized by using independent variables to define the exact geometry of the armature. The main goal is to maximize the muzzle kinetic energy of the projectile with 300-g mass including pressure and contact current constraints. Finite-element method (FEM) is used to calculate the muzzle kinetic energy of the EML for different armature geometries. Genetic algorithm is used as the optimization method. Since the contact resistance between the armature and the rail affects the distribution of contact current density, contact resistance is also modeled in FEM. It is observed that armature shape optimization study increases the muzzle kinetic energy to 596 kJ and the muzzle velocity to 1993 m/s.