Time-stepping Finite Element Model Research Articles

Analysis of DC bias characteristics of transformer by using fixed-point time-step FEM and dynamic J–A hysteresis model

The injection of the Direct Current (DC) bias component will lead to oversaturation of the transformer core and affect its safe operation. In this paper, the vector magnetic potential A and winding current I are used as the variables solved in the time-step finite element method to simulate the nonlinear transient magnetization characteristics of the transformer under DC bias, and the fixed-point reluctivity is introduced to deal with the nonlinear iterative problem. The field-circuit coupling relationship is established through the electromagnetic induction law, and the two-dimensional time-step finite element model of the transformer core is found. The dynamic J–A hysteresis model is used to deal with the hysteresis effect of iron cores. The fixed-point reluctivity of difference form is introduced to solve the problem of uneven transition and multi-value of magnetization curve with hysteresis in the iterative process. The determination scheme for the equivalent thickness of the core model and the initial iterative value are discussed. A laminated core transformer is made for experiments, and the accuracy and applicability of the model proposed in this paper are verified by comparing the calculation and experimental results. The influence of different voltages and different DC bias components on the electromagnetic characteristics of the transformer is analyzed.

Coupled Electromagnetic–Fluid–Thermal Analysis of a Fully Air-Cooled Pumped Storage Generator Motor

With the continuous increase in the capacity of the pumped storage generator motor, the overheating of the rotor area is becoming increasingly severe, which has a significant effect on the safe and reliable operation of the machine. The heat dissipation of the machine rotor by fully air-cooled is one of the key technologies to develop the new generation of pumped storage generator motors. In this paper, the electromagnetic field and fluid–thermal coupled field of a pumped storage generator motor are analyzed. The 2D transient time-step finite element model of the electromagnetic field of a pumped storage generator motor is established, and the eddy current loss of damping bars of the rotor is calculated by the finite element method. The additional loss of the rotor pole surface is calculated by analytical method. The mathematical and geometric models of the 3D fluid–thermal coupled field of the pumped storage generator motor are established and calculated. The complex fluid velocity distribution and the temperature distribution at different positions of the rotor under fully air-cooled fanless cooling conditions are investigated in detail. The calculated temperature of field winding is compared with the measured value, and the result shows that the calculated result coincident well with the test data. This research provides the technical reference for the development and temperature rise calculation for large pumped storage generator motors.

Loss Distribution in Stator End Region of Turbo-Generator during Asynchronous Operation after Different Excitation Faults

A turbo-generator during asynchronous operation after the excitation fault can absorb lots of reactive power and result in the increase of the leakage flux and losses in the stator end region. In order to study the loss distribution of the stator end structural components during asynchronous operation, this paper presents a method combining the 2-D field-circuit coupled time-stepping finite element model (FCCTSFEM) with the 3-D transient electromagnetic field in the end region of the turbo-generator. The asynchronous processes of the turbo-generator under the open- and short-circuit faults of field winding are calculated by FCCTSFEM, and 3-D transient electromagnetic field and the losses in the stator end region of the turbo-generator are calculated. From the detailed performance evaluations by the 3-D finite-element analysis, the flux densities and loss distributions of the stator end structural components are compared under different excitation faults. The influence of the metal shield material on the flux densities and losses of the stator end region is studied. The variations of the losses in different stator end structural components are revealed along with the conductivity of the metal shield. The results could provide a theoretical basis for improving the asynchronous operating ability of the turbo-generator after the excitation fault.

Power Tracking Excitation Control and Its Parameter Optimization of Dual-Excited Synchronous Generator

A dual-excited synchronous generator (DESG) with two field windings on the rotor has better dynamic characteristics and high stability. However, the realization of the function needs a reasonable excitation control strategy. In this article, a power tracking excitation control (PTEC) is proposed to improve the operating performances of the DESG. The dynamic processes of a 300-MW DESG with the PTEC are calculated after the disturbance of the torque and reactive power by the time-stepping finite element model, and the results are superior to those adopting the traditional dual-channel excitation control. To further improve the dynamic characteristic of the DESG, the sensitivities of the control parameters of the PTEC to the dynamic characteristic indices are studied. The fuzzy control rules are built based on the sensitivity analysis results and the control parameters are optimized by the fuzzy control method. It revealed the variation laws of the optimized control parameters along with the active and reactive power deviations and their variable rates. The results show that the DESG adopting the optimized control parameters has better dynamic characteristics. The study can provide the theoretic basis for enhancing the system damping effect and suppressing the system oscillation.

Influence of Rotor Slot Wedge Materials on Rotor Losses of Turbogenerator During Loss of Excitation

A short period of steady-state asynchronous operation after loss of excitation can improve the reliability of turbogenerator. The rotor damping structure of the turbogenerator can provide asynchronous torque and, thus, play an important role in improving the asynchronous operating ability. The rotor slot wedges as a part of rotor damping structure often made of aluminum, beryllium bronze, or stainless steel. The different materials of the rotor slot wedges can affect not only the asynchronous operating ability of the turbogenerator but also the rotor losses. The selection of material for the rotor slot wedges is therefore a key factor that should be carefully considered in the design of turbogenerator. In this article, the effect of the rotor slot wedges made of different materials on the asynchronous operating ability, rotor loss densities, and loss distributions of the turbogenerator after loss of excitation is investigated by time-stepping finite element model. The variations of the asynchronous operating ability and the rotor losses are revealed along with the rotor slot wedge conductivity. The rotor regions where the losses are significantly affected by the rotor slot wedge material are obtained. The results provide theoretic basis for improvement of the asynchronous operating ability and reduction of the rotor loss of turbogenerator.

A direct field‐circuit coupled analytical modelling method for permanent magnet motor operation performance analysis

In this paper, the analytical relationship among supply voltage, current, and structure parameters of the permanent magnet (PM) motor is cleverly deduced by using an intermediate-flux linkage. After further consideration of boundary conditions, the direct field-circuit coupled analytical model in integrated matrix form is subsequently constructed. Using this model, the vector potentials and currents of the motor can be calculated simultaneously, and the electromagnetic performance, such as the output torque, winding flux linkage, and so on can be further calculated by the vector potentials. Because the control parameters and motor structure parameters are both considered in the derivation process, the proposed analytical model can be used to analyse the motor operation performance under different control strategies. Its validity is finally verified on a 10-pole/12-slot PM motor. The results of the proposed direct field-circuit coupled analytical model are compared with those of field-circuit coupled time-stepping finite element model and experiment under speed-current double closed-loop and current closed-loop control strategies, respectively. The results of the proposed model are proved well with finite element simulation and experimental results.

Asynchronous Operating Ability of Turbo Generator With Different Field Discharge Resistors

Asynchronous operation of a turbo generator after the loss of field caused by the excitation fault can avoid large-scale blackout and, therefore, improve the reliability of the power systems. In order to consume the magnetic energy stored in the field winding as soon as possible, a field discharge resistor (FDR) is often connected to the field winding after the excitation fault, but it may affect the asynchronous operating ability of the turbo generator and result in the overvoltage of the field winding. In order to study the influence of the FDR on the asynchronous operating ability of turbo generator, a field-circuit coupled time-stepping finite-element model is established, and the experimental validation is performed on a model machine. For a 300-MW turbo generator, the electromagnetic characteristics, such as torque pulsation, air-gap radial flux density, and flux density distribution, are calculated and compared under different FDRs. The variation of the asynchronous operating ability along with the increase of the value of the FDR is revealed. Under the consideration of the withstanding voltage of field winding, the suitable value of the FDR that can improve the asynchronous operating ability is obtained. The results could provide a theoretical basis for improving the asynchronous operating ability of the turbo generator.

Finite‐element calculation of electromagnetic characteristics and steady‐state stability of dual‐excited synchronous generator

The Dual-Excited Synchronous Generator (DESG) has two sets of field windings. The magnitudes and directions of the two field currents can be regulated, so that the excitation magneto-motive force can be in any direction. The electromagnetic characteristics of the DESG may be different with those of the Traditional Synchronous Generator (TSG) for the different rotor structures of the two generators. To obtain better electromagnetic characteristics, a time-stepping finite element model (T-S FEM) of the DESG is established. The air-gap radial flux density, saturation, active and reactive power of the DESG in single- and dual-axis excitation modes are calculated and compared with those of the TSG. The electromagnetic characteristics affected by the different ratio of q-axis field current to d-axis field current are studied. On this basis, an excitation control strategy that can enhance the steady-state stability is proposed, and the steady-state stability limits with and without excitation control are calculated by the T-S FEM. A 10-kW DESG is developed to verify the correctness of the simulation results. The results show that the DESG with dual-axis excitation has better electromagnetic characteristics and stronger reactive power ability, and the steady-state stability limit of the DESG is increased obviously through the excitation control.

Dynamic Simulation of Unbalanced Magnetic Force in Doubly-Fed Induction Machine with Inter-turn Short-Circuited Stator

In the presented work, a dynamic model is provided for the wound-rotor induction machines with short-circuited stator winding. Both inter-turn phase-to-ground and inter-turn phase-to-phase short circuit faults are considered in the provided model. The self- and mutual-inductances of the windings of the faulty machine are the parameters of the provided state-space equations. As well as the machine electromagnetic torque and its stator and rotor currents, the waveform of the unbalanced magnetic force (UMF) in the faulty induction machine is predicted in the provided model. The UMF of the faulty machine is expressed by a static function of the machine currents. The parameters of the UMF function are obtained by using the Maxwell definition. The machine inductances and the air gap flux density distribution are obtained by means of winding function method. Since the exact waveforms of the machine turn functions are considered in computation of the air gap flux density, the special harmonics are taken into account inherently in the provided model. Finally, the developed model is verified by means of the time-stepping finite element model.

Damping and demagnetization analysis of a cylindrical linear electromagnetic buffer under impact load

This paper investigates the damping and demagnetization effect of an electromagnetic buffer (EMB) under impact load. The motional eddy currents are calculated first, and the Ampere circuital theorem is employed to calculate the induced magnetic field. The demagnetization effect is formulated by the magnetic Reynolds number with a correction coefficient km. Following this, the time-step finite element (FE) model of the buffering system is constructed based on the nonlinear B–H curve. The accuracy and feasibility of the FE model is preliminarily verified by small-scale impact test. The characteristics of damping displacement, velocity, damping force and damping coefficient are obtained. Then, the demagnetization effect is analysed by eddy current, magnetic field distribution, through the intensive impact load test at room temperature and time-step FE model. The value of km is obtained through the intensive impact test and the simplified expression of critical velocity. The results show that the demagnetization effect is obvious with the increase of velocity. By introducing the correction coefficient of magnetic Reynolds number, the eddy current demagnetization process is more realistic.

Eddy current loss and its magnetization effect of electromagnetic buffer under intensive impact load

In this paper, a high-energy density electromagnetic buffer (EMB) is studied and analysed for the violent acceleration and high velocity of intensive impact loads. First, the design requirements of the EMB are proposed to select reasonable structure and magnetic circuit parameters. The equivalent current model is used to introduce the primary eddy current affected by demagnetization effect and the induced secondary eddy current. The magnetization process is studied by dividing the conductor tube into the approach end and the departure end. Considering the nonlinear damping and eddy current interaction between primary and secondary, a primary-secondary eddy current loss coupled nonlinear time-step finite element model (FEM) is established to obtain the spatiotemporal distribution characteristics of eddy current. Finally, a test experiment with weak impact, medium impact and intensive impact was carried out. The measured displacement, velocity, damping force, and time nodes responses during buffering are consistent with the established time-step FEM results. The proposed high-energy density EMB can effectively complete the impact buffering process. It is reasonable to obtain the eddy current loss and its magnetization law from the established FEM which is suitable for shock buffering with different impulse strength.

Influence of Rotor Damping Structure on Speed Fluctuation and Asynchronous Operating Ability of Turbogenerators With Loss of Excitation

The asynchronous operation of turbogenerators with the loss of excitation can avoid equipment damage and improve the reliability of power systems. The rotor damping that provides asynchronous torque plays an important role in asynchronous operation. In order to study the influence of rotor damping structures—comprised of damping bars, slot wedges, and core—on asynchronous operating ability of turbogenerators, a time-stepping finite-element model is established and verified by the experiment on a model machine. By using this model, the relationship between the rotor damping structures and speed fluctuation during asynchronous operating process is studied. The asynchronous operating ability is compared in terms of the separate and combined effects of the rotor damping structures. Considering the material options for rotor slot wedges, the influence of aluminum, beryllium bronze, and stainless steel slot wedges on the speed fluctuation and the asynchronous operating ability is also studied. The study shows that the speed fluctuation of turbogenerators with the loss of excitation depends on the asymmetry of the rotor winding structure and the asynchronous operating ability depends on the average damping torques. The results provide theoretical basis for an approach to the enhancement of power system stability by improving rotor damping structures of turbogenerators.

Impact of Real Air-Gap Nonuniformity on the Electromagnetic Forces of a Large Hydro-Generator

In this paper, an accurate two-dimensional time-stepping finite-element model of a large hydro-generator considering a nonuniform air gap for computing the magnetic-flux density and the electromagnetic forces is developed and presented. The 74-MVA industrial hydro-generator is modeled using an actual air gap obtained from a monitoring system having eight capacitive sensors installed on its stator teeth. First, the method consisted in creating geometrically the real air gap in the finite-element model. Then, the latter was experimentally validated. The study showed that the impact of the real air gap on the hydro-generator performance could be found in the electromagnetic force density and in the radial magnetic-flux density as well. Furthermore, the considered real air-gap shape contributes to induce many higher magnitude forces at rotating frequency and its multiples that can excite the natural frequencies of the generator structure. Moreover, the computed dynamic rotating net force considering poles displacement is evaluated as 29% of the average value of the static net force.

Rotor Interturn Short Circuit Impact on Large Hydrogenerator Magnetic Quantities

In this paper, a two-dimensional time-stepping finite-element model of a large hydrogenerator considering field interturn short circuits (ITSCs) default is developed and presented. The study quantified the impact of the degree of rotor ITSC on the radial magnetic flux density, radial force density, unbalanced magnetic pull, and electromagnetic torque of a 74-MVA industrial large hydrogenerator with 76 poles. The proposed numerical model was validated by comparing computed and experimentally measured magnetic flux density of a chosen healthy machine; good agreement between measured and computed results is obtained. Moreover, a detection method using two search coils installed on stator teeth is used. This method allows by inspection of the peak value the quantification of the degree of ITSC. The average value of the magnetic flux density of the defective pole decreases linearly (more than 5%) with the increase of the number of ITSCs; as well, the unbalanced magnetic pull increases with a polynomial of degree 2 with the increase of the degree of ITSC.

The influence of damping resistance on first swing stability of turbine generator considering stator transient

Generally, the ignored stator transient of turbine generator result in the unidirectional electromagnetic torque caused by damping resistance is neglected. While, the unidirectional electromagnetic torque has a braking effect which can reduce the rotor acceleration following the disturbance and improve the stability of power system. With a 300 MW turbine generator as an example, the large disturbance characteristic and First Swing Stability (FSS) limit are calculated by Time-Step Finite Element Model (T-S FEM) and three practical models of turbine generator in this paper. The unidirectional electromagnetic torque caused by stator transient is investigated and its important role in FSS is analyzed. Since there are several material options for damping windings, the influence of damping resistance on the large disturbance characteristic and FSS limit are calculated and compared under different damping resistance. The result shows that the FSS limits calculated by the practical model with stator transient are increased than that without stator transient; the FSS limits of turbine generator with damping windings made from stainless steel are larger than that made from aluminum and beryllium bronze by the four kinds of generator models. The result provides theoretic basis of generator modeling for precise simulation of power systems.

An Analytical Model for the Computation of No-Load Eddy-Current Losses in the Rotor of a Permanent Magnet Synchronous Machine

This paper describes an analytical model for computing the rotor eddy-current losses in the case of permanent magnet synchronous machines, based on a formal resolution of Maxwell’s equations. We focus on the computation of the eddy currents in the machine magnets, in which the diffusion equation is analytically solved, using an accurate electromagnetic model of the stator slotting. The model originality lies in its capacity of taking into account both the diffusion phenomenon and the magnet’s finite length over the pole pitch, imposing that the total current over the magnet’s surface should be zero at each instant. This important problem is studied by solving a Fredholm integral equation. A validation using a 2-D time-stepping finite-element model is also performed, and the obtained losses are shown to be in good agreement with those given by the analytical method, for a shorter computation time.

Fast Steady-State Field-Circuit Model for SMPM-BLdc Motors Driven From 120° and 180° Quasi-Square Wave Inverters

A consistent and computationally efficient finite-element model for the simulation of the steady-state operation of surface-mounted permanent magnet brushless dc motors driven from quasi-square wave inverters is presented. The methodology combines the magnetostatic finite-element and the steady-state time-periodic circuit models with time averaging. A weak field-circuit coupling is established through the effective constant current and lumped parameters estimated at various loading conditions. The performance characteristics, determined via the proposed model for two different motors, are comparable with those obtained from the comprehensive time-stepping finite-element model, with the execution time being approximately a hundred times shorter for the former.

The influence of turbine generator rotor damping structure and material on first swing stability

In this paper, we study the influence of rotor damping structure and material on First Swing Stability (FSS) of turbine generator connected to power system after three-phase short circuit. Considering the complex rotor damping structure of turbine generator, we make crucial improvements in finite element discrete strategy reflecting skin effect of eddy current and establish field-circuit-network coupled time-step finite element model. We test this model by the experiment of 7.5kW model machine. Based on this model, we take a 300MW turbine generator as an example to study the influence of damping bar, rotor iron core and conductive slot wedge on FSS. We investigate the importance of the rotor damping structure to FSS and find its impact is not negligible. By comparing the FSS limits affected by three components of rotor damping structure respectively, we conclude that the effect of rotor slot wedge and iron core is not linear superposition but Coupling relationship. Since we have several rotor slot wedge materials to choose from and the conductivity of these materials is different, we establish the relationship between FSS limit and conductivity of rotor slot wedge. The result shows that the FSS limit gradually increases as the conductivity of rotor slot wedge changes from σal (conductivity of aluminum alloy) to 0.05σal.

Influence of Different Practical Models on the First Swing Stability of Turbine Generators

There are two popular practical models of synchronous generators used in power system simulation, both based on Park equations, defined as assumed A and assumed B respectively, according to the different assumptions. To study the influence of the different models on the first swing stability calculation precision, the physical essence of the two assumptions are revealed in theory, and it is obtained that assumed A takes account of the mutual leakage flux linkage between field and damping windings and neglects the self-leakage flux linkage of damping winding, the opposite of assumed B. Taking a 300-MW turbine generator as an example, first swing stability limits calculated by two practical models are compared; simulation results are verified by the time-step finite-element model. The influence of line reactance and excitation system on first swing stability limits is studied. Results show that the first swing stability limit calculated by the practical model with assumed A is closer to the result of the time-step finite-element model, since assumed A takes account of the larger mutual leakage flux linkage. Therefore, the practical model with assumed A is more accurate. The result provides reasonable reference to select synchronous generator models in power system simulation.

Analysis of Influence to Electric Spindle Losses Caused by Carrier Ratio in Frequency Converter

Aiming at analyzing the influence to ceramic electric spindle and metal electric spindle caused by carrier ratio in frequency converter, in this paper, the time-step finite element model was built based on SPWM method. The changing law of the loss in different carrier ratios were gained by simulation. The result shows that the greatest impact by carrier ratio is solid loss, the least is core loss. The ceramic electric spindle is less impact by carrier ratio than metal electric spindle. Additionally, the corresponding carrier ratio with minimum loss in both ceramic electric spindle and metal electric spindle were found.