Modeling Of Electrical Machines Research Articles

Electrical Machines Thermal Model: Advanced Calibration Techniques

Thermal analysis is a key aspect in electrical machine design and for those operating with severe duty where a high-reliability thermal analysis is required. This paper presents a comprehensive analysis of techniques for calibrating generic thermal model of electrical machines. The proposed approach combines two existing experimental methods commonly used in thermal testing of electrical devices. The first method uses a short-duty transient excitation to derive the winding thermal parameters, whereas the second method uses a steady-state excitation to estimate the thermal parameters related to the heat transfer from the winding. Both experimental methods are based on a well-defined heat source provided by a constant current (dc) excitation. For reference, alternative existing methods for calibrating thermal models, are usually combining the winding thermal data predictions and a set of experimentally derived temperatures from dc tests. Such approach, however, might be inadequate if not supported by extensive experimental data. This frequently leads to a significant rate of inaccuracy, thus having a significant impact on the reliability of temperature predictions. The main advantage of newly proposed approach is the reducing of the number of variable parameters and a more systematic calibration process. Additionally, a detailed test procedure for generic thermal model calibration is presented and discussed.

Electromagnetic performance with and without considering the impact of rotation on convective cooling

Accurate thermal modelling of electrical machines is important for electromagnetic performance determination of a design. This study presents the impact of rotation on convective cooling of a through-ventilated motor – a design equivalent to the Tesla S 60 traction motor design. Machine temperatures after steady state with and without considering rotation effects are compared, and the influence on the machine continuous performance is investigated.

Efficient Modeling of Six-Phase PM Synchronous Machine-Rectifier Systems in State-Variable-Based Simulation Programs

Many advanced energy conversion systems utilize multiphase (e.g., six or more phases) electrical machines that feed high-count-pulse (e.g., 12 or more pulses) rectifiers for supplying dc power. Efficient simulation of such power systems in commonly-used state-variable-based programs requires fast and accurate models of electrical machines and power electronic converters with compatible interfaces. As an alternative to the existing $qd$ and voltage-behind-reactance (VBR) machine models, this paper develops a constant-parameter VBR model for six-phase permanent magnet synchronous machines to offer computationally efficient interface. For system-level studies where the switching details of rectifiers can be neglected, a multiple-reference-frame parametric-average-value model is developed for the 12-pulse rectifiers that provides fast simulation and preserves the dominant ac harmonics of interest. The accuracy and numerical efficiency of the proposed machine-converter models are verified using the detailed and alternative existing models.

A Finite-Element Method Framework for Modeling Rotating Machines With Superconducting Windings

Electrical machines employing superconductors are attractive solutions in a variety of application domains. Numerical models are powerful and necessary tools to optimize their design and predict their performance. The electromagnetic modeling of superconductors by finite-element method (FEM) is usually based on a power-law resistivity for their electrical behavior. The implementation of such constitutive law in conventional models of electrical machines is quite problematic: the magnetic vector potential directly gives the electric field and requires using a power-law depending on it. This power-law is a non-bounded function that can generate enormous uneven values in low electric field regions that can destroy the reliability of solutions. The method proposed here consists in separating the model of an electrical machine in two parts, where the magnetic field is calculated with the most appropriate formulation: the H-formulation in the part containing the superconductors and the A-formulation in the part containing conventional conductors (and possibly permanent magnets). The main goal of this work is to determine and to correctly apply the continuity conditions on the boundary separating the two regions. Depending on the location of such boundary -- in the fixed or rotating part of the machine -- the conditions that one needs to apply are different. In addition, the application of those conditions requires the use of Lagrange multipliers satisfying the field transforms of the electromagnetic quantities in the two reference systems, the fixed and the rotating one. In this article, several exemplary cases for the possible configurations are presented. In order to emphasize and capture the essential point of this modeling strategy, the discussed examples are rather simple. Nevertheless, they constitute a solid starting point for modeling more complex and realistic devices.

Use of reluctance network modelling and software component to study the influence of electrical machine pole number on hybrid electric vehicle global optimization

In the paper, the global optimization of hybrid electric vehicle (HEV) components and control is performed using genetic algorithm and dynamic programming. Reluctance network modelling (RNM) is used to describe the behaviour of the electrical machine (EM). The pole number is considered as a design variable in the EM model. A software component is built from this model and is used in Matlab for a sizing by optimization. The influence of the EM pole number on the system optimization is analysed. Contrary to the low differences observed on the energy efficiency of the vehicle, the machine shape is highly impacted.

Mixed-Order Finite-Element Modeling of Magnetic Material Degradation Due to Cutting

As a part of manufacturing of electrical machines, electrical sheets are cut to the desired shape by various cutting techniques, such as punching and laser cutting. This cutting process degrades the magnetic material near the cut edge, which should be included in the finite-element modeling of electrical machines. However, due to the nature of the cutting effects, the existing finite-element modeling of the cutting effect results in computationally heavy simulations. This paper investigates the application of mixed-order elements to model the cutting effect. The second-order nodal triangular elements are used near the cut edge, whereas transition/first-order elements are applied in the remaining solution domain. Furthermore, the accuracy of the presented method is analyzed with the traditional method. According to the simulations, the mixed-order elements returned accurate results significantly faster than the traditional finite-element-based approaches. Furthermore, the effect of the cutting on the machine performance is also studied by comparing its results briefly.

Direct Coupling Method for Coupled Field-Circuit Thermal Model of Electrical Machines

A direct coupling method for coupled field-circuit thermal model of electrical machines is proposed, by which the temperature distributions in the lumped-parameter thermal network and finite-element region are solved simultaneously without iterative calculation procedure. Each thermal resistance in the lumped-parameter thermal network is seen as a one-dimensional finite element. The lumped-parameter thermal network and the finite-element region are linked with the two kinds of boundaries, namely: equivalent convective and equivalent temperature. The users can take advantage of both methods together for more accurate and efficient thermal modeling of the electrical machines using the direct coupling method. An outer-rotor permanent magnet machine with an uneven distribution of ac copper loss in the winding region is used to highlight the benefits of the proposed method. The proposed method is verified by comparing with the indirect method and experiments as well.

Analytical Model of Electrical Machines in Business Software

Analytical Model of Electrical Machines in Business Software

Split ratio optimization of high torque density PM BLDC machines considering copper loss density limitation and stator slot leakage

The paper deals with analytical modeling and design optimization of electrical machines as basic energy conversion elements in power systems. A new method is proposed for designing high torque density PM BLDC (Permanent Magnet Brushless Direct Current) machines with analytically derived optimal split ratio, applicable even to large high pole count machines with considerable impact of the stator slot leakage and with limited value of copper loss density. The method relies on the fact that the product of the electric loading and the current density does not depend on the machine size, while it is primarily determined by the cooling conditions. Moreover, the method also considers the influence of the stator slot leakage on the optimal split ratio. It is shown that the method provides an accurate optimum of the machine design for a wide range of machine sizes and cooling conditions. At the same time, the optimum design can be found for different machine sizes without any need to update the input data. It is shown that the impact of the stator slot leakage is significant for large machines with a high pole count, where an increase of the leakage shifts the optimum towards larger values of the split ratio. The results of the analytical optimization are thoroughly verified by computer simulations using finite element analysis (FEA).

Optimal Sizing of Traction Motors Using Scalable Electric Machine Model

This paper presents a novel method for optimal sizing of traction motors based on vehicle level targets. The method employs a scalable electric machine model inside the multiobjective optimization (MOO) algorithm. A reference motor geometry is scaled in axial and radial directions in the optimization routines according to the values of the design variables. The optimization candidates are the scaled versions of the reference motor and their performance is evaluated using the computationally inexpensive scalable electric machine model. The approach is demonstrated on a vehicle comprising in-wheel motors. The design variables are the rated torque and the base speed of the motor while the considered vehicle level design objectives are the maximization of driving performance and the minimization of energy consumption and unsprung mass. MOO approach considers the objective functions simultaneously and derives the Pareto-optimal solutions in both the objective functions and the design variables domains. The analysis is repeated with New European Driving Cycle and the Worldwide Harmonized Light Vehicles Test Procedure to present the influence of driving pattern on the optimization results.

The Study of Permanent Magnets Synchronous Machine (PMSM) of the Autonomous Electric Power Supply System (ASE), compatible with the Concept of a More Electric Aircraft (MEA)

Based on the analysis and mathematical models of synchronous electric machines (motor/generator), basing on permanent magnets, presented in this paper, the main importance of alternator AC power sources in the form of starter/generator (for conventional aircraft) and in the form of integrated unit starter (motor)/AC synchronous generator S/G AC (with respect to advanced aircraft concept in terms of more electric aircraft) was highlighted. Additionally, through the analysis and selected simulations of the on-board autonomous power supply system of the modern aircrafts, sources of electrical energy (synchronous motor/generator, integrated unit starter/AC generator) were located in board autonomic power system ASE (EPS, PES). Main components of this system are the electro-energetic power system EPS and the energo-electronic power system PES. In addition, the analysis and exemplary simulations of main electricity sources based on mathematical models have contributed to highlighting the main practical applications in accordance with the concept of MEA.

A Sparse Minimal-Order Dynamic Model of Power Networks Based on dq0 Signals

Today the dq0 reference frame is mainly used for modeling and control of traditional electric machines and small power sources. A current challenge is to merge various dq0-based models appearing in recent literature to obtain a complete model of a large power system. To this end, in this paper we propose a model describing the dynamics of large transmission networks based on dq0 quantities. The proposed model is based on a standard network topology, uses sparse system matrices, and is of minimal order. We also demonstrate how this model may be used to construct a small-signal description of a complete system that includes the transmission network, generators, and loads. Results are illustrated on the basis of a long transmission line, and using the 118-bus test case network. This paper is accompanied by a free software package.

Prediction and Measurement of the Heat Transfer Coefficient in a Direct Oil-Cooled Electrical Machine With Segmented Stator

The heat transfer coefficient (HTC) is a critical parameter that is required for accurate thermal modeling of electrical machines. This is often achieved from empirical correlations of ideal geometries or computational fluid dynamics (CFD) simulations. This paper presents a novel technique using double-sided thin film heat flux gauges for measuring the HTC from a direct oil-cooled electrical machine with segmented stator. While thin film gauges are often used in transient measurements of the HTC on gas turbine components, their application to electrical machines has been largely unexplored. This is the topic of this paper. Due to the large viscosity of the coolant, the transient technique was found to be inadequate and a steady-state adaptation for oil-cooled machines was developed. This paper explores the challenges linked with this measurement technique when applied to oil-cooled machines, and develops new nondimensional correlations of the Nusselt number with Reynolds number. These correlations are applicable to machines with different geometries, flow, and coolant properties. The experimental results were compared to CFD simulations and existing pipe flow correlations. It is shown that these underpredict the HTC by approximately 60% at Re = 20. The discrepancy gradually decreases to around 10% at Re = 200.

Electromagnetic and vibration finite element model for early fault detection in permanent magnet machine

Electrical machines are integrated widely in novel applications like hybrid electric vehicles. The field of machine prognosis is expending and evolving rapidly. It aims to assure the proper operation of the machine. Finite element model is the best way to model and optimize electrical machine. In this paper, we will take advantage of the accuracy of finite element method to generate the electromagnetic and vibration model of electrical machine in healthy state and faulty state. We aim to observe the performance of the machine in the two cases and extract a useful measured parameter that will be beneficial in fault prognosis.

Parametric model of electric machines based on exponential Fourier approximations of magnetic air gap flux density and inductance

PurposeThis study aims to present a parametric model of a novel electrical machine, based on a slotless air gap winding, allowing for fast and precise magnetic circuit calculations.Design/methodology/approachApproximations of Fourier coefficients through an exponential function deliver the required nonlinear air gap flux density and inductance. Accordingly, major machine characteristics, such as back-EMF and torque, can be calculated analytically with high speed and precision. A physical model of the electrical machine with air gap windings is given. It is based on a finite element analysis of the air gap magnetic flux density and inductance. The air gap height and the permanent magnetic height are considered as magnetic circuit parameters.FindingsIn total, 11 Fourier coefficient matrixes with 65 sampling points each were generated. From each, matrix a two-dimensional surface function was approximated by using exponentials. Optimal parameters were calculated by the least-squares method. Comparison with the finite element model demonstrates a very low error of the analytical approximation for all Fourier coefficients considered. Finally, the dynamics of an electrical machine, modeled using the preceding magnetic flux density approximation, are analyzed in MATLAB Simulink. Required approximations of the phase self-inductance and mutual inductance were given. Accordingly, the effects of the two magnetic circuit parameters on the dynamics of electrical machine current as well as the electrical machine torque are explained.Originality/valueThe presented model offers high accuracy comparable to FE-models, needing only very limited computational complexity.

Magnetic Modeling of a Linear Synchronous Machine With the Spectral Element Method

The field calculus for electrical machines (EMs) is realized solving subdomain problems. Most often, the latter are solved using either finite element analysis (FEA) or the semi-analytical solution of a Laplace or Poisson equation obtained by separation of variables. The first option can capture complex geometries but becomes slow for high accuracy, whereas the second is fast but limited to simple periodic geometries and linear or infinite permeable materials. This paper presents the 2-D implementation of the spectral element method (SEM) for the modeling of EMs. The polynomial basis functions used to approximate the solution in each domain are reaching exponential convergence similar to the semi-analytical solution. Moreover, each element can be represented by a non-square shape resulting in the possibility to model complex geometries. Following the results in this paper, significantly fewer degrees of freedom are needed for the SEM to achieve the approximation similar to the FEA, and consequently less memory and computational time are required.

Reduced Basis Finite Element Modeling of Electrical Machines with Multiconductor Windings

Finite element (FE) analysis of electrical machines with multiconductor windings can be computationally costly. This paper proposes a solution to this problem, using a reduced basis approach. The field-circuit problem is first solved in a single slot only with a set of different boundary conditions. These precomputed solutions are then used as shape functions to approximate the solution in all slots of the full problem. A polynomial interpolation method is also proposed for coupling the slot domains with the rest of the geometry, even if the geometries or meshes do not fully conform on the boundary. The method is evaluated on several test problems both in the frequency and time domains. According to the simulations, accurate solutions are obtained, 54-90 times faster as compared with the established FE approach.

Modeling of synchronous electric machines for real-time simulation and automotive applications

Recent research in the field of vehicle electrification has indicated that synchronous machines, which include the permanent magnet synchronous machine (PMSM) and the externally excited synchronous machine (EESM), represent a viable solution for electric propulsion. A challenging problem for synchronous machines drives employed in automotive applications is to obtain accurate mathematical models which can deal with parametric variation and which are suitable for real-time simulations and synthesis of control laws. The goal of this paper is to provide a mathematical modeling framework for synchronous machines that can answer to this challenging problem. To this end, using the rotor reference frame, the mathematical models of PMSMs and EESMs are constructed taking into account also the parametric variation due to magnetic saturation and temperature variation. Then, a complex state-space bilinear model for both EESM and PMSM with parametric variation due to magnetic saturation and temperature are developed. Considering the parametric variation as a polytopic bounded disturbance, it is then shown how to split the bilinear complex model in two PWA variable parameter state-space models suitable for a cascade control structure. Based on the developed models, a dynamic unified simulator was constructed in Matlab®/Simulink®. Measurement data obtained in a real test-bench system were used to verify the accuracy of the simulator. The discrete-time simulator was then integrated in an industrial hardware-in-the-loop test bench for real-time evaluation of a current control scheme in EESM drives.

Parallel Performance of Multi-Slice Finite-Element Modeling of Skewed Electrical Machines

The multi-slice method allows approximation of the 3-D phenomena without carrying out a full 3-D analysis, e.g., in skewed radial flux electrical machines. The idea is to divide a 3-D machine into several 2-D finite-element models along the axis, connected by electrical circuits. Here we show how the multi-slice method is perfect for parallel computation; the computation efficiency is close to that of 2-D models in modern parallel hardware. The results are shown to agree with 3-D computation and experimental results.

Rotor Damping Effects in Dynamic Modeling of Three-Phase Synchronous Machines Under the Stator Interturn Faults—Winding Function Approach

Condition monitoring is used for early detection of incipient faults in electrical machines. Accurate modeling and simulation of the faulty machines can help to design effective condition monitoring systems. Three-phase synchronous machines (TSMs) are widely used for electrical power generation at power plants. Winding function theory offers effective, quick, and rather simple method for modeling and simulation of faulty electrical machines; however, this method only includes real windings of the machine. Rotor damping effects have important role in dynamic performance of the TSMs. Fictitious short-circuited windings (damper windings) on the rotor direct and quadrature axes are used to model these effects in the Park's vector model. This paper offers an approach to include similar damper windings in the winding function approach for modeling TSMs with interturn fault in the stator winding. Simulation results show creation or amplification of some frequency components in the stator line current as well as the rotor field current due to the interturn fault whose frequencies are equal to the rotor speed and its integer multiples. The frequency components are also present in the circulating fault current within the shorted turns. Experimental results approve the simulation results.