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The conventional mechanical design approach of cooling jackets serves the goal of heat dissipation to keep motor temperature below the maximum allowable limit for thermal protection. However, the desired motor performance cannot be effectively achieved by this approach since it only employs heat transfer mechanism. Therefore, a detailed algorithm is developed to provide a constructive cooling design process to achieve the desired performance of a permanent magnet (PM) traction motor. In the preprocessing stage, a two-way electromagnetic (EM) and thermal co-analysis method is developed for preinvestigation of motor temperature and torque to set the goal for the cooling requirement. In the solver, a shape and size optimization method is utilized to get the optimal cooling design for fulfilling the requirement. Further, a multiphysics finite-element analysis model is developed for structural optimization to ensure safe minimal weight of cooling design for the improvement in torque and power density. In the validation step, unlike using only computational fluid dynamics (CFD) to predict motor temperature, a two-way coupling of EM and CFD model is utilized to ensure the design goals of both torque and temperature for several operating conditions. Finally, the design optimization of a cooling jacket for an interior PM synchronous motor is conducted by implementing this algorithm.

Structural analysis of single-sided axial-flux permanent magnet (AFPM) machines for automotive cooling applications is presented in this article. First, the machine configuration and various magnetic materials for this machine, namely, electrical steel (ES) and soft magnetic composite (SMC), are introduced. Second, analytical modeling of the axial electromagnetic force is established to identify the components having a significant influence on the machine vibration and noise. Third, the electromagnetic forces for AFPM machines with different magnetic materials and machine eigenmodes are studied based on finite-element analysis. By using 2-D fast Fourier transform (2-D-FFT), the spatial and temporal orders of the electromagnetic force are obtained to verify the analytical modeling. Finally, by coupling the results from electromagnetic analysis and modal analysis, the vibration and noise for AFPM machines with different magnetic materials are investigated. The results show that the application of different magnetic materials greatly affects the vibration and noise characteristics of single-sided AFPM machines.

Developing a permanent magnet synchronous machine (PMSM) for direct-drive electric vehicle (EV) has challenges such as obtaining high torque density and low torque ripple. The PMSM should have high pole numbers owing to low-speed operation, thereby increasing the use of rare earth magnets and cost. Therefore, in this article a consequent pole (CP) rotor topology is proposed in which the permanent magnet (PM) volume is reduced when compared with conventional surface PMSM (SPMSM). However, replacing south poles in an SPMSM with induced steel poles can increase torque ripple and reduce torque density. In order to improve torque density in a CP PMSM, structural modifications such as multilayer windings and non-ferromagnetic barriers have been proposed in the literature. These modifications increased the torque density while increasing the torque ripple. Therefore, this article proposes a novel two-level optimization method based on gradient descent algorithm, to address the challenges of improving torque density and reducing torque ripple simultaneously in a CP PMSM. Initially, an expression for the magnet pole arc angle is derived for CP PMSM based on magnetic equivalent circuit. A two-level optimization is performed on a baseline CP PMSM to determine the optimal magnet pole arc. The torque production and torque ripples of the optimized design are validated by simulation and experimental results.

Few of the challenges with development of a single on–board motor for direct–drive electric vehicles include high torque density and low torque ripple. Therefore, in this paper, a 36–slot, 34–pole consequent pole six–phase permanent magnet synchronous machine (PMSM) has been optimized to address the aforementioned challenges for direct–drive application. Existing literature on optimization processes that rely solely on finite element models are restricted to three–phase machines only and also take longer computation time. Therefore, this paper proposes a novel optimization approach based on supervised machine learning for six–phase PMSM. In this approach, a non–conventional extended dual dq– frame model that accounts for higher order space harmonics in inductances and flux linkages has been developed and used for accurate computation of average torque and torque ripple of six–phase PMSM. Using the performance characteristics obtained from the extended dual dq –frame model for a set of initial design candidates, support vector regression algorithm is employed for supervised machine learning and increasing solutions in the design space. Furthermore, pareto front is used for selecting optimal machine models with maximum torque density and reduced torque ripple. Multi–objective trade–offs and comparison of initial and optimized designs based on average torque, torque ripple, efficiency and cost are performed.

Permanent magnet (PM) synchronous machines (PMSMs) with concentrated windings (CW) exhibit high content of space harmonics leading to non–sinusoidal distribution of PM flux linkage and phase inductances in addition to the non-sinusoidal wave shape of the induced electromotive force. The ideal single reference frame-based PMSM model considers these parameters to be sinusoidal and does not include the effect of harmonics. Hence, computation of electromagnetic torque using ideal model can lead to deviation from the actual waveform. In this paper, a novel analytical model for electromagnetic torque has been derived using multiple reference frames (MRF) incorporating non-sinusoidal aspects of CW PMSM. Initially, the PM flux linkage and inductances in abc frame are extended by incorporating higher order harmonics. Then, the extended model is transformed into dq –axis using MRF rotating at speeds of dominant harmonics in PM flux linkages and inductances, the fundamental being the electrical rotor frequency. Based on this MRF model, a comprehensive electromagnetic torque model for the CW PMSM is derived. Simulation and experiments are conducted on a CW PMSM to validate the proposed model under different operating conditions.

The 3-phase windings of interior permanent magnet synchronous machines (IPMSMs) used in electric vehicles (EVs) for traction can also be utilized for charging a battery. This integrated charging technology eliminates the on-board charger, leading to a significant reduction in the overall weight and cost of the EV. However, during integrated charging, the induced magnetic fields across the IPMSM windings are unbalanced, which could lead to addition of harmonic current components at the battery side, demagnetization, noise, and vibrations. This paper provides a novel design solution by implementing asymmetrical damper bars in the IPMSM rotor to mitigate unbalanced magnetic fields during integrated charging, and, thus, overcome the aforementioned issues. However, the bars introduced could affect the useful torque production of the machine during traction. Therefore, a magnetic equivalent circuit model based differential evolutionary algorithm is proposed and implemented to optimize the IPMSM rotor structure with dampers to achieve balanced magnetic fields during integrated charging operation and satisfactory traction performance. A comprehensive performance analysis of the optimally designed traction IPMSM equipped with integrated charging capability under both operating conditions is presented in this paper using finite element analysis.

Non-oriented electrical steels are indispensable materials for use in electric motors as magnetic cores. It is desired that the magnetic properties of the steel sheets be optimal and uniform in all the directions in the sheet plane. Thus, knowing the magnetic properties of the steel sheets in all the directions is crucial for the design of the electric motors. However, the magnetic properties of non-oriented electrical steels are usually measured by standard Epstein frame method, which normally only gives the overall magnetic properties in the rolling and transverse directions, and the magnetic properties in other directions are usually not known. In this research, magnetic Barkhausen noise (MBN) technique is utilized to characterize the local magnetic response of the processed non-oriented electrical steel. By rotating the MBN sensor to all the directions in the sheet plane, the local magnetic responses are obtained. The measured MBN is then directly compared to the crystallographic texture (texture factor) measured in the same direction. In this way, the local magnetic response of the steel sheet can be correlated to the crystallographic texture. It was found that magnetic Barkhausen noise technique was able to detect the difference in magnetic response induced by magnetocrystalline anisotropy if the effect of the residual stress can be eliminated. This would provide a potential technique for the characterization of magnetic properties of non-oriented electrical steel.

High power density, high efficiency, wide constant power speed range, lower torque ripple, and manufacturability are the major concerns of future electrical machines for electric vehicle (EV) propulsion applications. Towards this, permanent magnet synchronous machines (PMSMs) are the most relevant candidate for EVs mainly due to their high power/torque density, wide constant power speed range, compact size and higher efficiency than their counterpart induction machines. However, the focus of automakers on phasing out vehicles powered solely by internal combustion engines necessitates further improvement of the performance of EV traction machines. This paper highlights four critical design areas which significantly impact on the performance of PMSMs for EV propulsion application: i) new materials and their feasibility in manufacturing; ii) innovative topologies/structural design solutions; iii) design approaches for efficient thermal management; and iv) optimized design approaches, and provides insights to each area based on recent research and development recorded in the literature.

Stator slot shifting is widely implemented in fractional–slot wound permanent magnet synchronous machines for reduction of high spatial harmonic contents resulting in improved efficiency and flux–weakening performance. Existing method involves using twice the number of stator slots present thereby resulting in a winding topology with a coil pitch of 2. However, in this process, many slot–pole combinations, especially with odd slot numbers are neglected. Therefore, this paper proposes a procedure for stator slot shifting for n–phase fractional–slot wound machines considering all feasible slot–pole combinations. The slot–plot combinations are analyzed for performance attributes including winding factor, total harmonic distortion, minimum cogging torque and maximum torque per unit winding losses. Further, a non–dominated sorting genetic algorithm is used for optimal slot–pole selection for each phase number. The resultant machine performance characteristics of a sample best design candidate is verified using experimental data and finite element analysis.

This paper performs a comprehensive comparative analysis of copper and aluminum wound permanent magnet synchronous machines (PMSMs) for high– speed application. While general studies have been conducted in literature on copper and aluminum windings in terms of conductivity, losses and mass density, the impact of these winding materials on the overall machine performance has not been analyzed broadly. Thus, this paper considers a fractional– slot wound PMSM developed for high–speed traction application and analyzes the performance with copper and aluminum windings in terms of torque density, peak efficiency, operating speed range and variation of winding losses with temperature. Furthermore, in order to assess these machines traction capability, a drive–cycle based analysis is conducted for common drive cycles including urban, highway and worldwide lightweight test cycle (WLTC) for a commercially available Ford Focus vehicle. Performance characteristics in terms of torque–speed characteristics and maximum energy density efficiency were compared for both machines.

Replacing half of the number of poles in a conventional surface permanent magnet synchronous machine (PMSM) reduces the use of rare earth materials delivering similar performance. However, in such a consequent pole configuration certain slot–pole numbers deliver high magnitudes of even order harmonics in the induced EMF waveforms leading to unbalanced magnetic force. Further, utilizing concentrated windings (CW) in the stator adds to this space harmonic content. In literature, slot–pole combinations were selected based on fundamental winding factor, cogging torque and net force on the machine, neglecting space harmonics content in inductance and induced EMF waveforms. Motivated by the drawbacks in the existing methods, in this paper, a novel inductance harmonics factor and EMF harmonics factor have been modelled using winding function method for a consequent pole multiphase CW PMSM. Furthermore, a gradient descent algorithm–based approach is implemented to optimally select slot–pole combination, with reduced inductance and EMF harmonics, for three–, five– and six–phase FSCW PMSM, with little prior knowledge about structural information of the machine. The inductance and induced EMF harmonics for optimal slot–pole combinations obtained from the algorithm are verified using finite element and experimental analysis.

Existing literature on 3-phase combined star-delta winding topologies only focuses on even slot numbers or conventional multiples of 6, since they emulate a 6-phase configuration with a phase difference of 30° between the star and delta connected sets. Contrarily, if a turns ratio of √3 can be achieved with proper coil and turns distribution, unconventional odd slot numbers and non-multiples of 6 can be implemented resulting in various possible design solutions with minimum spatial harmonic contents. Therefore, this paper focuses on modeling and analysis of a novel star-delta winding configuration using unconventional odd slot numbers for fractional-slot wound machines towards maximum torque density and reduced space harmonic content. Initially, a generalized analytical model using winding function theory for any slot-pole combination is presented. Furthermore, a comprehensive comparative analysis of a novel odd slot-pole combination and a conventional topology is presented in terms of spatial harmonic contents, saliency, torque density, torque ripple, rated machine efficiency and overall operating speed range.

Parameter estimation and self-commissioning methods for interior permanent magnet motor drive are moving toward a maturing technology as an integral part of electric drive design. In this paper, parameter estimation as a part of self-commissioning method is presented. This method does not involve high frequency current injection in any part of the test procedure. The proposed method involves a self-commissioning method to calculate the resistance and then proceeds toward online estimation of d-axis and q-axis inductances and permanent magnet flux linkage. At the last stage of the method, it calculates online, the resistance variation with winding temperature for Permanent Magnet motor without saliency.

Multiphase concentrated wound (CW) permanent magnet synchronous machines (PMSMs) have high content of space harmonics in the magneto-motive force (MMF) waveforms. These harmonics result in distorted voltage waveforms and cause additional losses thereby deteriorating the machine's performance. However, the magnitude of space harmonics in multi-phase machines is lesser when compared to three-phase CW PMSM. In order to eliminate and/or reduce space harmonics even further in the MMF waveforms, this paper investigates non-conventional phase angle displacements for a six-phase 36-slot/34-pole CW PMSM. The six-phase CW PMSM considered has two independent three-phase windings. Conventional six-phase CW PMSM have phase angle displacements of 60° (symmetrical configuration) or 30° (asymmetrical configuration) between the two-phase sets. Based on star of slots method, a number of possible phase shifts between the two sets of three phase windings are investigated for reduced MMF harmonics, improved demagnetization and other performance characteristics for the 36-slot/34-pole PMSM and are compared along with conventional phase displacement angles of 60 ° and 30 °.

With advent in permanent magnet synchronous machine (PMSM) structure and inverter topologies, accurate parameter determination is of significance for high-performance control, analysis, and making critical decisions on inter-dependent design parameter variations for machine optimization. However, the machine parameters, including permanent magnet (PM) flux linkage and dq -axis inductances, vary during operation with machine nonlinearities such as magnetic saturation, temperature rise, and the introduction of spatial- and time-harmonic contents contributing toward inaccuracies during machine parameter determination. While classical dq -axis modeling fails to accommodate non-sinusoidal winding distributions and the effects of temperature rise, finite-element analysis (FEA) is computationally expensive and coupling of electromagnetic and thermal analysis including current harmonics becomes complex. Therefore, in this paper, a novel magnetic equivalent circuit model incorporating the effects of temperature rise and current harmonics has been developed for parameter determination of PMSMs. A lumped thermal model is implemented to determine the temperatures at each point of the machine. The proposed coupled electromagnetic and thermal model has been validated for various operating conditions of a fractional-slot distributed wound laboratory PMSM with FEA and experimental investigations.

Most of the demagnetization detection techniques are based on single sensor diagnosis such as analysis of stator current [1], acoustic noise [2], or torque [3]. However, single sensor demagnetization detection has inherent uncertainties due to fault models and motor operating environments. Hence, multi-sensor information fusion is an effective way to solve such uncertainties and improve demagnetization detection accuracy and improve motor control stability. This paper explores the use of acoustic noise and torque ripple for on-line PM demagnetization detection by using the multisensor information fusion method. Both noise and torque signals are first analyzed and processed by wavelet transforms for de-noising and feature value extraction. Moreover, multi-sensor information fusion is applied to estimate the demagnetization ratio based on the support vector machine (SVM) training set. The proposed demagnetization detection approach is experimentally verified on a laboratory PMSM and compared with singlesensor detection method.

Fractional slot concentrated windings (FSCW) permanent magnet synchronous machines (PMSM) have high content of space harmonics in the magnetomotive force (MMF) due to which the harmonic inductance is much larger than the magnetizing inductance [1]. These inductance harmonics lead to high torque ripple and low power factor. In case of FSCW, the coils are full pitched and cannot be chorded like in distributed windings to reduce inductance harmonics and also a suitable rotor structure have small impact on reduction of these harmonics. However, the space harmonic content in the FSCW PMSM vary significantly with the choice of slot-pole combination. Thus, the inductance harmonics can be modeled and minimized using an optimal choice of machine phases (m), stator slot numbers (S) and rotor poles (P). State of the art: [2] has presented the selection of slot, pole and phase numbers for reducing harmonic leakage inductance specifically for single layer CW PMSM. In [3], a detailed procedure for slot-pole selection based on inductances for single and double layer windings are provided. However, these are restricted for odd phase numbers and the selection process is time consuming. In this paper, the impact of winding layers, phase belt, slots, poles, and phase numbers on inductance harmonics has been studied. Further, an Adapative gradient (Adagrad) algorithm based approach is implemented to optimally select these parameters with little prior knowledge about the structural data.

Integrated charging (IC) technology in electric vehicles (EVs) employing conventional power electronics and motor drivetrain components facilitates level 3 fast charging capabilities with reduction in overall weight and cost of the vehicle. However, when the winding inductances of 3-phase interior permanent magnet synchronous machines (IPMSMs) are realized as line inductors for battery charging, due to machine saliency, the magnetic fields produced by the sinusoidal AC supply results in 1) asymmetrical voltages in the air-gap as a function of rotor position and 2) relatively high magnitudes of oscillating torques causing harmful noise and vibrations. This can lead to significant AC losses with risk of permanent magnet demagnetization in the machine. Since the same motor is employed for traction application as well, it is of significance to optimally design the machine for IC operation. Thus, this paper exclusively investigates three IPMSM rotor configurations to be employed for IC operation in EV. This paper firstly presents a conventional dq-axis circuit model based damper design approach implemented for mitigating the saliency effect during IC. Then, a comparative performance analysis of the rotor configurations with damper bars during IC operation on machine saliency; asymmetrical voltage waveforms; oscillating electromagnetic torque; permanent magnet operating point and magnet losses is performed using finite-element analysis (FEA). Results obtained are analyzed and discussed.

In order to design and control a permanent magnet synchronous machine (PMSM) for superior performance over a wide speed range, comprehensive testing methods with accurate measurements are of paramount importance. Moreover, in order to extract the maximum operating capability of the machine with inverter and magnetic saturation, accurate determination of dq-axis inductances over a wide speed range is essential. In this paper, a comparative analysis of three inductance determination methods based on stand-still and moving conditions of the machine is performed. The chosen test methods for measurement and calculation of d- and q-axis inductances are validated experimentally using a laboratory interior permanent magnet synchronous machine (IPMSM) prototype. Merits and demerits of these methods are thereafter analyzed comprehensively in terms of complexity of the methodology implemented, accuracy of parameters determined taking into account effects due to harmonics and temperature, scope and applicability of each of the test methods.

The magnetic properties of non–oriented electrical steel (NOES) vary significantly with respect to the microstructure and crystallographic texture of the final steel sheets, which, in turn, are highly dependent upon the thermomechanical processing parameters used during hot rolling, cold rolling and annealing. This paper performs an exploratory performance analysis of NOES for use in high–speed traction motors, emphasizing the importance of obtaining an appropriate crystallographic texture to achieve the desired magnetic properties by controlling the annealing temperature and holding time. A 3.2% Si NOES annealed at 860°C for 24 hours after hot rolling can result in reduced core losses after cold rolling and final annealing. This material was chosen for the performance analysis of a laboratory scale high–speed, high–power traction motor (45 kW, 10,000 rpm) using finite element analysis (FEA). The motor using the NOES is compared to that using a commercially available grain–oriented electrical steel (GOES) to highlight the feasibility and advantages of NOES for high–speed motor applications. In addition, the motor performance using the NOES is compared to that using commercial NOES to understand the scope of improvement obtained by optimizing the microstructure and texture of the steel sheet.

This paper investigates aluminium and copper windings for a permanent magnet synchronous machine (PMSM) developed for direct–drive electric vehicle (EV) application. Previously, studies have been conducted on comparison of these windings in terms of thermal and electrical conductivity, cost and mass density. However, the impact of these windings on the machine’s performance in terms of efficiency and torque has not been analysed. In this paper, for the same machine volume and geometry, a comparative analysis of PMSMs with copper and aluminium windings has been performed in terms of efficiency, torque, weight, operating speed range, ohmic losses and temperatures. Furthermore, as these machines are developed for direct–drive EV application, drive–cycle-based analysis was conducted for urban and highway cycles for a 2013 Ford Focus vehicle dynamics model. For these drive cycles, analysis in terms of torque speed characteristics and maximum energy density efficiency for both the machines has been performed.

Direct-drive electric vehicle motors have requirements such as high-torque, low-speed and a constant power speed range (CPSR) between 3 and 5 depending on the tire size. Furthermore, these motors must deliver lower cogging torque and torque ripple when compared to conventional electric vehicle high-speed motors due to absence of any damping mechanism. Surface permanent magnet synchronous machines (SPMSMs) with distributed winding configuration are found to favor the aforementioned characteristics for the above application. However, in spite of the lower CPSR requirements for direct-drive application, SPMSMs suffer from poor flux weakening operation. Various rotor structural modifications as well as optimal PM sizing solutions are proposed in literature. However, they fail to take into account the stator slotting effect which significantly affects the flux weakening operation of the machine. Thus, in order to alleviate the challenges involved in realizing a SPMSM as a direct-drive motor, Response Surface Methodology (RSM) is implemented with magnet size and stator slot dimensions as design variables in an effort to optimize the characteristic current and further enhance the CPSR of the machine. Finite element models of the optimal machine are used to verify the output power- and torque-speed characteristics over entire operating range calculated from analytical equations.

Surface Permanent Magnet (SPM) synchronous machines with fractional slot concentrated windings (FSCW) have been found to provide high torque density with low torque ripple and cogging torque, making them suitable for direct-drive electric vehicle (EV) application. This paper initially analyses a 3-phase 36/30 FSCW SPM machine for direct-drive application in terms of its space harmonics, steady-state characteristics and losses over a wide speed range using winding function theory and MTPA control in conjunction with finite element analysis (FEA). It was found that the 3-phase machine produces high space harmonics in the flux density which resulted in increased magnet eddy current loss and high stator leakage inductance which leads to extended constant power speed range (CPSR) as well. Since, the CPSR requirement for a direct-drive EV motor is lesser than that of a high-speed EV motor, there is scope for reducing the stator leakage inductance. Hence, a 6-phase 36/30 FSCW SPM machine employing the same stator, rotor and current rating as that of the 3-phase machine is investigated in an effort to reduce space harmonics, stator leakage inductance and magnet eddy current losses while delivering the desired output characteristics. Also, an analytical method to calculate the 6-phase machine d- and q-axis inductances from winding and slot permeance functions are proposed. Thereafter, a comparative performance analysis is conducted on both the 3-phase and 6-phase machines designed and results are discussed.

Removal of the gear-box from a conventional all-electric vehicle (EV) power-train and incorporating direct-drive topology is expected to improve motor-to-wheel efficiency. Firstly, this paper discusses the merits and challenges of a novel direct-drive scheme employing a single on-board motor in an EV. Thereafter, motor design targets established for such an application in a typical super-mini EV are discussed. A novel bottom-up approach based on maximum-torque-per-ampere (MTPA) control and winding function theories of PM machines is proposed to design an on-board direct-drive surface permanent magnet (PM) machine with fractional-slot concentrated-windings in the stator. A typical direct-drive motor is designed employing the proposed approach and its performance is analyzed using its electromagnetic model in conjunction with finite element analysis and MTPA control scheme over the entire speed range of the motor. Comparative analysis of results obtained from analytical calculations and finite element analysis is performed. It is also shown that the proposed direct-drive scheme in EV is worth considering for advancement of state-of-the-art EV drive-train systems technology.

The beneficial nature of employing power electronics and drive components in conventional electric vehicle (EV) towards level 3 charging capability has propelled research activities towards integrated charging (IC) technology. However, alternating magnetic fields produced in the air-gap by AC charging currents and the stationary nature of the rotor leads to unusual loss and magnet operating characteristics. Since the same permanent magnet synchronous motor (PMSM) will be used for both traction and IC, it is important to understand the machine's behaviour during IC to optimally design the machine for both applications. Hence, this paper exclusively investigates: 1) permanent magnet operation; 2) electrical and magnet losses; 3) temperature rise; and 4) effect of winding inductances on voltages and currents, in both surface and interior traction PMSMs employed for IC in EVs. Results obtained from investigations conducted on laboratory interior and surface PMSMs using finite element analysis and experimentation are analysed and discussed.

Understanding the need for improvement in efficiency of an electric vehicle drivetrain system, this paper exclusively discusses various design aspects of a permanent magnet machine drive for direct-drive electric vehicles (EV). Firstly, the motivation to employ a direct-drive configuration in EV is discussed. Thereafter, initial electric machine rating design considerations for a typical Supermini or B-segment EV employing a direct-drive configuration is discussed. Furthermore, employing an existing stator, investigations are performed through analytical equations and designed machines to understand different permanent magnet machine design aspects with regards to selection of: number of poles, type of permanent magnet rotor, stator winding configuration and number of phases. The study performed here will assist in providing decision points on various structural design indices of the machine before venturing into the FEA based permanent magnet machine design and assessment for the direct-drive EV application.

GaN nanorods were grown by plasma assisted molecular beam epitaxy on intrinsic Si (111) substrates which were characterized by powder X-ray diffraction, field emission scanning electron microscopy, and photoluminescence. The current–voltage characteristics of the GaN nanorods on Si (111) heterojunction were obtained from 138 to 493 K which showed the inverted rectification behavior. The I-V characteristics were analyzed in terms of thermionic emission model. The temperature variation of the apparent barrier height and ideality factor along with the non-linearity of the activation energy plot indicated the presence of lateral inhomogeneities in the barrier height. The observed two temperature regimes in Richardson's plot could be well explained by assuming two separate Gaussian distribution of the barrier heights.