Design Optimization and Experimental Verification of Permanent Magnet Synchronous Motor Used in Electric Compressors in Electric

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Article Design Optimization and Experimental Veriﬁcation of Permanent Magnet Synchronous Motor Used in Electric Compressors in Electric Vehicles

Soo-Whang Baek 1 and Sang Wook Lee 2,*

1 Department of Automotive Engineering, Honam University, 417 Eodeung-daero, Gwangsan-gu, Gwangju 62399, Korea; [email protected] 2 Department of Mechanical Design Engineering, Wonkwang University, 460 Iksan-daero, Iksan-si, Jeollabuk-do 54538, Korea * Correspondence: [email protected]; Tel.: +82-63-850-6968

Received: 9 April 2020; Accepted: 3 May 2020; Published: 6 May 2020

Featured Application: Optimal design of permanent magnet synchronous motors (PMSMs) used in electric compressors in electric vehicles. Based on the proposed optimization method, the eﬃciency and cogging torque characteristics of the PMSM can be improved.

Abstract: In this study, a shape design optimization method is proposed to improve the efficiency of a 3 kW permanent magnet synchronous motor (PMSM) used in an electric compressor intended for use in an electric vehicle. The proposed method improves the efficiency performance of the electric compressor by improving the torque characteristics of the initial PMSM model. The dimensions of the rotor were set as the design variables and were chosen to maximize efficiency and reduce cogging torque. During the determination of the design points with conventional Latin hypercube design, the experimental points may be closely related to each other. Therefore, the optimal Latin hypercube design was used to optimally distribute the experimental points evenly and improve the space filling characteristics. The Kriging model was used as an interpolation model to predict the optimal values of the design variables. This allowed the formulation of more accurate prediction models with multiple design variables, complex reactions, or nonlinearities. A genetic algorithm was used to identify the optimal solution for the design variables. It was used to satisfy the objective function and to determine the optimal design variables based on established constraints. The optimal design results obtained based on the proposed shape optimization method were confirmed by finite element analyses. For practical verification, the optimal model of the prototype PMSM of an electric compressor was manufactured, and a 1.5% improvement in its efficiency performance was confirmed based on an experimental dynamometer test.

Keywords: optimal design; metamodeling; electric compressor; permanent magnet; synchronous motor

1. Introduction As the environmental pollution of internal combustion engine vehicles becomes serious, interest in eco-friendly vehicles and hybrid electric vehicles (HEVs) are increasing worldwide [1]. Among them, electric vehicles (EVs) are in the spotlight as pollution-free automobiles that reduce fuel eﬃciency [2] and have no harmful emissions because they use only electric energy in the system instead of the engine of an internal combustion engine [3]. Therefore, EV has been proposed as one of the methods to solve fossil fuel depletion and environmental problems, and research on it has been actively conducted worldwide [4].

Appl. Sci. 2020, 10, 3235; doi:10.3390/app10093235 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 3235 2 of 16

Recently, the PMSM has been used in parts for electric vehicles because it has excellent efficiency characteristics compared with induction motors [5]. PMSM is a structure in which a permanent magnet is embedded in the iron core of the rotor, and the magnetic flux weakening operation area can be widened depending on the difference in inductance of the d-q axis [6]. Because of these advantages, it is widely used in EV or HEV where variable speed operation is required [7]. An electric compressor for air conditioning of electric vehicles has been developed, and by applying high-efficiency PMSM to the compressor, it has the advantage of increasing fuel efficiency regardless of the vehicle’s driving speed [8]. Optimal design is essential to meet the various design requirements of PMSM. Optimal design is a method of finding the value of a design variable and obtaining an optimal solution within a limited design area [9]. The previous researches on the optimal design of PMSM can be divided into two categories. First, there are studies using the magnetic equivalent circuits (MEC) model [10,11]. In [10], it was proposed as a study on optimization using MEC model. It has been reported that the MEC optimization method combined with the optimization algorithm can optimize the volume and energy loss of PMSM. In addition, a novel MEC model of PMSM was developed to obtain maximum efficiency, minimum weight and price [11]. However, MEC-based design has a problem in that it is difficult to accurately consider the nonlinearity of parameters. Second, there are studies that combine numerical analysis methods of electrical devices such as finite element analysis (FEA) with optimal design algorithms [12,13]. FEA was performed to take into account the nonlinearity of permanent magnets and electrical steel sheets, which are difficult to consider in MEC. In [12], an optimal design of PMSM based on dynamic characteristics and finite element analysis of PMSM was performed. Design variables that influenced the efficiency characteristics of PMSM were selected and the efficiency and response characteristics were improved through experiments. In [13], the authors announced the optimization design process of PMSM for electric compressors of air conditioners applied to electric vehicles and hybrid vehicles. Research on the optimal design of PMSM using the response surface method has been carried out. In particular, the response surface method is often used in the optimization design of permanent magnet motors. The response surface method typically uses a second order polynomial regression model. However, it is difficult to accurately predict the optimum value because the response surface method becomes highly nonlinear and yields an unstable high-order prediction function. As a similar study related to PMSM, the rated efficiency was improved through the optimum design of 110 W small brushless direct current (BLDC) motor [14]. In addition, a study was conducted to improve the performance of the electric variable valve timing system for improving fuel efficiency and emission of automobiles [15]. Cogging torque is one of the most representative components of torque ripple in PMSM. This phenomenon can be a critical issue to automotive applications that need precision control of the PMSM and are sensitive to noise and vibration. Therefore, recently, studies to improve efficiency and reduce cogging torque have been actively conducted, and mainly focused on reducing the cogging effect by adjusting the combination of pole slot number, pole arc, and core shape [16,17]. Furthermore, the study of [18] performed multi-purpose shape optimization of PMSM based on FEA and particle swarm optimization algorithms. Unlike the existing methods, the proposed rule of start point selection takes an advantage of minimizing the search time. A study has been conducted on the multi-purpose optimized design PMSM of fractional slotted windings [19]. The optimization results demonstrated the accuracy of the proposed model with comparison to numerical models such as FEA, but with much faster computational performance which makes it much more suitable to be used in evolutionary optimization design approaches. Most of the previous studies were applied to the optimal design using metamodels created in one way [20,21]. In general, FEA’s design of experiment (DOE) consists of a modeling process using CAD Appl. Sci. 2020, 10, 3235 3 of 16 tools, an FEA analytical condition setting process, a FEA process, and a post-process for extracting and configuring results. A lot of DOE has to be done to get reliable and optimal design results. AsAppl. a Sci. related 2020, 10 study,, x FOR PEER Taguchi REVIEW method was used to optimize the efficiency and cogging3 torqueof 15 of BLDC motors used in automotive electric oil pumps. However, to obtain DOE results, 336 FE analyses extracting and configuring results. A lot of DOE has to be done to get reliable and optimal design for five design variables were required [22]. results. ThisAs study a related differs study, from Taguchi previous method studies was givenused to that optimize five designthe efficiency variables and werecogging selected torque forof the DOEBLDC and 54 motors experiments used in automotive were performed. electric Tooil improvepumps. However, the efficiency to obtain of theDOE design results, variable 336 FE analyses distribution, the optimalfor five design Latin hypercubevariables were design required (OLHD) [22]. [23,24] was used with an equal number of levels for all the designThis study variables differs that from has previous a better studies fill performance given that five than design Latin variables hypercube were selected design (LHD)for the [25]. NumerousDOE and studies 54 experiments have been publishedwere performed. on metamodeling To improve conductedthe efficiency based of the on thedesign application variable of a singledistribution, method [26 the,27 optimal]. However, Latin hypercube there are design suitable (OLHD) metamodels [23,24] was for used each with optimal an equal design number problem. of Correspondingly,levels for all the the design metamodels variables that need has to abe better written fill performance and compared than Lati in variousn hypercube ways. design Given (LHD) that the prediction[25]. Numerous performance studies of thehave metamodel been published affects on the metamodeling reliability of conducted the optimal based design, on the it application is necessary to of a single method [26,27]. However, there are suitable metamodels for each optimal design problem. evaluate the accuracy of each metamodel. Therefore, we evaluated three representative metamodels, Correspondingly, the metamodels need to be written and compared in various ways. Given that the includingprediction Kriging performance [28], multilayer of the metamodel perceptron affects (MLP) the reliability [29], and of ensemble the optimal of design, decision it is tree necessary (EDT) [30], and comparedto evaluate thethe metamodelingaccuracy of each results. metamodel. The predicted Therefore, performances we evaluated ofthree the metamodelsrepresentative were evaluatedmetamodels, and compared including basedKriging on [28], the multilayer root-mean-square perceptron error(MLP) (RMSE) [29], and test, ensemble the results, of decision and tree Kriging was selected(EDT) [30], as and the compared best metamodel. the metamodeling In this paper, results. Kriging The predicted model performances can evaluate of the models metamodels with many designwere variables, evaluated complex and compared responses, based or strongon the root-m nonlinearitiesean-square more error accurately. (RMSE) test, the results, and TheKriging genetic was selected algorithm as the (GA) best [31 metamodel.] was used In for this the paper, determination Kriging model of thecan optimalevaluate designmodels variableswith basedmany on the design objective variables, functions complex and responses, constraints or strong set for nonlinearities the optimization. more accurately. To verifyThe genetic the validity algorithm of the (GA) proposed [31] was optimizationused for the determination design results, of the the optimal characteristics design variables of the initial based on the objective functions and constraints set for the optimization. and the optimal models (back-electromotive force (EMF), cogging torque, and torque ripple) were To verify the validity of the proposed optimization design results, the characteristics of the initial evaluatedand the based optimal on models finite element(back-electromotive analyses, andforce the(EMF), results cogging were torque, compared. and torque To verifyripple) feasibility,were the proposedevaluated optimizationbased on finite methodelement analyses, was applied and the to results the design were ofcompared. a 3 kW To PMSM verify used feasibility, in an the electric compressor,proposed and optimization the method’s method performance was applied was to comparedthe design withof a the3 kW results PMSM obtained used in froman electric the initial modelcompressor, with finite and element the method’s analysis. performance Finally, prototype was compar PMSMsed with were the fabricatedresults obtained and dynamometerfrom the initial tests weremodel performed with finite to confirm element the analysis. suitability Finally, of the prototype proposed PMSMs shape were optimization fabricated design.and dynamometer tests were performed to confirm the suitability of the proposed shape optimization design. 2. PMSM for Electric Compressor 2. PMSM for Electric Compressor The compressor of a vehicle operated by a conventional internal combustion engine is driven by the drivingThe force compressor of the engine. of a vehicle Correspondingly, operated by a conventi when theonal compressor internal combustion is operating, engine the is driven output by power the driving force of the engine. Correspondingly, when the compressor is operating, the output of the engine is reduced. In addition, given that the engine contains various mechanical components, power of the engine is reduced. In addition, given that the engine contains various mechanical unnecessary power consumptions occur that lead to increased fuel consumption. To solve this problem, components, unnecessary power consumptions occur that lead to increased fuel consumption. To an electricsolve this compressor problem, drivenan electric by compressor a motor was driven developed. by a motor The was electric developed. compressor The electric has ancompressor advantage in that ithas can an be advantage mounted in onthat an it can electric be mounted vehicle on based an electric on the vehicle utilization based ofon thethe utilization energy of of the the high-voltage energy batteryof ofthe the high-voltage electric vehicle. battery The of systemthe electric used vehicle. to cool The an electricsystem vehicleused to iscool composed an electric of avehicle high-voltage is battery,composed an inverter, of a high-voltage and an electric battery, compressor, an inverter, and and is an shown electric in compressor, Figure1. and is shown in Figure 1.

FigureFigure 1. 1.Cooling Cooling componentscomponents of of an an electric electric vehicle. vehicle. Appl. Sci. 2020, 10, 3235 4 of 16 Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 15

FigureFigure2 2 shows shows the the shape shape of of an an initial initial PMSM PMSM model model used used for for an an electric electric compressor. compressor. The The PMSM PMSM selectedselected forfor thisthis studystudy hashas anan interiorinterior permanentpermanent magnetmagnet (IPM)(IPM) typetype withwith anan 88 polepole/12/12 slotslot structurestructure withwith aa concentrated concentrated winding winding method method in considerationin consideratio ofn vibrationof vibration and and noise. noise. Initial Initial designs designs have beenhave establishedbeen established to satisfy to satisfy the given the speciﬁcations. given specificatio Thens. current The densitycurrent ofdensity the stator of the winding stator iswinding designed is designed to be less than 72 Arms/mm2 at maximum speed. The reference temperature condition is 20 to be less than 7 Arms/mm at maximum speed. The reference temperature condition is 20 ◦C. The speciﬁcations°C. The specifications of the initial of the model initial are model listed are in Tablelisted1 in. Table 1.

FigureFigure 2.2.Shape Shape of of conventional conventional permanent permanent magnet magnet synchronous synchronous motor (PMSM) motor for(PMSM) an electric for compressor.an electric Tablecompressor. 1. Speciﬁcations of the initial model of permanent magnet synchronous motor (PMSM) (rpm: revolutions per minute, EMF: electromotive force). Table 1. Specifications of the initial model of permanent magnet synchronous motor (PMSM) (rpm: revolutions per minute, EMF: electromotiveItems force). Unit Value

ItemsInput voltageUnit VValue 380 Rated speed rpm 6000 Required specification Input voltage V 380 Rated outputRated speed power rpm W 6000 3000 Required specification OperationRated output frequency power W Hz 3000 400 Stator’sOperation outer diameterfrequency Hz mm 400 93 Stator’sStator’s inner outer diameter diameter mm mm 93 51 Rotor’sStator’s outer inner diameter diameter mm mm 51 50.2 Mechanical dimension Rotor’s outer diameter mm 50.2 Mechanical dimension Shaft diameter mm 20 AirShaft gap lengthdiameter mm mm 20 0.4 StackAir gap length length mm mm 0.4 60 Stack length mm 60 CoilCoil turns turns 40 40 ElectricalElectrical dimension dimension mmmm CoilCoil thickness thickness 0.9 0.9 ElectricalElectrical steel steel 35PN23035PN230 MaterialMaterial - - PermanentPermanent magnet magnet N42UH N42UH Back-EMF(@1000rpm) Vrms 27.8 Back-EMF(@1000rpm)Cogging torque(peak to peak) Nm V rms 0.3479 27.8 Characteristics CoggingTorque(@rated torque(peak speed) to peak) Nm Nm 4.775 0.3479 Characteristics Torque(@ratedInput current(@rated speed) speed) Arms Nm 12.85 4.775 InputEfficiency(@rated current(@rated speed) % Arms 91.40 12.85 Efficiency(@rated speed) % 91.40 3. Design Optimization 3. Design Optimization 3.1. Rotor Shape Optimization Process 3.1. Rotor Shape Optimization Process The proposed optimization process was performed by taking into account the rotor shape of the The proposed optimization process was performed by taking into account the rotor shape of the PMSM as a design variable and by taking into account the efficiency and cogging torque. The PMSM as a design variable and by taking into account the e ciency and cogging torque. The proposed proposed optimization process for the design of PMSM isffi illustrated in Figure 3. optimization process for the design of PMSM is illustrated in Figure3. The proposed optimization process is as follows. Depending on the design specifications of the initial model, design variables are selected that improve the efficiency and reduce cogging torque characteristics. To execute the DOE, the design variables were determined using OLHD. The efficiency and cogging torque characteristics of the sampling models were calculated based on finite element analyses. To ensure the accuracy of the DOE results, metamodeling of multipurpose functions and constraints used the following three techniques: Kriging model, MLP, and EDT. For the evaluation of the predictive performance of the metamodel, the best approximation modeling method was adopted Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 15

Appl. Sci. 2020, 10, 3235 5 of 16

based on the comparison of the results of RMSE. The objective functions and constraints were set to achieve the required target speciﬁcations. To obtain the values of the design variables of the optimal model, metamodeling results were obtained with the optimal GA algorithm. Finally, if the target designAppl. Sci. result2020, 10 does, x FOR not PEER appear, REVIEW the optimization process is restarted by adjusting the design variables.5 of 15

Figure 3. Proposed optimization process.

The proposed optimization process is as follows. Depending on the design specifications of the initial model, design variables are selected that improve the efficiency and reduce cogging torque characteristics. To execute the DOE, the design variables were determined using OLHD. The efficiency and cogging torque characteristics of the sampling models were calculated based on finite element analyses. To ensure the accuracy of the DOE results, metamodeling of multipurpose functions and constraints used the following three techniques: Kriging model, MLP, and EDT. For the evaluation of the predictive performance of the metamodel, the best approximation modeling method was adopted based on the comparison of the results of RMSE. The objective functions and constraints were set to achieve the required target specifications. To obtain the values of the design variables of the optimal model, metamodeling results were obtained with the optimal GA algorithm. Finally, if the target design resultFigure does 3.not Proposed appear, optimization the optimization process. process is restarted by adjusting the design variables. AccordingAccordingThe proposed to to this thisoptimization optimization optimization proce process, process,ss is as the follows. the mechan mechanical Dependingical dimensions dimensions on the ofdesign the of thestator specifications stator and androtor, of rotor, i.e., the thei.e.,initial diameter the model, diameter of design the of thecore variables core and and the are the stack selected stack length, length, that were im wereprove fixed. fixed. the Five Five efficiency design design variables and variables reduce of of thecogging the rotor rotor torqueshape shape werecharacteristics. selected as Toshown execute in Figure the 4 DOE,4.. the design variables were determined using OLHD. The efficiency and cogging torque characteristics of the sampling models were calculated based on finite element analyses. To ensure the accuracy of the DOE results, metamodeling of multipurpose functions and constraints used the following three techniques: Kriging model, MLP, and EDT. For the evaluation of the predictive performance of the metamodel, the best approximation modeling method was adopted based on the comparison of the results of RMSE. The objective functions and constraints were set to achieve the required target specifications. To obtain the values of the design variables of the optimal model, metamodeling results were obtained with the optimal GA algorithm. Finally, if the target design result does not appear, the optimization process is restarted by adjusting the design variables. FigureFigure 4. 4. RotorRotor shape shape design design variables. variables. According to this optimization process, the mechanical dimensions of the stator and rotor, i.e., the diameterTable2 shows of the the core range and of the the stack five designlength, variables were fixed. used Five for design the optimization variables of thethe rotorrotor shapeshape Table 2 shows the range of the five design variables used for the optimization of the rotor shape ofwere the selected PMSM. asX1 shownis the magnetin Figure length, 4. X2 is the magnet width, X3 is the distance between the center of the PMSM. X1 is the magnet length, X2 is the magnet width, X3 is the distance between the center and the inner diameter of rotor, X4 is the distance between the center and the magnet, and X5 is the and the inner diameter of rotor, X4 is the distance between the center and the magnet, and X5 is the distance between the center and the barrier. These design variables were chosen to optimize the rotor distance between the center and the barrier. These design variables were chosen to optimize the rotor shape because they affect the efficiency and cogging torque of the PMSM. In addition, the ranges of the shape because they affect the efficiency and cogging torque of the PMSM. In addition, the ranges of upper and lower limits for each design variable are also listed. The design variables and ranges were the upper and lower limits for each design variable are also listed. The design variables and ranges determined based on the consideration of the PMSM’s manufacturability. were determined based on the consideration of the PMSM’s manufacturability.

Figure 4. Rotor shape design variables.

Table 2 shows the range of the five design variables used for the optimization of the rotor shape of the PMSM. X1 is the magnet length, X2 is the magnet width, X3 is the distance between the center and the inner diameter of rotor, X4 is the distance between the center and the magnet, and X5 is the distance between the center and the barrier. These design variables were chosen to optimize the rotor shape because they affect the efficiency and cogging torque of the PMSM. In addition, the ranges of the upper and lower limits for each design variable are also listed. The design variables and ranges were determined based on the consideration of the PMSM’s manufacturability.

Appl. Sci. 2020, 10, 3235 6 of 16

Table 2. Ranges of the design variables

Parameters Lower (XL) Upper (XU) Unit Remark

X1 12 15 mm Magnet length X 1.5 3.0 mm Magnet width Appl. Sci. 20202 , 10, x FOR PEER REVIEW 6 of 15 Distance between the center and the inner X 22 25 mm 3 diameter of rotor Table 2. Ranges of the design variables X4 22 25 mm Distance between the center and the magnet

ParametersX5 Lower20 (XL) Upper (X 23U) Unit mm Distance between Remark the center and the barrier X1 12 15 mm Magnet length X2 1.5 3.0 mm Magnet width The objectiveX3 function22 used 25 to maximize mm Distance eﬃciency between is expressedthe center and by the Equationinner diameter (1). of rotor In addition, the constraintX4 that should22 be lower 25 than mm the cogging Distance torque between of the the initialcenter and model the magnet of 0.3479 Nm, as indicated byX5 Equation 20 (2). 23 mm Distance between the center and the barrier

ObjectiveThe objective function: function used to maximize efficiency is expressed by Equation (1). In addition, the • constraint that should be lower than the cogging torque of the initial model of 0.3479 Nm, as indicated by Equation (2). • Objective function: Maximize the eﬃciency. (1)

Constraints: Maximize the efficiency. (1) • • Constraints:

CoggingCogging torque torque< <0.3479 0.3479 NmNm (2) (2)

3.2. Design of Experiment 3.2. Design of Experiment SamplingSampling points points were were selected selected withwith thethe OLHD.OLHD. OLHD OLHD has has the the advantag advantagee of of distributing distributing the the experimentalexperimental points points evenly evenly usingusing optimaloptimal conditions.conditions. This This technique technique has has improved improved projection projection propertiesproperties and and spatial spatial fill fill properties properties comparedcompared withwith the existing existing LHD. LHD. The The number number ofof experimental experimental pointspoints was was determined determined based on on consideration consideration of ofthe the range range of design of design variables variables listed listedin Table in 2. Table The 2. Thetotal total number number of samples of samples was determin was determineded to be 54. to This be 54. number This was number chosen was to ensure chosen that to ensurea sufficient that a suffinumbercient numberof experimental of experimental points ex pointsisted for existed all five for design all five variables. design variables.Figure 5 shows Figure the5 shows sample the sampledistribution distribution maps mapsof all ofthe all design the design variables. variables. The sample The sample points points were chosen were chosen so that so there that were there no were nooverlapping overlapping points. points.

(a) (b)

FigureFigure 5. 5.Sample Sample distribution distribution maps maps ofof optimaloptimal Latin hypercube design design (OLHD): (OLHD): (a ()a )XX1; 1(;(b)b X) 2X; (2c;() Xc)3;X 3; (d)(dX)4 X;(4e; ()eX) 5X.5.

The efficiency and cogging torque characteristics of the samples selected by OLHD were calculated via FE analyses, and are listed in Appendix A. The efficiency and cogging torque characteristics of each sample were obtained based on two-dimensional (2D) FE analyses.

Appl. Sci. 2020, 10, 3235 7 of 16

The efficiency and cogging torque characteristics of the samples selected by OLHD were calculated via FE analyses, and are listed in AppendixA. The e fficiency and cogging torque characteristics of each sample were obtained based on two-dimensional (2D) FE analyses. Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 15 3.3. Metadmodeling 3.3. Metadmodeling BasedBased on theon the DOE DOE results results described described inin thethe previous section, section, we we created created a metamodel a metamodel for the for the objectiveobjective function function and constraint.and constraint. Most Most of the of existingthe existing studies studies have have proposed proposed metamodels, metamodels, but accuracybut evaluationsaccuracy were evaluation not performed.s were not Furthermore,performed. Furthermore, searches for searches optimal for values optimal of designvalues variablesof design have beenvariables conducted. have Therefore, been conducted. to evaluate Therefore, the metamodelto evaluate the accuracy, metamodel the bestaccuracy, metamodel the best wasmetamodel selected by comparingwas selected the RMSE by comparing test outcomes the RMSE according test outcomes to the eaccordingfficiency to and the cogging efficiency torque and cogging characteristics. torque Thecharacteristics. Kriging model [28], an interpolation model type, passes the test points accurately and is suitable for The Kriging model [28], an interpolation model type, passes the test points accurately and is approximation without random errors. Therefore, a numerically robust model was provided. The estimation suitable for approximation without random errors. Therefore, a numerically robust model was equation for the Kriging model was defined to eliminate bias, thus minimizing error variance. provided. The estimation equation for the Kriging model was defined to eliminate bias, thus MLPminimizing [29] is error a type variance. of deep learning algorithm and has the advantage of expressing a nonlinear relationshipMLP between [29] is a inputtype of and deep output learning variables. algorithm In and particular, has the advantage metamodels of expressing can be created a nonlinear even when thererelationship are plenty between of data. input However, and output if there variables. are many In particular, parameters metamodels that depend can be on created the know-how even when of the user,there accuracy are plenty may of be data. deteriorated However, and if there training are ma timeny parameters may be required. that depend on the know-how of the Theuser, EDTaccuracy [30] may has be a featuredeteriorated that and allows training the generationtime may be ofrequired. multiple decision trees (DTs) and the predictionThe of anEDT output [30] has value a feature as the that average allows value the generation of all the outputsof multiple predicted decision by trees each (DTs) DT forand a the specific inputprediction value. The of instabilityan output value and performance as the average variance value of of all the the DT outputs model predicted were reduced by each compared DT for a with specific input value. The instability and performance variance of the DT model were reduced the use of a single DT. Additionally, the predictive power was improved and the performance was compared with the use of a single DT. Additionally, the predictive power was improved and the excellent in large datasets. However, parameters (depth, number of DTs, etc.) must be determined in performance was excellent in large datasets. However, parameters (depth, number of DTs, etc.) must advance.be determined As the depth in advance. of DT As becomes the depth deeper, of DT becomes the DT modeldeeper, becomesthe DT model complicated becomes complicated and leads to an increaseand ofleads the to calculation an increase complexity.of the calculation Figure complexity.6 shows Figure the conceptual 6 shows the diagram conceptual of the diagram Kriging of the model, MLP,Kriging and EDT model, used MLP, for metamodelingand EDT used for in metamodeling this study. in this study.

(a) (b) (c)

FigureFigure 6. Conceptual 6. Conceptual diagram: diagram: (a ()a) Kriging; Kriging; ((b) multilayer perceptron perceptron (MLP); (MLP); (c) ensemble (c) ensemble of decision of decision tree (EDT).tree (EDT).

GivenGiven that that the the predictive predictive performance performance ofof the me metamodeltamodel affects aﬀects the the reliability reliability of the of optimal the optimal design,design, the predicted the predicted performance performance was was compared compared based based on on the the RMSERMSE test. The The RMSE RMSE values values should should be usedbe to evaluateused to evaluate the accuracy the accuracy of the interpolation of the interp model.olation Themodel. predictive The predictive performance performance of the metamodelof the metamodel was evaluated based on the RMSE test and was calculated according to Equation (3) [32]. was evaluated based on the RMSE test and was calculated according to Equation (3) [32].

tv 1 ntest RMSE 1 X 2 (3) RMSE = [y(Xi) yˆ(Xi)] (3) ntest − i=1 where ntest is the number of test points for metamodel validation, y(Xi) is the value of the real function, whereandntest yˆ(Xisi) the is the number value of the test metamodel. points for metamodel validation, y(Xi) is the value of the real function, and yˆ(XiThe) is thepredicted value performance of the metamodel. of the metamodel was evaluated as an output variable of efficiency Theand predictedcogging torque performance through ofthe the RMSE metamodel test. The was comparison evaluated of asthe an RMSE output test variable results ofof e ﬃtheciency and coggingmetamodels torque for throughthe objective the RMSEfunction test. is shown The comparison in Figure 7. ofThe the lower RMSE the test value results of the of RMSE the metamodels is, the for thebetter objective the predictive function performance is shown will in Figure be. As7 shown. The in lower Figure the 7, valuethe Kriging of the model RMSE yielded is, the the better best the predictiveprediction performance performance will as be.a metamodel As shown of in efficiency Figure7 and, the cogging Kriging torque. model However, yielded if the the best number prediction of design variables, objective functions, and constraints are different, different metamodels for each performance as a metamodel of eﬃciency and cogging torque. However, if the number of design characteristic may yield the best predictive performances. In this study, Kriging metamodels that Appl. Sci. 2020, 10, 3235 8 of 16

Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 15 variables,Appl. Sci. objective 2020, 10, x functions,FOR PEER REVIEW and constraints are diﬀerent, diﬀerent metamodels for each characteristic8 of 15 yielded the best predictive performances for each of the output variables were selected for optimal may yield the best predictive performances. In this study, Kriging metamodels that yielded the best yieldeddesign. the best predictive performances for each of the output variables were selected for optimal predictive performances for each of the output variables were selected for optimal design. design.

(a) (b) (a) (b) FigureFigure 7. Root-mean-square7. Root-mean-square errorerror (RMSE) test test results results of metamodels of metamodels for the for objective the objective function: function: (a) (a)EffiFigureEfficiency;ciency; 7. Root-mean-square ( b(b)) CoggingCogging torque. torque. error (RMSE) test results of metamodels for the objective function: (a) Efficiency; (b) Cogging torque. 3.4. Global3.4. Global Searching Searching with with the the GA GA 3.4. Global Searching with the GA GA wasGA was developed developed to investigateto investigate optimal optimal designdesign variables variables with with an an approximate approximate model. model. GA is GA is commonlycommonlyGA used was used todeveloped createto create solutions to solutions investigate forfor optimizationoptimal design and and variables search search problems, with problems, an approximate thus thusrelying relying onmodel. inspired on GA inspired inis in vivocommonlyvivooperators, operators, used such to create as as mutation, mutation,solutions crossover, for crossover, optimization and se andlection and selection search [31]. GA problems, [31 was]. used GA thus wasto determinerelying used on to theinspired determine optimal in the design variables based on the objective function mentioned above and constraints set for optimal optimalvivo designoperators, variables such as mutation, based on crossover, the objective and se functionlection [31]. mentioned GA was used above to determine and constraints the optimal set for designdesign. variables Figure 8 basedshows onthe the respective objective 200 function iteration mentioned convergence above profiles and constraints of each of setthe forfive optimal design optimal design. Figure8 shows the respective 200 iteration convergence profiles of each of the five design.variables Figure investigated 8 shows in the this respective study. The 200 convergenc iteration econvergence yielded design profiles variables of each that of were the adjustedfive design for designvariablesoptimal variables efficiency investigated investigated and in cogging this study. in torque. this The study. convergenc The convergencee yielded design yielded variables design that were variables adjusted that for were adjustedoptimal for efficiency optimal eandfficiency cogging and torque. cogging torque.

(a) (b) (a) (b)

FigureFigure 8. Convergence 8. Convergence proﬁles profiles of of design design variables:variables: ( (aa) )XX1;1 (;(b)b X)2X; (2c;() Xc3); X(d3);( Xd4;) (eX)4 X;(5.e ) X5. Table 3 compares the values of the initial and optimal model design variables. The shape of the TableoptimalTable3 comparesmodel 3 compares was the determined the values values of ofby thethe the initial proposed and and optimal optimaloptimization model model designprocess. design variables. Figure variables. The9 illustrates shape The of shape thethe of the optimaloptimalcomparison modelmodel between was determinedthe determined initial and by byoptimal the the proposed proposed models. op optimizationtimization process. process. Figure Figure 9 illustrates9 illustrates the the comparisoncomparison between between the the initial initial and and optimal optimal models.models. Table 3. Comparison of design variables. Table 3. Comparison of design variables. ParametersTable 3. ComparisonInitial of design Optimal variables. Unit ParametersX1 Initial14.3 Optimal12.4 Unitmm ParametersXX12 14.3 Initial2 12.42.7 Optimalmmmm Unit XX23 23.82 23.32.7 mmmm X1 14.3 12.4 mm XX34 23.823.2 23.323.7 mmmm X2 2 2.7 mm XX45 23.221.3 23.721.9 mmmm X3 23.8 23.3 mm X5 21.3 21.9 mm X4 23.2 23.7 mm X5 21.3 21.9 mm Appl. Sci. 2020, 10, 3235 9 of 16 Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 15

Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 15

Figure 9. Comparison of initial and optimal models. Figure 9. Comparison of initial and optimal models. 4. Verification of Simulations and Experiments 4. Verification of Simulations and Experiments 4.1. Simulation Results Figure 9. Comparison of initial and optimal models. 4.1. Simulation Results In this study, the electromagnetic analyses of the no-load and load characteristics of PMSM were 4. Verification of Simulations and Experiments performedIn this tostudy, compare the electromagnetic the characteristics analyses of the initialof the no-load and the optimaland load models. characteristics In general, of PMSM in the were case ofperformed an electric to motor,compare magnetic the characteristics properties of occur the initia almostl and linearly the optimal except models. for the In electrical general,part in the of case the 4.1. Simulation Results end-windingof an electric motor, along the magnetic stacking properties length in occur the axial almo direction.st linearly To except evaluate for the the electrical validity of part the of analytical the end- modelwindingIn andthis along thestudy, optimizationthe the stacking electromagnetic designlength procedurein analysesthe axial presented of direction. the no-load in To the andevaluate previous load characteristicsthe section, validity the characteristicsof of the PMSM analytical were of performedPMSMmodel wereand tothe predicted compare optimization withthe characteristics two-dimensional design procedure of the FE initiapresent analysisl anded based inthe the optimal on previous the electromagnetic models. section, In general, the field characteristics simulationin the case ofsoftwareof anPMSM electric JMAG-Designer were motor, predicted magnetic (v18.0,with properties two-dimensional JSOL Corporation,occur almo stFE linearly Tokyo, analysis Japan).except based forTo on the ensure the electrical electromagnetic analytical part of accuracy, the end-field windingmodelsimulation geometries along software the used stacking JMAG-Designer high-quality length in meshes (v18.0,the axial withJSOL direction. 35,100 Corporation, elements To evaluate Tokyo, and 22,300the Japan). validity nodes. To ensureof the analyticalanalytical modelaccuracy, and model the optimization geometries useddesign high-quality procedure meshpresentes edwith in 35,100the previous elements section, and 22,300 the characteristics nodes. of4.1.1. PMSM No-Load were Analysis predicted with two-dimensional FE analysis based on the electromagnetic field simulation4.1.1.Figure No-Load software10a Analysis shows JMAG-Designer the line voltage (v18.0, of back-EMF JSOL Corporation, at 1000 rpm atTokyo, no-load Japan). conditions. To ensure The back-EMFanalytical accuracy,waveformFigure model is 10a a majorshows geometries factorthe line used that voltage ahigh-qualityffects of theback-EMF torque mesh ates characteristics. 1000 with rpm 35,100 at no-loadelements As the conditions. and shape 22,300 of theThe nodes. back-EMFback-EMF waveformwaveform resemblesis a major thefactor sinusoidal that affects wave the with torque lesser characteristics. distortion, a smallerAs the shape torque of ripple the back-EMF response 4.1.1. No-Load Analysis iswaveform generated. resembles The maximum the sinusoidal value wave of the with no-load lesser back-EMF distortion, with a smaller harmonics torque is ripple 38.557 response V for the is initialgenerated.Figure model The10a and showsmaximum 40.566 the V line value for voltage the of optimal the of no-load back-EMF model. back-EMF at At 1000 the maximumrpmwith at harmonics no-load operating conditions. is 38.557 speed V The offor theback-EMF the PMSM initial waveformatmodel 12,000 and rpm, is40.566 a themajor V maximum for factor the optimal that back-EMF affects model. isthe 486.792 At torque the maximum V. characteristics. It can be operating observed As speed thatthe shape it of has the aof marginPMSM the back-EMF at of 12,000 18.8% waveformregardingrpm, the maximum theresembles IGBT withstandback-EMF the sinusoidal voltageis 486.792 wave specification V. with It can lesser be of observed distortion, 600 V used that a in itsmaller thishas a study. margin torque Figure ofripple 18.8% 10 bresponse showsregarding the is generated.distributionthe IGBT withstandThe ratio maximum of each voltage harmonic value specification of orderthe no-load based of onback-EMF600 the V total used with harmonic in harmonicsthis distortionstudy. is Figure38.557 (THD) V10b analysisfor shows the initial of the modelback-EMFdistribution and waveform.40.566 ratio Vof foreach Whenthe harmon optimal the fundamentalic model.order based At the component on maximum the total of operatingharmonic the back-EMF speeddistortion waveformof the (THD) PMSM is analysis increased, at 12,000 of rpm,thethe eback-EMF ffitheciency maximum iswaveform. improved. back-EMF When It can is the486.792 be fundamental observed V. It can that becomp the observed fundamentalonent of that the it back-EMF has wave a margin component waveform of 18.8% of is the regardingincreased, optimal themodelthe efficiencyIGBT is improved withstand is improved. by voltage 2% compared It canspecification be observed with the of initial th 6at00 the model.V fundamentalused in this wavestudy. component Figure 10b of theshows optimal the distributionmodelFigure is improved 11 ratio shows of by each the 2% comparison harmon comparedic order ofwith the thebased cogging initial on torque themodel. total characteristics harmonic distortion of the initial (THD) and theanalysis optimal of themodels. back-EMF The optimum waveform. model’s When coggingthe fundamental torque is comp 0.2778onent Nm, of which the back-EMF is smaller waveform than the constraintis increased, of the efficiency initial model is improved. of 0.3479 Nm.It can Based be observed on FE analyses, that the fundamental the cogging torquewave component of the optimal of the model optimal was modelreduced is byimproved 20.2% compared by 2% compared with the with initial the model. initial model.

(a) (b)

Figure 10. Comparison of the back-electromotive force (EMF) characteristics between the initial and the optimal models at no-load conditions (rotation speed at 1000 revolutions per minute (rpm): (a) (a) (b) Waveform; (b) Harmonic. Figure 10. Comparison of the back-electromotive force (EMF) characteristics between the initial and theFigure optimal 11 showsmodels theat no-load comparison conditions of the(rotat (rotation coggingion speed torque at at 1000 characteristics revolutions per of minute the initial (rpm): and( (aa)) the optimalWaveform; models. (b ))The Harmonic.Harmonic. optimum model’s cogging torque is 0.2778 Nm, which is smaller than the constraint of the initial model of 0.3479 Nm. Based on FE analyses, the cogging torque of the optimal modelFigure was reduced11 shows by the 20.2% comparison compared of with the thecogging initial torquemodel. characteristics of the initial and the optimal models. The optimum model’s cogging torque is 0.2778 Nm, which is smaller than the constraint of the initial model of 0.3479 Nm. Based on FE analyses, the cogging torque of the optimal model was reduced by 20.2% compared with the initial model. Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 15

Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 15 Appl. Sci. 2020, 10, 3235 10 of 16 Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 15

Figure 11. Comparison of the cogging torque characteristics. Figure 11. Comparison of the cogging torque characteristics. 4.1.2. Load Analysis Figure 11. Comparison of the cogging torque characteristics. 4.1.2. Load Analysis Figure 11. Comparison of the cogging torque characteristics. 4.1.2.Owing Load Analysisto the characteristics of the compressor with constant torque characteristic load, the PMSM4.1.2.Owing Load must Analysis tomaintain the characteristics an increased of theefficiency compressor at the wi ratedth constant operating torque conditions characteristic to achieve load, thean Owing to the characteristics of the compressor with constant torque characteristic load, the efficiencyPMSM must improvement maintain aneffect. increased The characteristics efficiency at ofthe the rated rated operating torque ofconditions the PMSM to forachieve electric an PMSMOwing must maintainto the characteristics an increased eofffi ciencythe compressor at the rated wi operatingth constant conditions torque ch toaracteristic achieve an eload,fficiency the compressorsefficiency improvement used for the coolingeffect. The of the characteristics electric vehi clesof theare comparedrated torque in Figureof the 12.PMSM At this for time, electric the improvementPMSM must emaintainffect. The characteristicsan increased efficiency of the rated at torque the rated of the operating PMSM for conditions electric compressors to achieve used an ratedcompressors power is used 3 kW, for and the the cooling rated of speed the electric is 6000 vehirpm.cles Additionally, are compared the incharacteristics Figure 12. At are this applicable time, the forefficiency the cooling improvement of the electric effect. vehicles The arecharacteristics compared in of Figure the 12rated. At torque this time, of thethe rated PMSM power for iselectric 3 kW, torated the powerrated load is 3 kW,of 4.775 and Nm. the rated The peak-to-peak speed is 6000 varpm.lue Additionally,of torque ripple the was characteristics calculated toare be applicable 2.16 Nm andcompressors the rated used speed for is the 6000 cooling rpm. Additionally,of the electricthe vehi characteristicscles are compared are applicable in Figure to12. the At ratedthis time, load the of forto thethe ratedinitial load model, of 4.775 and 1.34Nm. Nm The for peak-to-peak the optimal va model.lue of Thetorque torque ripple ripple was of calculated the optimal to be model 2.16 Nmhas 4.775rated Nm.power The is peak-to-peak3 kW, and the value rated of speed torque is 6000 ripple rpm. was Additionally, calculated to the be2.16 characteristics Nm for the are initial applicable model, improvedfor the initial by 38%model, compared and 1.34 with Nm thefor theinitial optimal model. model. Based The on torquethis analysis, ripple ofthe the rated optimal efficiency model was has andto the 1.34 rated Nm load for theof 4.775 optimal Nm. model. The peak-to-peak The torque va ripplelue of of torque the optimal ripple modelwas calculated has improved to be 2.16 by 38%Nm 92.0%improved for theby 38%initial compared model, andwith 93.5% the initial for themodel. optimal Based model, on this thus analysis, improving the rated the efficiencyefficiency was by comparedfor the initial with model, the initial and 1.34 model. Nm Based for the on optimal this analysis, model. the The rated torque effi rippleciency of was the 92.0% optimal for model the initial has approximately92.0% for the 1.5%.initial model, and 93.5% for the optimal model, thus improving the efficiency by model,improved and by 93.5% 38%for compared the optimal with model, the initial thus model. improving Based the on effi thisciency analysis, by approximately the rated efficiency 1.5%. was approximately 1.5%. 92.0% for the initial model, and 93.5% for the optimal model, thus improving the efficiency by approximately 1.5%.

Figure 12. Comparison of the rated torque characteristics. Figure 12. Comparison of the rated torque characteristics. Figure 12. Comparison of the rated torque characteristics. FigureFigure 1313 shows the flux flux distributions and magnetic flux flux densities of of the initial and optimal Figure 12. Comparison of the rated torque characteristics. models,models,Figure respectively. 13 shows TheThe the leakageleakage flux distributions fluxflux thatthat did did and not not magnetic contribute contribute flux to to the thedensities output output andof and the magnetic magnetic initial saturationand saturation optimal at atmodels, the iron respectively. core was alsoThe leakageanalyzed. flux Based that didon thnote contributeproposed rotorto the shape output optimization and magnetic process, saturation an the ironFigure core 13 was shows also analyzed. the flux distributions Based on the proposedand magnetic rotor shapeflux densities optimization of the process, initial anand increased optimal increasedat the iron amount core was of magnetic also analyzed. flux flowed Based through on the theproposed stator’s rotorcore in shape the case optimization of the optimal process, model. an amountmodels, of respectively. magnetic flux The flowed leakage through flux that the did stator’s not contribute core in the caseto the of output the optimal and magnetic model. In saturation addition, Inincreased addition, amount improvements of magnetic offlux magnetic flowed through flux flow the stator’sand the core effect in the ofcase the of thevariation optimal ofmodel. the improvementsat the iron core of was magnetic also analyzed. flux flow Based and the on e ffthecte proposed of the variation rotor shape of the optimization magnetoresistance process, were an magnetoresistanceIn addition, improvements were obtained. of magneticThese improved flux flow the back-EMFand the andeffect reduced of the the variation cogging torque,of the obtained.increased Theseamount improved of magnetic the back-EMF flux flowed and through reduced the the stator’s cogging core torque, in the as case explained of the optimal in the previous model. asmagnetoresistance explained in the previouswere obtained. section. These The maximumimproved magneticthe back-EMF flux densityand reduced of the therotor cogging was 1.9 torque, T for section.In addition, The maximum improvements magnetic of flux magnetic density offlux the rotorflow wasand 1.9 the T foreffect both theof initialthe variation and the optimalof the bothas explained the initial in andthe previousthe optimal section. models. The Thismaximum density magnetic was not flux saturated. density Correspondingly,of the rotor was 1.9 it Twas for models.magnetoresistance This density were was obtained. not saturated. These improved Correspondingly, the back-EMF it was and therefore reduced considered the cogging that torque, it was thereforeboth the consideredinitial and thethat optimalit was properly models. designed. This dens ity was not saturated. Correspondingly, it was properlyas explained designed. in the previous section. The maximum magnetic flux density of the rotor was 1.9 T for therefore considered that it was properly designed. both the initial and the optimal models. This density was not saturated. Correspondingly, it was therefore considered that it was properly designed.

(a) (b)

Figure 13. FluxFlux distribution distribution(a) and and magnetic magnetic flux ﬂux density: ( (aa)) Initial Initial model;( model;b) ( (bb)) optimal optimal model. model. Figure 13. Flux distribution(a) and magnetic flux density: (a) Initial model;(b) (b) optimal model.

Figure 13. Flux distribution and magnetic flux density: (a) Initial model; (b) optimal model. Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 15 Appl. Sci. 2020, 10, 3235x FOR PEER REVIEW 1111 of of 1615 Appl.4.2. ExperimentalSci. 2020, 10, x FOR Results PEER REVIEW 11 of 15 4.2. ExperimentalTo verify the Results proposed optimal design process, a prototype of the optimal PMSM was fabricated. 4.2. Experimental Results The prototypeTo verify the PMSM proposed motor optimal assembly, design stator, process, and rotor, a prototype are shown of the in Figure optima 14,l PMSM and the was experimental fabricated. To verify the proposed optimal design process, a prototype of the optimal PMSM was fabricated. Thesetup prototypeTo is verify illustrated thePMSM proposed in Figuremotor optimal assembly,15. design stator, process, and rotor, a prototype are shown of thein Figure optimal 14, PMSM and the was experimental fabricated. The prototype PMSM motor assembly, stator, and rotor, are shown in Figure 14, and the experimental Thesetup prototype is illustrated PMSM in Figure motor assembly,15. stator, and rotor, are shown in Figure 14, and the experimental setup is illustrated in Figure 1515..

(a) (b) (c) (a) (b) (c) Figure 14. PMSM prototype(a) for an electric compressor:(b) (a) Stator; (b) rotor;(c) (c) motor assembly. Figure 14. PMSM prototype for an electric compressor: (a) Stator; (b) rotor; (c) motor assembly. Figure 14. PMSMPMSM prototype prototype for an electric compressor: ( (aa)) Stator; Stator; ( (b)) rotor; rotor; ( c) motor assembly.

Figure 15. Experimental setup for motor dynamo testing. Figure 15. Experimental setup for motor dynamo testing. Figure 15. Experimental setup for motor dynamo testing. The results of the Figurecogging 15. Experimentaltorque experiment setup for are motor compared dynamo testing.and shown in Figure 16. The The results of the cogging torque experiment are compared and shown in Figure 16. The optimum optimumThe resultsmodel ofyielded the cogging a cogging torque torque experiment of 0.2153 areNm comparedwhich is reducedand shown by 37.1% in Figure compared 16. The to modelThe yielded results a coggingof the cogging torque oftorque 0.2153 experiment Nm which are is reducedcompared by 37.1%and shown compared in Figure to 0.3369 16. NmThe optimum0.3369 Nm model generated yielded in the a cogging initial model. torque It of is 0.2153expected Nm that which the coggingis reduced torque by 37.1%characteristics compared have to generatedoptimum inmodel the initial yielded model. a cogging It is expected torque thatof 0.2153 the cogging Nm which torque is characteristics reduced by have37.1% been compared improved to 0.3369been improved Nm generated based inon the rotor initial shape model. optimization. It is expected The resultsthat the of cogging the cogging torque torque characteristics experiment have are based0.3369 onNm rotor generated shape optimization.in the initial model. The results It is expected of the cogging that the torque cogging experiment torque characteristics are compared have and beencompared improved and basedshown on in rotor Figure shape 16. Theoptimization. optimum Themodel results yielded of the a coggingcogging torquetorque experiment of 0.2153 Nm, are shownbeen improved in Figure based16. The on optimum rotor shape model optimization. yielded a cogging The results torque of of the 0.2153 cogging Nm, torque which wasexperiment reduced are by comparedwhich was and reduced shown by in 39.2% Figure compared 16. The optimumto 0.3369 Nmmodel of yieldedthe initial a coggingmodel. Ittorque is expected of 0.2153 that Nm, the 39.2%compared compared and shown to 0.3369 in NmFigure of the16.initial The optimum model. It ismodel expected yielded that thea cogging cogging torque torque of characteristics 0.2153 Nm, whichcogging was torque reduced characteristics by 39.2% comparedhave been to improved 0.3369 Nm based of the on initialrotor shapemodel. optimization. It is expected However, that the havewhich been was improvedreduced by based 39.2% on compared rotor shape to optimization. 0.3369 Nm of However, the initial there model. are severalIt is expected reasons that for the coggingthere are torque several characteristics reasons for theha veexistence been improved of pulsation based in onthe rotor cogging shape torque optimization. waveform However, that are existencecogging torque of pulsation characteristics in the cogging have torquebeen improved waveform based that are on attributedrotor shape to theoptimization. harmonic component However, thereattributed are several to the harmonicreasons for component the existence of theof pulsationpole number. in the It coggingis known torque that thewaveform number thatof pole are ofthere the are pole several number. reasons It is known for the that existence the number of pulsation of pole harmonics in the cogging is mainly torque caused waveform by the shape that error are attributedharmonics tois mainlythe harmonic caused componentby the shape of error the ofpole the number. stator generated It is known during that manufacturing. the number of This pole is ofattributed the stator to generated the harmonic during component manufacturing. of the Thispole isnumber. also a factor It is thatknown adversely that the aﬀ ectsnumber the coggingof pole harmonicsalso a factor is thatmainly adversely caused affectsby the theshape cogging error ofto rquethe stator that cannot generated be easily during considered manufacturing. at the designThis is torqueharmonics that is cannot mainly be caused easily consideredby the shape at theerror design of the stage. stator Thus, generated its complementary during manufacturing. method needs This tois alsostage. a factorThus, itsthat complementary adversely affects method the cogging needs toto rquebe studied that cannot further. be easily considered at the design bealso studied a factor further. that adversely affects the cogging torque that cannot be easily considered at the design stage. Thus, its complementary method needs to be studied further. stage. Thus, its complementary method needs to be studied further.

Figure 16. Comparison of the experimental cogging torque characteristics. Figure 16. Comparison of the experimental cogging torque characteristics. The experimentalFigure results 16. Comparison of motor of dynamo the experimental testing for cogging the initial torque and characteristics. optimal models are presented Figure 16. Comparison of the experimental cogging torque characteristics. in Figure 17. The measurement targets include the rated efficiency in response to the rated load. Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 15 Appl. Sci. 2020, 10, 3235 12 of 16 The experimental results of motor dynamo testing for the initial and optimal models are presented in Figure 17. The measurement targets include the rated efficiency in response to the rated Theload. input The input direct direct current current voltage voltage was 380 was V. 380 To compareV. To compare the operating the operating characteristics, characteristics, the PMSM the PMSM motor wasmotor started was started and had and an initialhad an speed initial of speed 6000 rpm,of 6000 while rpm, the while load torquethe load was torque continually was continually increased increaseduntil it reached until it the reached rated loadthe rated of 4.775 load Nm of 4.775 during Nm the during experiment. the experiment. The experimental The experimental results showed results showedthat the ratedthat the effi ratedciency efficiency of the initial of the model initial was mo 91.4%,del was and 91.4%, that ofand the that optimal of the model optimal was model 92.9%, was at 92.9%,the rated at operatingthe rated operating conditions conditions (rotational (rotational speed of 6000speed rpm of 6000 and outputrpm and power output of 3power kW). Theof 3 ratedkW). Theefficiency rated testefficiency characteristics test characteristics were also found were to also be approximately found to be approximately 1.5% lower than 1.5% the analysis.lower than This the is analysis.expected This to be is attributed expected to to be the attributed difference to between the difference the physical between properties the physical considered properties in considered the design, inthe the analysis design, used the for analysis the same used material, for the and same the mate physicalrial, and properties the physical applied properties to the prototype, applied asto well the prototype,as the component as well tolerancesas the component of the magnetic tolerances materials of the generated magnetic duringmaterials the generated manufacturing during of the prototypes,manufacturing assembly of the tolerances, prototypes, and assembly errors attributed tolerances, to test and equipment errors attributed settings. Tableto test4 summarizes equipment settings.the simulation Table 4 and summarizes experimental the resultssimulation from and each experimental model. results from each model.

(a)

(b)

Figure 17. Comparison of of experimental experimental motor motor dynamometer dynamometer test results:test results: (a) Initial (a) Initial model; model; (b) optimal (b) optimal model. model. Table 4. Simulation and experimental results.

ItemsTable 4. Simulation and experimental Initial results. Optimal Unit RatedItems eﬃ ciency Initial 92.0 Optimal 93.5 Unit % Simulation CoggingRated torque efficiency 0.347992.0 93.50.2778 % Nm Simulation RatedCogging eﬃciency torque 0.3479 91.4 0.2778 92.9 Nm % Experiment CoggingRated torque efficiency 0.2778 91.4 92.9 0.2153 % Nm Experiment Cogging torque 0.2778 0.2153 Nm Appl. Sci. 2020, 10, 3235 13 of 16

5. Conclusions In this study, the optimization of the rotor shape of the PMSM used in electric compressors was conducted. Accordingly, the rated efficiency and cogging torque characteristics of the rated output 3 kW PMSM were optimized. The design variables consisted of 54 experimental points without overlapping points with OHLD within the range of the designated design variables. For the approximate modeling, three metamodels were implemented to analyze the predicted accuracy. Among them, Kriging yielded the best characteristics. Additionally, the GA was selected as the optimal design variable that satisfied the objective function and constraints. The suitability of the proposed rotor shape optimization was analyzed based on FE analyses based on the selected optimal design variables. For practical verification, a prototype of the optimal model of PMSM was produced, and experiments confirmed the improvements of the efficiency and cogging torque characteristics compared with those of the initial model. According to the proposed optimization that was verified experimentally, the rated efficiency characteristics were improved by 1.5% compared with the initial model, while the cogging torque was reduced to 22.5%. In the future, the driving efficiency of the motor is expected to be improved when the electric compressor system of the test vehicle will be implemented.

Author Contributions: Conceptualization, S.-W.B.; Methodology, S.-W.B.; Software, S.-W.B.; Validation, S.-W.B. and S.W.L.; Writing—original draft preparation, S.-W.B.; Writing—review and editing, S.W.L.; and S.-W.B.; Funding acquisition, S.-W.B. All authors have read and agreed to the published version of the manuscript. Funding: This paper was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIT) (no. 2017R1C1B5075525); This study is the result of a research carried out as a part of “Green Vehicle Component Cluster Project” supported by the Ministry of Trade, Industry and Energy (MOTIE) and Korea Institute for Advancement of Technology (KIAT) (P0000760). Acknowledgments: The author express gratitude to Koh-A Jung Gong Co., Ltd. and PIDOTECH for their technical support. Conﬂicts of Interest: The authors declare no conﬂict of interest.

Appendix A

Table A1. Characteristics of samples obtained from optimal Latin hypercube design (OLHD) using ﬁnite element (FE) analyses.

Eﬃciency Cogging Number X X X X X 1 2 3 4 5 (%) Torque (Nm) 1 12.000 2.000 24.167 22.998 22.267 91.87 0.2746 2 12.956 2.306 23.625 23.000 21.166 91.91 0.2774 3 14.833 2.333 23.278 24.278 21.389 92.35 0.2816 4 12.352 2.250 22.833 23.091 21.458 92.98 0.2939 5 12.400 2.528 22.889 23.389 21.056 93.21 0.2881 6 14.111 2.150 24.444 22.889 21.000 92.88 0.3242 7 12.785 1.946 24.611 23.952 20.766 92.38 0.3438 8 12.380 2.720 23.300 23.700 21.900 91.55 0.2778 9 12.222 2.916 24.556 24.275 22.000 92.35 0.3412 10 13.889 2.139 24.161 24.109 22.833 91.37 0.2751 11 13.558 2.111 24.670 24.662 22.056 93.06 0.2736 12 13.215 2.889 23.444 23.222 22.278 93.06 0.3176 13 14.733 1.890 23.891 23.840 21.634 91.42 0.2765 14 12.122 2.472 23.778 23.611 22.389 93.44 0.3272 15 13.482 2.417 22.444 23.667 20.500 93.58 0.3385 16 14.971 2.194 23.948 24.749 21.433 93.01 0.2761 17 13.347 2.444 23.111 24.555 21.833 91.11 0.2863 18 14.933 2.250 22.611 23.555 20.944 93.41 0.3026 19 14.444 2.667 22.945 22.723 22.777 92.74 0.2855 Appl. Sci. 2020, 10, 3235 14 of 16

Table A1. Cont.

Eﬃciency Cogging Number X X X X X 1 2 3 4 5 (%) Torque (Nm) 20 13.668 2.639 22.722 23.667 21.704 91.51 0.2969 21 14.556 2.167 23.556 22.835 22.479 91.85 0.3275 22 12.631 1.833 24.831 23.322 22.500 93.13 0.3438 23 13.055 2.611 22.778 24.833 20.947 92.96 0.2973 24 14.723 1.778 22.712 23.722 20.832 91.49 0.2989 25 13.444 2.833 23.832 24.597 22.150 91.08 0.2779 26 13.000 1.750 22.608 24.500 21.611 91.12 0.3045 27 14.855 2.320 23.721 23.411 21.501 93.27 0.2771 28 12.345 2.972 23.883 24.381 20.722 91.27 0.2774 29 12.784 1.872 23.575 23.942 22.667 93.41 0.2781 30 14.234 1.652 24.738 23.166 20.665 92.99 0.2741 31 12.611 2.055 24.445 22.453 21.835 92.56 0.2737 32 14.278 2.540 24.388 23.444 22.611 93.34 0.2738 33 13.111 1.847 22.325 23.213 21.748 91.03 0.3178 34 13.344 2.298 24.000 24.390 20.889 93.21 0.2965 35 14.834 2.556 25.000 24.885 22.407 92.97 0.2833 36 13.667 1.691 24.056 22.584 20.556 92.63 0.2755 37 13.879 2.695 23.167 24.117 21.927 93.38 0.2829 38 14.056 1.639 24.666 22.662 22.216 93.67 0.2734 39 14.667 2.642 22.459 22.444 22.857 92.53 0.3112 40 13.250 2.235 23.088 24.722 22.711 93.04 0.2836 41 12.489 2.057 24.331 22.832 22.958 92.83 0.2751 42 13.367 2.762 22.503 24.978 21.222 92.91 0.3053 43 14.999 2.922 24.278 22.333 20.390 92.36 0.2941 44 14.145 2.452 22.271 22.553 21.333 92.61 0.2911 45 13.265 1.721 22.389 24.944 22.942 92.94 0.2839 46 12.256 1.622 23.378 22.385 22.113 92.49 0.2781 47 14.325 2.996 24.944 22.278 21.218 92.33 0.2735 48 13.650 1.583 23.051 24.220 20.333 91.37 0.2847 49 12.444 2.389 22.455 22.722 20.222 92.71 0.9267 50 13.777 1.944 22.222 22.192 20.389 92.21 0.3221 51 13.458 2.805 24.246 22.111 20.221 92.19 0.3333 52 12.798 1.558 22.060 23.833 20.167 93.45 0.3445 53 14.795 2.685 22.794 22.056 20.056 92.15 0.2736 54 13.075 1.500 22.001 22.001 20.001 92.11 0.3511

References

1. Yilmaz, M.; Krein, P.T. Review of battery charger topologies, charging power levels, and infrastructure for plug-in electric and hybrid vehicles. IEEE Trans. Power Electron. 2013, 28, 2151–2169. [CrossRef] 2. Chukwu, U.C.; Mahajan, S.M. Real-time management of power systems with V2G facility for smart-grid applications. IEEE Trans. Sustain. Energy 2014, 5, 558–566. [CrossRef] 3. Babin, A.; Rizoug, N.; Mesbahi, T.; Boscher, D.; Hamdoun, Z.; Larouci, C. Total cost of ownership improvement of commercial electric vehicles using battery sizing and intelligent charge method. IEEE Trans. Ind. Appl. 2018, 54, 1691–1700. [CrossRef] 4. Loiselle-Lapointe, A.; Whittal, I.; Christenson, M. Electric Vehicles: Impacts of Mileage Accumulation and Fast Charging. World Electr. Veh. J. 2016, 8, 249–262. [CrossRef] 5. De Almeida, A.T.; Ferreira, F.J.; Baoming, G. Beyond Induction Motors—Technology Trends to Move Up Eﬃciency. IEEE Trans. Ind. Appl. 2013, 50, 2103–2114. [CrossRef] 6. Yang, Z.; Shang, F.; Brown, I.P.; Krishnamurthy, M. Comparative study of interior permanent magnet, induction, and switched reluctance motor drives for EV and HEV applications. IEEE Trans. Transp. Electrif. 2015, 1, 245–254. [CrossRef] 7. Lu, C.; Ferrari, S.; Pellegrino, G. Two Design Procedures for PM Synchronous Machines for Electric Powertrains. IEEE Trans. Transp. Electrif. 2017, 4, 98–107. [CrossRef] Appl. Sci. 2020, 10, 3235 15 of 16

8. Jung, T.-U. Development of Hybrid Electric Compressor Motor Drive System for Hybrid Electrical Vehicles. J. Power Electron. 2009, 9, 960–968. 9. Jolly, L.; Jabbar, M.A.; Qinghua, L. Design optimization of permanent magnet motors using response surface methodology and genetic algorithms. IEEE Trans. Magn. 2005, 41, 3928–3930. [CrossRef] 10. Hwang, C.-C.; Cho, Y.H. Effects of leakage flux on magnetic fields of interior permanent magnet synchronous motors. IEEE Trans. Magn. 2001, 37, 3021–3024. [CrossRef] 11. Ilka, R.; Alinejad-Beromi, Y.; Yaghobi, H. Techno-economic Design Optimisation of an Interior Permanent-Magnet Synchronous Motor by the Multi-Objective Approach. IET Electr. Power Appl. 2018, 12, 972–978. [CrossRef] 12. Hong, G.; Wei, T.; Ding, X. Multi-objective Optimal Design of Permanent Magnet Synchronous Motor for High Effciency and High Dynamic Performance. IEEE Access 2018, 6, 23568–23581. [CrossRef] 13. Cho, S.; Jung, K.; Choi, J. Design Optimization of Interior Permanent Magnet Synchronous Motor for Electric Compressors of Air-Conditioning Systems Mounted on EVs and HEVs. IEEE Trans. Magn. 2018, 54, 1–5. [CrossRef] 14. Baek, S. Optimum shape design of a BLDC motor for electric continuous variable valve timing system considering efficiency and torque characteristics. Microsyst. Technol. 2018, 24, 4441–4452. [CrossRef] 15. Lee, S.; Baek, S. A study on the improvement of the cam phase control performance of an electric continuous variable valve timing system using a cycloid reducer and BLDC motor. Microsyst. Technol. 2020, 26, 59–70. [CrossRef] 16. Ortega, A.J.P.; Paul, S.; Islam, R.; Xu, L. Analytical model for predicting effects of manufacturing variations on cogging torque in surface-mounted permanent magnet motors. IEEE Trans. Magn. 2016, 52, 3050–3061. [CrossRef] 17. Zhou, Y.; Li, H.; Meng, G.; Zhou, S.; Cao, Q. Analytical calculation of magnetic field and cogging torque in surface-mounted permanent-magnet machines accounting for any eccentric rotor shape. IEEE Trans. Ind. Electron. 2015, 62, 3438–3447. [CrossRef] 18. Lee, J.H.; Kim, J.W.; Song, J.Y.; Kim, Y.J.; Jung, S.Y. A Novel Memetic Algorithm Using Modified Particle Swarm Optimization and Mesh Adaptive Direct Search for PMSM Design. IEEE Trans. Magn. 2016, 52, 1–4. [CrossRef] 19. Edhah, S.O.; Alsawalhi, J.Y.; Al-Durra, A.A. Multi-Objective Optimization Design of Fractional Slot Concentrated Winding Permanent Magnet Synchronous Machines. IEEE Access 2019, 7, 162874–162882. [CrossRef] 20. Chung, S.U.; Kim, J.W.; Chun, Y.D.; Woo, B.C.; Hong, D.K. Fractional Slot Concentrated Winding PMSM with Consequent Pole Rotor for a Low-Speed Direct Drive Reduction of Rare Earth Permanent Magnet. IEEE Trans. Energy Convers. 2015, 30, 103–109. [CrossRef] 21. Kwon, J.W.; Lee, J.H.; Zhao, W.L.; Kwon, B.I. Flux-Switching Permanent Magnet Machine with Phase-Group Concentrated-Coil Windings and Cogging Torque Reduction Technique. Energies 2018, 11, 2758. [CrossRef] 22. Yoon, K.-Y.; Baek, S.-W. Robust design optimization with penalty function for electric oil pumps with BLDC motors. Energies 2019, 12, 153. [CrossRef] 23. Guo, H.; He, H.; Sun, F. A combined cooperative braking model with a predictive control strategy in an electric vehicle. Energies 2013, 6, 6455–6475. [CrossRef] 24. Ma, P.; Zhou, Y.; Shang, X.; Yang, M. Firing accuracy evaluation of electromagnetic railgun based on multicriteria optimal Latin hypercube design. IEEE Trans. Plasma Sci. 2017, 45, 1503–1511. [CrossRef] 25. Shin, P.S.; Woo, S.H.; Koh, C.S. An optimal design of large scale permanent magnet pole shape using adaptive response surface method with Latin hypercube sampling strategy. IEEE Trans. Magn. 2009, 45, 1214–1217. [CrossRef] 26. Zhang, B.S.; Song, B.W.; Mao, Z.Y.; Tian, W.L.; Li, B.Y.; Li, B. Novel parametric modeling method and optimal design for savonius wind turbines. Energies 2017, 10, 301. [CrossRef] 27. Li, Y.K.; Song, B.W.; Mao, Z.Y.; Tian, W.L. Analysis and optimization of the electromagnetic performance of a novel stator modular ring drive thruster motor. Energies 2018, 11, 1598. [CrossRef] 28. Gong, J.; Gillon, F.; Canh, J.T.; Xu, Y.Proposal of a Kriging output space mapping technique for electromagnetic design optimization. IEEE Trans. Magn. 2017, 53, 1–4. [CrossRef] 29. Zhang, L.; Tian, F. Performance study of multilayer perceptrons in a low-cost electronic nose. IEEE Trans. Instrum. Meas. 2014, 36, 1670–1679. [CrossRef] Appl. Sci. 2020, 10, 3235 16 of 16

30. Franzese, G.; Visintin, M. Probabilistic ensemble of deep Information networks. Entropy 2020, 22, 100. [CrossRef] 31. Baek, S.; Kwon, B. Optimum design of a single-phase line-start PM motor considering eﬃciency, maximum torque, and starting torque. IEEE Trans. Magn. 2012, 48, 4850–4859. [CrossRef] 32. Yan, C.; Zhu, J.; Shen, X.; Fan, J.; Mi, D.; Qian, Z. Ensemble of regression-type and interpolation-type metamodels. Energies 2020, 13, 654. [CrossRef]

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