2 nd International Conference on Engineering Optimization

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1 2 nd International Conference on Engineering Optimization September 6-9, 2010, Lisbon, Portugal Brushless Permanent Magnet Motor Losses Minimization with Constraints in Perspective of Life Cycle Assessment T. H. Pham 1, P. Wendling 1, P. Lombard 2, V. Leconte 2, J. L. Coulomb 3 1 Magsoft Corporation, Clifton Park, New York, USA, tan@magsoft-flux.com 2 Cedrat S.A., Meylan, France 3 G2ELAB, INPG, Saint Martin d Heres, France Abstract The off the shelf (commercially available) brushless permanent magnet motor is evaluated for electromagnetic losses minimization in order to increase motor efficiency. The proposed analysis is conducted with the perspective of satisfying global thinking approach to the evaluation by Life Cycle Assessment. This will be done in an attempt to reduce the power consumption impact of the brushless permanent magnet motor in its industrial application. The key electromagnetic losses components are the stator winding resistive losses, the motor magnetic material iron core losses and the rotor magnet eddy current losses. These electromagnetic losses are computed through finite element dynamic computation that simulates the motor real life operations. As such the power budget can be visualized to depict the impact of different losses components and can be used to develop a targeted losses reduction strategy. The motor geometry features such as the rotor magnet shape and the stator lamination details (i.e. slot opening, tooth width) along with the motor physical properties (i. e. motor current, materials) are considered as design parameters for the optimization process to minimize the electromagnetic losses. Two optimization strategies and algorithms are considered for comparison. The first strategy is engineering oriented and requires a level of motor design expertise for effective execution. It consists of performing a Screening to extract the most influential parameters. Then a transformation is performed, utilizing a smaller number of key design parameters, into a 2 steps optimization process. This approach entails laying the ground work that employs concise preparation by reducing the number of parameters and the optimization domain. The result is that the evaluation of the objective functions and constraints becomes more economical. The second strategy is Stochastic based and uses Genetic Algorithm to automatically find the minimum motor electromagnetic losses for the given design parameters. This approach results in a more robust, computationally intensive process requiring more finite elements solutions. During the design optimization procedure, there are trade-offs in terms of quantity of materials and the type of (regular or advanced) materials employed. These factors effectively illustrate the importance of Life Cycle Assessment to evaluate the environment cost. Utilization of this procedure results in an impact to the financial cost along with reduction of operating cost, affording insight to the true impact of the design optimization over the motor life rather just its electromagnetic performances. Keywords: electromagnetic losses, finite element, optimization, life cycle assessment. 1. Introduction Electric motors use a significant amount of electrical energy during their operating life. Among them, brushless permanent magnet motors constitute an ever increasing segment, adding value with the decreased cost to permanent magnets and motor drives. They are widely used in the day to day industrial applications, such as pumps, fans and compressor drives [1]. The resulting trade-offs of the lower manufacturing costs of brushless permanent magnet motors are low motor performances and efficiency. This is a result of economizing costs by using generic materials for laminations and magnets instead of using high end and high performance materials. This practice was acceptable in the past when energy costs were cheap and there was less of an awareness about energy conservation. Today, the industry is still subject to economic and business constraints while facing the challenge of meeting higher efficiency and reducing the environment impacts. All these factors (economical, energetic and environmental) require the design engineer to consider a global thinking approach to project design known as Life Cycle Assessment instead of the motor performances and manufacturing costs alone. In this paper, an existing industrial brushless permanent magnet used in pump applications is examined for its energy efficiency. Optimization processes are applied through simulations of motor finite element model in combination of numerical optimization routines, to yield improved motor efficiency under the guideline of Life Cycle Assessment. 1

2 2. Brushless Permanent Magnet Motor Characteristics, Power Budget and Design Improvement Goals 2.1. Motor General Characteristics The motor to be optimized in terms of performances and efficiency is a 4 pole, 3 phase winding Y connected, 24 slots brushless permanent magnet motor. It has been used as motor for pump applications at 2000 rpm. The motor drive is 48 Volts sine drive capable of delivering 50 Amps max. The magnet material used in the current design is ceramic magnet with a remanent flux density Br of 0.41 Tesla. The steel lamination for the stator stack is M19 24 gauge equivalent (0.64 mm thick). The summary of the main dimensional characteristics of the motor are described in Table 1. Table 1: Motor Dimensions Value Unit Stator OD 96.0 mm Rotor OD 50.0 mm Gap 0.5 mm Stack Length 50.0 mm Magnet Lhickness 5.5 mm The motor cross section and outline [2] with the magnets in black being radially magnetized outward whereas the magnets in grey are radially magnetized inward (see Figure 1.) Figure 1: Brushless Permanent Magnet Cross Section and Outline 2.2. Motor Power Budget Analysis The motor published efficiency is 55% at 2000 RPM. It corresponds to 2.45 N.m shaft torque at 30 Amps rms. The total motor losses are 420 Watts in which 381 Watts are attributed to stator winding copper losses. The electromagnetic finite element software Flux [3] is used to estimate the motor core losses in the stator laminations. The computed core losses are only about 2.42 Watts. The motor friction losses due bearings are also estimated at 30 Watts. The magnet eddy current losses are non-existent as the magnet electrical resistivity is very high Motor Design Improvement Goals The biggest contributor to the motor total losses is the winding copper losses due the high motor operating current. Further analysis shows that this level of motor current is required to meet the motor output torque requirement of 2.5 N.m at 2000 rpm. There are two ways to reduce the winding losses. The first one is to lower the winding resistance by using thicker wire. However, this method may increase the difficulty of the manufacturing process by making the motor harder to wind resulting in higher manufacturing cost. The second is to lower the motor 2

3 operating current by either adding more turns to the stator winding or increasing the flux density in the air gap with a stronger magnet. The later method is preferred as the cost of magnet material change is less than the cost of rewinding the stator winding while having more losses reduction. Take note that the motor core losses in the stator laminations are not significant when compared to the stator winding copper losses. The losses reduction by changing the lamination, for example, to higher performances materials or thinner is not big enough to offset the increase costs. These above observations lead us to set the design improvement goals of reducing the stator winding copper losses while meeting the motor torque requirement. In parallel, the motor torque ripples which can induce vibrations and noises will also be reduced in the design improvement scope. 3. Design Improvement Process Using Electromagnetic FEA Tool FLUX and Optimizer Tool GOT The design improvement goals described in section 2.3 are formulated using the optimizer tool GOT [4] which exchanges optimization parameters with the electromagnetic FEA tool FLUX which in turn provides motor performance results. The optimization tool and the FEA tool interact with each other to provide update information on the design parameters selected and performances needed for the objective functions and constraints Electromagnetic Finite Element Computation of Motor Performances For the purpose of optimizing the motor efficiency by reducing the motor losses while maintaining the motor torque output requirement, the electromagnetic finite element package, FLUX is used to compute the motor performance in running operations at 2000 rpm. FLUX is a general, multi-purpose electromagnetic finite element package that is adapted for electric motor performance computation. FLUX motion features include translating and rotating motion, in addition to external circuit connections making it possible to model the motor windings and power supply. For the magnetic field modeling, it takes into account magnetic material saturation and eddy currents in conductive materials. Figure 2 shows the motor finite element model and mesh. Periodicity conditions are applied to reduce the motor model size to a 1 pole model resulting in a smaller number of finite elements and nodes, thus, a shorter computation time. Figure 2: Brushless Permanent Magnet 1 Pole Finite Element Model and Mesh The motor running operations at 2000 rpm is simulated in time stepping mode over 1 electric cycle which is half of 1 mechanical cycle or 180 mechanical degrees with the rotor rotating at 1 deg/step. At each step, the finite element magnetic field solutions are solved simultaneously with the electric circuit equations (energized windings) and the electromechanical equations (rotating motion). Consequently, all the physical phenomena such as eddy currents in a conductor and harmonic effects are fully taken into account for the motor performance computations. Figure 3 displays the model flux density map and arrows that show the motor saturation. The rotor is rotated of 20 deg. The current in the windings are 30 Amps RMS and the magnet Br is 0.41 Tesla. The maximum saturation in the stator is less than 1.5 Tesla. That means that the motor is not saturated (saturation less than 1.8 Tesla for M19 material) under its full load capacity. 3

4 Figure 3: Motor Flux Density Map and Arrows Saturation The torque variation over 1 electric cycle is displayed in Figure 4. The average torque value T_ave is 2.51 N.m with the minimum torque value T_min is 2.42 N.m and the maximum torque value is 2.56 N.m. Figure 4: Torque Variation over 1 Electric Cycle 180 Deg. The torque ripples, T_ripples, is defined in Eq.(1) below and is equal to 5.58%. The torque ripples are due from the harmonic components of the phase back emf voltage and the cogging torque resulting from the stator slots and rotor poles interactions. ( T _ max T _ min) T _ ripples = (1) T _ ave 3.2 Motor Losses Computation and Efficiency There are 4 main components of the motor losses Losses motor : 1) First component: Winding copper losses P cu that are defined by Eq.(2) as: cu 2 3 phi rms P = R (2) where R ph and I rms are respectively the winding phase resistance and the RMS value of the sinusoidal motor phase current. 2) Second component: Motor core losses consist only of the stator core losses. The rotor core losses are negligible as the rotor is rotating at synchronous speed with the stator field. The stator core losses P fe are computed using the electromagnetic finite element solutions in terms of the flux density B and its time derivative db/dt developed by Bertotti [5]. They are defined as in Eq.(3) with 3 components: P hys, P eddy and P excess P = P + P + P (3) fe hyst P hys, P eddy and P excess [6] are respectively the hysteresis losses component, the eddy current losses component and the excess losses component. They are defined respectively in Eq.(4) through their average power over a period T in a finite element subdivision as: eddy excess 4

5 Hysteresis losses component: dp = K k fb (4a) hys K h is the computed hysteresis core losses coefficient depending on the lamination material. k f is the stator stacking factor which depends on the lamination thickness (0.93 to 0.97). B m is the peak flux density in the finite element subdivision and f is the electrical frequency. Eddy current losses component: 1 T σ 2 db t dpeddy = k f d dt (4b) T 0 12 dt where σ is the lamination material conductivity, d is the lamination thickness and B is the flux density value in the finite element subdivision. h f m ( ) 2 Excess losses component: 1 T db t dpeddy = K ek f dt T 0 dt K e is the excess core losses coefficient computed depending on the lamination material. ( ) 3 2 (4c) Table 2: Core Losses Coefficients and Physical Values of M19 M19 24 Gauge M19 26 Gauge M19 29 Gauge Thickness in mm, d D Elec. freq. in Hz F Conductivity in S/m σ 2.00E6 2.00E6 2.00E6 Hyst. loss. coef. K h Excess. loss. coef. K e Stacking factor K f Number of lam. N lams Core Losses in Watts P fe Table 2 gives the core losses coefficients and physical values of the M19 material used for the motor operating at 2000 rpm with different lamination thickness, 24 gauge, 26 gauge and 29 gauge. The average motor core losses calculated by Flux using Eq.(4) over 1 electric cycle period are 2.42 Watts for the stator stack made of M19 24 Gauge material. Changing the lamination material from M19 24 Gauge to 26 Gauge and 29 Gauge provides only a gain respectively of 0.43 Watts and 0.68 Watts! 3) The third component of the motor losses is the mechanical losses due to bearing friction and rotor windage. It is a fixed value at 2000 rpm and is equal to 30 Watts. 4) The last component of the motor losses is the magnet eddy current losses due to stator field variation and slotting effects. The magnet eddy current losses occur when the magnet material is conductive such as sintered NdFeB or SmCo and can be set up to be calculated during the finite element simulation. However, in our case, the magnet materials are either ceramic or bonded NdFeB with very low conductivity. Consequently, it is neglected here. The total losses calculated for Losses motor are: = To calculate the motor efficiency, we need to compute the motor mechanical output power P out defined as: P T ω (5) out = ave where T ave is the average motor torque and ω is the motor speed in rad/s. Pout is 2.51 x = Watts. We can now define the motor efficiency Eff as in Eq.(6) below and Eff calculated is % : Pout Eff = (6) P + Losses ( ) out 3.3. Optimizer Tool GOT The optimizer tool GOT which stands for General Optimization Tool [4], is a general purposed numerical optimization tool developed at G2ELAB, France. It features an extensive library of optimization deterministic and stochastic algorithms such as SQP, GA, etc GOT can also deal with constrained or unconstrained optimization motor 5

6 problems with mono or multi-objective functions. GOT can be connected to an external solver such as Flux to provide motor performances computation for the optimization objective function or constraints Motor Design Improvement Optimization Process using GOT and Flux For our motor design improvement optimization in terms of minimizing the motor losses and reducing the torque ripples, it is a coupled iterative process between the optimizer tool GOT and the motor performances computation tool Flux. Based on the design restrictions and requirements, objective functions and constraints are defined along with design parameters [7]. The motor finite element model is then created accordingly in Flux with parameterized geometry (magnet arc, magnet length, etc..), mesh and physical properties (drive current, magnet remanent flux density, etc..). At each optimization iteration, the design parameters are calculated in GOT and passed into Flux to modify the finite element model. Flux in turn computes the performances of the newly-defined motor model and returns the motor losses and torque ripples to GOT for the next iteration. 4. Motor Losses Minimization and Torque Ripples Reduction Using GOT-Flux optimizer and solver exchange, we can define our motor losses minimization and torque ripples reduction in the scope of design improvement Optimization design parameters Initial analysis of the motor performances allows us to identify 2 types of design parameters: 1) Physical properties design parameters which deal mainly with motor losses minimization a. Motor drive current AIrms b. Magnet remanent flux density ABr 2) Geometric design parameters which are for torque ripples reduction by shaping the stator lamination and the magnet a. Magnet arc A_BetaM, magnet edge A_Edge and magnet thickness A_LM b. Stator slot opening A_SO, stator slot angle A_SOAng and stator tip thickness A_TGD 4.2. Objective function and constraints The objective is to minimize the motor losses of the motor operating at 2000 rpm Losses motor. The objective function is then simply defined as F obj = Losses motor The motor torque ripples T_ripples is initially evaluated at 5.58%. It can be used directly as an objective function to be minimized. However, it is more realistic to define the torque ripples reduction as a constraint to be less than 4.5% as shown in Eq.(7). That represents about 1% torque ripples reduction and it reflects more the manufacturing process. T _ ripples (7) Generally, minimizing the motor losses and reducing the torque ripples would yield motor design with lower average torque, T_ave. Consequently, it is necessary to define a torque constraint to meet the average torque design requirement of 2.5 N.m. The average torque constraint is defined in Eq.(8) below as: 2.5 T _ ave 0 (8) 4.3. Optimization Stategies Two optimization strategies are investigated and examined for the motor losses minimization and torque ripples reduction. Initial design performances computation and analysis provide a motor power budget where the stator winding copper losses are significant and from the magnetic stand point, the motor is well below the material saturation. Based on these findings, a screening process allows us to segregate the motor losses minimization and the torque ripples reduction into 2 sequential optimization problems [8]: First, motor losses optimization and then torque ripples reduction on the resulting design motor losses optimization. This 2 steps optimization process is compared with the single step multi-constraints losses and torque ripples minimization Screening and 2 Steps Optimization Results Optimization Process 1 A screening process is applied in our motor losses minimization and it results in identifying the physical properties parameter AIrms, motor drive current as the major contributor to the stator winding copper losses, thus the motor losses. Take note that reducing the motor drive current will also reduce the motor operating torque; hence there is a need of boosting back the motor torque by using more performant magnet (stronger remanent flux density Br). This leads us to define the first step optimization process in minimizing F obj while subjecting to the average torque 6

7 constraint of Eq. (8). The 2 parameters selected are AIrms that can vary from 10 Amps to 30 Amps and ABr that can vary from 0.41 T to 0.80 T. Figures 7a and 7b show respectively the objective function convergence and the values of the average torque constraint during the first step optimization process. The Sequential Quadratic Programming optimization algorithm is used to find the minimum losses. Figure 7a: Motor Losses Objective Function Figure 7b: Average Torque Constraint Variation The design parameter optimum values of the first step of the optimization process 1 are listed in Table 3 in green. The motor phase current is reduced from 30 Amps to Amps whereas the magnet remanent flux density is increased from 0.41 T to 0.8 T after only 3 SQP iterations. After the first optimization step yielded the minimum losses motor design meeting the torque constraint, we perform the second step optimization which consists of shaping the motor magnetic circuit such as the stator tooth geometry and the magnet shape to reduce the torque ripples. The torque ripples defined in Eq.(1) is now the objective function and the average torque constraint of Eq.(8) is also enforced in this optimization step. The design parameters selected are geometric and are for the stator: the stator slot opening A_SO, the stator tooth angle A_SOAng, the stator tooth tip thickness A_TGD. For the magnet, they are: the magnet thickness A_LM, the magnet arc span A_BetaM and the magnet edge height A_Edge. Figures 8a and 8b show respectively the objective function T_Ripples convergence and the values of the average torque constraint during the second step optimization process. The stochastic optimization algorithm Genetic Algorithm is used to find the minimum torque ripples after 999 iterations. The design parameter optimum values of the first step of the optimization process 1 are listed in Table 3 in blue. The optimum design yielded by the optimization process shows a significant losses reduction of Watts while meeting the average torque and the torque ripples constraints. Figure 8a: Convergence of Torque Ripples Objective Function Optimization Process 1-2 nd step 7

8 Figure 8b: Variation of the Torque Constraint Optimization Process 1-2 nd step 4.5. Multi-Constraints Torque Ripples and Losses Minimization Optimization Process 2 Whereas the previous optimization process involves more engineering analysis and user intervention, this process is more black-box concept. In this perspective, after the design parameters are selected, the objective function defined and the constraints are set, the optimization algorithm such as Genetic Algorithm takes over to search the vast design domain to yield the optimum design. The objective function is defined as the motor losses to be minimized subjected to the torque ripples constraint of Eq.(7) and the average torque constraints of Eq.(8). All the design parameters, physical and geometric described in section 4.1. are selected as optimization parameters. The optimum values obtained as shown in Table 3 in magenta. Table 3 shows the values of the design parameters, the motor losses, the average torque and torque ripples for the initial design, the optimum design of optimization process 1 in two steps and the optimum design of optimization process 2. Table 3: Init Design Parameters and Performances vs. Optimum designs (Process 1 2 Steps and Process 2) Name Initial Optimum 1 Optimum 2 Motor Phase Current (Amps rms) A_IRMS Magnet Br A_Br Slot Opening in mm A_SO Stator Tooth Angle in deg. A_SOAng Tooth Tip Thickness in mm A_TGD Magnet Thickness in mm A_LM Magnet Arc Angle in deg. A_BetaM Magnet Edge Height in mm A_Edge Motor Losses in Watts Losses motor Average Torque in N.m T_Ave Torque Ripples in % T_Ripples Figure 9a: Motor Losses Objective Function Optimization Process 2 8

9 Figures 9a and 9b show respectively the convergence of the losses objective function and the variation of the torque constraints during the optimization process 2. After reaching the design with lower losses of Watts (without mechanical losses) after 20 iterations, the Genetic Algorithm could not improve the design further, except for very small losses reduction and small constraint variations. Figure 9b: Constraints Variations Optimization Process 2 Figures 10a and 10b show respectively the optimum motor geometry obtained with optimization process 1 and optimization process 2. Take note that both optimum designs exhibit variable air gap feature for torque ripples reduction. Figure 10a: Optimum Geometry Process 1 Figure 10b: Optimum Geometry Process 2 5. Design Comparison and Life Cycle Assessment 5.1. Design Optimization Summary Designs from optimization process 1 and optimization process 2 are compared in terms of geometric changes along with material changes. Both optimization processes reduce the motor drive current to reduce the motor winding losses, thus minimizing the motor losses. To meet the average torque requirement, the magnet strength is increased with higher performance magnet with higher Br or the magnet length is increased (optimization process 2) to add more magnetic fluxes across the air gap. To meet the torque ripples, the stator tooth shape is modified along with the magnet shape at the edge areas. Overall, designs from both optimization processes present motor losses and torque ripples reduction while meeting the torque requirement. Design from optimization process 1, however, results in better efficiency improvement than the design from optimization process 2 (80.03% vs %) Costs Assessment The optimized designs result in geometric and material changes. 9

10 For the stator laminations, only the geometric changes are considered in order to reduce the torque ripples. The impact of the stator lamination geometric changes is in terms of new lamination tool of which the cost can be amortized over time. However, the resulting lower torque ripples have for effects less shaft vibrations thus less bearing failure along with longer bearing life. We decide again using thinner laminations for the stator stacks as the number of laminations increases along with the costs while the core losses gain is minimal as shown in Table 2. For the magnet, the optimized designs require new magnet material with higher magnet strength which has higher $/kg. Furthermore, to compensate for the lower motor drive current, we thicken the magnet (especially for the optimization process 2 design) to provide more magnetic flux across the air gap. A bigger and stronger magnet leads to much higher magnet cost for the optimized design when compared to the original design. The new magnet shape with thinner edges also requires new molding tool that can be amortized over time. Overall, the optimized design requires new tooling investments and has higher material costs. Optimization process 2 design has a larger magnet but less expensive magnet material compared to the magnet of optimization process 1 design, thus making both magnet costs equivalent. 5.3 Efficiency Improvement and Assessment Optimization process 1 design has an efficiency of 80.03%. The total motor losses are Watts compared to Watts, showing a reduction of Watts which is significant over the lifetime of the motor. Furthermore, less motor losses mean the motor temperature rise will be less resulting in a reduced chances of motor failure and longer motor life. Optimization process 2 design has an efficiency of 70.67%. The total motor losses are Watts. This corresponds to a reduction of Watts. The motor temperature rise would be about half of the original design whereas the temperature rise of optimization process 1 design is about 1/3 of the original design one. 5.4 Life Cycle Assessment When taking into consideration the efficiency gain and the cost increase, optimization process 1 design presents the most attractive solution over the long terms. It has the biggest motor losses reduction as the saving in energy would quickly offset the material cost increases and tooling change costs [9]. 6. Conclusion The off the-shelf (commercially available) brushless permanent magnet motor has been analyzed and optimized to increase its efficiency. The optimization process was approached in two ways. The first approach that is more engineering oriented yields a higher efficiency design whereas the second one, which is black-box oriented, relies only on numerical solutions and yields an improved design but compared with approach 1, not the most optimum design. This demonstrates that in the field of engineering optimization of industrial devices, we cannot totally rely on the black box approach as the physical problem often presents complex objective functions and is subjected to numerous constraints. The optimum design obtained is always attached with increased costs of new materials or tooling changes, but in terms of Life Cycle Assessment where the environment cost of the optimized design is also examined with its efficiency and operating cost reduction, the optimum design represents the most environmentally economical solution. References [1] J. R. Hendershot Jr., T. J. E. Miller, Design of Brushless Permanent-Magnet Motors, Magna Physics Publications Oxford Science Publications, [2] PC-BDC 9.0, SPEED Software, SPEED LAB, Glasgow, United Kindom, [3] FLUX 10, CEDRAT S. A., Meylan, France, [4] GOT Version 3, G2ELAB, INPG, Saint Martin d Heres, France, [5] G. Bertotti, A. Boglietti, M. Chiampi, F. Fiorillo, M. Lazzari, An Improved Estimation Of Iron Losses In Rotating Electrical Machines, IEEE Trans. On Magnetics, Vol. 27, No. 6, , Nov [6] F. Fiorillo, A. Novikov, An Improved Approach To Power Losses In Magnetic Laminations Under Non-Sinusoidal Induction Waveform, IEEE Trans. On Magnetics, Vol. 26, No. 5, , Sept [7] D. Cho, H. Jung, C. Lee, Induction Motor Design For Electric Vehicle Using a Niching Genetic Algorithm, IEEE Trans. Ind. Appl., Vol. 37, No. 4, , July/August [8] Y. Kano, T. Kosaka, N. Matsui, Optimum Design Approach For A Two-Phase Switched Reluctance Compressor Drive, IEEE Trans. Ind. Appl., Vol. 46, No. 3, , May/June [9] V. Debusschere and al., Minimization Of Life Cycle Energy Cost Of A Single Phase Induction Motor, Electric Machines and Drives Conferencs 2009, IEMDC 09, , May