Design and Optimization Tools for High-Efficiency Three-Phase Induction Motors R.L.J. Sprangers1 , J.J.H. Paulides1 , K.O. Boynov1 , J. Waarma2 , E.A. Lomonova1 EINDHOVEN UNIVERSITY OF TECHNOLOGY1 P.O. box 513, 5600 MB Eindhoven, The Netherlands Phone: +31 (0)40 247-2310 Fax: +31 (0)40 243-4364 Email:
[email protected] URL: http://w3.ele.tue.nl/nl/epe/
VOSTERMANS VENTILATION B.V.2 P.O. Box 3025, 5902 RA Venlo, The Netherlands Phone: +31 (0)77 389-3232 Fax: +31 (0)77 382-0893 Email:
[email protected] URL: www.vostermans.com
Keywords , , ,
Abstract An Expert System (ES) for the analysis and design optimization of low-power, three-phase induction motors (IMs) is presented. The ES is based on analytical models, which are carefully selected from literature, and coupled together to calculate motor performance characteristics. These performance characteristics are computed within a few seconds. Also, validation of the ES calculation results against measurements on four test motors shows that the analysis results are reasonably accurate. Additionally, the ES is applied to redesign a case study motor and a prototype of the new design is realized. The theoretical design results are validated against measurement performed on the prototype. This validation shows that the design optimization works, though a more accurate description of the lamination material B(H) characteristic is desirable to improve the accuracy of the ES.
Introduction Among the various types of electric motors, the induction motor (IM) has manifested itself as the workhorse of industry. In comparison to other motor types, the IM has several advantages such as low production cost, low maintenance cost, high reliability and its ability to run directly from the grid. However, the IM its main disadvantage is a relatively low efficiency. During the last two decades, a significant part of the IM research has been directed towards cheaper and more reliable control of IMs, such as field-oriented sensorless control [1]. In variable speed applications, the improved control methods can give a significant increase in the total system efficiency [2]. However, due to the world-wide desire to reduce electric energy consumption, the efficiency requirements for electric motors intended for constant speed applications are increasing. To maintain its position as workhorse of industry, the common design of such IMs should be reconsidered, especially for low power IMs. However, proper design tools are required in order to investigate the influence of changes in design and materials. One valuable tool for IM analysis is Finite Element Analysis (FEA). However, FEA requires relatively long computational times and it does not provide any analytical insight into the physical phenomena that determine the behavior of the machine. This makes FEA less suitable as a design tool. Tools based on analytical methods, such as SPEED [3] and RMxprt [4], are faster and more suitable for design, but the large number of coefficients and model choices require extensive knowledge in order to use the software. Furthermore, commercially available tool are relatively expensive and do not provide any access to the software code. The aim of this work is to develop suitable analysis and design tools for three-phase IMs, such that a minimal number of tuning parameter is required. Such tools are also known as Expert Systems (ES), and
1
2
3
4
A
5
6
7
8
9
B
10 11 12
C
Figure 1: Full pitch distributed winding
1
2
3
4
5
6
A
7
B
8
9
10 11 12
C
Figure 2: Short pitch distributed winding
should be fast, sufficiently accurate and easy-to-use. In this work, the ES should be applicable for threephase IMs with an output power ranging from 100 W up to 5 kW. Suitable analytical models are selected from the widely available literature to predict the electric and magnetic behavior of the motor. These models are then coupled by a solving algorithm to form an analysis tool. Additionally, an optimization procedure is described based on the analysis tool, and applied to redesign a case study motor. The main contribution of this work is the method used to couple the analytical models and the validation of its results by means of measurements. It is shown that relatively simple analytical models can be used to create a sufficiently accurate ES. Additionally, the results of the optimization procedure are validated by means of a prototype. Based on the results, some of the limitations of the optimization procedure are discussed, including the influence of critical dimension tolerances, lamination material characteristics and the accuracy of the magnetic model.
Preliminary design choices The design of a three-phase IM is initiated by the definition of the desired specifications for the motor. Table I shows an overview of the specification parameters for a three-phase IM. From these specifications, suitable preliminary design choices are then selected. These design choices include sizing of the motor, definition of the winding layout, material selection and preliminary sizing of the main magnetic flux path. The selection and calculation of the preliminary design parameters is discussed briefly in this section.
Sizing and winding selection The main dimensions of a motor include the stator outer diameter, Dse , the rotor diameter, Dr , the shaft diameter, Dsha f t , the axial length, l, and the air gap length, δ. For a mass produced motor, these parameters are normally limited by manufacturing possibilities. However, for new designs, motor sizing can be performed based on empirical methods to obtain an initial estimation of the main dimensions. The equations used for motor sizing can be found in literature [5, 6]. After defining the main dimensions of the motor, a winding lay-out for the stator winding can be selected. In this work, only distributed stator windings are considered for the three-phase IM. It is desirable to design the stator winding such that a sinusoidal magneto-motive force (mmf) distribution is produced with minimized harmonic distortion. To reduce the harmonic distortion of the mmf distribution, several methods can be employed. For example, coil distribution spreads the phase coils along several slots to reduce mmf harmonics, as shown in Fig. 1. Also, short pitching shifts the upper part of the winding with respect to the lower part to reduce mmf harmonics, as shown in Fig. 2. Both methods influence the harmonic mmf amplitude as well as the fundamental mmf amplitude, and the influence on the νth spatial harmonic can be calculated by the distribution factor, kd,ν and the pitch factor, k p,ν , respectively. Equations for these factors can be found in literature [5, 6]. Additionally, rotor skewing is usually applied to reduce the effects of stator slot harmonics. A skew pitch, τskew , equal to the stator slot pitch, τus , is recommended to effectively cancel slot harmonics. The influence of skewing on the νth mmf harmonic
Table I: Specification parameters for the desired three-phase motor
Symbol Vph fs TN n p Top,s Top,r Tamb
Unit V Hz W rpm ◦C ◦C ◦C
Description Stator phase voltage (rms) Stator excitation frequency Nominal torque Nominal speed Number of pole pairs Stator operating temperature Rotor operating temperature Ambient temperature
geometry, slip initialization
i+1 Em 1 Em
magnetic model
No electric model
i Em,new
εemf < εacc ?
Yes Characteristics calculation
Figure 3: Schematic overview of the proposed coupling algorithm
is given by the skew factor, ksq,ν , which is computed as given in [5, 6]. The total winding factor is then kw,ν = kd,ν k p,ν ksq,ν .
(1)
The number of stator slots is usually selected such that a minimum slot pitch τmin us ≈ 7 mm can be employed [6]. Furthermore, only integer values of the number of slots per pole per phase, q, are considered here, which limits the possible values of Qs . Using these rules, the maximum possible value of Qs is often selected to obtain maximum reduction of the mmf harmonics. For the number of rotor slots, Qr , a suitable choice can now be selected from tables provided in literature [5, 6] depending on Qs and p.
Material selection and lamination design The selection of the materials for the IM is limited here to the magnetic lamination material and the rotor cage conducting material. For the rotor cage material, a choice must be made between various aluminium alloys and copper alloys. For the lamination material, also many different materials are available. In both cases, a trade-off should be made between efficiency and cost. The developed ES could be used to automate this trade-off. Following the lamination material selection, an initial design for the lamination dimensions will be calculated. The design of the stator and rotor laminations is largely defined by six parameters, namely the stator yoke height, hys , the stator slot height, hss , the stator tooth width, bds , the rotor yoke height, hyr , the rotor slot height, hsr , and the rotor tooth width, bdr . To calculate preliminary values for these parameters, an initial value for the amplitude of the fundamental magnetic flux density in the air gap, Bˆ δ,1 , is selected, usually between 0.5 and 0.8 T. The peak fundamental magnetic flux density in the yokes is then calculated as Bˆ ys/r,1 = αi Bδ,1
πDs/r l 0 , 4pkFe lhys/r
(2)
where Ds = Dr − 2δ is the stator air gap diameter, l 0 = l + 2δ is the effective motor length, kFe is the lamination stacking factor and the factor αi takes flux flattening due to stator and rotor tooth saturation into account [6]. For the preliminary design, αi = 0.64 can be used. Further, the apparent peak fundamental magnetic flux density in the teeth, Bˆ 0ds/r,1 , is calculated as Bˆ 0ds/r,1 =
Ds/r l 0 τus/r sin Bˆ δ . kFe lbds/r Ds/r
(3)
For the preliminary design, it is assumed that the actual peak fundamental magnetic flux density in the teeth, Bˆ ds/r,1 , is equal to Bˆ 0ds/r,1 . Finally, Eqs. (2) and (3), are used to determine values for hys , hyr , bds and bdr such that the peak magnetic flux densities in the teeth and yokes do not exceed Bmax = 1.6 T. The remaining dimension details of the stator and rotor slots depend on the type of slot that is selected. An overview of commonly used slot types is shown in literature [5, 6]. In this work, the slot dimension details are selected during the preliminary design and fixed during the design optimization.
Electromagnetic modeling To optimize the efficiency of the IM, a fast and sufficiently accurate electromagnetic model is desired. This electromagnetic model is often divided into separate models for the magnetic behaviour and the electric behaviour. The coupling between these two models can be taken into account by means of an iterative algorithm. An overview of the proposed coupling algorithm is shown in Fig. 3.
geometry, emf initialization αi1
=
αik+1 αi1
2 π
calculate Uˆδ
no calculate Uˆds , Uˆdr
calculate k ksat , αi,new
k αi,new
εαi < εacc ?
yes
calculate Uˆys , Uˆyr
Figure 4: Algorithm for magnetic model analysis
The algorithm can be used to calculate motor performance at any desired operating speed, nop , between zero and synchronous speed, nsyn = (60 fs ) /p. The operating slip, s, is calculated as s=
nop nsyn − nop = 1− . nsyn nsyn
(4)
For a given geometry and operating slip, all required model parameters are initialized and an initial estimation of the emf, Em1 , is selected. Then, Em1 is used as an input for the magnetic and electric model 1 is calculated from the electric model analysis results. The error between evaluation. A new emf, Em,new the initial and the new emf is calculated as i Em i εem f = i − 1 , (5) Em,new where i indicates the iteration step. If εiem f is larger than the desired maximum error, εmax , the next iteration step, i + 1, is initiated. This process is repeated until a sufficiently small error between Emi and i Em,new is reached. After each iteration step, a new estimation of the emf, Emi+1 , is calculated as i Emi+1 = Emi +Cem f Em,new − Emi , (6) where Cem f is the emf relaxation constant. Finally, when εem f has converged, performance characteristics can be calculated from the magnetic and the electric model analysis results.
Magnetic model The magnetic model is based on the lumped parameter model shown in Fig. 5. The model represents one half of the main flux path of the motor and accounts only for the fundamental space harmonic. The depicted elements represent the reluctance of the stator and rotor yokes, the stator and rotor teeth and the air gap. Furthermore, the source term represents the mmf produced by the stator winding for the fundamental space harmonic. The analysis of the magnetic circuit is performed in an inverse manner, such that the mmf drops are calculated as a function of the estimated emf. In the calculation of the mmf accross the iron parts, the non-linear B(H) characteristic of the lamination material given by the lamination manufacturer is used. An example is shown in Fig. 20 by the curve labeled ’B(H) original’. An overview of the algorithm used to analyse the magnetic model is shown in Fig. 4. After the initialisation of the magnetic model parameters, the peak magnetic flux density in the air gap, Bˆ δ,1 , is calculated from the emf estimation, Emi , as √ i 2Em , (7) Bˆ δ,1 = 2π fs kw,1 αi lτ ps Ns where τ ps is the stator pole pitch and Ns is the number of turns per phase of the stator winding. Then, the peak mmf across the air gap reluctance element, Uˆ δ , and the peak mmfs accross the stator and rotor teeth, Uˆ ds and Uˆ dr , are calculated using the non-linear B(H) characteristic and the equations described in [6]. In the calculation of Uˆ δ , the effective lengthening of the air gap due to the slot openings is accounted for by the Carter coefficient, kC [7]. Also, in the calculation of Uˆ ds and Uˆ dr , the width of the stator and rotor teeth is corrected by subtracting 0.1 mm to account for the influence of punching on the edges of the laminations [6]. Once Uˆ δ , Uˆ ds and Uˆ dr are known, the tooth saturation factor, ksat , is calculated as ksat =
Uˆ ds + Uˆ dr . Uˆ δ
(8)
ˆm Θ
Uˆys /2
Uˆds
Uˆyr /2
Uˆdr
Is
Uˆδ
Figure 5: Lumped parameter main flux path model
Vph
Rs
Lσ,s
RF e
Em Lm
0 Ir Lσ,r
Rr0
1−s s
· Rr0
Figure 6: Single phase electric equivalent circuit
A new value for the flux flattening factor, α1i,new , is then found by interpolating ksat on the αi (ksat ) characteristic given in [6]. The error between the initial and the new flux flattening factor is calculated as αk εkαi = k i − 1 , (9) αi,new where k indicates the iteration step. If εkαi is larger than εmax , the next iteration step, k + 1, is initiated by calculating a corrected flux flattening factor as k k k αk+1 = α +C α − α (10) αi i i,new i , i where Cαi is the flux flattening factor relaxation constant. Finally, when αi has converged, the mmfs across the stator and rotor yoke, Uˆ ys and Uˆ yr , are calculated using the non-linear B(H) characteristic and the equations given in [6]. A correction factor, cs/r , is applied in these calculations to account for the non-sinusoidal distribution of Hys/r due to the non-linearity of lamination materials. Then, the total mmf required to magnetize half of the main flux path is found as Uˆ ys Uˆ yr + , Uˆtot = Uˆ δ + Uˆ ds + Uˆ dr + 2 2 and the effective air gap, δe f = Uˆtot /Uˆ δ kC δ, is calculated.
(11)
Electric model The electric model is based on the single phase electric equivalent circuit shown in Fig. 6. It is assumed that the motor operates in balanced conditions and only the fundamental time harmonic is taken into account. The parameters of the model shown in Fig. 6 include the stator resistance, Rs , the stator leakage 0 , the core loss resistance, R inductance, Lσ,s , the rotor resistance, R0r , the rotor leakage inductance, Lσ,r Fe and the magnetizing inductance, Lm . The calculation of the parameter values will be discussed briefly. Resistance parameters Firstly, the resistance of a stator phase winding, Rs , is calculated from the stator winding conductivity at operating temperature, σs,op , the number of parallel wires, a p , the wire diameter, Dwire , and the average turn length, lturn . The average turn length is estimated using empirical equations of the form lturn = 2l + aτcoil + b,
(12)
where τcoil is the average coil pitch. The parameters a and b need to be tuned towards the production process of the motor manufacturer for each number of pole pairs, p. Also, skin and proximity effects are assumed to be negligible due to the small wire diameters used in low-power IMs. Secondly, the rotor resistance, R0r is calculated. Initially, the dc resistance of a skewed rotor bar, Rbar , and the dc resistance of a rotor ring segment, Rring , are computed. These calculations are based on the material conductivity at operating temperature, σr,op and the bar and ring dimensions. However, the skin effect due to slot leakage flux, which links part of the rotor bars, will effectively increase the bar resistance for high slip values. The increase in Rbar is accounted for by the skin effect resistance factor, kR . An analytical method to calculate kR as function of the operating slip is given in [5, 6]. Now, the rotor resistance, R0r , is calculated as # 2 " N k k R 12 s p,1 ring d,1 kR (s) Rbar + , (13) R0r = Qr ksq,1 2 sin2 πp Qr
Finally, the core loss resistance is calculated as 3Em2 , (14) PFe where PFe presents the total iron core loss. The calculation of PFe will be discussed later in this section. RFe =
Inductance parameters The magnetizing inductance, Lm , represents the fundamental magnetic flux in the main flux path of the motor that links both the stator and the rotor windings. This flux is known as the main flux. Its value is computed from the result of the magnetic model, and given by Lm =
6µ0 τ ps l 0 (kw,1 Ns )2 π2 pδe f
(15)
Only the main flux contributes to the production of useful torque. All additional flux is considered 0 . In total, the leakage inductance leakage flux, and is represented by the leakage inductances, Lσ,s and Lσ,r can be divided into five different components, namely: 1. Air gap leakage inductance, Lδ , which models all harmonic fluxes in the main flux path other than the fundamental one. The stator and rotor values for Lδ are computed using the equations given in [6]. 2. Slot leakage inductance, Lu , which models the leakage flux inside a slot between two teeth. The stator and rotor values for Lu are found using the equations given in [6], though the equation for the rotor value is based on the work of Richter [8]. 3. Tooth tip or zig-zag leakage inductance, Ld , which models the leakage flux that crosses the air gap back and forth between the tooth tips. The stator and rotor values of Ld are calculated using the equations given in [6]. 4. End winding leakage inductance, Lw , which models the leakage flux that flows in the air that surrounds the stator end winding and the rotor end ring. The stator and rotor values of Lw are found using the equations given in [5]. 5. Skew leakage inductance, Lsq , which models the part of the fundamental magnetic flux in the main flux path that does not link both the stator and the rotor windings due to skewing. The value of Lsq is calculated using the equation given in [6]. Finally, the total leakage inductances of the stator and rotor are calculated as Lsσ = Lδ,s + Lu,s + Ld,s + Lw,s + Lsq , (16) # 2 " Lw,r 12 Ns kd,1 k p,1 0 Lrσ = Lδ,r + Ld,s + Lsq + , (17) kL Lu,r + Qr ksq,1 2 sin2 πp Qr where kL account for a reduction in the rotor slot leakage inductance due to the rotor bar skin effect. Analytical equations to calculate kL can be found in [5, 6].
Losses and efficiency The losses of the IM are divided into four components, namely ohmic losses, fundamental iron losses, mechanical losses and additional losses. Firstly, the stator and rotor ohmic losses, Pohm,s and Pohm,r , are computed as 2 Pohm,s = 3 |I¯s | Rs
2 Pohm,r = 3 |I¯r | R0r .
(18)
Secondly, the fundamental iron losses in the stator yoke, PFe,ys , the stator teeth, PFe,ds , the rotor yoke, PFe,yr , and the rotor teeth, PFe,dr are calculated separately using the equations given in [6]. These equations use the specific loss coefficient of the lamination material, P15 , for which the value specified by the lamination steel manufacturer is adopted. The total fundamental iron loss is calculated as PFe = PFe,ys + PFe,ds + PFe,yr + PFe,dr . (19) Thirdly, the mechanical losses, Pmech , account mainly for bearing friction losses. However, in case rotor cooling fins are present on the end rings, rotor windage losses should be added to Pmech . Finally, the additional losses, Pad , model ohmic and iron losses due to parasitic effects, and are estimated as 0.5% of the input power. For given slip, s, the mechanical output power, Pout , and the efficiency, η, of the motor are then calculated as 1−s 2 − Pmech . (20) Pout = 3 |I¯r | R0r s Pout η = . (21) Pout + Pohm + PFe + Pmech + Pad
Model validation To validate the electromagnetic model of the ES, it is applied to analyse the performance of four test motors. The results of the analysis are compared to measurement results. Some specification parameters of the test motors are given in Table II. The nominal output power, PN , of the test motors is between 100 W and 1500 W. Figures 7 to 14 show a comparison between the ES analysis results and the measurement results for the four test motors. The comparison is based on characteristics for the output torque versus speed, T (n), and the stator phase current versus speed, Iph (n). All characteristics are described in per unit (p.u.) values. It can be seen from figures 7, 9, 11 and 13 that the torque calculated by the ES matches well with the measured torque for low slip values. For high slip values, the accuracy of the ES decreases. However, the uncertainty of the measured data is also larger for high slip values, due to high rotor ohmic loss and it associated temperature rise. Furthermore, it can be seen from figures 8, 10, 12 and 14 that the stator phase current calculated by the ES generally matches well with the measured current. However, a discrepancy can be seen at low slip values, especially close to zero slip. Several possible causes of the discrepancy are manufacturing tolerances, variation in the lamination material properties and inaccuracies of the magnetic model. These problems will be discussed more thoroughly in the next section.
Design optimization Methodology The presented analytical models are used to implement an optimization procedure. For fixed main dimensions, the geometrical parameters hys , hss , bds , hyr , hsr and bdr are optimized to give maximum efficiency. Thus, in effect, the balance between the amount of conducting material and the amount of lamination material is optimized. A schematic overview of the optimization algorithm is shown in Fig. 17. This algorithm is implemented in MATLAB and is built around the ’fmincon’ optimization function, which is part of the optimization toolbox [9]. Firstly, an initial design is generated using the preliminary design choices discussed previously. For the resulting geometry, the stator winding coils are then designed such that the fundamental magnetic air gap flux density found from the magnetic model matches with the induced voltage calculated from the electric model. Equation (7) is used to calculate Ns , and the wire diameter, Dwire , is found as s 4kCu SCu,s Dwire = , (22) zQ π where zQ is the number of conductors per slot, SCu,s is the stator slot area and kCu = 0.63 is the slot fill factor, which does not include the slot insulation. Finally, when the coil design is finished, the Expert System is used to calculate the performance of the motor design at nominal speed and the optimization function decides whether the performance is satisfactory or not. If the design is considered optimal, the characteristics of the new design are calculated. However, if the design is not considered optimal, a new geometry is proposed and the previous steps are repeated.
Case study The presented optimization procedure is applied to redesign a low-power, 6-pole induction motor with a nominal speed of 895 rpm. The B(H) curve of the lamination material, as specified by the manufacturer, is shown in Fig. 20 as ’B(H) original’. For the new design, an efficiency increase of 9.9% with respect to the original design is predicted by the ES. This improvement is mainly due to a reduction of the stator
Table II: Test motor specification parameters
Symbol Vph fs p sN
Unit V Hz -
Motor 1 230 50 1 0.09
Value Motor 2 Motor 3 230 230 50 50 2 2 0.093 0.06
Motor 4 230 50 3 0.13
Description Test motor number Stator phase voltage (rms) Stator excitation frequency Number of pole pairs Nominal slip
6 Stator phase current (p.u.)
Output torque (p.u.)
4 3 2 1 0 0
Model Measurement 500
1000
1500 2000 Speed (rpm)
2500
5 4 3 2 1 0 0
3000
Figure 7: Test motor 1 - Torque comparison
Stator phase current (p.u.)
Output torque (p.u.)
1000
2.5 2 1.5 1 Model Measurement 500
1000
2 1.5 1 0.5 0 0
1500
Model Measurement 500
1000
1500
Speed (rpm)
Figure 10: Test motor 2 - Current comparison
3
5 Stator phase current (p.u.)
Output torque (p.u.)
3000
Figure 9: Test motor 2 - Torque comparison
2.5 2 1.5 1 0.5 0 0
Model Measurement 500
1000
Stator phase current (p.u.)
2 1.5 1 Model Measurement
Model Measurement 500
1000
1500
200
400 600 Speed (rpm)
800
3 2.5 2 1.5 1 0.5 0 0
1000
Figure 13: Test motor 4 - Torque comparison
Model Measurement 200
400 600 Speed (rpm)
800
1000
Figure 14: Test motor 4 - Current comparison 3 Stator phase current (p.u.)
3 2.5 2 1.5 1
0 0
1
3.5
2.5
0.5
2
Figure 12: Test motor 3 - Current comparison
3
0 0
3
Speed (rpm)
Figure 11: Test motor 3 - Torque comparison
0.5
4
0 0
1500
Speed (rpm)
Output torque (p.u.)
2500
2.5
Speed (rpm)
Output torque (p.u.)
1500 2000 Speed (rpm)
3
3
0 0
500
Figure 8: Test motor 1 - Current comparison
3.5
0.5
Model Measurement
Model Measurement 200
400 600 Speed (rpm)
800
1000
Figure 15: Design validation - Torque comparison
2.5 2 1.5 1 0.5 0 0
Model Measurement 200
400 600 Speed (rpm)
800
1000
Figure 16: Design validation - Current comparison
constraints, fixed dimensions initial design
new geometry
geometry
No
Expert System
stator coil design
optimal design?
Yes
calculate characteristics
Figure 17: Overview of the optimization algorithm
ohmic loss, Pohm,s , by approximately 56% with respect to the original design. Part of this reduction is realized by a reduction of the air gap length, which leads to lower magnetizing current. However, additionally, the optimization has provided a design with more space for the stator windings and less lamination material in the stator. As a result, Rs has decreased by approximately 29% and PFe,s has decreased by approximately 46%, according to the calculations. To validate the efficiency improvement, a prototype is constructed for the newly designed motor. A comparison between ES simulation results and measurements is shown in Figures 15 and 16 in terms of T (n) and Iph (n) characteristics. A good match between the calculated torque and the measured torque can be seen in Fig. 15. However, Fig. 16 shows that the measured phase current is generally larger than the calculated phase current. At the rated operating point, the phase current error is approximately 20%, whereas it increases up to approximately 45% at no-load operation. The increased phase current leads to an increase in Pohm,s , and consequently to a lower efficiency. In total, the measured rated efficiency of the prototype has increased by approximately 7% with respect to the original motor, whereas an increase of 9.9% was predicted. To determine the origin of the phase current mismatch, no-load measurements are performed on the prototype motor under varying excitation voltages. From these measurements, the magnetizing current, Im , is calculated as a function of Vph and compared to similar results obtained from the ES. Additionally, no-load simulation are performed using a 2D FEA model for the prototype motor. A comparison of the results is shown in Fig. 18. It can be seen that Im is underestimated by the ES along the entire voltage range. However, the 2D FEA results do not match with the measurement results either. One possible origin of the difference between the 2D FEA simulations and the measurements can be tolerances on critical dimensions of the motor. The prototype is simulated by 2D FEA with a 10% increase in δ and a 10% decrease in tooth width, separately. The results of both variations are shown in Fig. 19. However, it can be seen that the increase in δ barely influences the result, whereas the decreased in tooth width increases the error.
1.5
2
FEM − original Expert System Measurements
Magnetizing current (p.u.)
Magnetizing current (p.u.)
2
1 0.5 0 0.5
0.6
0.7
0.8 0.9 1 Phase voltage (p.u.)
1.1
1.2
2
1.5 1 B(H) original B(H) var 1 B(H) var 2 B(H) var 3
0.5
1000
2000 3000 4000 5000 Magnetic field strength (A/m)
6000
7000
Figure 20: Original B(H) curve and B(H) curve variations for no-load simulations
Magnetizing current (p.u.)
Magnetic flux density (T)
0.5
0.6
0.7
0.8 0.9 1 Phase voltage (p.u.)
1.1
1.2
1.3
Figure 19: Magnetizing current versus phase voltage: dimension variation
2
0 0
Measurements 1
0 0.5
1.3
Figure 18: Magnetizing current versus phase voltage
1.5
FEM − original FEM − increased δ FEM − decreased Bds
1.5
FEM − original FEM − B(H) var 1 FEM − B(H) var 2 FEM − B(H) var 3 Measurements
1 0.5 0 0.5
0.6
0.7
0.8 0.9 1 Phase voltage (p.u.)
1.1
1.2
1.3
Figure 21: Magnetizing current versus phase voltage: B(H) curve variation
Another possible origin of the mismatch between the 2D FEA results and the measurements shown in Fig. 18 can be the lamination material properties. Several variations on the original B(H) characteristic are investigated. Variations one and two, shown in Fig. 20 by ’B(H) var 1’ and ’B(H) var 2’ respectively, include a 5% decrease and a 5% increase of the flux density that defines the original B(H) characteristic. For the third variation, indicated by ’B(H) var 3’ in Fig. 20, the magnetic field strength of the original B(H) characteristic is multiplied by a factor of 10. The results of the 2D FEA simulations with altered B(H) curves are shown in Fig. 21. It can be seen that only variation three is able to correct the error for low excitation voltages, which suggests that the relative permeability of the linear part of the B(H) curve is much lower than expected. Also, it can be seen that only variation 2 is able to reduce Im for large Vph , which suggests the saturation flux density of the B(H) curve to be larger than expected.
Conclusions An Expert System (ES) for analysis and design optimization of three-phase induction motors (IMs), based on analytical electric and magnetic models, is implemented and validated against measurements. It is shown that the ES can be used to predict the motor performance relatively accurate. Also, the models are implemented into an optimization procedure to optimize the motor for high efficiency. A prototype for a case study design is realized and measurements show that it has a higher efficiency than the original motor. However, the measured efficiency improvement is smaller than expected due to an unexpectedly large magnetizing current. No-load measurements of the prototype and 2D FEA simulations show that tolerances of the air gap length and the tooth width are not the main cause of the magnetizing current mismatch. In fact, simulations performed with different variations on the original B(H) curve show that an incorrect definition of the B(H) curve is more likely to be the cause of the mismatch. However, to verify this, a thorough measurement of the B(H) characteristic is required. Furthermore, it can be seen from Fig. 18 that the magnetic model of the ES does not account for main flux path saturation properly. A more accurate (analytical) magnetic model, such as the model proposed in [10], can be considered to improve the ES accuracy. Finally, it should be noted that ES could be extended further, for example with an analytical thermal model [11]. In its current form, however, the developed ES can calculate full characteristics within a few seconds, and with reasonable accuracy. Therefore, it provides a powerful tool to investigate the influence of changes in the design choices with the aim of improving motor efficiency.
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