Performance Analysis of Unskewed Asymmetrical Rotor for LV Induction Motors

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Degree project in

Asymmetrical Rotor for LV Induction Motors

USMAN SHAUKAT

Stockholm, Sweden 2012 Electrical Engineering Master of Science

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Performance Analysis of Unskewed Asymmetrical Rotor for LV Induction Motors

USMAN SHAUKAT

Master of Science Thesis in Electrical Energy Conversion (E2C) School of Electrical Engineering

Royal Institute of Technology Stockholm, Sweden, October 2012

Supervisor: Alexander Stening (KTH), Rathna Chitroju (ABB) Examiner: Chandur Sadarangani, Professor

XR-EE-E2C 2012:018

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Abstract

This master thesis presents a comparative analysis of the starting per- formance and losses at rated operation for a 15 kW , 4-pole industrial in- duction motor, mounted with standard skewed, unskewed and unskewed asymmetrical die-cast aluminium rotors through measurements and simulations.

It is a well-known fact that rotor skewing suppresses the synchronous torques at low speeds and also reduces the audible noise of the machine.

However, the casting process results in a low resistive path between the rotor bars and the iron laminations, for skewed rotors, this promotes the flow of inter-bar currents. These currents, flowing between the rotor bars, increase the harmonic torques during a start and create additional losses at rated operation. For standard unskewed rotors, these losses are ideally zero, but these rotors may produce high audible noise. Studies have shown that rotors with asymmetrical rotor slot pitch can reduce the audible noise level in unskewed machines. By removing the skew, the inter-bar current losses are suppressed to a negligible level; ultimately increased machine efficiency is obtained. In this work the electrical performance is verified through measurements on the built prototypes.

Direct-on-line starts and rated performance for motors with diﬀerent rotor slot arrangements is simulated using 2D FEM tool FCSmek. The three prototypes are tested in the laboratory according to IEC 60034- 2-1 standard and the simulation results are in good agreement with the measured results. An additional test for the measurement of high frequency delta connected stator winding currents for each prototype machine is also performed, in order to study the losses induced in the stator winding.

Results have shown that by introducing the proposed asymmetry in the rotor slots, the synchronous torques at low speeds are suppressed effectively, thus, improving the starting performance of the asymmetrical rotor compared to the standard unskewed rotor. Additionally, a higher pull-out torque is obtained for the unskewed rotor motor compared to the standard skewed rotor motor. However, the losses were more or less re-distributed in the unskewed rotor motor, resulting in similar efficiency as the standard skewed rotor motor. One important observation is that; to capture the inter-bar current losses which are es- timated to be 5.5% of the total losses, requires more accurate methods of measurements than the existing. And sufficient repeatability must be achieved; alternatively one should rely on statistical data obtained from measurements on several number of motors.

Keywords: Induction motor, skewed rotor, inter-bar currents, starting performance, asymmetrical rotor slots, 2D FEM, syn- chronous torques.

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Utvärdering av Asymmetrisk Rotor Utan Spårsneddning för Asynkronmotorer

Detta examensarbete presenterar en jämförande studie av startegenska- per och förluster vid märkdrift för en 15 kW , 4-polig asynkronmotor, utrustad med olika typer av högtrycksgjutna aluminiumrotorer. Mät- ningar och simuleringar utförs då motorn utrustas med en symmetrisk rotor, med och utan spårsneddning, samt även för en asymmetrisk rotor utan spårsneddning.

Sneddning av rotorspåren i asynkronmotorer är vanligt förekommande, det används för att reducera asynkrona och synkrona moment vid låga varvtal samt för att minska det elektromagnetiska ljudet från motorn.

Men avsaknaden av spårisolation i högtrycksgjutna rotorer resulterar i att strömmar kan ledas fritt mellan spåren, dessa tvärströmmar ökar kraftigt med spårsneddningen. Tvärströmmarna ökar de asynkrona mo- menten vid en start, och kan även öka tillsatsförlusterna vid märkdrift.

Genom att använda rotorer utan spårsneddning kan dessa strömmar re- duceras till en försumbar nivå, och optimalt uppnås därmed en högre vekningsgrad.

Genom simuleringsprogrammet FCSmek, vilket använder Finita Ele- ment Metoden, beräknas startegenskaper och förluster vid märkdrift då motorn utrustas med de olika rotorerna. Motsvarande mätningar utförs på prototypmotorer enligt mätstandarden IEC 600-34-2-1, resultaten visar god korrelation med simuleringarna. Ett extra prov utförs även för att studera hur de högfrekventa strömmarna i statorlindningen påver- kas av rotordesignen. Resultaten visar att ett högre startmoment och ett högre kipmoment uppnås då rotorn ej har spårsneddning, men till en kostnad av ökade synkrona moment vid låga varvtal. Detta problem reducerades då en spårasymmetri infördes. Förbättrade startegenskaper uppnås därför med den asymmetriska rotorn jämfört med den symmet- riska rotorn utan spårsneddning. Mätningarna visade att de totala för- lusterna var mer eller mindre oförändrade för de tre rotorerna, vilket även gällde tillsatsförlusterna. Detta indikerar att förlusterna omförde- lades i motorn, snarare än att de reducerades, då spårsneddning ej an- vändes. Det konstaterades även att noggrannare mätmetoder med högre repeterbarhet krävs för att med precision kunna jämföra förändringen av tvärströmsförlusterna, som för de studerade motorerna uppskattades till 5.5% av de totala förlusterna.

Sökord: Asynkronmotor, induktionsmotor, tvärströmmar, starte- genskaper, asymmetrisk rotor, 2D FEM, synkrona moment.

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Acknowledgment

This master degree project was conducted in cooperation between ABB LV Motors (Västerås) and KTH (Stockholm). First of all, I would like to thank Allah Almighty for helping me all the way to reach this point. I would like to thank the Electrical Energy Conversion (E2C) department in KTH and ABB for providing me the op- portunity to work at one of the world’s leading engineering company.

I would like to thank Alexander Stening who was my supervisor in KTH. He had given me patient explanation about the theory, guided me very well, taught me how to work in the right direction and encouraged me all the way.

Also, I would like to thank my supervisor Rathna Chitroju from ABB LV Mo- tors, who gave me great help during my thesis work and did the detailed proofread of the report. I am especially thankful to him for introducing me to LaTeX. His profound nature gave me great impression.

I also want to thank my examiner Professor Chandur Sadarangani for his kind- ness and valuable guidance for my studies at KTH.

Last but not least, I would like to thank my parents, my brother, sisters and all the family members for their moral and ﬁnancial support throughout my study work;

my dear friends Arslan Zafar, Amit Kumar Jha, Ibrahim Bilal and Ali Shaheen for being an inspirational source and a helping hand through this journey.

Usman Shaukat

Västerås, October 2012.

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List of Symbols & Abbreviations

I Average line current [A]

I0 No-load average line current [A]

Is Stator current [A]

I_r Rotor current [A]

Iab Winding current in one phase [A]

L Axial length of machine [mm]

N_r Rated mechanical speed [rpm]

PN Rated power [W ]

P_T, P_loss Total power losses [W ]

P_in Input power [W ]

P0 No-load input power [W ]

Pout Output power [W ]

P_K Constant losses [W ]

PL Load losses [W ]

PLL Additional load losses or Stray load losses [W ]

P_{f e} Iron losses [W ]

Pf w Friction & windage losses [W ]

Pcu1, Ps Stator copper losses [W ]

P_cu2, P_r Rotor copper losses [W ]

Q_s Number of stator slots [...]

Qr Number of rotor slots [...]

R Stator line to line resistance [Ω]

R_N Stator winding resistance from rated load test [Ω]

R_||0 Line to line resistance from no-load test [Ω]

R_s Stator winding resistance [Ω]

Rr Rotor winding resistance [Ω]

R^′_r Rotor winding resistance refer to stator side [Ω]

R_tot Total locked rotor resistance [Ω]

T Output torque [N m]

T_N Rated torque [N m]

U_N Rated voltage [V ]

U0 No-load voltage [V ]

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Xtot Total locked rotor reactance [Ω]

X_sl Stator leakage reactance [Ω]

X_rl^′ Rotor leakage reactance referred to stator side [Ω]

f₍₁₎ Fundamental frequency [Hz]

fN Rated frequency [Hz]

fs Sampling frequency [Hz]

f_c Cut-oﬀ frequency [Hz]

ω Synchronous speed [rad/sec]

ωr Rotor mechanical speed [rad/sec]

ρ Inter-bar resistivity [Ωm]

ϕ Induced ﬂux [W b]

θ0 Initial slot pitch angle [rad]

b₀ Initial slot width [mm]

θ_c Inlet cooling temperature during tests [⁰C]

θw Reference winding temperature [⁰C]

s₍₁₎ Fundamental slip [...]

Ki,δi i^th modulation coeﬃcients [...]

γ Correlation coeﬃcient [...]

k_θ Winding temperature correction factor [...]

sθ Corrected slip value according to reference

coolant temperature [...]

p Number of stator pole pairs [...]

m Number of machine phases [...]

n Harmonic order [...]

η Eﬃciency [...]

nr Slot number [...]

FFT Fast Fourier Transform FEM Finite Element Method

FEMM Finite Element Method Magnetics

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List of Figures

1.1 Efficiency classes for electrical motors(50 Hz, 4-pole) [5] . . . . 2 1.2 A simple sketch of unskewed and skewed rotors [3] . . . 3 1.3 Illustration of inter-bar current flow between bars through lamination core 3 1.4 Starting torque curves with different inter-bar resistivity for a)Skewed

rotor motor b)Unskewed rotor motor[7] . . . 4 1.5 a) Components of stray-load losses for 0.2-37 kW induction motors

[7],[9]. b) Total rotor losses as a function of rotor skew and inter-bar resistivity [3] . . . 5 2.1 Semi-closed stator slot shape . . . 8 2.2 Distribution of losses in induction machines . . . 9 2.3 Diﬀerent test methods for eﬃciency measurement according to IEC 60034-

2-1 standard . . . 12 3.1 One-pole geometry of diﬀerent asymmetrical rotor slot arrangements

a)Dual 24-32 rotor slot design b)Progressive sinusoidal rotor slot design c)Dual+progressive sinusoidal rotor slot design . . . 14 3.2 One-pole geometry of rotor slots for diﬀerent rotor designs a) Standard

unskewed b) Dual 24-32+progressive c) Progressive sinusoidal . . . 16 3.3 Smoothening of residual loss data [14] . . . 20 4.1 2D FEM simulation results of the starting performance for three rotor

designs . . . 22 4.2 2D FEM simulated flux density in the airgap for three rotor designs . . 24 4.3 Harmonic spectrum of airgap flux density for three rotor designs . . . . 24 4.4 2D FEM simulation for the rated torque of different rotor designs . . . . 25 4.5 Torque harmonics at rated operation for three rotor designs . . . 26 4.6 Delta circulating stator currents at rated operation for three rotor designs 28 4.7 High frequency harmonic components in 2D FEM simulated winding

current I_ab at rated operation for three rotor designs . . . 29 5.1 Validation of 2D FEM simulation results for the starting performance of

standard unskewed rotor case . . . 32

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5.2 2D FEM simulated and measured results for high frequency stator winding currents for standard unskewed rotor case . . . 35 5.3 Measured torque-speed and current-speed curves for standard skewed

and standard unskewed rotor motors . . . 36 5.4 Measured variation of torque with time at high sampling frequency for

skewed and unskewed rotor motors . . . 39 5.5 Measured results for high frequency stator winding current for standard

skewed and standard unskewed rotor motors . . . 41 5.6 Measured torque-speed and current-speed curves for three rotor designs 41 5.7 Torque variation with time for motor with diﬀerent rotor prototypes . . 43 5.8 Measured winding current I_ab at rated operation for three rotor designs 45 5.9 High frequency components in measured winding current Iab at rated

operation for three rotor designs . . . 46 A.1 Rotor slot dimensions . . . 53 B.1 Single phase equivalent circuit for locked rotor condition . . . 55

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List of Tables

3.1 General motor speciﬁcations . . . 15

4.1 Simulated starting properties for the three rotor designs . . . 23

4.2 Summary of losses at rated operation for three rotor designs . . . 27

5.1 Starting performance parameters obtained from 2D FEM simulation and measurements for standard unskewed rotor case . . . 33

5.2 Loss comparison of analytical, simulated and measured results for standard unskewed rotor case . . . 34

5.3 Measurement results of starting performance for standard skewed and standard unskewed rotor motors . . . 36

5.4 Equivalent circuit parameters for standard skewed and standard unskewed rotor motors . . . 37

5.5 Measured losses for standard skewed and standard unskewed rotor motors 40 5.6 Measurement results of the starting performance for three rotor designs 42 5.7 Equivalent circuit parameters for standard skewed, standard unskewed and asymmetrical rotor motors . . . 42

5.8 Summary of measured losses for motor with three rotor designs . . . 44

6.1 Stray losses for three rotor designs . . . 48

A.1 Slot dimensions and pitch angles for standard rotor . . . 53

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Introduction

Electrical machines provide a low cost and efficient solution for converting electrical energy to mechanical energy and vice versa. From hydro and turbo generators of several hundred mega watts to few watts micro-motors used for surgical applications, electrical machines have a wide range of applications with different power ratings [1]. The huge advancement in power electronics have made it possible to have highly efficient electric machines and drives with torque and speed control.

Induction motor, invented in 1886, is one of the most commonly used electrical machine in industrial sector. Direct on-line start, low-cost, simplicity and robust- ness are key features associated with these motors.

Need for high eﬃciency motors

Electric motors used in industrial applications consume 30% to 40% of generated electrical energy of the world. In European countries, the electric motor systems have 70% share in the total electricity consumption [2]. In Sweden, single and three phase induction motors, ranging from 0.75 to 375 kW , have 90% share in the total electricity consumption by all kind of electric motors [3]. These statistics suggest that a small reduction in the losses of induction motor will have signiﬁcant impact on the energy consumption, keeping in view the number of motors being manufac- tured and the life time of each motor.

Today, the focus is on producing high efficiency motors to minimize the energy consumption. According to the new EU regulations, all the motors purchased must meet IE2 efficiency standards. It has also been decided that by 2015, the direct- on-line start motors, ranging between 7.5 kW to 375 kW must meet IE3 efficiency standard or IE2 efficiency standard with variable speed drive attached.[5]. A new version of efficiency standard IEC-60034-30 [4], including the efficiency classes of three-phase single-speed cage-induction motors, has been introduced. The energy efficiency class IE4 (Super-Premium Efficiency) is also under consideration. The different efficiency classes for synchronous and asynchronous motors (50 Hz 4-pole)

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Figure 1.1: Eﬃciency classes for electrical motors(50 Hz, 4-pole) [5]

are shown in ﬁgure 1.1.

The emerging calculation methods, powerful computational capacity, the advancement in materials and improved manufacturing techniques have made it possible for the motor designers to work on possible solutions for improving the existing motor designs in eﬃciency point of view.

1.1 Thesis background

Induction motors with skewed rotor

Small to medium size induction motors are generally equipped with die-cast aluminium skewed rotors. Rotor skewing by one stator slot pitch is a common technique utilized by motor manufacturers to suppress the asynchronous torques [6] and reduce the audible noise of the motor[7], [8]. A simple sketch of skewed and unskewed rotors is shown in ﬁgure 1.2.

It is known fact that casting process results in low contact resistive paths between the rotor bars through the iron core laminations. Rotor skewing under these conditions result in the ﬂow of currents through these low contact resistive paths.

These are called inter-bar currents or cross-currents which result in losses known as inter-bar current losses.

The concept of inter-bar current ﬂow is illustrated in ﬁgure 1.3(a) and 1.3(b).

Two small sections between the rotor bars are shown for both skewed and unskewed rotors. In case of an unskewed rotor, the ﬂux(directed into the page) linked by these

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1.1. THESIS BACKGROUND

s

(a) Unskewed rotor

s

(b) Rotor skewed by one stator slot pitch

Figure 1.2: A simple sketch of unskewed and skewed rotors [3]

sections is independent of the axial position of the rotor, As a result, the current induced will ﬂow only between rotor bars and the short-circuit ring, completing the current path, as shown in 1.3(a).

For a skewed rotor, the flux linked by the element and the resulting induced current both depend upon the axial position of rotor. Considering this effect along the total length of the rotor, it can be found that current will flow between the rotor

(a) Unskewed rotor (b) Skewed rotor

Figure 1.3: Illustration of inter-bar current ﬂow between bars through lamination core

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(a) (b)

Figure 1.4: Starting torque curves with diﬀerent inter-bar resistivity for a)Skewed rotor motor b)Unskewed rotor motor[7]

bars taking into consideration the low resistive path as shown in ﬁgure 1.3(b). The magnitude of these currents will depend upon the time derivative of ﬂux creating them. The harmonic inter-bar currents produce large asynchronous torques during the direct-on-line start of induction motors.

Figure 1.4(a) is an interesting result from [7]. It shows that the total torque for skewed rotor motors largely depends upon the inter-bar resistivity value. For low resistivity values, even skewing is ineﬀective in suppressing the asynchronous torques. The resultant asynchronous torques in skewed rotor motors are prolonged even above their synchronous speed, resulting in a decrease of accelerating torque with a reduction of pull-out torque. In some cases, the motor could face a starting problem. For unskewed rotor motors, the starting torque and pull-out torque was found to be independent of the inter-bar resistivity as shown in ﬁgure 1.4(b). How- ever, large asynchronous torques are present at low speed for unskewed rotors.

Measurements in the past have shown that for small to medium sized induction motors, the stray losses can vary from 0.5% to 3% of the total input power [12].

The different stray loss components are shown in figure 1.5(a). The surface losses¹ contributes around 40% of the total stray losses. The inter-bar current losses con- tribute 30% in the total stray losses. For a 4-pole, 15 kW 36/28 slot induction motor the variation of total rotor losses, as a function of rotor skew and inter-bar resistivity, is shown in figure 1.5(b) [7], [10]. It can be seen that the stray losses increase with increase in skewing angle, reducing the overall efficiency of induction motor. These above mentioned reasons make skewing an unattractive choice with die-cast aluminium rotor bars.

1The surface losses are caused by high frequency ﬂux that results in eddy currents on the rotor surface. These losses can be suppressed using non-machined rotors [9].

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1.2. THESIS OBJECTIVES

Surface losses¹

40%

Inter-bar current losses

30%

Pulsation losses

17%

High frequency

losses 10%

Leakage flux losses

3%

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Figure 1.5: a) Components of stray-load losses for 0.2-37 kW induction motors [7],[9]. b) Total rotor losses as a function of rotor skew and inter-bar resistivity [3]

Unskewed rotors on the other hand help in eliminating inter-bar currents, sim- plify and improve the casting process. The total torque for unskewed rotor motors is independent of the inter-bar resistivity. However, the drawbacks associated with symmetrical unskewed rotors are high audible noise and large synchronous and asynchronous torques at low speed [6] which can prolong the starting time and limit the motor from reaching its rated speed [3], [7].

Asymmetrical slot rotors have been the focus of research for many years in order to gain the advantage of having unskewed rotor bars in terms of increasing the eﬃciency, suppressing the braking torques and reducing the audible noise in the motor. Studies carried out in [3], [7], [10] and [11] have shown promising results in this regard. It has been found that by proper asymmetrical modulation of rotor slots, the radial airgap forces associated with high noise level can be suppressed, while the joule losses are maintained at a reasonable level with reduction in synchronous torque at low speed. Hence, induction motor with asymmetrical unskewed rotor is expected to achieve higher eﬃciency with acceptable noise level compared to the standard skewed rotor motor.

1.2 Thesis objectives

The objective of this thesis is to analyse the performance of a 15 kW , 4-pole, 36/28 slot industrial induction motor mounted with standard skewed, unskewed and unskewed asymmetrical rotors. The performance analysis is based on measuring the losses in the motor at rated operation according to IEC standard test procedures, and torque measurements during a direct-on-line start. Accurate determination of

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high frequency stator winding currents to determine the high frequency copper losses are also of interest. Based on the measurement results, a comparative analysis is made between diﬀerent rotor types and the diﬀerences are highlighted and explained.

1.3 Thesis outline

The outline of chapters in this thesis report are described as follows:

• Chapter 2 includes details about harmonics in induction machines, the dis- tribution of losses in induction machine and a review on standard eﬃciency measurement methods.

• In Chapter 3, theory about the asymmetrical rotor slots is explained. It also includes details about the investigated motor with diﬀerent rotor prototypes.

The method of analysis used in carrying out the 2D FEM simulations and measurements is presented in this chapter.

• Chapter 4 includes the 2D FEM simulation results for the starting perfor- mance and losses at rated operation for the diﬀerent rotor prototypes. The simulation results for the high frequency stator(delta connected) winding currents for the three rotor designs is presented in this chapter.

• Chapter 5 includes the measurement results and the comparisons for the investigated motors mentioned in chapter 3. Firstly, the simulation results presented in previous chapter are validated against measurements for the standard unskewed rotor case. Secondly, a comparison of measurement results for standard skewed and standard unskewed motors is presented. Finally, the measurement results of standard skewed, standard unskewed and asymmetrical unskewed rotor motors are compared and explained.

• Chapter 6 includes conclusions and future work.

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Chapter 2

Harmonics in Induction Machines, Distribution of Losses & Standard Eﬃciency Measurement Methods

2.1 Harmonics in induction machines

2.1.1 Space harmonics

The harmonics in the airgap magnetic field are known as space harmonics. These harmonics cause additional noise, vibration and adversely affect the starting performance of induction motors [17]. Space harmonics are by-products of the rotating magnetic field production mechanism inside electrical machines, hence they cannot be completely eliminated. However, they can be suppressed to a greater level by proper design optimization. The space harmonics in an electrical machine can produce forward or backward rotating waves, depending upon the harmonic order. For symmetrical three-phase machines, the general expression for space harmonics of order n, created by the stator winding is;

Space harmonics, n = 1± 6k (2.1)

where, k = 0, 1, 2, 3, ....

Harmonics such as 7^th and 13^th result in forward rotating mmf waves with speed equals to ω/7 and ω/13, respectively. On the other hand, 5^th and 11^th space har- monics result in backward rotating mmf waves with speed equals to ω/5 and ω/11, respectively. The n^th space harmonic in general has a speed equal to 1/n times the speed of the fundamental synchronous speed of the motor, but contains n times more peaks than the fundamental. Therefore, the space harmonics and the fundamental component created by the stator winding have same frequency in stator reference frame [6].

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The space harmonic of order n induces a current in rotor of frequency given by;

f_2(n) = [n(1− s(1))± 1]·f(1) (2.2) In equation 2.2, the positive(+) or negative (-) sign depends on the value of n giving backward or forward rotating waves, respectively [6].

Studies have shown that the for 36/28 slot induction motors, the torque dips due to 7^th(space harmonic) and 19^th(stator slot harmonic) forward rotating waves can aﬀect the starting characteristics [7]. If the resultant torque dip becomes lower than the required load torque, it can result in an unsuccessful start of the motor.

2.1.2 Slot harmonics

The stator of the induction machine consists of semi-closed slots as shown in ﬁgure 2.1.

Figure 2.1: Semi-closed stator slot shape

The stator slot openings result in the variation of air gap permeance, distorting the main ﬂux and create space harmonics. These harmonics are known as the stator slot harmonics. In contrast, with closed rotor slot design, the high frequency rotor slot harmonics are expected to have low magnitude compared to stator slot harmonics [18]. The general expression for the stator and rotor slot harmonics is given by;

Stator slot harmonics = 1±n·Qs

p (2.3)

Rotor slot harmonics = 1±n·Qr

p (2.4)

where n is an integer representing the order of slot harmonic, p is the number of pole pairs. Q_s and Q_r are the total number of stator and rotor slots, respectively.

The stator slot harmonics induces currents in rotor of frequency given by;

[n·Qs

p (1− s(1))± s(1)]·f(1) (2.5)

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2.2. DISTRIBUTION OF LOSSES IN INDUCTION MACHINES

The rotor slot harmonics induces currents in stator of frequency given by;

[n·Qr

p (1− s(1))± 1]·f(1) (2.6) where, f₍₁₎ is the fundamental line frequency and s₍₁₎ is the fundamental slip. In a standard unskewed rotor the slot harmonics result in;

• High frequency currents which can cause an increase in stray losses of the motor [7].

• Production of torque harmonics, noise and vibrations in induction machine due to interaction of stator ﬁelds and rotor harmonic currents [3].

2.1.3 Phase belt harmonics

They are created due to concentration of MMF in slots [7]. The general expression for phase belt harmonics for three phase machine is given by;

n = 1± 6k (2.7)

2.2 Distribution of losses in induction machines

The classification of the different losses occurring in induction machine is well described in [13] and [14]. The total losses in the induction machine are usually defined as the difference between the input and the output power.

P_T = P_in− Pout (2.8)

where P_T, P_in and P_out are the total power losses, the input power and the output power of the machine in watts, respectively.

According to the IEC 60034-2-1 [14], the total power losses in an induction machine can be mainly categorized as shown in ﬁgure 2.2.

Figure 2.2: Distribution of losses in induction machines

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Constant losses, P_k

The constant losses, as seen from ﬁgure 2.2, consist of iron losses, friction and windage losses. The constant losses always occur in the machine, independent of load. The iron losses are further categorized as hysteresis losses and eddy current losses. These losses are dependent upon the magnetic properties of the material, lamination thickness and frequency. Some harmonic losses occurring on the surface of the iron and in the teeth are also included in iron loss category [14].

Load losses, P_L

The load losses consist of the ohmic losses occurring in the stator winding and in the rotor bars. These are given as;

Stator copper losses, Pcu1 = 3·Is²·Rs (2.9) Rotor copper losses, Pcu2= 3·I_r²·Rr (2.10) Additional load losses or stray load-losses, P_LL

The losses that occur at rated load condition in the active metal parts other than conductor and in active iron are considered as additional load losses or stray-load losses. The load current dependent ﬂux pulsations that cause eddy currents are also considered in this category of losses [14].

2.3 Methods for eﬃciency measurement

Two common methods for determining the eﬃciency of electrical machines are presented in [16]. These are;

• Direct method

• Indirect method

In case of the direct method, the eﬃciency of the motor is determined simply by ﬁnding the ratio of input active electric power and the output mechanical power.

η = Pout

(2.11) where, P_out=T·wr is output mechanical power in watts. P_in is the input electrical power in watts.

The indirect method of eﬃciency measurement is based on the input active electric power and the total losses in the machine calculated from tests.

η = Pin− Ploss

(2.12)

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2.4. STANDARDS FOR EFFICIENCY MEASUREMENT

where, the total losses consist of the constant losses, the load losses and the additional stray load-losses.

P_loss= P_T = P_K+ P_L+ P_LL (2.13) Indirect method is considered more accurate for determining the eﬃciency of machines; provided that the stray-load losses are determined accurately [16].

2.4 Standards for eﬃciency measurement

Four major standards for measuring the eﬃciency of electrical machines are presented in [16]. These are;

• IEEE 112

• IEC 60034-2-1

• CSA C390

• JEC37

IEC 600-34-2-1 and IEEE 112B standards include both direct¹ and indirect eﬃciency measurement methods. IEC 600-34-2-1 was introduced in September 2007 and it includes the method to determine the additional stray losses. The older version of IEC standard, IEC 600-34-2, deﬁned stray losses as 0.5% of the total losses occurring in the machine.

Comparison of IEEE and IEC standards

A comparison between the loss determination methods, utilized in IEC and IEEE standards [15] [16], are presented as follows.

• In order to determine the stator copper losses, the IEEE standard requires the measurement of reference stator winding in cold condition and at diﬀerent operating conditions along with temperature measurements. This requires the temperature sensor to be used during the test hence, this procedure cannot be performed on motors that are in service. On the other hand, according to IEC standard test method, the resistance is directly measured for the highest and the lowest operating points, without the need of temperature sensors.

• In IEC standard, the method to ﬁnd the iron losses includes the factor of voltage drop across the stator resistance; as the load on the motor changes. On the other hand, the IEEE standard considers the iron losses to be independent of load, which could lead to inaccurate results.

1The direct method is known as "Method A" in the IEEE 112 standard.

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• In case of stray losses, the two standards deploy similar techniques. First the residual stray losses in the machine are determined. A linear regression analysis technique is then used to smoothen the curve in order to determine the actual stray losses in the machine [16]. A small difference between the two standards is the correlation coefficient value that is used in the curve fitting process. IEEE 112 specifies a value of 0.9 while IEC uses 0.95 [15].

• Regarding the methods to ﬁnd the rotor copper and friction losses, both standards describes similar techniques.

In this thesis work, the test methods for determining losses and efficiency of different machines are followed according to IEC 600-34-2-1 standard [14]. A block diagram showing different test methods for efficiency measurement according to IEC standard are shown in figure 2.3.

Efficiency measurement methods [IEC 60034-2-1]

Direct Method

Torque Meter Test

Dynamometer Test

Dual Supply Back to Back Test

Indirect Method

Calorimetric Method

Single Supply Back to Back Test No-Load Test

Heat-run test (Load test Equivalent Circuit

Method

Reversed Rotation and Removed Rotor Test

EH-Star Test

Load test with torque measurment (residual loss method)

Gives total losses

Gives constant losses

Gives stray losses Gives load losses

Figure 2.3: Diﬀerent test methods for eﬃciency measurement according to IEC 60034-2-1 standard

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Chapter 3

Asymmetrical Rotor Slot Arrangement

& The Investigated Motors

3.1 Asymmetrical rotor slot arrangement

The noise and vibration can be reduced to a greater extent by introducing asymmetry in rotating structure [3]. Asymmetry can be introduced in both rotor and stator, later is more complex from the manufacturing point of view. A detail method of introducing asymmetry in rotor slots has been presented in [3]. Based on this study an improved modulation function for designing asymmetrical rotors has been developed in [10]. The diﬀerent asymmetrical rotor slot arrangements are discussed as follows.

3.1.1 Dual rotor slot arrangement

The main theme of this type of asymmetrical rotor slot design is to combine two diﬀerent rotor slot combinations, with their respective slot pitch angles, into a single rotor. In this way, the combined advantages of both rotor slot arrangements can be achieved. An example of a dual rotor slot geometry, combining 24 and 32 rotor slots in a single rotor design, is shown in ﬁgure 3.1(a).

3.1.2 Progressive sinusoidal rotor slot arrangement

Asymmetrical rotor slot arrangement can also be achieved by varying the slot pitch angles and corresponding slot width, as a function of sine-wave as given in equation 3.1 and equation 3.2, respectively [10].

θ(nr) = θ0(nr) +

∑n i=1

Kisin( i.θ0(nr) + δi) (3.1)

bnr = b0(nr) θ(nr+ 1)− θ(nr)

θ₀(n_r+ 1)− θ0(n_r) (3.2)

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where n_r is the slot number, θ₀ is the initial slot pitch angle and b₀ is the initial slot width. K_i and δ_i are the modulation coeﬃcients.

An example of progressive rotor slot arrangement is shown in ﬁgure 3.1(b).

3.1.3 Dual + Progressive rotor slot arrangement

Another method to introduce asymmetry in rotor slots is by combining the properties of both dual and progressive asymmetrical rotor slot arrangements. This results in design named as dual+progressive rotor slot arrangement. This is shown in 3.1(c).

(a) (b) (c)

Figure 3.1: One-pole geometry of diﬀerent asymmetrical rotor slot arrangements a)Dual 24-32 rotor slot design b)Progressive sinusoidal rotor slot design c)Dual+progressive sinusoidal rotor slot design

3.2 The investigated motors

The general speciﬁcations of the four motors investigated in this work are shown in table 3.1. The stator was kept the same in all the tests with diﬀerent rotor prototypes.

3.2.1 Rotor prototypes

The four rotor prototypes namely; a)Standard unskewed b)Standard skewed c) Dual 24-32+progressive d)Progressive sinusoidal were investigated. Some details about the rotor slot arrangement, for each prototype, is given as follows:

• The two prototypes: standard skewed and standard unskewed rotors have same rotor slot design.

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3.2. THE INVESTIGATED MOTORS

Table 3.1: General motor speciﬁcations Rated power, PN 15 kW

Rated voltage, UN 400 V Rated frequency, fN 50 Hz No. of stator poles 4

Stator winding Delta connected 3-cross concentric No. of stator slots 36

No. of rotor slots 28

Core material M600-50A Machine length 205 mm Shaft height 160 mm Airgap length 0.55 mm Insulation class B

• The dual 24-32+progressive rotor prototype have asymmetrical rotor slots.

The rotor slot dimensions and slot pitch angles were obtained by setting mod- ulation coeﬃcients i = 24 and K24= 1.7 in equation 3.2.

• The rotor slot dimensions and slot pitch angles for progressive sinusoidal rotor prototype were obtained by setting modulation coeﬃcients i = 4, 8 ; K₄= 2.65 and K₈ = 2.2 in equation 3.2.

The slot widths and slot pitch angles for each prototype are given in appendix A. The idea behind choosing particular modulation coeﬃcients for asymmetrical rotor slot design is to suppress the synchronous torques at zero speed as presented in [10].

3.2.2 Simulation tool- FCSmek

A 2D FEM simulation tool FCSmek¹was used to simulate the diﬀerent rotor designs and the performance of motors were analyzed. Some features of FCSmek and the geometry creation process in FCSmek are illustrated as follows:

• The losses simulated in FCSmek includes the losses due to high frequency components of current.

• At present, it is not possible to simulate skewed rotor cases in FCSmek.

• The simulation time largely depends upon the time step chosen for each simulation and the mesh settings including size, shape & order of element.

1FCSmek is a base program in ADEPT. ADEPT is an in-house ABB calculation tool.

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• In FCSmek, the stator and rotor geometries are created using FEMM². De- pending upon the machine input parameters in ADEPT, FCSmek generates the FEMM ﬁles for the corresponding stator and rotor geometries along with a LUA script [20] ﬁle readable in FEMM.

• The LUA script ﬁle for the standard rotor geometry was modiﬁed in order to obtain the desired asymmetrical rotor geometries.

The one-pole geometry of standard stator and diﬀerent rotor designs, created in FCSmek are shown in ﬁgure 3.2.

(a) (b) (c)

Figure 3.2: One-pole geometry of rotor slots for diﬀerent rotor designs a) Standard unskewed b) Dual 24-32+progressive c) Progressive sinusoidal

3.2.3 Method of analysis

The method of analysis used during simulation and measurement work is presented in this section.

3.2.3.1 Simulations

The starting performance of the machine with diﬀerent rotor designs were simu- lated using a time step of 250 µ sec for a total of 80 fundamental periods. This corresponds to a sampling frequency of 4 kHz. The simulation was initialized with a rotor speed of -750 rpm. The purpose of doing this is to avoid the switching transients in the motoring region during the direct on-line start condition and also to capture the asynchronous torques, due to 5^th space harmonics, occurring in neg- ative speed range. A rotor inertia value of 2.25 Kgm² was set in order to reduce the acceleration time of the rotor and to capture the diﬀerent phenomenon of interest in

2FEMM is a free-ware tool known as Finite Element Method Magnetics [19].

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the torque curve. In general, a higher value of rotor inertia is avoided as it prolongs the simulation time.

The starting performance curves obtained from 2D FEM simulations contain high frequency components in it. A 3^rd order low-pass butter worth filter was used in order to filter out these curves. The sampling frequency, fs for the low pass filter was set to 50 Hz with cut-off frequency, f_c to 35 Hz.

For rated operation, the simulations were carried out with time stepping of 100 µ sec for a total of 200 periods. The simulation results were used in order to de- termine the high frequency stator winding currents, air-gap ﬂux density, torque harmonics and losses in the machines at rated operation.

3.2.3.2 Measurements Starting performance

The torque-speed curves for the different cases were recorded by operating the motor between rated and zero speed range. However, due to the low sampling frequency of recording equipment in the laboratory, it was difficult to determine the impact of synchronous and asynchronous torques at low speed. To capture these low speed parasitic effects, an oscilloscope with a 5 kHz sampling frequency was used to capture the torque variation with time for different cases.

High frequency stator winding currents

An oscilloscope of 50 kHz sampling frequency was used to capture the high fre- quency currents, ﬂowing in stator winding, for diﬀerent cases.

Eﬃciency

To determine eﬃciency, indirect method was used in this study. The standard methods used to determine individual loss components given in equation 2.13, are discussed as follows.

1. Constant losses, P_K using no-load test: The constant losses, P_K consists of frictional and windage losses, P_{f w}and the iron losses, P_{f e}. These losses are determined by performing a no-load test [14] on the machine, recording the variation of input power at no-load with terminal voltage, Uo. The voltage was varied between 20% to 125% of the rated voltage. During no-load test, the total losses in the machine equal the no-load input power, Po, and is the sum of stator copper losses, Ps and the constant losses, PK. The constant losses are given as shown in equation 3.3.

P_K = P_o− Ps= P_{f e}+ P_{f w} (3.3)

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P_s = 1.5·Io2·R_||o (3.4) where Io, is the no-load average line current in amperes. R_||o, the line to line resistance in ohm, is determined after the lowest voltage reading during the no-load test.

Using the no-load loss points that show no signiﬁcant saturation eﬀect, a curve is developed showing relationship between the constant losses and the square of no-load terminal voltage. This curve is extrapolated to zero-voltage axis and the intercept to that gives the friction and windage losses in the machine. These losses are independent of the load.

After ﬁnding the friction and windage losses, another curve can be plotted for diﬀerent load points giving relationship between P_{f e} = P_K-P_{f w} and the no-load terminal voltage, U_o. At any desired load point, the iron losses can be found corresponding to voltage, Ur taking resistive voltage drop in the stator winding into account as given in equation 3.6.

U_r =

√ (U−

√3.I.R. cos φ 2 )²+ (

√3.I.R. sin φ

2 )² (3.5)

where, cos(φ) = √^P¹

3.U.I, sin(φ) =^√1− cos(φ)

U is the average terminal voltage, P₁ is the input power in watts, R is the winding resistance in ohms and I is the average line currents in amperes.

2. Load losses, PL using heat-run test: The load losses include the stator cop- per losses, P_sand rotor copper losses, P_r, at rated load operation. During the load test or heat-run test, the machine is loaded at rated supply power and is operated until thermal equilibrium is achieved (gradient of 2 K per hour).

At the end of test the power, current, voltage, resistance, slip, frequency and winding temperature at rated conditions are noted.

The incorrect stator copper losses are determined at any load point using equation 3.6.

Ps= 1.5·I²·R (3.6)

The stator winding resistance is corrected to reference coolant temperature of 25^oC to obtain the correct value of stator copper losses;

Ps,θ = Ps·kθ (3.7)

kθ= 225 + θw+ 25− θc

225 + θw

(3.8)

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where, k_θ is the temperature correction factor for winding, θ_c is the inlet coolant temperature during test and θ_w is the reference winding temperature depending upon the insulation class.

Similarly, the rotor copper losses for a given load point is determined using equation 3.9.

P_r= (P₁+ P_s+ P_{f e})·s (3.9) The corrected rotor copper losses are given as;

P_r,θ = (P1− Ps,θ− Pf e)·sθ (3.10)

sθ= s·kθ (3.11)

3. Stray losses, PLL using residual loss method: The additional load losses are determined using partial load test with torque measurement. Firstly, the residual losses, PLr for each load point are determined by subtracting the output power, load losses and constant losses from the input power. This is shown in equation (3.12).

P_Lr = P1− P2− PL− PK (3.12) The residual losses can be expressed as a function of square of torque given as;

P_Lr = A·T²+ B (3.13)

The losses given by equation 3.13 are smoothed using linear regression analysis as shown in figure 3.3. In figure 3.3, A is the slope, B is the intercept, i is the number of load points and γ is the correlation coefficient. Once the value of A is stable, the value of additional load losses for every load point is determined by the following expression.

P_LL= A·T² (3.14)

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Figure 3.3: Smoothening of residual loss data [14]

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Chapter 4

2D FEM Simulation Results

4.1 Starting performance for three rotor designs

In this section the simulated starting performance and key performance characteristics of the investigated motors having different rotor designs is presented. As the simulation of skewed rotor case needs 3D FEM tool, whereas FCSmek is a 2D FEM tool, only the unskewed cases (symmetrical and asymmetrical) were possible to simulate using FCSmek. The 2D FEM simulated starting performance curves for the three different rotor designs are shown in figure 4.1. The rotor speed was varied from -750 rpm to 1500 rpm as shown in figure 4.1(a) and the corresponding torque varia- tion for three cases, at sampling frequency of 4 kHz, is shown in figure 4.1(b), 4.1(c) and 4.1(d). For comparative analysis, the higher order frequency components were filtered out using a low-pass filter. The 2D FEM simulated current-speed curves for three rotor designs are also shown in figure 4.1(f).

Figure 4.1(e) shows the ﬁltered starting torque-speed curves for the three rotor designs. It can be observed that:

• The impact of 5^th, 7^th space harmonic and 17^th, 19^th stator slot harmonics can be seen in the resulting torque speed curves. The 7^th and 19^th harmonics having forward rotation create torque dips in the motoring region.

• At zero speed, the synchronous torques for standard unskewed rotor are negligible. For asymmetrical rotor designs, small synchronous torques are present at zero speed. However, the synchronous torques at zero speed are well suppressed with chosen modulation coeﬃcients, compared to results presented in [11]. Hence, the motors with asymmetrical rotor prototypes were expected to undergo successful start during prototype testing.

• At 214 rpm, (¹₇ of the synchronous speed of motor), there are big ﬂuctuations in the torque-speed curves for all the cases. Synchronous torques are experi- enced by all the rotor designs at this speed due to 28 rotor slots. Synchronous torque is also present around 150 rpm for all rotor designs due to 36 stator

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0 0.5 1 1.5 2 2.5

−750

−500

−250 0 250 500 750 1000 1250 1500

Time [s]

Speed[rpm]

(a) Speed variation with time

0 0.5 1 1.5 2 2.5

−400

−200 0 200 400 600 800 1000

Time [s]

Torque[Nm]

Original Filtered

(b) Standard unskewed

0 0.5 1 1.5 2 2.5

−400

−200 0 200 400 600 800 1000

Time [s]

Torque[Nm]

Original Filtered

(c) Dual 24-32+progressive

0 0.5 1 1.5 2 2.5

−400

−200 0 200 400 600 800 1000

Time [s]

Torque[Nm]

Original Filtered

(d) Progressive sinusoidal

−500 −250 0 250 500 750 1000 1250 1500

−100 0 100 200 300 400 500 600 700

Speed [rpm]

Torque[Nm]

Standard unskewed Dual 24−32+progressive Progressive sinusoidal

Pull−out torque

Starting torque

(e) Torque-speed curves comparison

0 500 1000 1500

0 50 100 150 200 250

Speed [rpm]

Current[A]

Standard unskewed Dual 24−32+Progressive Progressive sinuosidal

(f) Current-speed curves comparison

Figure 4.1: 2D FEM simulation results of the starting performance for three rotor designs

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4.2. PERFORMANCE OF MOTORS AT RATED OPERATION

slots. It can also be seen that the synchronous torques are suppressed for the progressive sinusoidal rotor design compared to the other two rotor designs.

This shows that the chosen modulation coeﬃcients, for introducing asymmetry in rotor designs, not only helped in suppressing the synchronous torques at zero speed but also suppressed the synchronous torques due to 7^th space harmonic.

• It is diﬃcult to analyse the asynchronous torque created by 7^thspace harmonic for the three cases, because of the synchronous torque occurrence at the same speed.

The values of starting torque, pull-out torque and starting current(RMS), simulated for three rotor designs, are summarized in table 4.1. These results are con- sistent with the ﬁndings in [10] and show that the studied asymmetrical rotors are capable of starting during direct-on-line.

Table 4.1: Simulated starting properties for the three rotor designs Starting Maximum Starting Rotor design torque torque current

[N m] [N m] [A]

Standard unskewed 258 303 209.7

Dual 24-32+progressive 237 303 209.2 Progressive sinusoidal 253 306 208.5

4.2 Performance of motors at rated operation

This section contains the performance of the investigated motors, having diﬀerent rotor designs, simulated at rated operation.

4.2.1 Air-gap ﬂux density

Figure 4.2 shows the simulation results of the airgap flux density of motor with three rotor designs for one electrical cycle. The fundamental component of airgap flux density can also be seen for each case. In order to analyse the harmonic content with their possible sources in the airgap flux density, FFT spectral analysis of flux density for the three rotor designs is shown in figure 4.3. It can be observed that:

• The value of the fundamental component of flux density was approximately 0.75 T for all the three cases. In figure 4.3, the magnitude of higher order flux density components is presented in terms of percentage of fundamental component value (taken as 100%).

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0 0.5 1 1.5 2 2.5 3

−1

−0.5 0 0.5 1

Space co-ordinate in the air gap [radians]

Fluxdensity[T]

Standard unskewed

0 0.5 1 1.5 2 2.5 3

−1

−0.5 0 0.5 1

Fluxdensity[T]

Dual 24−32+progressive

0 0.5 1 1.5 2 2.5 3

−1

−0.5 0 0.5 1

Fluxdensity[T]

Progressive sinusoidal

Figure 4.2: 2D FEM simulated ﬂux density in the airgap for three rotor designs

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 0

5 10 15 20 25 30 35 40 45 50

Harmonic number

%amplitudeoffundamentalfluxdensity

Standard

Dual 28−32+progressive Progessive Sinuosidal

1 ± 2m

1 ±^Qp^s

1 ± 2^Q_p^r

1 ± 2^Q_p^s 1 ±^Q_p^r

1 ± 4m

Figure 4.3: Harmonic spectrum of airgap ﬂux density for three rotor designs

Performance Analysis of Unskewed Asymmetrical Rotor for LV Induction Motors

Asymmetrical Rotor for LV Induction Motors

USMAN SHAUKAT

Performance Analysis of Unskewed Asymmetrical Rotor for LV Induction Motors

Abstract

Utvärdering av Asymmetrisk Rotor Utan Spårsneddning för Asynkronmotorer

Acknowledgment

List of Symbols & Abbreviations

List of Figures

List of Tables

Contents

Chapter 1

Introduction

1.1 Thesis background

1.2 Thesis objectives

1.3 Thesis outline

Chapter 2

Harmonics in Induction Machines, Distribution of Losses & Standard Eﬃciency Measurement Methods

2.1 Harmonics in induction machines

2.2 Distribution of losses in induction machines

2.3 Methods for eﬃciency measurement

2.4 Standards for eﬃciency measurement

Chapter 3

Asymmetrical Rotor Slot Arrangement

& The Investigated Motors

3.1 Asymmetrical rotor slot arrangement

3.2 The investigated motors

Chapter 4

2D FEM Simulation Results

4.1 Starting performance for three rotor designs

4.2 Performance of motors at rated operation