RESEARCH OF PERMANENT MAGNET GENERATOR WITH … · TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding 3 ABSTRACT In this thesis, a patented “bifilar” coil

KLAIPEDA UNIVERSITY

FACULTY OF MARINE ENGINEERING

DEPARTMENT OF ELECTRICAL ENGINEERING

I________________________HEREBY CONIFIRM

Head of department: prof. dr. Eleonora Guseinovienė

2013

BACHELOR STUDY PROGRAME OF ELECTRICAL ENGINEERING

(Code of studies 612H62003)

FINAL THESIS

RESEARCH OF PERMANENT MAGNET

GENERATOR WITH COMPENSATED

REACTANCE WINDINGS

Editor: ________________________

2013

Supervisors: Prof. dr. Eleonora Guseinovienė

Boris Rudnickij

2013

Authors: TEI-09 Oleg Lyan

HENALLUX Vincent Monet

2013

Klaipėda, 2013

TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding

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ABSTRACT

In this thesis, a patented “bifilar” coil (BC) type permanent magnet generator (PMG) is

constructed for scientific research and comparison with other technologies. The features, working

principle and elements of the BCPMG are analyzed.

The BCPMG is developed from the iron-cored “bifilar” coil topology based on (1) in an

attempt to overcome the problems with current rotary type generators, which have so far been

dominant on the market. One of the problems is armature reactance , which is usually bigger than

resistance . The circumstance creates difficulties for designers and operators of the generator.

That is why patented technology is offered to partially remove or absolutely neglect the reactance of

the machine. Drawings of the PMG parts and assembly are added. A finite element magnetic model

(FEMM) is presented and analyzed.

Also, this thesis contains an experimental analysis of the PMG characteristics, such as no-

load losses and EMF vs. speed, loaded voltage drop, power output and efficiency vs. load current at

different speeds.


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LIST OF TABLES

1.1. Table. “Alxion” constructors catalogue parameters ................................................................... 12

1.2. Table. “MOOG” constructors catalogue parameters .................................................................. 12

1.3. Table. Prototype generator specifications .................................................................................. 15

1.4. Table. Nominal characteristics of constructed TFPMDG .......................................................... 16

2.1. Existing magnet materials and parameters ................................................................................. 23

3.1. Table. Measurement device ........................................................................................................ 31

3.2. Table. Parameters of driving machines ...................................................................................... 31

3.3. Table. Motor current voltage data from A2. ............................................................................... 35

3.4. Table. Motor terminal voltage data from V2. ............................................................................. 35

3.5. Table. PMG terminal EMF frequency data from F. ................................................................... 36

3.6. Table. Power losses, calculated data. ......................................................................................... 37

3.7. Table. The parameters of calculated curves. .............................................................................. 38

5.1. Table. Practical parameters of the PMG topology ..................................................................... 46

5.2. Table. Consumed material quantity ............................................................................................ 46

0.1. Table. EMF and frequency data for phase A from V1, F ........................................................... 52

0.2. Table. EMF and frequency data for phase B from V1, F ........................................................... 53

0.3. Table. EMF and frequency data for phase C from V1, F ........................................................... 54

0.4. Table. 8,75 Hz, voltage and current data from F, V1, A1 .......................................................... 55

0.5. Table. 11,02 Hz, voltage and current data from F, V1, A1 ........................................................ 56


0.7. Table 17,80 Hz, voltage and current data from F, V1 and A1 ................................................... 58


0.9. Table. 28.80 Hz, voltage and current data from F, V1, A1 ........................................................ 60

0.10. Table. 44,00 Hz, voltage and current data from F, V1, A1 ...................................................... 61



0.13. Table. 8,75 Hz, power, losses, efficiency, power factor calculated data .................................. 64

0.14. Table. 11,02 Hz, power, losses, efficiency, power factor calculated data ................................ 65


0.16. Table. 17,8 Hz, power, losses, efficiency, power factor calculated data .................................. 67






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LIST OF EQUATIONS

3.1. Equation. Mean value is calculated by know formula of arithmetic mean from (14): ............... 35

3.2. Equation. Ohm's law formula from (15) as the law explained in (16 p. 54), also in (17): ......... 36

3.3. Equation. Electrical power calculation explained with (18) and (17): ....................................... 36

3.4. Equation. Joule’s first law (heating) formula explained (19): .................................................... 36

3.5. Equation. Synchronous impedance using Ohm’s law for AC circuits ....................................... 38

3.6. Equation. Reactance calculation from scalar vector formula ..................................................... 38

3.7. Equation. Short circuit current of SG with armature resistance (2 p. 330) ................................ 39

3.8. Equation. Vector and scalar representation of terminal voltage based on Kirchhoff’s II law ... 39

3.9. Equation. Relation between terminal voltage and load current .................................................. 39

3.10. Equation. Terminal voltage of PMG performance ................................................................... 39

3.11. Equation. 3 phase electric power of SG. .................................................................................. 41

LIST OF FIGURES

1.1. Fig. View of a synchronous AC generator ................................................................................. 10

1.2. Fig. In-runner PMG construction: (a) realistic view, (b) 3D CAD view ................................... 11

1.3. Fig. In-runner PMG construction 3D CAD view ....................................................................... 13

1.4. Fig. Non-slotted axial field PMG ............................................................................................... 14

1.5. Fig. Prototype axial flux PMG ................................................................................................... 15

1.6. Fig. The structure of the axial flux permanent magnet generators. (1) Stator core holder. (2)

Stator core. (3) Armature winding. (4) Rotor Disk. (5) Permanent Magnet ..................................... 16

1.7. Fig. PM wave energy converter generator.................................................................................. 17

2.1. Fig. Cross section view of PMG topology ................................................................................. 18

2.2. Fig. Axial section view of PMG topology .................................................................................. 19

2.3. Fig. Magnetic circuit model of PMG topology .......................................................................... 19

2.4. Fig. Single wound rod of PMG topology stator ......................................................................... 20

2.5. Fig. Permanent magnet rotor generator. (a) surface-mounted magnets. (b) Inset (buried)

magnets. (c) Buried magnet with radial magnetization. (d) Buried magnet with circumferential

magnetization (2 p. 355) .................................................................................................................... 21

2.6. Fig. Surface mounted magnets [1] on the ferromagnetic core [5] .............................................. 22

2.7. Fig. 3D isometric view of PMG construction ............................................................................ 22

2.8. Fig. Magnetic circuit flux lines of PMG topology with double magnets. .................................. 24


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2.9. Fig. Magnetic circuit flux lines of PMG topology with less magnets. ....................................... 24

2.10. Fig. Magnetic circuit flux lines of PMG while moving through steps. .................................... 25

2.11. Fig. 1/5 segment of patented PMG active material (3D model front view) ............................. 26

2.12. Fig. 1/5 segment of patented PMG active material (3D top view) ........................................... 26

2.13. Fig. Magnetic flux density vector plot (front view) ................................................................. 26

2.14. Fig. Magnetic flux density vector plot (top view) .................................................................... 27

2.15. Fig. Magnetic flux density continuous fringe plot on several sections: A – cross section of

magnet array, B – cross section of coils ............................................................................................ 27

2.16. Fig. Magnetic flux density continuous fringe plot on several sections: C – axial section of core

phase C, D – axial section of core phase A ....................................................................................... 27

2.17. Fig. 1/5 segment of patented PMG active material magnetic flux density with applied 3 phase

current 10A RMS .............................................................................................................................. 28

2.18. Fig. Magnetic flux density with applied 3 phase current 10A RMS axial section of first wound

rod (right side view) .......................................................................................................................... 28

2.19. Fig. Magnetic flux density with applied 3 phase current 10A RMS cross section of first array

of magnets (front view) ..................................................................................................................... 29

3.1. Fig. Arduino Nano V3.0 ............................................................................................................. 31

3.2. Fig. IGBT or MOSFET gate driver working principle ............................................................... 32

3.3. Fig. Gate driver “turning on” equivalent .................................................................................... 33

3.4. Fig. Gate driver “turned on” equivalent ..................................................................................... 33

3.5. Fig. Gate driver “turning off” equivalent ................................................................................... 34

3.6. Fig. Gate driver “turned off” equivalent ..................................................................................... 34

3.7. Fig. Mechanical and magnetic power losses versus frequency as TG signal ............................. 37

3.8. Fig. EMF vs. frequency as AC TG speed signal (OCC) ............................................................ 37

3.9. Fig. Linear relationship of reactance vs. frequency.................................................................... 38

3.10. Fig. Short circuit current vs. speed relationship ....................................................................... 39

3.11. Fig. Terminal voltage vs. load current performance characteristics at different speeds

(measured and calculated) ................................................................................................................. 40

3.12. Fig. Terminal voltage vs. load at different speeds (surface plot) ............................................. 40

3.13. Fig. Performance characteristics of independent synchronous generator: (a) equivalent circuit

diagram; (b) Terminal voltage vs. load current at constant rotating excitation field (2 p. 331) ........ 41

3.14. Fig. Power output vs. load current performance characteristics at different speeds (measured

and calculated) ................................................................................................................................... 41

3.15. Fig. Output power vs. load at different speeds (surface plot)................................................... 42


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3.16. Fig. Efficiency vs. load current performance characteristics at different speeds (measured and

calculated) .......................................................................................................................................... 42

3.17. Fig. Efficiency vs. load current at different speeds (surface plot) ............................................ 43

3.18. Fig. Efficiency vs. load current performance characteristics at different speeds (before

overload) ............................................................................................................................................ 43

3.19. Fig. Efficiency vs. load current performance characteristics at different speeds (after

overload) ............................................................................................................................................ 44


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LIST OF CONTENTS

INTRODUCTION…………………………………………………………………………… 9

1. OVERVIEW OF EXISTENT GENERATOR CONSTRUCTION TYPES……….. 10

1.1. The synchronous generator ...................................................................................... 10

1.2. Types of PM generator ............................................................................................ 11

2. DESIGN ASPECTS OF PMG………………………………………………………..17

2.1. Description of the prototype patent (1) .................................................................... 17

2.2. Materials .................................................................................................................. 23

2.3. Finite element magnetic model ................................................................................ 24

3. EXPERIMENTAL RESEARCH OF PMG………………………………………….. 29

3.1. Plan of the experiment ............................................................................................. 29

3.2. Measurement equipment and specifications ............................................................ 31

3.3. Electric schematic explanation ................................................................................ 32

3.4. Analysis of the results .............................................................................................. 35

3.4.1. No-load data analysis......................................................................................... 35

3.4.2. Load data analysis ............................................................................................. 38

4. GRATITUDE………………………………………………………………………... 45

5. CONCLUSIONS…………………………………………………………………….. 46

5.1. Parameters of the PMG and comparison ................................................................. 46

5.2. Material consumptions ............................................................................................. 46

5.3. Experiment characteristics ....................................................................................... 47

RECOMMENDATIONS…………………………………………………………………... 47

REFERENCE………………………………………………………………………………. 48

APPENDIX………………………………………………………………………………… 50


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INTRODUCTION

Relevance of the topic. Classic generators are based on electrical induction or electric

currents and magnetic fields. Each electric machine that uses permanent magnets, can act as a

generator or motor. One of existent problems of manufactured electric generators is that the coil

reactance , the most common, is greater than the active coil resistance . This fact creates

difficulties for designers and operators of generators. The proposed generator or motor should

partially or completely compensate reactance.

The object: Patented PMG prototype with reactance compensated winding.

The aim: Research the type of patented PMG, which is claimed to have significant internal

circuit reactance compensation by winding special coils and construction of before unseen machine.

Tasks:

1. Overview of present PMGs.

2. Review of patented PMG.

3. Prototype design.

4. Construction of prototype.

5. Finite element analysis of magnetic circuits.

6. Conduction of experiments.

7. Achieved data analysis.

Methods. Design aspects are evaluated with the help of literature, scientific articles and patent

analysis of existent PMG technologies. Prototype is designed and drawings are made with

SolidWorks. Magnetic analysis is conducted with FEMM (2D) and EMS add-on for SolidWorks

(3D). Electrical schematics are drawn with EAGLE CAD. Experiments are conducted in Klaipeda

university LAB facilities. Achieved data is analyzed and characteristics plotted with MS Excel.


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1. OVERVIEW OF EXISTENT GENERATOR CONSTRUCTION TYPES

1.1. The synchronous generator

The stator coils are positioned in slots, which are connected in series. The ends of the circuit

thus formed are the generator terminals.

For the rotor, there are 2 types:

salient pole rotor

non-salient pole rotor

Salient pole rotor usually has 4 or more poles.

Non-salient (smooth) pole rotor has 2 or 4 poles.

The coils are connected in series and placed on pole cores. There is an even number of

poles, successive around the wheel, North, South, North, South, etc... The windings of two

consecutive coils are reversed. The rotor is made laminated to reduce induced eddy current (2 p.

20).

1.1. Fig. View of a synchronous AC generator

In a PM generator, the rotor field windings are replaced by permanent magnets which do not

require additional excitation. As the permanent magnets are rotated, current is induced in the stator

windings.

PM generators offer several advantages: they have no rotor windings so they are less

complicated; they have high efficiencies; the gap field flux is not dependent on large pole pitches so

the machine requires less back iron and can have a greater number of smaller poles ; and they

usually require smaller and fewer support systems.


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1.2. Types of PM generator

Radial-flux permanent magnet generator with Internal Rotor (In-runner)

(a) (b)

1.2. Fig. In-runner PMG construction: (a) realistic view, (b) 3D CAD view

A typical radial-flux generator with permanent magnet poles rotating inside stationary

armature windings. The air-gap flux density is closely related to the remanence of the magnet and

the magnet working point (The Working Point is the point on the demagnetization curve where the

value of B & H corresponds to the actual working conditions of the magnet). So it is difficult to get

high air-gap flux densities with low remanence magnets in this configuration. The windings are

placed on the stator in slots, and the magnets are surface mounted on the rotor or buried in the rotor.

In general, the inner rotor machine possesses high torque/power capability, good heat

conduction and cooling properties making it ideal for high-speed, higher-power applications.

It has high efficiency and power/weight ratio (no rotor windings). The disadvantage is that

the magnets have to be implanted carefully so that the rotor does not fly apart (3) (4).


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As an example, a radial-flux permanent magnet generator with Internal Rotor from the

“Alxion” and “MOOG” constructors catalogues are respectively shown below:

1.1. Table. “Alxion” constructors catalogue parameters

The gravimetric power density of this PMG series is from to at a

rated speed of .

1.2. Table. “MOOG” constructors catalogue parameters

The gravimetric power density of this PMG series is from to at a

rated speed of .


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Radial-flux permanent magnet generator with External Rotor (Out-runner)

1.3. Fig. In-runner PMG construction 3D CAD view

As illustrated in figure above, the wound stator inside of external rotor configuration is

stationary, located in the center of the generator, while the magnets are mounted uniformly along

the internal circumference of the rotating drum supported by front and rear bearings.

The radial flux outer rotor machines are commonly used in hard disk drives, small computer

ventilation fans, and some blowers. This type of design is very efficient, low-cost, easy to

manufacture, and applicable for low-power applications such as wind generator. That type of

generator or motor can be driven with higher speeds rather than with internal rotor, because of

centrifugal forces (4) (5).

Axial flux permanent magnet generator

The axial flux machine is significantly different than the previous two because flux flows in

the axial direction vice radial direction and the windings are oriented radially vice axially.

A lot of different topologies exist, but here are some examples:

Double-Stator Slotted Axial-Flux Machine

The machine consists of two external stators and one inner rotor. The permanent magnets

are surface mounted or are embedded in the rotor disc. In all axial flux machines, the rotor rotates

relative to the stator with the flux crossing the air gap in the axial direction. The stator iron core is

laminated in the radial direction (6).

Double Rotor Slotted Axial-Flux Machine

This configuration is similar to that of the double-stator slotted axial-flux machine, except

that there is one stator and two rotors. The stator is located in the middle of the two rotors and

slotted on both sides (6). An example of non-slotted from (7) is shown below:


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1.4. Fig. Non-slotted axial field PMG

Axial-Flux Machine with Toroidal Winding

This kind of prototype generator has a simple construction and is often referred to as a Torus

machine. It is a slotless double-sided axial flux PM disc-typed machine. The two rotor discs are

made of mild steel and have surface-mounted PMs to produce an axially directed magnetic field in

the machine air gaps. The machine stator comprises a slotless toroidally wound strip-iron core that

carries a three-phase winding in a toroidal fashion by means of concentrated coils. The coils have a

rectangular shape according to the core cross section. The axially directed end-winding lengths are

relatively short, yielding low resistance and reduced power loss. The active conductor lengths are

the two radial portions facing the magnets, the polarities of which are arranged to induce additive

electromotive forces (EMFs) around a stator coil (6).


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Here is a prototype of an axial flux PMG (8):

1.5. Fig. Prototype axial flux PMG

By positioning the stator on both sides of the rotor, the magnetic flux on both sides of the

magnet can be utilized. In addition, by piling the rotor and the stator in the direction of the shaft, a

plurality of the air gap can be applied.

1.3. Table. Prototype generator specifications

Rated Power 1

Rated speed 840

No-load EMF 206

Number of rotors 7

Number of poles 12

Rotor size 140x6

Gap between rotors 6

Number of stators 6

Number of coils 9

Stator size 170x4

Number of loops per coil 53

Outside size 182x142

Weight 8,5

Cooling Natural

The gravimetric power density of this prototype at a rated speed of is


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In order to compare, here there is another prototype of an axial flux PMG (9):

1.6. Fig. The structure of the axial flux permanent magnet generators. (1) Stator core holder. (2)

Stator core. (3) Armature winding. (4) Rotor Disk. (5) Permanent Magnet

1.4. Table. Nominal characteristics of constructed TFPMDG

Load current 4

Output power of one module 400

Efficiency 90

Power factor 0,8985

Output power per active mass 0,298

Output power per volume 591

Active outer diameter of one module 166

Active inner diameter of one module, 96

Active thickness of one module, 47

Armature resistance 0,38

Direct synchronous reactance 6,824

Quadrature synchronous reactance 6,808

Output frequency 500

The disk-shaped profile of this prototype makes it very suitable for exploitation in wind

turbines. Also, the disk structure allows high rotational speed due to its ability to counteract

centrifugal forces acting on the permanent magnets.

In conclusion, the advantage of the axial flux model against the radial flux model is that they

can be designed to have a higher power/weight ratio resulting of the less core material and a higher

efficiency. Their disc shaped rotor and stator structure is also an advantage because suitable shape

and size to match the space limitation is crucial for some applications such as electric vehicle.


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Linear tubular permanent magnet generator

The mover of the tubular generator in study consists of iron core rings fixed on a shaft

alternated with permanent magnet rings magnetized in radial direction. They are used as linear

WEC (Wave Energy Converters) generator. An example from (10) is shown below

1.7. Fig. PM wave energy converter generator

2. DESIGN ASPECTS OF PMG

2.1. Description of the prototype patent (1)

In this section a “Hybrid Flux” permanent magnet generator topology with reactance

compensated windings is presented. The flux of this topology travels radially through the rotor and

axially through the stator.

The invention is in the field of generators and motors, and can be adapted to mechanical

rotational motion converting into electrical energy or electrical energy to translate mechanical

rotary motion.

Classic generators are based on electrical induction or electric currents and magnetic fields.

Each electric machine that uses permanent magnets, can act as a generator or motor. One of existent

problems of manufactured electric generators is that the coil reactance , the most common, is

greater than the active coil resistance. This fact creates difficulties for designers and operators of

generators. The proposed generator or motor should partially or completely compensate reactance.

The closest technical solution is the toroidal electric generator or motor, which is described

in the patent application EN 2011 036 (an application filed 2011-04-29). Toroidal generator or

motor proposed “bifilar” type of generator or motor, using “bifilar” (opposite) coil circuit mode.

Toroidal generator or motor magnetic flux passes through the coil windings, which set the air gap

between the magnets and the toroidal core. Air space has a large magnetic resistance; the fact

reduces the generator or motor power. The proposed “bifilar” type generator or motor does not have


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huge air gap between the magnetic core, cores have the ability to connect almost directly to the

magnets. This fact allows increasing the mentioned electrical machinery output.

(The proposed construction of the magnetic field direction changes from radial to axial and

vice versa. This circumstance prevents the coil-generated magnetic field to reach the point where

permanent magnets are demagnetized (coercive force).

Bifilar type generator or motor is constructed in order to reduce inductive coil reactance.

Due to the fact, the machine should give more power when working in the generator mode and

develop more power when working in the motor mode. This is achieved by applying “bifilar” coil

connection method. When the coils are physically separated, the mutual inductance determines the

total inductance of coils. While a current passes through a coil, the current having the same value

but opposite direction, these magnetic fields should partially or completely destroy each other and

hence destroy or decrease the total inductance. This type of generator or motor advantage when

compared to similar electric machines is the fact that each pair of inductive coils reactance is

reduced significantly.

Differences from other prototype are:

1. Type of “bifilar” generator or motor having permanent magnets wherein the coils are set out

at the air gap between the magnets and the core which has the ability to directly connect to

the magnets.

2. Type of “bifilar” generator or motor having permanent magnets, wherein the cores are not

toroidal and straight.

3. Type of “bifilar” generator or motor having permanent magnets is different in that it can

have an unlimited number of ferromagnetic cores.

2.1. Fig. Cross section view of PMG topology


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In figures 2.2–2.3, there is in reality not one but two series of magnets separated by a piece

of epoxy composed supporting slots for the cores [3] and mated to the shaft by a bearing. The Iron

or steel non-laminated core between the opposite pole magnet had been deleted because it was

useless, insignificant magnetic field passing through it, which is changed to radial direction,

differently from figure 2.3.

2.2. Fig. Axial section view of PMG topology

2.3. Fig. Magnetic circuit model of PMG topology

In figures 2.1–2.3 numberings are explained:

1) Magnets;

2) Windings;

3) Ferromagnetic cores;

4) Magnetic flux lines with direction arrow;

5) Iron or steel non-laminated core;

6) Rotor supporting part (non-magnetic);

7) Shaft.


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Stator

As shown in figure 2.4, each coil is wound on ferromagnetic cores [3]. The windings are

wound in one direction, then to the other [2] in order to have a same current with opposite

directions. These compensated windings should in theory limit the reactance. By turning the rotor,

the alternation of magnetic fields in ferromagnetic cores [3] and windings [2] creates an electrical

current. When the machine is operating in the generator mode, the current flowing in coil creates a

magnetic field that opposes the external magnetic field changes.

There are a total of 15 rods each wound with 2 coils. Each phase has 5 rods connected in

series.

2.4. Fig. Single wound rod of PMG topology stator

Rotor

As shown below, different topologies exist for rotor of PM generator or motor:

Surface-mounted magnets

As shown in figure 2.5 (a) the radially magnetized magnets are mounted on the steel-core

rotor structure. The relative permeability of the magnets material being near unity, it acts like a

large air gap. The effective air gap is therefore large, making (direct inductance) low. The

structure is magnetically non salient and thus . And, this topology, because of constant

magnetic gap between rotor and stator, can provide a square wave flux distribution (2 p. 356).

The inset (buried) magnets

For the inset (buried) topology, the magnets are embedded in the rotor steel as shown in

figure 2.5 (b) the construction provide a more secure magnet setting. The advantage is the

possibility to use straight magnets. Another advantage is the possibility to place the magnets to

acquire flux concentration in the air gap. Buried magnet machines can also have significant

structural issues in high-power applications.

The disadvantage is that some flux from the PM’s will ‘leak’ trough the rotor steel. This

means that this flux does not cross the air gap and contribute to the Eddy currents (2 p. 356).


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2.5. Fig. Permanent magnet rotor generator. (a) surface-mounted magnets. (b) Inset (buried)

magnets. (c) Buried magnet with radial magnetization. (d) Buried magnet with circumferential

magnetization (2 p. 355)

Inset (buried) magnet with radial magnetization.

As shown in figure 2.5 (c), the magnets are buried inside the rotor structure with radial

magnetization. For this configuration .

Inset (buried) magnets with circumferential magnetization.

As shown in figure 2.5 (d), the magnets are buried inside the rotor structure with

circumferential magnetization. Because of the flux-focusing effect, circumferential magnetization

yields a greater air gap flux rather than the radial magnetization. The structure is magnetically

salient, becomes large .


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Based on these topologies, it is chosen, that the magnets will be surface-mounted on the

rotor.

On the shaft [7] and the construction parts [5] and [6] are attached with magnets first It

consists of having the opportunity to rotate on its axis, rotor. The magnets [1] are mounted on the

magnetic construction [5].

Magnet poles of one magnet in each queue along the longitudinal axis are mounted in

opposite magnetic fields as shown in figures 2.6 and 2.2.

There are a total of 80 magnets. Each of the two parts of the two rotors is composed of 20 of

them.

2.6. Fig. Surface mounted magnets [1] on the ferromagnetic core [5]

2.7. Fig. 3D isometric view of PMG construction


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2.2. Materials

Magnets

The table below is an average of the magnets characteristics given the amount types of

permanent magnets existing.

2.1. Existing magnet materials and parameters

Magnets Typical

Typical

Typical

Curie

Temperature

Price extra

NdFeB

(sintered) 1,0-1,4 750-2000 200-440 310-400 +++

SmCo 0,8-1,1 600-2000 120-200 720 ++++

Low

temperature

coefficient

NdFeB

(bonded) 0,6-0,7 600-1200 60-100 310-400 ++

Low Eddy-

currents

Alnico 0,6-1,4 275 10-88 700-850 + Low Eddy-

currents

Ferrite 0,2-0,4 100-300 10-40 450 + High knee

point

The permanent magnet NdFeB has been chosen to develop the prototype because it has a

high remanence flux density which means a higher rotor excitation field. Therefore less copper is

needed to induce the same voltage in the windings. The Curie temperature of the NdFeB magnets is

enough for this application.

Between all types of NdFeB magnets, the N45 had been chosen because of a compromise

between prize and remanence (magnetic field). The N45 have a remanence between

tesla, a coercive force and a maximum operating temperature . The N48, 50

and 52 have a higher remanence but they are also much more expensive.

Wood Epoxy Fiber

The epoxy wooden fiber had been chose because it is a strong, cheap and easy to

manufacture material. There are also no eddy currents in those materials. This material is supporting

stator rods, as shown in drawings for Stator Slots and Stator Flanges (pp. 6–7).

Polyethylene

Material for the rotor had been chosen because it is light, so the rotor has less inertia. It is

also easy to manufacture, cheap and it is quite durable. More important, the rotor having no

windings it does not heat so the polyethylene won’t melt.

Wire

The copper wires used for the windings has 1 mm diameter. The choice of those wires had

been done because there were in stock so it was the cheapest way.


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2.3. Finite element magnetic model

A half of this PMG construction is unfolded into linear type and modeled in 2D

environment. Down below cores are shown as poles with wound coils around them and the magnets

from both sides surface mounted on iron plate. Another half of the generator is eliminated, because

it is impossible to have a full model in 2D environment.

2.8. Fig. Magnetic circuit flux lines of PMG topology with double magnets.

This topology has 4 magnets for 3 stator rods or 2 pole pairs for 3 phases. The original plan

was to put 10 permanents magnets on each of the four parts of the rotor. The reason is due to little

magnetic field interacting, if every second magnet from top and bottom is eliminated, there a half

area left for the other magnet pole, while the first one covers a full area flux, which causes high

cogging torques while spinning and only half of the flux from magnets is used. This problem has

been fixed by mounting 20 permanent magnets on each of the four parts of the rotor. With the

configuration, while the one coil faces one pole (north for example), the following two coils face 3

quarters of a south pole and a quarter of a north pole so the electromagnetic force of the coil A is

equal to the electromagnetic force of the coils BC.

2.9. Fig. Magnetic circuit flux lines of PMG topology with less magnets.


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A magnetic transition between rotor and stator is shown below in steps.

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step n

2.10. Fig. Magnetic circuit flux lines of PMG while moving through steps.

A 3D finite element analysis is made to show relationship between magnets and stator rods.

For that task a 1/5 segment of the generator is cut out and shown below. The numbering is the same

as in figures 2.1–2.3, 2.6.


26

2.11. Fig. 1/5 segment of patented PMG active material (3D model front view)

2.12. Fig. 1/5 segment of patented PMG active material (3D top view)

2.13. Fig. Magnetic flux density vector plot (front view)

1 5

1

1 1

3

3

3

2

2

2


27

2.14. Fig. Magnetic flux density vector plot (top view)

2.15. Fig. Magnetic flux density continuous fringe plot on several sections: A – cross section of

magnet array, B – cross section of coils

2.16. Fig. Magnetic flux density continuous fringe plot on several sections: C – axial section of core

phase C, D – axial section of core phase A

A

B

D

C


28

Further a 3 phase current is applied to show the relationship between wound stator and magnets.

2.17. Fig. 1/5 segment of patented PMG active material magnetic flux density with applied 3 phase

current 10A RMS

2.18. Fig. Magnetic flux density with applied 3 phase current 10A RMS axial section of first wound

rod (right side view)


29

2.19. Fig. Magnetic flux density with applied 3 phase current 10A RMS cross section of first array

of magnets (front view)

3. EXPERIMENTAL RESEARCH OF PMG

3.1. Plan of the experiment

In this part of thesis the plan of experiment is described. Several parameters are measured in

order to get full pictures of real characteristics. The conduction of experiment is described below.

Notice, every abbreviation corresponds to electronic schematic “BCPM Test & Control Circuit”.

Connection and mounting of the system:

1) PMG’s shaft is connected to the driving DC motor with mechanical coupler (G1-

M1);

2) A load block (resistors R, capacitors C, coils L) is connected to the terminals of the

PMG. The method of connection of PMG generating coils and load block is star with

0 wire (Y0-Y0);

3) Connection of measuring devices to circuit:

a. Voltmeter V1 is connected between A0 terminals, alternative AA’.

b. Voltmeter V2 is connected in parallel with armature M1.


30

c. Ampermeter A1 is connected in series with the A phase loading element.

d. Ampermeter A2 is connected in series with Armature M1.

e. Power meter P is connected the same way as V1 and A1 to corresponding

terminals.

f. Frequency meter Hz is connected the same way as V1.

4) Connection of DC motor M1 is more complex, because it is digitally controlled with

computer, microcontroller and power transistors.

a. Thyristor rectifier output provides 220VDC. Field winding is connected

directly to the output terminals.

b. Armature of the motor is connected in series with power transistor block Q1,

which contains 2 transistors inside protected with freewheel diodes as

described in (11). For this application Low Side IGBT and High Side Diode

are used to regulate the speed of the motor in 1 direction. Terminal 3 of Q1 is

connected directly to the “+” as one of the armature terminals of the M1, 2 –

directly to the “–” and 1 – to anther armature terminal. The motor is

controlled by transistor and protected by freewheel diode (terminals 31).

Terminals 6–7 connected to the Gate Driver, which has galvanic isolation

OK1 from the logic.

5) The system is prepared for experiment conduction.

Experimental data achievement:

1) No load characteristic:

a. The terminals of PMG are disconnected from the load, only V is left.

b. The control logic is powered on, the computer is running hyper terminal of

the Serial Communication between microcontroller, which listens to decimal

expression of 8 bits (0-255), which is controlling PWM;

c. The Power for the motor is turned on (SW1);

d. Increment the number and send to the logic.

e. While the M1 drives the PM ROTOR, take parameter measurements of each

meter each step until you reach maximum safe speed.

f. Transfer no load data to Microsoft Excel.

2) Load characteristics:

a. For this experiment asynchronous geared motor of the lathe is used to drive

the PMG. The shaft of PMG is driven with the knuckle of the lathe.

b. The gear ratio is chosen from smallest speed to the maximum safe.


31

c. Each gear switch step, while the lathe is spinning the PM rotor, the stator is

loaded and the measured data is transferred to MS Excel Sheet.

3.2. Measurement equipment and specifications

3.1. Table. Measurement device

Measurement

device Model AC/DC Max scale

Tolerance

class Use

Ampermeter M1500T3

1984 DC 1,5

DC motor

armature

Voltmeter M1600

1979 DC 1,5

DC motor

armature

Multimeter Agilent

U1241A AC/DC 1000V

PMG voltage

and frequency

Multimeter Mastech

MS8222H AC/DC 10A PMG current

3.2. Table. Parameters of driving machines

Driving machine Model Power Gearbox Speed Year

DC motor П-42 7,2

kW No 2800 rpm 1976

Induction motor

– Lathe

Красный

Пролетарий

1K62

10 kW Yes

(Multiple)

1450 rpm

(50, 63, 80, 100, 125, 160, 200,

250, 315, 400) 500, 630

1971

DC motor controlling logic

Used “Arduino Nano V3.0” module, which is manufactured in USA “GRAVITECH”. This

board Bread-Board friendly. A Mini-B USB socket (12).

3.1. Fig. Arduino Nano V3.0

Specifications:

Microcontroller Atmel ATmega328 (8 bit)


32

Logic level 5V

Voltage:

o Recommended 7–12V

o Maximum 6–20V

Digital outputs 14 (6 are PWM channels)

Analog inputs 8

Maximum current capabilities 40mA

Memory

o FLASH 32KB (2KB used for boot loader)

o SRAM 2KB

o EEPROM 1KB

Frequency 16MHz

Size

3.3. Electric schematic explanation

In section B2 of the electric schematic drawing, we can see thyristor rectifier. A rectifier is

an electrical device that converts alternating current (AC) to direct current (DC).

In section D5, D6, E5, E6, we can see Gate Driver. A gate driver is a power amplifier that

accepts a low-power input from a controller IC and produces a high-current drive input for the gate

of a high-power transistor such as an IGBT or power MOSFET.

In figure below, the arrows represent the path taking by the current when the transistor T0

(transistor from the opto-coupler 4N35) is open or not.

3.2. Fig. IGBT or MOSFET gate driver working principle

The equivalent circuit in figure 3.3 on the left symbolizes the behavior of the gate driver

when the transistor T0 is opening (red arrows). The transistor T1 is symbolized by a diode

(according to construction of NPN transistor). The transistor IGBT is symbolized by a capacitor and

http://en.wikipedia.org/wiki/Electric_power_conversion

http://en.wikipedia.org/wiki/Alternating_current

http://en.wikipedia.org/wiki/Direct_current

http://en.wikipedia.org/wiki/Power_amplifier

http://en.wikipedia.org/wiki/Integrated_circuit

http://en.wikipedia.org/wiki/IGBT

http://en.wikipedia.org/wiki/Power_MOSFET


33

a diode (according to the construction of IGBT). The current passes through the opto-coupler

transistor, 200 ohms resistance and NPN BC547 transistor’s base-emitter, while charging the

capacitance of IGBT gate, an NPN transistor amplifies the current and charges the gate faster,

which is shown in figure 3.4.

3.3. Fig. Gate driver “turning on” equivalent 3.4. Fig. Gate driver “turned on” equivalent

While base-emitter current flows through BC547, a collector current is amplified, but it is

limited by 50 Ohm resistor near to absolute maximum current of signal transistor (100mA). While

the gate of IGBT is charged to 10V the current is efficiently supplied for high power motor.

Equivalent circuits of the states, when the transistor is closed (blue arrows), shown in figures

3.5 and 3.6.


34

3.5. Fig. Gate driver “turning off” equivalent 3.6. Fig. Gate driver “turned off” equivalent

In figure 3.5 the transistor T0 is closed. The IGBT is symbolized as a capacitor and the

transistor PNP BC557 as a diode. Current flows from charged capacitor through the PN junction of

the transistor (emitter-base) and 2 resistors in series.

In figure 3.6 the emitter-base current is amplified, while discharging the capacitance through

the resistors, and limited by resistor.

The opto-coupler is used to transmit signal using light in order to protect the electronic

microcontroller (MCU) with galvanic isolation between.

The resistor R6 is a pull-down resistor. A pull-down resistor serves to secure the zero

of the opto-coupler (transistor).

The resistors R7 and R8 are situated respectively at the collector of the transistor BC547 and

the emitter of the transistor BC557. The resistor has been chosen in order to limit the current

going through the transistor and the IGBT capacitance.

The IGBT SKM150GB12T4 is a very important component in power

electronics. By applying voltage to gate of IGBT, it supplies current to the motor. The conduction

stops when it ceases to act on the gate. By changing the duty cycle of a PWM, we can control the

speed of the motor. The maximum voltage between the emitter and the collector the transistor can

withstand is . The continuous load current of the IGBT is .

In section B5, B6, C5 and C6 the speed sensor TCRT5000. The TCRT5000 are reflective

sensors which include an infrared emitter and phototransistor in a leaded package which blocks

visible light (13).

The resistor was chosen in order to make sure that the controller “sees” a voltage of

0V when the transistor is not opened.

The resistance was chosen in order to limit the current under , which is the

maximum forward current for the infrared emitting diode of the speed sensor.


35

In section C4, there is a temperature sensor LM35. The output voltage is linearly

proportional to the Celsius (Centigrade) temperature.

3.4. Analysis of the results

3.4.1. No-load data analysis

The No Load results of the experiment provide the information of power losses in

mechanical and magnetic (eddy currents) parts, the size of EMF induced.

3.3. Table. Motor current voltage data from A2

( ) 0 0,90 0,93 0,98 1,01 1,04 1,08 1,13 1,16 1,19 1,22

( ) 0 0,90 0,94 0,99 1,02 1,05 1,09 1,13 1,17 1,20 1,23

0,000 0,130 0,165 0,215 0,245 0,275 0,315 0,360 0,395 0,425 0,455

1,26 1,31 1,35 1,39 1,42 1,44 1,48 1,53 1,57 1,60 1,64 1,68

1,27 1,32 1,35 1,39 1,42 1,45 1,49 1,53 1,58 1,61 1,65 1,69

0,495 0,545 0,580 0,620 0,650 0,675 0,715 0,760 0,805 0,835 0,875 0,915

Where: – Mean armature current of the motor;

min, max – Electronic unstable measurement range.

3.1. Equation. Arithmetic mean (14)

∑

Applied arithmetic mean value for the armature current:

( ( ) ( ))

3.4. Table. Motor terminal voltage data from V2

0,0 6,0 7,8 10,2 11,4 12,4 13,9 15,8 17,2 18,4

0,0 6,1 7,9 10,3 11,5 12,5 14,0 15,9 17,3 18,5

0,00 6,05 7,85 10,25 11,45 12,45 13,95 15,85 17,25 18,45

0,00 0,07 0,09 0,12 0,14 0,16 0,18 0,21 0,23 0,24

21,1 22,6 23,7 24,7 25,7 25,6 26,8 28,1 29,1 30,1 31,1

21,1 22,7 23,8 24,8 25,8 25,7 26,9 28,2 29,1 30,2 31,2

21,10 22,65 23,75 24,75 25,75 25,65 26,85 28,15 29,10 30,15 31,15

0,28 0,31 0,33 0,36 0,37 0,39 0,41 0,44 0,46 0,48 0,50

where

– Mean terminal voltage of the motor;

– Armature resistance.

Applied arithmetic mean value for the armature voltage:


36

( ( ) ( ))

3.2. Equation. Ohm's law (15) (16 p. 54) (17)

where

– Resistance in ohms;

– Electric potential difference in volts;

– Electric current in amperes.

Applied Ohm’s law for the armature internal resistance voltage drop:

3.5. Table. PMG terminal EMF frequency data from Hz

0,00 7,52 11,45 15,10 17,18 19,32 22,17 25,58 28,18 29,97 31,99

0,00 7,77 11,52 15,15 17,22 19,27 22,23 25,65 28,22 30,04 32,03

0,000 7,645 11,485 15,125 17,200 19,295 22,200 25,615 28,200 30,005 32,010

33,76 36,15 38,47 40,40 39,48 41,11 42,94 44,53 46,73 33,76 36,15 38,47

33,92 36,24 38,50 40,45 39,42 41,14 42,95 44,77 46,75 33,92 36,24 38,50 33,840 36,195 38,485 40,425 39,450 41,125 42,945 44,650 46,74 33,840 36,195 38,485

Applied arithmetic mean value for the frequency:

( ( ) ( ))

In order to calculate the real mechanical and magnetic losses, we need to subtract Copper losses

from power fed to the motor.

3.3. Equation. Electrical power (18) (17)

where

– Electric charge in coulombs;

– Time in seconds;

Applied electric power equation for fed power:

3.4. Equation. Joule’s first law (heating) (19)

Applied Joule’s first law for copper losses in motor armature:

The mechanical and magnetic losses achieved from:


37

Copper losses are insignificant compared to mechanical and magnetic losses.

3.6. Table. Power losses, calculated data

0,00 0,79 1,30 2,20 2,81 3,42 4,39 5,71 6,81 7,84 9,01

0,00 0,01 0,02 0,03 0,03 0,04 0,06 0,07 0,09 0,10 0,12

0,00 0,78 1,28 2,18 2,77 3,38 4,34 5,63 6,72 7,74 8,89

10,44 12,34 13,78 15,35 16,74 17,31 19,20 21,39 23,43 25,18 27,26 29,42

0,14 0,17 0,19 0,22 0,24 0,26 0,29 0,33 0,37 0,40 0,44 0,48

10,30 12,17 13,58 15,12 16,50 17,05 18,90 21,06 23,05 24,78 26,82 28,94

Notice: other shown values are calculated the same way as in the example before.

The curve in figure 3.7 is plotted to show the relationship of power loss and speed, the trend line

equation describes it:

3.7. Fig. Mechanical and magnetic power losses versus frequency as TG signal

The no-load data tables of EMF vs. speed ( ) are placed in appendix tables 0.1 – 0.3. The

plot of the curves is shown in figure 3.8. All the mean value calculations are done using equation

3.1 in MS Excel.

3 plotted curves are shown as a linear relationships and very low difference in figure 3.8. A

trend line is added and equation describing the curve is generated.

3.8. Fig. EMF vs. frequency as AC TG speed signal (OCC)

ΔP(f) = 0,0001f3 + 0,0046f2 + 0,0262f + 0,1773

0

5

10

15

20

25

30

35

0 10 20 30 40 50 60

Po

we

r lo

sse

s , W

Frequency, Hz

Measured

Predicted

E(f) = 6,3244f + 1,1674

0

100

200

300

400

0 10 20 30 40 50 60

EMF,

V

Frequency, Hz

EMF vs Frequency A

EMF vs Frequency B

EMF vs Frequency c

Predicted


38

3.4.2. Load data analysis

Measured data from taken V1, Hz and A1 at different speeds and loads are placed in

appendix (0.4-0.12 tables). The same mean value equation is applied for voltage and current data.

The plot is constructed from raw data to show relationship of output characteristics ( ) at

different speeds. Armature active resistance is per phase.

Due to lack of accuracy in measurements, such as inductance in variable resistors, calculated

characteristics are added for comparison. The calculated parameters are presented in table below.

3.7. Table. The parameters of calculated curves

8,75 11,02 14,14 17,80 22,89 28,80 44,08 56,49 71,11

56,51 70,86 90,59 113,74 145,93 183,31 279,19 357,29 448,90

2,095 2,195 2,250 2,260 2,300 2,315 2,340 2,370 2,365

25,53 31,09 39,31 49,57 62,85 78,70 118,99 150,51 189,61

134,2 183,7 251,4 328,6 442,5 573,5 916,0 1204,6 1529,5

where

– Short circuit current in amperes;

– Synchronous reactance in ohms.

– Useful output power in watts;

Applied formula generated from trend line for EMF calculation:

3.5. Equation. Synchronous impedance using Ohm’s law for AC circuits

3.6. Equation. Reactance calculation from scalar vector formula

√

Relation between synchronous reactance and frequency is plotted in figure 3.9. A

linear trend line is added and equation describing the curve generated. That is stated to show, that

there is no non-linearity in PMG stator circuit.

3.9. Fig. Linear relationship of reactance vs. frequency

Xs (f) = 2,6141f + 3,6992 0

50

100

150

200

0 10 20 30 40 50 60 70 80

Re

acta

nce

, Ω

Frequency, Hz

Calculated

Predicted


39

Predicting short circuit current ( ) using correlated values of and .

3.7. Equation. Short circuit current of SG with armature resistance (2 p. 330)

√

Substitute curve equations of EMF and reactance and get

( )

√( )

√

which describes the curve in figure 3.10.

3.10. Fig. Short circuit current vs. speed relationship

3.8. Equation. Vector and scalar representation of terminal voltage based on Kirchhoff’s II law

( ) √ ( )

3.9. Equation. Relation between terminal voltage and load current

( )

described by equation 6.36 from (2 p. 330) if

Substitute of above equations to terminal voltage ( ).

3.10. Equation. Terminal voltage of PMG performance

( ) √ ( ) ( ( ) )

which is used in MS Excel to get results plotted in figure 3.11.

0,0

0,5

1,0

1,5

2,0

2,5

0 10 20 30 40 50 60 70 80

Cu

rre

nt,

A

Frequency, Hz

Predicted

Measured


40

3.11. Fig. Terminal voltage vs. load current performance characteristics at different speeds

(measured and calculated)

An interpolated surface plot is generated to have a better view.

3.12. Fig. Terminal voltage vs. load at different speeds (surface plot)

The curve of independent PMG displays armature voltage fall by quarter ellipse trajectory

because of synchronous reactance of the system as shown in figure 3.13. Measured curves seem

to be lower, because the load resistors have as explained in (2 p. 331), at small

load and short circuit, at .

0

50

100

150

200

250

300

350

400

450

500

0,0 0,5 1,0 1,5 2,0 2,5

Arm

atu

re V

olt

age

, V

Current, A

0,0 0,5 1,0 1,5 2,0 2,5

Current, A

70,80 Hz

56,50 Hz

44,08 Hz

28,80 Hz

22,89 Hz

17,80 Hz

14,14 Hz

11,08 Hz

8,75 Hz


41

3.13. Fig. Performance characteristics of independent synchronous generator: (a) equivalent circuit

diagram; (b) Terminal voltage vs. load current at constant rotating excitation field (2 p. 331)

The power output curves ( ) are calculated from ( ) performance

characteristics.

3.11. Equation. 3 phase electric power of SG

Assuming that , therefore the function describing the curves is:

( ) ( )

This equation is used in MS Excel to get results plotted below:

3.14. Fig. Power output vs. load current performance characteristics at different speeds (measured

and calculated)

Notice that measured curves are slightly lower than the calculated one, which is due to the

load device . Evaluated measured ( ) , while calculated is

( ) (the difference in frequency is insignificant). Maximum

power output points are shown in figure 3.14 for the best performance at different speeds

( )

0

200

400

600

800

1000

1200

1400

1600

0,0 0,5 1,0 1,5 2,0 2,5

Po

we

r, W

Current, A

0,0 0,5 1,0 1,5 2,0 2,5

Current, A

max P

70,80 Hz

56,50 Hz

44,08 Hz

28,80 Hz

22,89 Hz

17,80 Hz

14,14 Hz

11,08 Hz

8,75 Hz


42


3.15. Fig. Output power vs. load at different speeds (surface plot)

In order to calculate energy conversion efficiency curves, we have to use efficiency formula

(20 pp. 52-54):

where

– applied input power to the shaft in watts.

This equation is used in MS Excel to get results plotted in figure 3.16.

3.16. Fig. Efficiency vs. load current performance characteristics at different speeds (measured and

calculated)

All power losses consist of mechanical, magnetic and electric (20 p. 211):

Mechanical losses due to friction in bearings, ventilation.

0

20

40

60

80

100

0,0 0,5 1,0 1,5 2,0 2,5

Effi

cie

ncy

, %

Current, A

0,0 0,5 1,0 1,5 2,0 2,5

Current, A

70,80 Hz

56,50 Hz

44,08 Hz

28,80 Hz

22,89 Hz

17,80 Hz

14,14 Hz

11,08 Hz

8,75 Hz


43

Magnetic losses due to core hysteresis, eddy currents.

Electric losses due to electric resistance of the copper.


3.17. Fig. Efficiency vs. load current at different speeds (surface plot)

More plots are made in figure 3.18 – 3.19 to show efficiency vs. power output

performance ( ), where dots are ( ).

3.18. Fig. Efficiency vs. load current performance characteristics at different speeds

(before overload)

0

10

20

30

40

50

60

70

80

90

100

0 200 400 600 800 1000 1200 1400 1600 1800

Effi

cie

ncy

, %

Power, W

70,80 Hz 56,50 Hz 44,08 Hz 28,80 Hz 22,89 Hz

17,80 Hz 14,14 Hz 11,08 Hz 8,75 Hz


44

3.19. Fig. Efficiency vs. load current performance characteristics at different speeds

(after overload)

0

10

20

30

40

50

60

70

80

90

100

0 200 400 600 800 1000 1200 1400 1600 1800

Effi

cie

ncy

, %

Output Power, W


45

4. GRATITUDE

MITA (Agency of Science, Innovation and Technology) for VP2-1.3-ŪM-05-K “Inočekiai

LT” (Innovation checks) “2007-2013 growing economics program” for supporting project

“Research of innovative bifilar type electric generator or motor”.

EMWorks (ElectroMagneticWorks Inc.) for trial license of software EMS, a SolidWorks

add-on for electromagnetic analysis and simulation studies.


46

5. CONCLUSIONS

5.1. Parameters of the PMG and comparison

In table below parameters of patented and 2 more of reviewed generator types are shown.

5.1. Table. Practical parameters of the PMG topology

Parameters Symbol

Generator types

Fig. 2.7 Fig. 1.5 Table. 1.1.

Table

Load current 1,65 3,2

Output power 1500 2100 1307

Rated speed 840 840 650

No-Load EMF 446 206 390

Voltage at rated power 309 243

Efficiency 92,4 81 76

Rated Power factor 0,69

Total mass 55 8,5 10,4

Output power per active mass 38,4 117,65 125,67

Output power per volume 138

Number of rotors 2 7

Number of poles (pair poles) 20 (10) 12 12(6)

Number of coils 30 9

Number of loops per coil 375 53

Active diameter 150

Rotor inertia 29,58 2,24

Phase armature resistance 8,7 8,6

Phase synchronous reactance 186,7

Phase inductance 442,5 60

Output frequency 70

Cooling Natural Natural Natural

5.2. Material consumptions

5.2. Table. Consumed material quantity

Material Mass, kg Number of pcs. or pkg.

Copper 13 30 coils

Laminated steel 20,7 15 rods 20x25x352

Non-laminated steel 4,4 4 rings, 1 shaft, fasteners

NdFeB N45 magnets 3,3 80

Wood Epoxy Fiber 10,3 5 parts

Polyethylene 1,8 2 cylindroids

Bearings 0,2 3


47

5.3. Experiment characteristics

Power no-load losses vs. speed characteristic is a square function of speed (frequency),

which include friction, ventilation and iron losses (induction, eddy currents), at it

reaches of power loss.

No-load EMF vs. speed (frequency) characteristic has linear relationship.

As PMG is loaded, terminal voltage fall by quarter ellipse trajectory due to synchronous

reactance of the system as shown in figure 3.13.

Measured curves seem to be lower due to the load resistors with at small

load and short circuit, at .

Power Output vs. load current measured curves are slightly lower than the calculated one,

which are due to the load device . Measured ( ) ,

while calculated is ( ) . For applications a max power

output points are shown in figure 3.14 for the best performance at different

speeds ( ).

Efficiency covers a large area at different speeds and load currents, at efficiency

almost same ( ) . The bigger the speed, the bigger the load currents available

for higher efficiency, nominal thermal current is the limit, practically ,

, which is preferred to be rated, because magnet’s Curie temperature . The

machine can be driven to produce .

RECOMMENDATIONS

As for the thesis the research is incomplete. This is a bachelor final thesis, which leads to

continuity of scientific works and researches in future. These are the first tests of the

patented BC PMG, which has shown some abstract parameters of a single configuration. A

further development of the PMG and effect of coil configuration analysis is planned during

the summer and master studies.

Future plan for generator:

o Connect different types of loads for more accurate and rich analysis;

o Test different coil configurations;

o Test generator parts separately to discover the effect and describe the difference;

o Make a Simulink MATLAB model;

o Describe in equations and theory.

Preliminary all parameters can be modeled by a special simulation program EMS add-on for

SolidWorks.


48

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Technical University of Cluj-Napoca, Romania : s.n.

11. Semicron. SKM150GB12T4. [Datasheet] s.l. : Semicron, 2012.

12. Mellis, David; Arduino. Arduino Nano. Arduino. [Tinkle] Arduino, 2009 m. 8 15 d.

[Cituota: 2013 m. 01 13 d.] http://arduino.cc/en/Main/ArduinoBoardNano.

13. Vishay Semiconductors. Reflective Optical Sensor with Transistor Output. 1.8, D-

74025 Heilbronn, Germany : Vishay Semiconductors, 6 11, 2012. TCRT1000, TCRT1010

Technical data. 83752.

14. Arithmetic Mean. Wikipedia The Free Encyclopedia. [Online] Wikimedia Foundation

Inc, May 3, 2013. [Cited: May 29, 2013.] https://en.wikipedia.org/wiki/Arithmetic_mean.


49

15. Ohm's Law. Wikipedia The Free Encyclopedia. [Online] Wikimedia Foundation, May 3,

2013. [Cited: May 29, 2013.] http://en.wikipedia.org/wiki/Ohm's_law.

16. Millikan, Robert Andrews and Bishop, Edwin Sherwood. Elements of electricity.

Michigan : American Technical Society, 1917.

17. Pukys, Povilas, Stonys, Jonas and Virbalis, Arvydas. Teorinė elektrotechnika.

Elektros grandinių teorijos pagrindai. Kaunas : KTU leidykla Technologija, 2004. ISBN 9955-09-

561-X.

18. Electric Power. Wikipedia The Free Encyclopedia. [Online] Wikimedia Foundation Inc,

May 24, 2013. [Cited: May 29, 2013.] http://en.wikipedia.org/wiki/Electric_power.

19. Joule heating. Wikipedia The Free Encyclopedia. [Online] Wikimedia Foundation Inc,

April 22, 2013. [Cited: 05 29, 2013.] http://en.wikipedia.org/wiki/Joule%27s_first_law.

20. Gečys, Steponas, Kalvaitis, Artūras and Smolskas, Pranas. Elektros mašinos.

Sinchroninės mašinos. Nuolatinės srovės mašinos. [ed.] Rimantas Jonas Mukulys. Kaunas :

Technologija, 2010. Vol. II. ISBN 978-9955-25-774-5.

21. Mellis, David; Arduino. Arduino Nano. Arduino. [Online] Arduino, 8 15, 2009. [Cited:

01 13, 2013.] http://arduino.cc/en/Main/ArduinoBoardNano.

22. Kšanienė, Daiva; KLAIPĖDOS UNIVERSITETO SENATAS. NUTARIMAS DĖL

„KLAIPĖDOS UNIVERSITETO STUDENTŲ SAVARANKIŠKŲ RAŠTO IR MENO DARBŲ

BENDRŲJŲ REIKALAVIMŲ APRAŠO“ PATVIRTINIMO. 11 – 56, Klaipėda : KU Senatas, 4 9,

2010.


50

APPENDIX


51

LIST OF APPENDIX

1. Data tables of measured and calculated values for analysis.

2. Mechanical drawings of PMG prototype design.

3. Electrical drawings of DC drive control.


52

0.1. Table. EMF and frequency data for phase A from V1, Hz

Phase A

Frequency EMF

min max average min max average

6,94 7,02 6,980 42 45 43,5

9,96 10,00 9,980 62 64 63

14,94 14,99 14,965 95 96 95,5

16,40 16,60 16,500 104 107 105,5

19,44 19,45 19,445 124 125 124,5

22,04 22,15 22,095 141 142 141,5

26,06 26,11 26,085 166 168 167

28,26 28,29 28,275 180 182 181

30,03 30,19 30,110 192 193 192,5

31,80 31,84 31,820 203 204 203,5

33,72 33,76 33,740 216 217 216,5

36,76 36,80 36,780 235 236 235,5

39,50 39,93 39,715 252 255 253,5

41,67 41,72 41,695 264 265 264,5

41,8 41,86 41,830 275 277 276,0

43,59 43,61 43,600 276 277 276,5

45,58 45,62 45,600 289 290 289,5

48,06 48,11 48,085 305 306 305,5

50,55 50,62 50,585 322 321 321,5

49,53 49,44 49,485 313 314 313,5

51,00 51,06 51,030 323 324 323,5

52,65 52,71 52,680 333 334 333,5


53

0.2. Table. EMF and frequency data for phase B from V1, Hz

Phase B

Frequency EMF

min mat average min max average

7,44 7,58 7,51 46 50 48

11,44 11,48 11,46 72 74 73

15,48 15,53 15,505 98 100 99

17,73 17,79 17,76 113 114 113,5

19,81 19,86 19,835 126 127 126,5

22,45 22,46 22,455 143 144 143,5

25,93 25,96 25,945 165 167 166

28,55 28,58 28,565 182 183 182,5

30,45 30,5 30,475 195 195 195

31,15 31,24 31,195 199 199 199

34,36 34,39 34,375 219,7 220,3 220

36,87 36,93 36,9 226 227 226,5

39,03 39,08 39,055 249 249 249

40,4 40,43 40,415 258 258 258

42,09 42,12 42,105 268 270 269

43,85 43,87 43,86 280,6 280,6 280,6

45,9 45,95 45,925 294 294 294

48,41 48,47 48,44 309 319 314

50,83 50,88 50,855 325 326 325,5

52,95 52,98 52,965 338 338 338

54,7 54,75 54,725 349 349 349

54,14 54,35 54,245 345 346 345,5


54

0.3. Table. EMF and frequency data for phase C from V1, Hz

Phase C

Frequency EMF

min max average min max average

8,34 8,38 8,36 53 55 54

11,95 12 11,975 75 77 76

16,58 16,63 16,605 105 107 106

18,12 18,88 18,5 119 120 119,5

20,86 20,92 20,89 132 133 132,5

23,84 23,87 23,855 151 153 152

27,16 27,2 27,18 172 173 172,5

29,61 29,7 29,655 187 190 188,5

31,18 31,21 31,195 198 199 198,5

32,79 32,82 32,805 208 209 208,5

35,1 35,14 35,12 223 224 223,5

37,58 37,62 37,6 240 240 240

40,16 40,37 40,265 256 258 257

41,67 41,7 41,685 265 266 265,5

43,41 43,44 43,425 276 277 276,5

45,2 45,25 45,225 287 288 287,5

43,35 43,41 43,38 275 276 275,5

46,22 46,24 46,23 293 294 293,5

48,42 48,45 48,435 307 307 307

50,32 50,35 50,335 319 319 319

52,12 52,17 52,145 330 330 330

53,89 53,93 53,91 341 342 341,5


55

0.4. Table. 8,75 Hz, voltage and current data from Hz, V1, A1

8,75 56,5 56,5 56,51 0 0 0,000

8,75 45,6 46,1 45,85 0,76 0,82 0,790

8,75 44,8 45,3 45,05 0,79 0,84 0,815

8,75 44,2 45,3 44,75 0,82 0,89 0,855

8,75 43,7 44,5 44,10 0,88 0,96 0,920

8,75 42,9 43,2 43,05 0,91 0,99 0,950

8,75 41,8 42,7 42,25 0,99 1,07 1,030

8,75 41,3 42,2 41,75 1,05 1,11 1,080

8,75 39,2 40,2 39,70 1,08 1,16 1,120

8,75 38,1 38,7 38,40 1,13 1,24 1,185

8,75 36,5 37,4 36,95 1,2 1,32 1,260

8,75 35,5 36 35,75 1,28 1,39 1,335

8,75 33,7 34,5 34,10 1,38 1,46 1,420

8,75 31,9 32,5 32,20 1,46 1,58 1,520

8,75 29,9 30,7 30,30 1,54 1,66 1,600

8,75 25,7 26 25,85 1,58 1,71 1,645

8,75 22,4 23 22,70 1,67 1,8 1,735

8,75 19,8 20 19,90 1,76 1,9 1,830

8,75 15,9 16 15,95 1,89 2,01 1,950

8,75 10,3 10,5 10,40 1,85 2,02 1,935

8,75 6,1 6,3 6,20 1,99 2,11 2,050

8,75 0 0 0,00 2 2,19 2,095


56


11,02 70,9 70,9 70,86 0 0 0,000

11,02 53,8 54,2 54,00 0,95 0,99 0,970

11,02 53,5 53,5 53,50 0,97 1,01 0,990

11,02 52,28 53 52,64 1,03 1,07 1,050

11,02 51,9 52,2 52,05 1,08 1,1 1,090

11,02 50,8 51,2 51,00 1,1 1,15 1,125

11,02 49,9 50,1 50,00 1,16 1,21 1,185

11,02 48,8 49,1 48,95 1,24 1,27 1,255

11,02 47,6 47,7 47,65 1,27 1,31 1,290

11,02 46,1 46,5 46,30 1,27 1,32 1,295

11,02 44,8 45 44,90 1,34 1,38 1,360

11,02 43,3 43,4 43,35 1,43 1,45 1,440

11,02 41,3 41,4 41,35 1,49 1,53 1,510

11,02 39,4 39,5 39,45 1,55 1,6 1,575

11,02 37,4 37,5 37,45 1,63 1,69 1,660

11,02 34,9 35 34,95 1,7 1,74 1,720

11,02 27,9 28 27,95 1,76 1,77 1,765

11,02 24,4 24,5 24,45 1,82 1,87 1,845

11,02 20,7 20,8 20,75 1,88 1,94 1,910

11,02 16,7 16,8 16,75 1,98 2,04 2,010

11,02 11,3 11,3 11,30 2,04 2,11 2,075

11,02 6,2 6,3 6,25 2,11 2,15 2,130

11,02 2,09 2,09 2,09 2,17 2,22 2,195


57


14,14 90,6 90,6 90,59 0 0 0,000

14,14 74,4 74,5 74,45 0,82 0,85 0,835

14,14 73,6 74,2 73,90 0,85 0,88 0,865

14,14 72,8 73,3 73,05 0,9 0,92 0,910

14,14 71,4 72,2 71,80 0,94 0,99 0,965

14,14 71,9 72,3 72,10 1,01 1,04 1,025

14,14 68,7 69,4 69,05 1,07 1,12 1,095

14,14 67,1 67,6 67,35 1,16 1,2 1,180

14,14 63 63,4 63,20 1,2 1,24 1,220

14,14 61 61,1 61,05 1,25 1,31 1,280

14,14 57,8 57,9 57,85 1,33 1,4 1,365

14,14 54,2 54,3 54,25 1,45 1,51 1,480

14,14 53,3 53,4 53,35 1,53 1,58 1,555

14,14 45,5 45,6 45,55 1,66 1,71 1,685

14,14 40 40 40,00 1,8 1,85 1,825

14,14 34,7 34,8 34,75 1,88 1,95 1,915

14,14 30,9 31 30,95 1,79 1,84 1,815

14,14 28,1 28,4 28,25 1,84 1,9 1,870

14,14 24,5 24,5 24,50 1,88 1,95 1,915

14,14 20,4 20,5 20,45 1,95 2,02 1,985

14,14 15,7 15,8 15,75 2,01 2,07 2,040

14,14 11,4 11,5 11,45 2,06 2,11 2,085

14,14 6,7 6,7 6,70 2,09 2,16 2,125

14,14 2,23 2,23 2,23 2,12 2,2 2,160

14,14 0 0 0,00 2,25 2,25 2,250


58

0.7. Table 17,80 Hz, voltage and current data from Hz, V1 and A1

17,8 113,7 113,7 113,74 0 0 0,000

17,8 89,9 90 89,95 1,08 1,1 1,090

17,8 88,6 88,7 88,65 1,116 1,125 1,121

17,8 86,6 86,7 86,65 1,17 1,179 1,175

17,8 84,8 84,9 84,85 1,215 1,224 1,220

17,8 81,2 81,3 81,25 1,26 1,26 1,260

17,8 79,9 80 79,95 1,341 1,35 1,346

17,8 76,6 76,7 76,65 1,404 1,413 1,409

17,8 74,3 74,4 74,35 1,476 1,485 1,481

17,8 70,1 70,2 70,15 1,512 1,521 1,517

17,8 66,1 66,2 66,15 1,557 1,566 1,562

17,8 60,9 61 60,95 1,665 1,674 1,670

17,8 55,2 55,3 55,25 1,737 1,746 1,742

17,8 48,9 49 48,95 1,818 1,827 1,823

17,8 42,3 42,4 42,35 1,917 1,944 1,931

17,8 36 36 36,00 1,998 2,007 2,003

17,8 27,9 28 27,95 2,007 2,088 2,048

17,8 19 19,1 19,05 2,142 2,151 2,147

17,8 13,2 13,4 13,30 2,16 2,169 2,165

17,8 4,4 4,6 4,50 2,178 2,196 2,187

17,8 3,3 3,5 3,40 2,196 2,205 2,201

17,8 0 0 0,00 2,25 2,27 2,260


59


22,89 145,9 145,9 145,93 0 0 0,000

22,89 132,8 132,8 132,80 0,66 0,66 0,660

22,89 120,9 121 120,95 0,971957 0,971957 0,972

22,89 106,7 106,7 106,70 1,292826 1,292826 1,293

22,89 104,8 104,8 104,80 1,337391 1,337391 1,337

22,89 101,7 101,8 101,75 1,399783 1,399783 1,400

22,89 98,9 99 98,95 1,453261 1,453261 1,453

22,89 95,4 95,4 95,40 1,515652 1,515652 1,516

22,89 91,8 91,8 91,80 1,578043 1,578043 1,578

22,89 87,8 87,9 87,85 1,649348 1,649348 1,649

22,89 84,1 84,2 84,15 1,711739 1,711739 1,712

22,89 78,9 78,9 78,90 1,720652 1,729565 1,725

22,89 73,1 73,2 73,15 1,809783 1,809783 1,810

22,89 66,8 66,9 66,85 1,863261 1,863261 1,863

22,89 59,7 59,7 59,70 1,961304 1,961304 1,961

22,89 51,8 51,8 51,80 2,014783 2,032609 2,024

22,89 43,6 43,7 43,65 2,095 2,103913 2,099

22,89 47,3 47,3 47,30 2,130652 2,139565 2,135

22,89 29,3 29,4 29,35 2,157391 2,166304 2,162

22,89 19,6 19,6 19,60 2,201957 2,21087 2,206

22,89 14,8 14,8 14,80 2,228696 2,237609 2,233

22,89 7,1 7,2 7,15 2,246522 2,255435 2,251

22,89 2,9 3 2,95 2,246522 2,264348 2,255

22,89 0 0 0,00 2,3 2,3 2,300


60


28,8 183,3 183,3 183,31 0 0 0,000

28,8 155,0 155,0 155,00 1 1 1,000

28,8 121,9 122 121,95 1,534013 1,531321 1,533

28,8 119,1 119,2 119,15 1,567389 1,564528 1,566

28,8 115,3 115,3 115,30 1,617452 1,61434 1,616

28,8 111,2 111,3 111,25 1,659172 1,664151 1,662

28,8 106,5 106,6 106,55 1,71758 1,722264 1,720

28,8 101,3 101,3 101,30 1,775987 1,772075 1,774

28,8 96,2 96,3 96,25 1,826051 1,830189 1,828

28,8 89,6 89,6 89,60 1,834395 1,838491 1,836

28,8 84,1 84,2 84,15 1,884459 1,88 1,882

28,8 77,6 77,7 77,65 1,942866 1,938113 1,940

28,8 70,9 70,9 70,90 1,984586 1,987925 1,986

28,8 64 64,1 64,05 2,093057 2,095849 2,094

28,8 54,1 54,1 54,10 2,084713 2,087547 2,086

28,8 45,5 45,6 45,55 2,134777 2,129057 2,132

28,8 37,7 37,7 37,70 2,184841 2,18717 2,186

28,8 29,7 29,7 29,70 2,201529 2,203774 2,203

28,8 24,1 24,1 24,10 2,226561 2,228679 2,228

28,8 19,3 19,4 19,35 2,243248 2,245283 2,244

28,8 14,1 14,2 14,15 2,259936 2,261887 2,261

28,8 7,6 7,6 7,60 2,26828 2,270189 2,269

28,8 2,7 2,8 2,75 2,284968 2,278491 2,282

28,8 0 0 0,00 2,31 2,32 2,315


61


43,96 279,2 279,2 279,19 0,00 0,00 0,000

43,96 218,4 218,4 218,40 1,16 1,18 1,170

43,96 211,9 212 211,95 1,26 1,27 1,266

43,94 195,8 195,9 195,85 1,42 1,44 1,429

43,94 173,2 173,2 173,20 1,61 1,62 1,616

43,94 146,6 146,7 146,65 1,81 1,83 1,819

43,94 142,4 142,4 142,40 1,84 1,85 1,847

43,96 136,3 136,3 136,30 1,88 1,89 1,886

43,94 129,5 129,6 129,55 1,92 1,93 1,926

43,96 122,9 123 122,95 1,96 1,97 1,966

43,96 115,5 115,6 115,55 1,99 2,01 2,002

43,965 107,5 107,6 107,55 2,03 2,05 2,041

43,985 99,1 99,1 99,10 2,02 2,02 2,022

43,97 91,5 91,6 91,55 2,05 2,06 2,057

43,97 83,3 83,4 83,35 2,08 2,09 2,085

43,98 74,7 74,7 74,70 2,11 2,12 2,113

43,995 65,5 65,6 65,55 2,14 2,15 2,145

44,005 55,5 55,5 55,50 2,18 2,18 2,181

44,02 46,1 46,1 46,10 2,20 2,20 2,197

44,025 38,1 38,1 38,10 2,25 2,25 2,252

44,025 34 34,1 34,05 2,26 2,27 2,264

44,03 28,9 28,9 28,90 2,27 2,27 2,268

44,04 23,8 23,9 23,85 2,28 2,28 2,276

44,04 18,9 19 18,95 2,28 2,28 2,284

44,06 14,1 14,1 14,10 2,29 2,30 2,296

44,07 7,1 7,1 7,10 2,29 2,30 2,296

44,08 2,3 2,3 2,30 2,32 2,32 2,316

44,08 0 0 0,00 2,34 2,34 2,340


62


56,31 357,3 357,3 357,29 0,00 0,00 0,000

56,31 261,3 261,3 261,30 1,39 1,39 1,390

56,32 246,5 246,6 246,55 1,49 1,49 1,491

56,315 234,2 234,3 234,25 1,58 1,57 1,573

56,325 222,3 222,4 222,35 1,65 1,65 1,648

56,325 202,9 203 202,95 1,75 1,76 1,756

56,325 181,9 182 181,95 1,87 1,87 1,872

56,345 157,7 157,7 157,70 1,99 1,98 1,984

56,345 151,8 151,8 151,80 2,02 2,01 2,014

56,335 144,2 144,2 144,20 2,04 2,04 2,044

56,335 136,2 136,3 136,25 2,09 2,09 2,089

56,32 128 128,1 128,05 2,12 2,13 2,122

56,35 120 120,1 120,05 2,15 2,16 2,152

56,355 111,8 111,8 111,80 2,18 2,19 2,182

56,355 104,8 104,8 104,80 2,21 2,21 2,208

56,38 102,8 102,8 102,80 2,16 2,16 2,156

56,375 94,8 94,8 94,80 2,18 2,18 2,178

56,395 85,3 85,3 85,30 2,20 2,20 2,201

56,415 75,7 75,7 75,70 2,23 2,23 2,230

56,425 65,7 65,7 65,70 2,25 2,25 2,253

56,425 56,1 56,2 56,15 2,28 2,28 2,275

56,455 46 46 46,00 2,29 2,30 2,294

56,455 38,4 38,5 38,45 2,30 2,30 2,298

56,465 34,6 34,6 34,60 2,32 2,32 2,320

56,475 29,3 29,3 29,30 2,33 2,33 2,328

56,485 24 24 24,00 2,34 2,34 2,335

56,485 19,2 19,2 19,20 2,34 2,35 2,346

56,485 12,7 12,7 12,70 2,35 2,35 2,350

56,485 7,33 7,33 7,33 2,35 2,35 2,350

56,485 0 0 0,00 2,37 2,37 2,370


63


70,795 448,9 448,9 448,90 0,00 0,00 0,000

70,795 295,5 295,5 295,50 1,59 1,60 1,595

70,795 278,3 278,3 278,30 1,69 1,69 1,690

70,795 245,2 245,3 245,25 1,84 1,85 1,845

70,81 206 206,1 206,05 1,99 1,99 1,990

70,84 164,5 164,5 164,50 2,15 2,15 2,150

70,88 157,4 157,4 157,40 2,18 2,18 2,180

70,875 149,5 149,6 149,55 2,20 2,20 2,200

70,905 141,4 141,4 141,40 2,22 2,22 2,220

70,915 131,6 131,6 131,60 2,24 2,24 2,240

70,915 122,6 122,7 122,65 2,26 2,26 2,260

70,94 113,3 113,3 113,30 2,28 2,28 2,280

70,94 106,3 106,3 106,30 2,29 2,29 2,290

70,95 105,4 105,4 105,40 2,26 2,26 2,260

70,965 97,4 97,4 97,40 2,27 2,27 2,270

70,97 87,4 87,4 87,40 2,29 2,30 2,295

71 77,5 77,6 77,55 2,30 2,31 2,305

71 67,8 67,8 67,80 2,31 2,31 2,310

71,015 57,3 57,3 57,30 2,32 2,33 2,325

71,045 47,1 47,2 47,15 2,33 2,34 2,335

71,035 38,1 38,2 38,15 2,34 2,34 2,340

71,045 34,4 34,4 34,40 2,34 2,34 2,340

71,055 29,2 29,2 29,20 2,35 2,35 2,350

71,08 23,7 23,7 23,70 2,35 2,35 2,350

71,115 18,2 18,2 18,20 2,35 2,35 2,350

71,12 13,2 13,2 13,20 2,35 2,35 2,350

71,135 7,6 7,6 7,60 2,35 2,35 2,350

71,11 2,99 3 3,00 2,35 2,36 2,355

71,11 0 0 0,00 2,36 2,37 2,365


64

0.13. Table. 8,75 Hz, power, losses, efficiency, power factor calculated data

0,00 0,00 0,89 0,89 0,00 0,00 0,00

36,22 4,99 42,10 0,89 86,03 41,21 44,64 0,923

36,72 5,31 42,92 0,89 85,55 42,03 46,05 0,913

38,26 5,85 45,00 0,89 85,03 44,11 48,31 0,913

40,57 6,77 48,23 0,89 84,12 47,34 51,99 0,911

40,90 7,22 49,01 0,89 83,45 48,12 53,68 0,896

43,52 8,49 52,89 0,89 82,27 52,00 58,20 0,894

45,09 9,33 55,31 0,89 81,52 54,42 61,03 0,892

44,46 10,04 55,39 0,89 80,28 54,50 63,29 0,861

45,50 11,23 57,63 0,89 78,96 56,74 66,96 0,847

46,56 12,70 60,15 0,89 77,41 59,26 71,20 0,832

47,73 14,26 62,87 0,89 75,91 61,98 75,44 0,822

48,42 16,13 65,44 0,89 73,99 64,55 80,24 0,805

48,94 18,48 68,32 0,89 71,64 67,43 85,89 0,785

48,48 20,48 69,85 0,89 69,41 68,96 90,41 0,763

42,52 21,65 65,06 0,89 65,36 64,17 92,95 0,690

39,38 24,08 64,35 0,89 61,20 63,47 98,04 0,647

36,42 26,79 64,10 0,89 56,82 63,21 103,41 0,611

31,10 30,42 62,41 0,89 49,83 61,52 110,19 0,558

20,12 29,95 50,97 0,89 39,48 50,08 109,34 0,458

12,71 33,62 47,22 0,89 26,92 46,33 115,84 0,400

0,00 35,11 36,00 0,89 0,00 35,11 118,38 0,297


65


0,00 0,00 1,34 1,34 0,00 0,00 0,00 -

52,38 7,53 61,25 1,34 85,52 59,91 68,74 0,872

52,97 7,84 62,15 1,34 85,23 60,81 70,15 0,867

55,27 8,82 65,43 1,34 84,47 64,09 74,41 0,861

56,73 9,50 67,58 1,34 83,95 66,24 77,24 0,858

57,38 10,13 68,84 1,34 83,35 67,50 79,72 0,847

59,25 11,23 71,82 1,34 82,49 70,48 83,97 0,839

61,43 12,60 75,37 1,34 81,51 74,03 88,93 0,832

61,47 13,31 76,12 1,34 80,75 74,78 91,41 0,818

59,96 13,42 74,71 1,34 80,25 73,37 91,77 0,800

61,06 14,80 77,20 1,34 79,10 75,86 96,37 0,787

62,42 16,59 80,35 1,34 77,69 79,01 102,04 0,774

62,44 18,24 82,02 1,34 76,13 80,68 107,00 0,754

62,13 19,85 83,32 1,34 74,57 81,98 111,61 0,735

62,17 22,04 85,55 1,34 72,67 84,21 117,63 0,716

60,11 23,67 85,12 1,34 70,62 83,78 121,88 0,687

49,33 24,92 75,59 1,34 65,26 74,25 125,07 0,594

45,11 27,23 73,68 1,34 61,22 72,34 130,74 0,553

39,63 29,18 70,16 1,34 56,49 68,82 135,35 0,508

33,67 32,32 67,33 1,34 50,01 65,99 142,43 0,463

23,45 34,45 59,23 1,34 39,59 57,89 147,04 0,394

13,31 36,30 50,95 1,34 26,13 49,61 150,94 0,329

4,59 38,54 44,47 1,34 10,32 43,13 155,54 0,277


66


0,00 0,00 2,04 2,04 0,00 0,00 0,00 -

62,17 5,58 69,79 2,04 89,08 67,74 75,65 0,896

63,92 5,99 71,95 2,04 88,84 69,91 78,36 0,892

66,48 6,62 75,14 2,04 88,46 73,10 82,44 0,887

69,29 7,45 78,78 2,04 87,95 76,74 87,42 0,878

73,90 8,41 84,35 2,04 87,61 82,31 92,86 0,886

75,61 9,59 87,25 2,04 86,66 85,20 99,20 0,859

79,47 11,14 92,66 2,04 85,77 90,61 106,90 0,848

77,10 11,91 91,06 2,04 84,68 89,01 110,53 0,805

78,14 13,11 93,30 2,04 83,76 91,25 115,96 0,787

78,97 14,91 95,92 2,04 82,33 93,87 123,66 0,759

80,29 17,52 99,86 2,04 80,40 97,81 134,08 0,730

82,96 19,34 104,35 2,04 79,50 102,30 140,87 0,726

76,75 22,71 101,51 2,04 75,61 99,47 152,65 0,652

73,00 26,65 101,69 2,04 71,79 99,65 165,33 0,603

66,55 29,34 97,93 2,04 67,95 95,88 173,49 0,553

56,17 26,35 84,57 2,04 66,42 82,53 164,43 0,502

52,83 27,98 82,85 2,04 63,76 80,80 169,41 0,477

46,92 29,34 78,30 2,04 59,92 76,26 173,49 0,440

40,59 31,52 74,16 2,04 54,74 72,12 179,83 0,401

32,13 33,29 67,47 2,04 47,62 65,42 184,81 0,354

23,87 34,78 60,70 2,04 39,33 58,65 188,89 0,311

14,24 36,13 52,41 2,04 27,17 50,36 192,51 0,262

4,82 37,32 44,19 2,04 10,90 42,14 195,68 0,215

0,00 40,50 42,54 2,04 0,00 40,50 203,84 0,199


67


0,00 0,00 3,03 3,03 0,00 0,00 0,00 -

98,05 9,50 110,58 3,03 88,66 107,55 123,98 0,867

99,33 10,04 112,41 3,03 88,37 109,38 127,45 0,858

101,77 11,04 115,84 3,03 87,86 112,81 133,59 0,844

103,47 11,90 118,40 3,03 87,39 115,37 138,71 0,832

102,38 12,70 118,11 3,03 86,68 115,08 143,31 0,803

107,57 14,48 125,09 3,03 86,00 122,06 153,04 0,798

107,96 15,87 126,86 3,03 85,10 123,83 160,21 0,773

110,08 17,54 130,64 3,03 84,26 127,61 168,39 0,758

106,38 18,40 127,81 3,03 83,23 124,78 172,49 0,723

103,29 19,51 125,83 3,03 82,09 122,80 177,61 0,691

101,76 22,30 127,09 3,03 80,07 124,05 189,89 0,653

96,22 24,26 123,51 3,03 77,90 120,48 198,08 0,608

89,21 26,57 118,82 3,03 75,08 115,78 207,29 0,559

81,76 29,81 114,60 3,03 71,34 111,57 219,58 0,508

72,09 32,08 107,20 3,03 67,25 104,17 227,77 0,457

57,23 33,54 93,80 3,03 61,01 90,77 232,89 0,390

40,89 36,86 80,78 3,03 50,62 77,75 244,15 0,318

28,79 37,48 69,30 3,03 41,54 66,27 246,19 0,269

9,84 38,26 51,14 3,03 19,25 48,11 248,75 0,193

7,48 38,74 49,25 3,03 15,19 46,22 250,29 0,185

0,00 40,86 43,89 3,03 0,00 40,86 257,06 0,159


68


0,00 0,00 4,91 4,91 0,00 0,00 0,00 -

87,65 3,48 96,04 4,91 91,26 91,13 96,32 0,946

117,56 7,56 130,03 4,91 90,41 125,12 141,84 0,882

137,94 13,37 156,23 4,91 88,30 151,32 188,67 0,802

140,16 14,31 159,38 4,91 87,94 154,47 195,17 0,791

142,43 15,68 163,01 4,91 87,37 158,10 204,27 0,774

143,80 16,90 165,61 4,91 86,83 160,70 212,08 0,758

144,59 18,38 167,88 4,91 86,13 162,97 221,18 0,737

144,86 19,92 169,70 4,91 85,37 164,79 230,29 0,716

144,90 21,76 171,57 4,91 84,45 166,66 240,69 0,692

144,04 23,44 172,39 4,91 83,55 167,48 249,80 0,670

136,11 23,81 164,83 4,91 82,58 159,92 251,75 0,635

132,39 26,20 163,50 4,91 80,97 158,59 264,11 0,600

124,56 27,77 157,24 4,91 79,21 152,33 271,91 0,560

117,09 30,77 152,77 4,91 76,64 147,86 286,22 0,517

104,83 32,76 142,50 4,91 73,56 137,59 295,32 0,466

91,64 35,26 131,81 4,91 69,52 126,90 306,38 0,414

100,99 36,47 142,37 4,91 70,94 137,46 311,58 0,441

63,45 37,39 105,75 4,91 60,00 100,84 315,48 0,320

43,25 38,95 87,10 4,91 49,65 82,19 321,99 0,255

33,05 39,90 77,86 4,91 42,45 72,95 325,89 0,224

16,09 40,54 61,54 4,91 26,15 56,63 328,49 0,172

6,65 40,70 52,26 4,91 12,73 47,35 329,14 0,144

0,00 42,32 47,23 4,91 0,00 42,32 335,65 0,126


69


0,00 0,00 8,41 8,41 0,00 0,00 0,00 -

155,00 8,00 171,41 8,41 90,42 163,00 183,31 0,889

186,91 18,79 214,11 8,41 87,29 205,70 280,95 0,732

186,58 19,62 214,62 8,41 86,94 206,20 287,06 0,718

186,31 20,89 215,62 8,41 86,41 207,20 296,21 0,700

184,86 22,09 215,36 8,41 85,84 206,95 304,60 0,679

183,26 23,67 215,34 8,41 85,10 206,92 315,28 0,656

179,71 25,18 213,30 8,41 84,25 204,89 325,20 0,630

175,96 26,74 211,11 8,41 83,35 202,69 335,11 0,605

164,55 26,98 199,94 8,41 82,30 191,53 336,64 0,569

158,39 28,34 195,15 8,41 81,16 186,73 345,03 0,541

150,68 30,12 189,22 8,41 79,63 180,80 355,71 0,508

140,83 31,56 180,80 8,41 77,89 172,39 364,10 0,473

134,15 35,09 177,66 8,41 75,51 169,24 383,93 0,441

112,86 34,82 156,09 8,41 72,30 147,68 382,41 0,386

97,11 36,36 141,88 8,41 68,44 133,47 390,80 0,342

82,41 38,23 129,06 8,41 63,86 120,64 400,72 0,301

65,42 38,81 112,65 8,41 58,07 104,23 403,77 0,258

53,69 39,70 101,80 8,41 52,74 93,38 408,35 0,229

43,43 40,29 92,13 8,41 47,13 83,72 411,40 0,204

31,99 40,89 81,30 8,41 39,35 72,89 414,45 0,176

17,25 41,20 66,86 8,41 25,80 58,44 415,97 0,140

6,27 41,65 56,34 8,41 11,14 47,93 418,26 0,115

0,00 42,87 51,29 8,41 0,00 42,87 424,36 0,101


70


0,00 0,00 29,48 29,48 0,00 0,00 0,00 -

255,53 10,95 295,96 29,48 86,34 266,48 326,65 0,816

268,22 12,81 310,51 29,48 86,38 281,04 353,32 0,795

279,80 16,33 325,56 29,43 85,94 296,13 398,86 0,742

279,84 20,88 330,16 29,43 84,76 300,73 451,09 0,667

266,70 26,46 322,60 29,43 82,67 293,16 507,74 0,577

262,95 27,28 319,66 29,43 82,26 290,22 515,53 0,563

257,11 28,47 315,05 29,48 81,61 285,57 526,64 0,542

249,53 29,68 308,64 29,43 80,85 279,21 537,75 0,519

241,71 30,92 302,11 29,48 80,01 272,63 548,86 0,497

231,30 32,05 292,83 29,48 78,99 263,35 558,85 0,471

219,56 33,34 282,39 29,49 77,75 252,90 569,96 0,444

200,34 32,70 262,57 29,53 76,30 233,04 564,42 0,413

188,36 33,86 251,72 29,50 74,83 222,22 574,41 0,387

173,81 34,79 238,10 29,50 73,00 208,60 582,19 0,358

157,85 35,72 223,09 29,52 70,76 193,57 589,96 0,328

140,60 36,81 206,96 29,55 67,94 177,41 598,85 0,296

121,04 38,05 188,65 29,57 64,16 159,08 608,86 0,261

101,27 38,61 169,48 29,60 59,75 139,87 613,30 0,228

85,82 40,59 156,02 29,61 55,00 126,41 628,86 0,201

77,10 41,02 147,73 29,61 52,19 118,12 632,18 0,187

65,56 41,16 136,34 29,62 48,08 106,72 633,30 0,169

54,29 41,45 125,39 29,65 43,30 95,74 635,52 0,151

43,29 41,74 114,68 29,65 37,75 85,03 637,75 0,133

32,38 42,18 104,24 29,69 31,06 74,56 641,07 0,116

16,30 42,18 88,19 29,71 18,49 58,48 641,07 0,091

5,33 42,92 77,97 29,73 6,83 48,24 646,63 0,075

0,00 43,80 73,54 29,73 0,00 43,80 653,30 0,067


71


0,00 0,00 62,27 62,27 0,00 0,00 0,00 -

363,21 15,46 440,94 62,27 82,37 378,66 496,64 0,762

367,57 17,78 447,65 62,30 82,11 385,35 532,76 0,723

368,48 19,80 450,57 62,29 81,78 388,28 562,08 0,691

366,37 21,72 450,41 62,32 81,34 388,09 588,88 0,659

356,40 24,67 443,39 62,32 80,38 381,07 627,60 0,607

340,59 28,03 430,94 62,32 79,03 368,62 668,98 0,551

312,86 31,49 406,73 62,38 76,92 344,35 709,28 0,485

305,70 32,44 400,52 62,38 76,32 338,14 719,97 0,470

294,70 33,41 390,46 62,35 75,47 328,11 730,52 0,449

284,56 34,90 381,81 62,35 74,53 319,46 746,55 0,428

271,74 36,03 370,07 62,30 73,43 307,77 758,37 0,406

258,35 37,05 357,80 62,40 72,21 295,40 769,45 0,384

243,94 38,09 344,44 62,41 70,82 282,02 780,21 0,361

231,40 39,00 332,82 62,41 69,53 270,41 789,55 0,342

221,61 37,18 321,28 62,49 68,98 258,79 771,19 0,336

206,49 37,96 306,92 62,47 67,28 244,45 779,14 0,314

187,71 38,74 288,98 62,53 64,96 226,45 787,44 0,288

168,85 39,80 271,24 62,59 62,25 208,65 798,41 0,261

148,01 40,60 251,24 62,63 58,91 188,62 806,58 0,234

127,76 41,42 231,80 62,63 55,12 169,17 814,60 0,208

105,52 42,10 210,34 62,72 50,17 147,62 821,73 0,180

88,35 42,24 193,30 62,72 45,70 130,58 823,06 0,159

80,28 43,06 186,09 62,75 43,14 123,34 831,24 0,148

68,20 43,34 174,32 62,78 39,12 111,54 834,06 0,134

56,04 43,62 162,47 62,81 34,49 99,66 836,89 0,119

45,05 44,04 151,90 62,81 29,66 89,09 840,91 0,106

29,85 44,18 136,83 62,81 21,81 74,03 842,24 0,088

17,23 44,18 124,21 62,81 13,87 61,41 842,24 0,073

0,00 44,94 107,74 62,81 0,00 44,94 849,41 0,053


72


0,00 0,00 101,67 101,67 0,00 0,00 0,00 -

471,32 20,35 593,35 101,67 79,43 491,67 716,00 0,687

470,33 22,85 594,85 101,67 79,07 493,18 758,65 0,650

452,49 27,23 581,39 101,67 77,83 479,72 828,23 0,579

410,04 31,68 543,42 101,70 75,46 441,72 893,51 0,494

353,68 36,98 492,40 101,75 71,83 390,66 965,75 0,405

343,13 38,02 482,97 101,81 71,05 381,15 979,78 0,389

329,01 38,72 469,54 101,81 70,07 367,73 988,70 0,372

313,91 39,43 455,19 101,86 68,96 353,34 998,11 0,354

294,78 40,14 436,80 101,87 67,49 334,92 1007,24 0,333

277,19 40,86 419,92 101,87 66,01 318,05 1016,24 0,313

258,32 41,59 401,82 101,91 64,29 299,91 1025,59 0,292

243,43 41,95 387,29 101,91 62,85 285,38 1030,09 0,277

238,20 40,86 380,99 101,93 62,52 279,06 1016,74 0,274

221,10 41,22 364,27 101,95 60,70 262,32 1021,45 0,257

200,58 42,14 344,68 101,96 58,19 242,72 1032,77 0,235

178,75 42,50 323,27 102,01 55,30 221,26 1037,71 0,213

156,62 42,69 301,32 102,01 51,98 199,31 1039,96 0,192

133,22 43,25 278,50 102,04 47,84 176,47 1046,94 0,169

110,10 43,62 255,80 102,08 43,04 153,71 1051,88 0,146

89,27 43,80 235,14 102,07 37,96 133,08 1053,99 0,126

80,50 43,80 226,38 102,08 35,56 124,30 1054,13 0,118

68,62 44,18 214,90 102,10 31,93 112,80 1058,79 0,107

55,70 44,18 202,01 102,14 27,57 99,88 1059,16 0,094

42,77 44,18 189,15 102,20 22,61 86,95 1059,68 0,082

31,02 44,18 177,40 102,20 17,49 75,20 1059,75 0,071

17,86 44,18 164,27 102,23 10,87 62,04 1059,98 0,059

7,05 44,37 153,61 102,19 4,59 51,42 1061,86 0,048

0,00 44,75 146,93 102,19 0,00 44,75 1066,37 0,042

Documents

RESEARCH OF PERMANENT MAGNET GENERATOR WITH … · TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding 3 ABSTRACT In this thesis, a patented “bifilar” coil