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: ________________________
Supervisors: Prof. dr. Eleonora Guseinovienė
Boris Rudnickij
2013
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
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
resistance
, which is usually bigger than
. 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 noload 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
0.6. Table. 14,14 Hz, voltage and current data from F, V1, A1 ........................................................ 57
0.7. Table 17,80 Hz, voltage and current data from F, V1 and A1 ................................................... 58
0.8. Table. 22,89 Hz, voltage and current data from F, V1, A1 ........................................................ 59
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
0.11. Table. 56,40 Hz, voltage and current data from F, V1, A1 ...................................................... 62
0.12. Table. 71,90 Hz, voltage and current data from F, V1, A1 ...................................................... 63
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
0.15. Table. 14,14 Hz, power, losses, efficiency, power factor calculated data ................................ 66
0.16. Table. 17,8 Hz, power, losses, efficiency, power factor calculated data .................................. 67
0.17. Table. 22,89 Hz, power, losses, efficiency, power factor calculated data ................................ 68
0.18. Table. 28,80 Hz, power, losses, efficiency, power factor calculated data ................................ 69
0.19. Table. 44,00 Hz, power, losses, efficiency, power factor calculated data ................................ 70
0.20. Table. 56,40 Hz, power, losses, efficiency, power factor calculated data ................................ 71
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Research of PMG with compensated reactance winding
0.21. Table. 70,90 Hz, power, losses, efficiency, power factor calculated data ................................ 72
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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Research of PMG with compensated reactance winding
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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Research of PMG with compensated reactance winding
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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Research of PMG with compensated reactance winding
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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Research of PMG with compensated reactance winding
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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Research of PMG with compensated reactance winding
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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Research of PMG with compensated reactance winding
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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Research of PMG with compensated reactance winding
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
rated speed of
to
at a
to
at a
.
1.2. Table. “MOOG” constructors catalogue parameters
The gravimetric power density of this PMG series is from
rated speed of
.
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Research of PMG with compensated reactance winding
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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Research of PMG with compensated reactance winding
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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Research of PMG with compensated reactance winding
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
Rated speed
No-load EMF
Number of rotors
Number of poles
Rotor size
Gap between rotors
Number of stators
Number of coils
Stator size
Number of loops per coil
Outside size
Weight
Cooling
The gravimetric power density of this prototype at a rated speed of
1
840
206
7
12
140x6
6
6
9
170x4
53
182x142
8,5
Natural
is
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Research of PMG with compensated reactance winding
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
Output power of one module
Efficiency
Power factor
Output power per active mass
Output power per volume
Active outer diameter of one module
Active inner diameter of one module,
Active thickness of one module,
Armature resistance
Direct synchronous reactance
Quadrature synchronous reactance
Output frequency
4
400
90
0,8985
0,298
591
166
96
47
0,38
6,824
6,808
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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Research of PMG with compensated reactance winding
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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Research of PMG with compensated reactance winding
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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Research of PMG with compensated reactance winding
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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Research of PMG with compensated reactance winding
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
structure is magnetically non salient and thus
(direct inductance) low. The
. 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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Research of PMG with compensated reactance winding
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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TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
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
Typical
Curie
Temperature
Price
200-440
310-400
+++
600-2000
120-200
720
++++
0,6-0,7
600-1200
60-100
310-400
++
Alnico
0,6-1,4
275
10-88
700-850
+
Ferrite
0,2-0,4
100-300
10-40
450
+
Typical
Typical
NdFeB
(sintered)
1,0-1,4
750-2000
SmCo
0,8-1,1
NdFeB
(bonded)
Magnets
extra
Low
temperature
coefficient
Low Eddycurrents
Low Eddycurrents
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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TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
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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TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
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 n
Step 7
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.
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TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
2
3
2
3
1
2
1
1
3
1
5
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)
26
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
2.14. Fig. Magnetic flux density vector plot (top view)
B
A
2.15. Fig. Magnetic flux density continuous fringe plot on several sections: A – cross section of
magnet array, B – cross section of coils
D
C
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
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
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)
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TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
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 (G1M1);
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.
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TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
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.
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TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
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
Ampermeter
Voltmeter
Multimeter
Multimeter
Model
AC/DC
M1500T3
1984
M1600
1979
Agilent
U1241A
Mastech
MS8222H
Max scale
Tolerance
class
DC
1,5
DC
1,5
AC/DC
1000V
AC/DC
10A
Use
DC motor
armature
DC motor
armature
PMG voltage
and frequency
PMG current
3.2. Table. Parameters of driving machines
Driving machine
Model
DC motor
П-42
Power
7,2
kW
Induction motor
– Lathe
Красный
Пролетарий
1K62
10 kW
Gearbox
Speed
Year
No
2800 rpm
1976
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)
31
TEI-09, O.Lyan, V.Monet








Logic level
Voltage:
o Recommended
o Maximum
Digital outputs
Analog inputs
Maximum current capabilities
Memory
o FLASH
o SRAM
o EEPROM
Frequency
Size
Research of PMG with compensated reactance winding
5V
7–12V
6–20V
14 (6 are PWM channels)
8
40mA
32KB (2KB used for boot loader)
2KB
1KB
16MHz
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
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TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
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.
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TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
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.
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TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
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
(
(
)
)
1,26
1,27
0,495
Where:
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
1,31 1,35 1,39 1,42 1,44 1,48 1,53 1,57 1,60 1,64 1,68
1,32 1,35 1,39 1,42 1,45 1,49 1,53 1,58 1,61 1,65 1,69
0,545 0,580 0,620 0,650 0,675 0,715 0,760 0,805 0,835 0,875 0,915
– 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
0,0
0,00
0,00
21,1
21,1
21,10
0,28
22,6
22,7
22,65
0,31
6,0
6,1
6,05
0,07
7,8
7,9
7,85
0,09
23,7
23,8
23,75
0,33
10,2
10,3
10,25
0,12
24,7
24,8
24,75
0,36
11,4
11,5
11,45
0,14
25,7
25,8
25,75
0,37
12,4
12,5
12,45
0,16
25,6
25,7
25,65
0,39
13,9
14,0
13,95
0,18
26,8
26,9
26,85
0,41
15,8
15,9
15,85
0,21
28,1
28,2
28,15
0,44
17,2
17,3
17,25
0,23
29,1
29,1
29,10
0,46
30,1
30,2
30,15
0,48
18,4
18,5
18,45
0,24
31,1
31,2
31,15
0,50
where
– Mean terminal voltage of the motor;
– Armature resistance.
Applied arithmetic mean value for the armature voltage:
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TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
(
(
)
(
))
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
0,00
7,52
7,77
11,45
11,52
15,10
15,15
17,18
17,22
19,32
19,27
22,17
22,23
25,58
25,65
28,18
28,22
29,97
30,04
31,99
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
33,92
36,15
36,24
38,47
38,50
40,40
40,45
39,48
39,42
41,11
41,14
42,94
42,95
44,53
44,77
46,73
46,75
33,76
33,92
36,15
36,24
38,47
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:
36
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
Copper losses are insignificant compared to mechanical and magnetic losses.
3.6. Table. Power losses, calculated data
10,44
0,14
10,30
0,00
0,00
0,00
0,79
0,01
0,78
1,30
0,02
1,28
2,20
0,03
2,18
2,81
0,03
2,77
3,42
0,04
3,38
4,39
0,06
4,34
5,71
0,07
5,63
6,81
0,09
6,72
7,84
0,10
7,74
9,01
0,12
8,89
12,34
0,17
12,17
13,78
0,19
13,58
15,35
0,22
15,12
16,74
0,24
16,50
17,31
0,26
17,05
19,20
0,29
18,90
21,39
0,33
21,06
23,43
0,37
23,05
25,18
0,40
24,78
27,26
0,44
26,82
29,42
0,48
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:
35
Power losses , W
30
25
20
ΔP(f) = 0,0001f3 + 0,0046f2 + 0,0262f + 0,1773
15
Measured
10
Predicted
5
0
0
10
20
30
40
50
60
Frequency, Hz
3.7. Fig. Mechanical and magnetic power losses versus frequency as TG signal
( ) are placed in appendix tables 0.1 – 0.3. The
The no-load data tables of EMF vs. speed
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.
400
EMF, V
300
EMF vs Frequency A
200
EMF vs Frequency B
E(f) = 6,3244f + 1,1674
100
EMF vs Frequency c
0
Predicted
0
10
20
30
40
50
60
Frequency, Hz
3.8. Fig. EMF vs. frequency as AC TG speed signal (OCC)
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TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
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
different speeds. Armature active resistance is
) at
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
56,51
2,095
25,53
134,2
11,02
70,86
2,195
31,09
183,7
14,14
90,59
2,250
39,31
251,4
17,80
113,74
2,260
49,57
328,6
22,89
145,93
2,300
62,85
442,5
28,80
183,31
2,315
78,70
573,5
44,08
279,19
2,340
118,99
916,0
56,49
357,29
2,370
150,51
1204,6
71,11
448,90
2,365
189,61
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.
Reactance, Ω
200
150
100
Calculated
50
Xs (f) = 2,6141f + 3,6992
0
0
10
20
30
40
50
60
70
Predicted
80
Frequency, Hz
3.9. Fig. Linear relationship of reactance vs. frequency
38
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
( ) using correlated values of
Predicting short circuit current
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.
2,5
Current, A
2,0
1,5
Predicted
1,0
Measured
0,5
0,0
0
10
20
30
40
50
60
70
80
Frequency, Hz
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.
39
Armature Voltage, V
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
500
450
400
350
300
250
200
150
100
50
0
70,80 Hz
56,50 Hz
44,08 Hz
28,80 Hz
22,89 Hz
17,80 Hz
14,14 Hz
11,08 Hz
0,0
0,5
1,0
1,5
2,0
2,5
0,0
Current, A
0,5
1,0
1,5
2,0
2,5
8,75 Hz
Current, A
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
load and short circuit,
at
as explained in (2 p. 331),
at small
.
40
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
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:
1600
max P
1400
70,80 Hz
Power, W
1200
56,50 Hz
1000
44,08 Hz
800
28,80 Hz
600
22,89 Hz
400
17,80 Hz
200
14,14 Hz
0
0,0
0,5
1,0
1,5
2,0
2,5
0,0
Current, A
0,5
1,0
1,5
Current, A
2,0
2,5
11,08 Hz
8,75 Hz
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
( )
41
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
An interpolated surface plot is generated to have a better view.
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.
100
70,80 Hz
Efficiency, %
80
56,50 Hz
44,08 Hz
60
28,80 Hz
40
22,89 Hz
17,80 Hz
20
14,14 Hz
0
0,0
0,5
1,0
1,5
Current, A
2,0
2,5
0,0
0,5
1,0
1,5
2,0
Current, A
2,5
11,08 Hz
8,75 Hz
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.
42
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding

Magnetic losses due to core hysteresis, eddy currents.

Electric losses due to electric resistance of the copper.
An interpolated surface plot is generated to have a better view.
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
( ).
100
90
80
Efficiency, %
70
60
50
40
30
20
10
0
0
200
400
600
800
1000
1200
1400
1600
1800
Power, W
70,80 Hz
56,50 Hz
44,08 Hz
28,80 Hz
17,80 Hz
14,14 Hz
11,08 Hz
8,75 Hz
22,89 Hz
3.18. Fig. Efficiency vs. load current performance characteristics at different speeds
(before overload)
43
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
100
90
80
Efficiency, %
70
60
50
40
30
20
10
0
0
200
400
600
800
1000
1200
1400
1600
1800
Output Power, W
3.19. Fig. Efficiency vs. load current performance characteristics at different speeds
(after overload)
44
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
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.
45
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
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
Load current
Output power
Rated speed
No-Load EMF
Voltage at rated power
Efficiency
Rated Power factor
Total mass
Output power per active mass
Output power per volume
Number of rotors
Number of poles (pair poles)
Number of coils
Number of loops per coil
Active diameter
Rotor inertia
Phase armature resistance
Phase synchronous reactance
Phase inductance
Output frequency
Cooling
Generator types
Fig. 1.5
Table. 1.1.
Fig. 2.7
Table
3,2
1,65
2100
1307
1500
840
650
840
206
390
446
243
309
81
76
92,4
0,69
8,5
10,4
55
117,65
125,67
38,4
138
2
7
20 (10)
12
12(6)
30
9
375
53
150
2,24
29,58
8,6
8,7
186,7
60
442,5
70
Natural
Natural
Natural
5.2. Material consumptions
5.2. Table. Consumed material quantity
Material
Copper
Laminated steel
Non-laminated steel
NdFeB N45 magnets
Wood Epoxy Fiber
Polyethylene
Bearings
Mass, kg
13
20,7
4,4
3,3
10,3
1,8
0,2
Number of pcs. or pkg.
30 coils
15 rods 20x25x352
4 rings, 1 shaft, fasteners
80
5 parts
2 cylindroids
3
46
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
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
reaches
it
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
Measured curves seem to be lower due to the load resistors with
load and short circuit,

at
3.13.
at small
.
Power Output vs. load current measured curves are slightly lower than the calculated one,
which are due to the load device
(
while calculated is
. Measured
)
(
)
,
. 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
almost same (
)
efficiency
. 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
machine can be driven to produce
,
. The
.
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.
47
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
REFERENCE
1. Pašilis, Aleksas Alfonsas and Guseinovienė, Eleonora. Bifilar type generator or motor.
LT 2012 019 Lithaunia, March 12, 2012. Electric Machines.
2. Sen, Paresh C. Principles of Electric Machines and Power Electronics. Kingston,
Ontario : John Wiley & Sons, 1997. Vol. II. ISBN 0-471-02295-0.
3. Rucker, Jonathan E. Design and Analysis of a Permanent Magnet Generator for Naval
Applications. Chapel Hill : s.n., June 2005.
4. Ocak, İ. Tarımer and C. Performance Comparision of Internal and External Rotor
Structured Wind Generators Mounted from Same Permanent Magnets on Same Geometry. Kaunas :
s.n., 2009. ISSN 1392 – 1215.
5. Centrifugal Force. Wikpedia The Free Encyclopedia. [Online] Wikimedia Foundation Inc,
May 7, 2013. [Cited: June 2, 2013.] http://en.wikipedia.org/wiki/Centrifugal_force.
6. Yicheng Chen, Pragasen Pillay and Azeem Khan. PM Wind Generator Comparison of
Different Topologies. 2004.
7. Vansompel, Hendrik. Maximizing the Energy Output of an Axial-Flux PermanentMagnet. Gent : s.n.
8. Hideki Kobayashi, Yuhito Doi, Koji Miyata, Takehisa Minowa. Design of the axialflux permanent magnet coreless generator for the multi-megawatts wind turbine. Kitago, Echizenshi, Fukui : s.n.
9. Seyedmohsen Hosseini, Javad Shokrollahi Moghani, Nima Farrokhzad Ershad, and
Bogi Bech Jensen. Design, Prototyping, and Analysis of a Novel Modular Permanent Magnet
Transverse Flux Disk Generator. Amirkabir University of Technology, Tehran and Technical
University of Denmark (DTU), Kongens Lyngby : s.n., 2010.
10. C. A. Oprea, C. S. Martis, F. N. Jurca, D. Fodorean, L. Szabó. Permanent Magnet
Linear Generator for Renewable Energy Applications: Tubular vs. Four-Sided Structures.
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, D74025 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.
48
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
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 9955-09561-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.
49
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
APPENDIX
50
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
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.
51
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
0.1. Table. EMF and frequency data for phase A from V1, Hz
Phase A
min
6,94
9,96
14,94
16,40
19,44
22,04
26,06
28,26
30,03
31,80
33,72
36,76
39,50
41,67
41,8
43,59
45,58
48,06
50,55
49,53
51,00
52,65
Frequency
max
7,02
10,00
14,99
16,60
19,45
22,15
26,11
28,29
30,19
31,84
33,76
36,80
39,93
41,72
41,86
43,61
45,62
48,11
50,62
49,44
51,06
52,71
average
6,980
9,980
14,965
16,500
19,445
22,095
26,085
28,275
30,110
31,820
33,740
36,780
39,715
41,695
41,830
43,600
45,600
48,085
50,585
49,485
51,030
52,680
min
42
62
95
104
124
141
166
180
192
203
216
235
252
264
275
276
289
305
322
313
323
333
EMF
max
45
64
96
107
125
142
168
182
193
204
217
236
255
265
277
277
290
306
321
314
324
334
average
43,5
63
95,5
105,5
124,5
141,5
167
181
192,5
203,5
216,5
235,5
253,5
264,5
276,0
276,5
289,5
305,5
321,5
313,5
323,5
333,5
52
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
0.2. Table. EMF and frequency data for phase B from V1, Hz
Phase B
min
7,44
11,44
15,48
17,73
19,81
22,45
25,93
28,55
30,45
31,15
34,36
36,87
39,03
40,4
42,09
43,85
45,9
48,41
50,83
52,95
54,7
54,14
Frequency
mat
7,58
11,48
15,53
17,79
19,86
22,46
25,96
28,58
30,5
31,24
34,39
36,93
39,08
40,43
42,12
43,87
45,95
48,47
50,88
52,98
54,75
54,35
average
7,51
11,46
15,505
17,76
19,835
22,455
25,945
28,565
30,475
31,195
34,375
36,9
39,055
40,415
42,105
43,86
45,925
48,44
50,855
52,965
54,725
54,245
min
46
72
98
113
126
143
165
182
195
199
219,7
226
249
258
268
280,6
294
309
325
338
349
345
EMF
max
50
74
100
114
127
144
167
183
195
199
220,3
227
249
258
270
280,6
294
319
326
338
349
346
average
48
73
99
113,5
126,5
143,5
166
182,5
195
199
220
226,5
249
258
269
280,6
294
314
325,5
338
349
345,5
53
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
0.3. Table. EMF and frequency data for phase C from V1, Hz
Phase C
min
8,34
11,95
16,58
18,12
20,86
23,84
27,16
29,61
31,18
32,79
35,1
37,58
40,16
41,67
43,41
45,2
43,35
46,22
48,42
50,32
52,12
53,89
Frequency
max
8,38
12
16,63
18,88
20,92
23,87
27,2
29,7
31,21
32,82
35,14
37,62
40,37
41,7
43,44
45,25
43,41
46,24
48,45
50,35
52,17
53,93
EMF
average
8,36
11,975
16,605
18,5
20,89
23,855
27,18
29,655
31,195
32,805
35,12
37,6
40,265
41,685
43,425
45,225
43,38
46,23
48,435
50,335
52,145
53,91
min
53
75
105
119
132
151
172
187
198
208
223
240
256
265
276
287
275
293
307
319
330
341
max
55
77
107
120
133
153
173
190
199
209
224
240
258
266
277
288
276
294
307
319
330
342
average
54
76
106
119,5
132,5
152
172,5
188,5
198,5
208,5
223,5
240
257
265,5
276,5
287,5
275,5
293,5
307
319
330
341,5
54
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
0.4. Table. 8,75 Hz, voltage and current data from Hz, V1, A1
8,75
8,75
8,75
8,75
8,75
8,75
8,75
8,75
8,75
8,75
8,75
8,75
8,75
8,75
8,75
8,75
8,75
8,75
8,75
8,75
8,75
8,75
56,5
45,6
44,8
44,2
43,7
42,9
41,8
41,3
39,2
38,1
36,5
35,5
33,7
31,9
29,9
25,7
22,4
19,8
15,9
10,3
6,1
0
56,5
46,1
45,3
45,3
44,5
43,2
42,7
42,2
40,2
38,7
37,4
36
34,5
32,5
30,7
26
23
20
16
10,5
6,3
0
56,51
45,85
45,05
44,75
44,10
43,05
42,25
41,75
39,70
38,40
36,95
35,75
34,10
32,20
30,30
25,85
22,70
19,90
15,95
10,40
6,20
0,00
0
0,76
0,79
0,82
0,88
0,91
0,99
1,05
1,08
1,13
1,2
1,28
1,38
1,46
1,54
1,58
1,67
1,76
1,89
1,85
1,99
2
0
0,82
0,84
0,89
0,96
0,99
1,07
1,11
1,16
1,24
1,32
1,39
1,46
1,58
1,66
1,71
1,8
1,9
2,01
2,02
2,11
2,19
0,000
0,790
0,815
0,855
0,920
0,950
1,030
1,080
1,120
1,185
1,260
1,335
1,420
1,520
1,600
1,645
1,735
1,830
1,950
1,935
2,050
2,095
55
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
0.5. Table. 11,02 Hz, voltage and current data from Hz, V1, A1
11,02
11,02
11,02
11,02
11,02
11,02
11,02
11,02
11,02
11,02
11,02
11,02
11,02
11,02
11,02
11,02
11,02
11,02
11,02
11,02
11,02
11,02
11,02
70,9
53,8
53,5
52,28
51,9
50,8
49,9
48,8
47,6
46,1
44,8
43,3
41,3
39,4
37,4
34,9
27,9
24,4
20,7
16,7
11,3
6,2
2,09
70,9
54,2
53,5
53
52,2
51,2
50,1
49,1
47,7
46,5
45
43,4
41,4
39,5
37,5
35
28
24,5
20,8
16,8
11,3
6,3
2,09
70,86
54,00
53,50
52,64
52,05
51,00
50,00
48,95
47,65
46,30
44,90
43,35
41,35
39,45
37,45
34,95
27,95
24,45
20,75
16,75
11,30
6,25
2,09
0
0,95
0,97
1,03
1,08
1,1
1,16
1,24
1,27
1,27
1,34
1,43
1,49
1,55
1,63
1,7
1,76
1,82
1,88
1,98
2,04
2,11
2,17
0
0,99
1,01
1,07
1,1
1,15
1,21
1,27
1,31
1,32
1,38
1,45
1,53
1,6
1,69
1,74
1,77
1,87
1,94
2,04
2,11
2,15
2,22
0,000
0,970
0,990
1,050
1,090
1,125
1,185
1,255
1,290
1,295
1,360
1,440
1,510
1,575
1,660
1,720
1,765
1,845
1,910
2,010
2,075
2,130
2,195
56
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
0.6. Table. 14,14 Hz, voltage and current data from Hz, V1, A1
14,14
14,14
14,14
14,14
14,14
14,14
14,14
14,14
14,14
14,14
14,14
14,14
14,14
14,14
14,14
14,14
14,14
14,14
14,14
14,14
14,14
14,14
14,14
14,14
14,14
90,6
74,4
73,6
72,8
71,4
71,9
68,7
67,1
63
61
57,8
54,2
53,3
45,5
40
34,7
30,9
28,1
24,5
20,4
15,7
11,4
6,7
2,23
0
90,6
74,5
74,2
73,3
72,2
72,3
69,4
67,6
63,4
61,1
57,9
54,3
53,4
45,6
40
34,8
31
28,4
24,5
20,5
15,8
11,5
6,7
2,23
0
90,59
74,45
73,90
73,05
71,80
72,10
69,05
67,35
63,20
61,05
57,85
54,25
53,35
45,55
40,00
34,75
30,95
28,25
24,50
20,45
15,75
11,45
6,70
2,23
0,00
0
0,82
0,85
0,9
0,94
1,01
1,07
1,16
1,2
1,25
1,33
1,45
1,53
1,66
1,8
1,88
1,79
1,84
1,88
1,95
2,01
2,06
2,09
2,12
2,25
0
0,85
0,88
0,92
0,99
1,04
1,12
1,2
1,24
1,31
1,4
1,51
1,58
1,71
1,85
1,95
1,84
1,9
1,95
2,02
2,07
2,11
2,16
2,2
2,25
0,000
0,835
0,865
0,910
0,965
1,025
1,095
1,180
1,220
1,280
1,365
1,480
1,555
1,685
1,825
1,915
1,815
1,870
1,915
1,985
2,040
2,085
2,125
2,160
2,250
57
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
0.7. Table 17,80 Hz, voltage and current data from Hz, V1 and A1
17,8
17,8
17,8
17,8
17,8
17,8
17,8
17,8
17,8
17,8
17,8
17,8
17,8
17,8
17,8
17,8
17,8
17,8
17,8
17,8
17,8
17,8
113,7
89,9
88,6
86,6
84,8
81,2
79,9
76,6
74,3
70,1
66,1
60,9
55,2
48,9
42,3
36
27,9
19
13,2
4,4
3,3
0
113,7
90
88,7
86,7
84,9
81,3
80
76,7
74,4
70,2
66,2
61
55,3
49
42,4
36
28
19,1
13,4
4,6
3,5
0
113,74
89,95
88,65
86,65
84,85
81,25
79,95
76,65
74,35
70,15
66,15
60,95
55,25
48,95
42,35
36,00
27,95
19,05
13,30
4,50
3,40
0,00
0
1,08
1,116
1,17
1,215
1,26
1,341
1,404
1,476
1,512
1,557
1,665
1,737
1,818
1,917
1,998
2,007
2,142
2,16
2,178
2,196
2,25
0
1,1
1,125
1,179
1,224
1,26
1,35
1,413
1,485
1,521
1,566
1,674
1,746
1,827
1,944
2,007
2,088
2,151
2,169
2,196
2,205
2,27
0,000
1,090
1,121
1,175
1,220
1,260
1,346
1,409
1,481
1,517
1,562
1,670
1,742
1,823
1,931
2,003
2,048
2,147
2,165
2,187
2,201
2,260
58
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
0.8. Table. 22,89 Hz, voltage and current data from Hz, V1, A1
22,89
22,89
22,89
22,89
22,89
22,89
22,89
22,89
22,89
22,89
22,89
22,89
22,89
22,89
22,89
22,89
22,89
22,89
22,89
22,89
22,89
22,89
22,89
22,89
145,9
132,8
120,9
106,7
104,8
101,7
98,9
95,4
91,8
87,8
84,1
78,9
73,1
66,8
59,7
51,8
43,6
47,3
29,3
19,6
14,8
7,1
2,9
0
145,9
132,8
121
106,7
104,8
101,8
99
95,4
91,8
87,9
84,2
78,9
73,2
66,9
59,7
51,8
43,7
47,3
29,4
19,6
14,8
7,2
3
0
145,93
132,80
120,95
106,70
104,80
101,75
98,95
95,40
91,80
87,85
84,15
78,90
73,15
66,85
59,70
51,80
43,65
47,30
29,35
19,60
14,80
7,15
2,95
0,00
0
0,66
0,971957
1,292826
1,337391
1,399783
1,453261
1,515652
1,578043
1,649348
1,711739
1,720652
1,809783
1,863261
1,961304
2,014783
2,095
2,130652
2,157391
2,201957
2,228696
2,246522
2,246522
2,3
0
0,66
0,971957
1,292826
1,337391
1,399783
1,453261
1,515652
1,578043
1,649348
1,711739
1,729565
1,809783
1,863261
1,961304
2,032609
2,103913
2,139565
2,166304
2,21087
2,237609
2,255435
2,264348
2,3
0,000
0,660
0,972
1,293
1,337
1,400
1,453
1,516
1,578
1,649
1,712
1,725
1,810
1,863
1,961
2,024
2,099
2,135
2,162
2,206
2,233
2,251
2,255
2,300
59
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
0.9. Table. 28,80 Hz, voltage and current data from Hz, V1, A1
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
28,8
183,3
155,0
121,9
119,1
115,3
111,2
106,5
101,3
96,2
89,6
84,1
77,6
70,9
64
54,1
45,5
37,7
29,7
24,1
19,3
14,1
7,6
2,7
0
183,3
155,0
122
119,2
115,3
111,3
106,6
101,3
96,3
89,6
84,2
77,7
70,9
64,1
54,1
45,6
37,7
29,7
24,1
19,4
14,2
7,6
2,8
0
183,31
155,00
121,95
119,15
115,30
111,25
106,55
101,30
96,25
89,60
84,15
77,65
70,90
64,05
54,10
45,55
37,70
29,70
24,10
19,35
14,15
7,60
2,75
0,00
0
1
1,534013
1,567389
1,617452
1,659172
1,71758
1,775987
1,826051
1,834395
1,884459
1,942866
1,984586
2,093057
2,084713
2,134777
2,184841
2,201529
2,226561
2,243248
2,259936
2,26828
2,284968
2,31
0
1
1,531321
1,564528
1,61434
1,664151
1,722264
1,772075
1,830189
1,838491
1,88
1,938113
1,987925
2,095849
2,087547
2,129057
2,18717
2,203774
2,228679
2,245283
2,261887
2,270189
2,278491
2,32
0,000
1,000
1,533
1,566
1,616
1,662
1,720
1,774
1,828
1,836
1,882
1,940
1,986
2,094
2,086
2,132
2,186
2,203
2,228
2,244
2,261
2,269
2,282
2,315
60
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
0.10. Table. 44,00 Hz, voltage and current data from Hz, V1, A1
43,96
43,96
43,96
43,94
43,94
43,94
43,94
43,96
43,94
43,96
43,96
43,965
43,985
43,97
43,97
43,98
43,995
44,005
44,02
44,025
44,025
44,03
44,04
44,04
44,06
44,07
44,08
44,08
279,2
218,4
211,9
195,8
173,2
146,6
142,4
136,3
129,5
122,9
115,5
107,5
99,1
91,5
83,3
74,7
65,5
55,5
46,1
38,1
34
28,9
23,8
18,9
14,1
7,1
2,3
0
279,2
218,4
212
195,9
173,2
146,7
142,4
136,3
129,6
123
115,6
107,6
99,1
91,6
83,4
74,7
65,6
55,5
46,1
38,1
34,1
28,9
23,9
19
14,1
7,1
2,3
0
279,19
218,40
211,95
195,85
173,20
146,65
142,40
136,30
129,55
122,95
115,55
107,55
99,10
91,55
83,35
74,70
65,55
55,50
46,10
38,10
34,05
28,90
23,85
18,95
14,10
7,10
2,30
0,00
0,00
1,16
1,26
1,42
1,61
1,81
1,84
1,88
1,92
1,96
1,99
2,03
2,02
2,05
2,08
2,11
2,14
2,18
2,20
2,25
2,26
2,27
2,28
2,28
2,29
2,29
2,32
2,34
0,00
1,18
1,27
1,44
1,62
1,83
1,85
1,89
1,93
1,97
2,01
2,05
2,02
2,06
2,09
2,12
2,15
2,18
2,20
2,25
2,27
2,27
2,28
2,28
2,30
2,30
2,32
2,34
0,000
1,170
1,266
1,429
1,616
1,819
1,847
1,886
1,926
1,966
2,002
2,041
2,022
2,057
2,085
2,113
2,145
2,181
2,197
2,252
2,264
2,268
2,276
2,284
2,296
2,296
2,316
2,340
61
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
0.11. Table. 56,40 Hz, voltage and current data from Hz, V1, A1
56,31
56,31
56,32
56,315
56,325
56,325
56,325
56,345
56,345
56,335
56,335
56,32
56,35
56,355
56,355
56,38
56,375
56,395
56,415
56,425
56,425
56,455
56,455
56,465
56,475
56,485
56,485
56,485
56,485
56,485
357,3
261,3
246,5
234,2
222,3
202,9
181,9
157,7
151,8
144,2
136,2
128
120
111,8
104,8
102,8
94,8
85,3
75,7
65,7
56,1
46
38,4
34,6
29,3
24
19,2
12,7
7,33
0
357,3
261,3
246,6
234,3
222,4
203
182
157,7
151,8
144,2
136,3
128,1
120,1
111,8
104,8
102,8
94,8
85,3
75,7
65,7
56,2
46
38,5
34,6
29,3
24
19,2
12,7
7,33
0
357,29
261,30
246,55
234,25
222,35
202,95
181,95
157,70
151,80
144,20
136,25
128,05
120,05
111,80
104,80
102,80
94,80
85,30
75,70
65,70
56,15
46,00
38,45
34,60
29,30
24,00
19,20
12,70
7,33
0,00
0,00
1,39
1,49
1,58
1,65
1,75
1,87
1,99
2,02
2,04
2,09
2,12
2,15
2,18
2,21
2,16
2,18
2,20
2,23
2,25
2,28
2,29
2,30
2,32
2,33
2,34
2,34
2,35
2,35
2,37
0,00
1,39
1,49
1,57
1,65
1,76
1,87
1,98
2,01
2,04
2,09
2,13
2,16
2,19
2,21
2,16
2,18
2,20
2,23
2,25
2,28
2,30
2,30
2,32
2,33
2,34
2,35
2,35
2,35
2,37
0,000
1,390
1,491
1,573
1,648
1,756
1,872
1,984
2,014
2,044
2,089
2,122
2,152
2,182
2,208
2,156
2,178
2,201
2,230
2,253
2,275
2,294
2,298
2,320
2,328
2,335
2,346
2,350
2,350
2,370
62
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
0.12. Table. 71,90 Hz, voltage and current data from Hz, V1, A1
70,795
70,795
70,795
70,795
70,81
70,84
70,88
70,875
70,905
70,915
70,915
70,94
70,94
70,95
70,965
70,97
71
71
71,015
71,045
71,035
71,045
71,055
71,08
71,115
71,12
71,135
71,11
71,11
448,9
295,5
278,3
245,2
206
164,5
157,4
149,5
141,4
131,6
122,6
113,3
106,3
105,4
97,4
87,4
77,5
67,8
57,3
47,1
38,1
34,4
29,2
23,7
18,2
13,2
7,6
2,99
0
448,9
295,5
278,3
245,3
206,1
164,5
157,4
149,6
141,4
131,6
122,7
113,3
106,3
105,4
97,4
87,4
77,6
67,8
57,3
47,2
38,2
34,4
29,2
23,7
18,2
13,2
7,6
3
0
448,90
295,50
278,30
245,25
206,05
164,50
157,40
149,55
141,40
131,60
122,65
113,30
106,30
105,40
97,40
87,40
77,55
67,80
57,30
47,15
38,15
34,40
29,20
23,70
18,20
13,20
7,60
3,00
0,00
0,00
1,59
1,69
1,84
1,99
2,15
2,18
2,20
2,22
2,24
2,26
2,28
2,29
2,26
2,27
2,29
2,30
2,31
2,32
2,33
2,34
2,34
2,35
2,35
2,35
2,35
2,35
2,35
2,36
0,00
1,60
1,69
1,85
1,99
2,15
2,18
2,20
2,22
2,24
2,26
2,28
2,29
2,26
2,27
2,30
2,31
2,31
2,33
2,34
2,34
2,34
2,35
2,35
2,35
2,35
2,35
2,36
2,37
0,000
1,595
1,690
1,845
1,990
2,150
2,180
2,200
2,220
2,240
2,260
2,280
2,290
2,260
2,270
2,295
2,305
2,310
2,325
2,335
2,340
2,340
2,350
2,350
2,350
2,350
2,350
2,355
2,365
63
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
0.13. Table. 8,75 Hz, power, losses, efficiency, power factor calculated data
0,00
36,22
36,72
38,26
40,57
40,90
43,52
45,09
44,46
45,50
46,56
47,73
48,42
48,94
48,48
42,52
39,38
36,42
31,10
20,12
12,71
0,00
0,00
4,99
5,31
5,85
6,77
7,22
8,49
9,33
10,04
11,23
12,70
14,26
16,13
18,48
20,48
21,65
24,08
26,79
30,42
29,95
33,62
35,11
0,89
42,10
42,92
45,00
48,23
49,01
52,89
55,31
55,39
57,63
60,15
62,87
65,44
68,32
69,85
65,06
64,35
64,10
62,41
50,97
47,22
36,00
0,89
0,89
0,89
0,89
0,89
0,89
0,89
0,89
0,89
0,89
0,89
0,89
0,89
0,89
0,89
0,89
0,89
0,89
0,89
0,89
0,89
0,89
0,00
86,03
85,55
85,03
84,12
83,45
82,27
81,52
80,28
78,96
77,41
75,91
73,99
71,64
69,41
65,36
61,20
56,82
49,83
39,48
26,92
0,00
0,00
41,21
42,03
44,11
47,34
48,12
52,00
54,42
54,50
56,74
59,26
61,98
64,55
67,43
68,96
64,17
63,47
63,21
61,52
50,08
46,33
35,11
0,00
44,64
46,05
48,31
51,99
53,68
58,20
61,03
63,29
66,96
71,20
75,44
80,24
85,89
90,41
92,95
98,04
103,41
110,19
109,34
115,84
118,38
0,923
0,913
0,913
0,911
0,896
0,894
0,892
0,861
0,847
0,832
0,822
0,805
0,785
0,763
0,690
0,647
0,611
0,558
0,458
0,400
0,297
64
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
0.14. Table. 11,02 Hz, power, losses, efficiency, power factor calculated data
0,00
52,38
52,97
55,27
56,73
57,38
59,25
61,43
61,47
59,96
61,06
62,42
62,44
62,13
62,17
60,11
49,33
45,11
39,63
33,67
23,45
13,31
4,59
0,00
7,53
7,84
8,82
9,50
10,13
11,23
12,60
13,31
13,42
14,80
16,59
18,24
19,85
22,04
23,67
24,92
27,23
29,18
32,32
34,45
36,30
38,54
1,34
61,25
62,15
65,43
67,58
68,84
71,82
75,37
76,12
74,71
77,20
80,35
82,02
83,32
85,55
85,12
75,59
73,68
70,16
67,33
59,23
50,95
44,47
1,34
1,34
1,34
1,34
1,34
1,34
1,34
1,34
1,34
1,34
1,34
1,34
1,34
1,34
1,34
1,34
1,34
1,34
1,34
1,34
1,34
1,34
1,34
0,00
85,52
85,23
84,47
83,95
83,35
82,49
81,51
80,75
80,25
79,10
77,69
76,13
74,57
72,67
70,62
65,26
61,22
56,49
50,01
39,59
26,13
10,32
0,00
59,91
60,81
64,09
66,24
67,50
70,48
74,03
74,78
73,37
75,86
79,01
80,68
81,98
84,21
83,78
74,25
72,34
68,82
65,99
57,89
49,61
43,13
0,00
68,74
70,15
74,41
77,24
79,72
83,97
88,93
91,41
91,77
96,37
102,04
107,00
111,61
117,63
121,88
125,07
130,74
135,35
142,43
147,04
150,94
155,54
0,872
0,867
0,861
0,858
0,847
0,839
0,832
0,818
0,800
0,787
0,774
0,754
0,735
0,716
0,687
0,594
0,553
0,508
0,463
0,394
0,329
0,277
65
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
0.15. Table. 14,14 Hz, power, losses, efficiency, power factor calculated data
0,00
62,17
63,92
66,48
69,29
73,90
75,61
79,47
77,10
78,14
78,97
80,29
82,96
76,75
73,00
66,55
56,17
52,83
46,92
40,59
32,13
23,87
14,24
4,82
0,00
0,00
5,58
5,99
6,62
7,45
8,41
9,59
11,14
11,91
13,11
14,91
17,52
19,34
22,71
26,65
29,34
26,35
27,98
29,34
31,52
33,29
34,78
36,13
37,32
40,50
2,04
69,79
71,95
75,14
78,78
84,35
87,25
92,66
91,06
93,30
95,92
99,86
104,35
101,51
101,69
97,93
84,57
82,85
78,30
74,16
67,47
60,70
52,41
44,19
42,54
2,04
2,04
2,04
2,04
2,04
2,04
2,04
2,04
2,04
2,04
2,04
2,04
2,04
2,04
2,04
2,04
2,04
2,04
2,04
2,04
2,04
2,04
2,04
2,04
2,04
0,00
89,08
88,84
88,46
87,95
87,61
86,66
85,77
84,68
83,76
82,33
80,40
79,50
75,61
71,79
67,95
66,42
63,76
59,92
54,74
47,62
39,33
27,17
10,90
0,00
0,00
67,74
69,91
73,10
76,74
82,31
85,20
90,61
89,01
91,25
93,87
97,81
102,30
99,47
99,65
95,88
82,53
80,80
76,26
72,12
65,42
58,65
50,36
42,14
40,50
0,00
75,65
78,36
82,44
87,42
92,86
99,20
106,90
110,53
115,96
123,66
134,08
140,87
152,65
165,33
173,49
164,43
169,41
173,49
179,83
184,81
188,89
192,51
195,68
203,84
0,896
0,892
0,887
0,878
0,886
0,859
0,848
0,805
0,787
0,759
0,730
0,726
0,652
0,603
0,553
0,502
0,477
0,440
0,401
0,354
0,311
0,262
0,215
0,199
66
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
0.16. Table. 17,8 Hz, power, losses, efficiency, power factor calculated data
0,00
98,05
99,33
101,77
103,47
102,38
107,57
107,96
110,08
106,38
103,29
101,76
96,22
89,21
81,76
72,09
57,23
40,89
28,79
9,84
7,48
0,00
0,00
9,50
10,04
11,04
11,90
12,70
14,48
15,87
17,54
18,40
19,51
22,30
24,26
26,57
29,81
32,08
33,54
36,86
37,48
38,26
38,74
40,86
3,03
110,58
112,41
115,84
118,40
118,11
125,09
126,86
130,64
127,81
125,83
127,09
123,51
118,82
114,60
107,20
93,80
80,78
69,30
51,14
49,25
43,89
3,03
3,03
3,03
3,03
3,03
3,03
3,03
3,03
3,03
3,03
3,03
3,03
3,03
3,03
3,03
3,03
3,03
3,03
3,03
3,03
3,03
3,03
0,00
88,66
88,37
87,86
87,39
86,68
86,00
85,10
84,26
83,23
82,09
80,07
77,90
75,08
71,34
67,25
61,01
50,62
41,54
19,25
15,19
0,00
0,00
107,55
109,38
112,81
115,37
115,08
122,06
123,83
127,61
124,78
122,80
124,05
120,48
115,78
111,57
104,17
90,77
77,75
66,27
48,11
46,22
40,86
0,00
123,98
127,45
133,59
138,71
143,31
153,04
160,21
168,39
172,49
177,61
189,89
198,08
207,29
219,58
227,77
232,89
244,15
246,19
248,75
250,29
257,06
0,867
0,858
0,844
0,832
0,803
0,798
0,773
0,758
0,723
0,691
0,653
0,608
0,559
0,508
0,457
0,390
0,318
0,269
0,193
0,185
0,159
67
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
0.17. Table. 22,89 Hz, power, losses, efficiency, power factor calculated data
0,00
87,65
117,56
137,94
140,16
142,43
143,80
144,59
144,86
144,90
144,04
136,11
132,39
124,56
117,09
104,83
91,64
100,99
63,45
43,25
33,05
16,09
6,65
0,00
0,00
3,48
7,56
13,37
14,31
15,68
16,90
18,38
19,92
21,76
23,44
23,81
26,20
27,77
30,77
32,76
35,26
36,47
37,39
38,95
39,90
40,54
40,70
42,32
4,91
96,04
130,03
156,23
159,38
163,01
165,61
167,88
169,70
171,57
172,39
164,83
163,50
157,24
152,77
142,50
131,81
142,37
105,75
87,10
77,86
61,54
52,26
47,23
4,91
4,91
4,91
4,91
4,91
4,91
4,91
4,91
4,91
4,91
4,91
4,91
4,91
4,91
4,91
4,91
4,91
4,91
4,91
4,91
4,91
4,91
4,91
4,91
0,00
91,26
90,41
88,30
87,94
87,37
86,83
86,13
85,37
84,45
83,55
82,58
80,97
79,21
76,64
73,56
69,52
70,94
60,00
49,65
42,45
26,15
12,73
0,00
0,00
91,13
125,12
151,32
154,47
158,10
160,70
162,97
164,79
166,66
167,48
159,92
158,59
152,33
147,86
137,59
126,90
137,46
100,84
82,19
72,95
56,63
47,35
42,32
0,00
96,32
141,84
188,67
195,17
204,27
212,08
221,18
230,29
240,69
249,80
251,75
264,11
271,91
286,22
295,32
306,38
311,58
315,48
321,99
325,89
328,49
329,14
335,65
0,946
0,882
0,802
0,791
0,774
0,758
0,737
0,716
0,692
0,670
0,635
0,600
0,560
0,517
0,466
0,414
0,441
0,320
0,255
0,224
0,172
0,144
0,126
68
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
0.18. Table. 28,80 Hz, power, losses, efficiency, power factor calculated data
0,00
155,00
186,91
186,58
186,31
184,86
183,26
179,71
175,96
164,55
158,39
150,68
140,83
134,15
112,86
97,11
82,41
65,42
53,69
43,43
31,99
17,25
6,27
0,00
0,00
8,00
18,79
19,62
20,89
22,09
23,67
25,18
26,74
26,98
28,34
30,12
31,56
35,09
34,82
36,36
38,23
38,81
39,70
40,29
40,89
41,20
41,65
42,87
8,41
171,41
214,11
214,62
215,62
215,36
215,34
213,30
211,11
199,94
195,15
189,22
180,80
177,66
156,09
141,88
129,06
112,65
101,80
92,13
81,30
66,86
56,34
51,29
8,41
8,41
8,41
8,41
8,41
8,41
8,41
8,41
8,41
8,41
8,41
8,41
8,41
8,41
8,41
8,41
8,41
8,41
8,41
8,41
8,41
8,41
8,41
8,41
0,00
90,42
87,29
86,94
86,41
85,84
85,10
84,25
83,35
82,30
81,16
79,63
77,89
75,51
72,30
68,44
63,86
58,07
52,74
47,13
39,35
25,80
11,14
0,00
0,00
163,00
205,70
206,20
207,20
206,95
206,92
204,89
202,69
191,53
186,73
180,80
172,39
169,24
147,68
133,47
120,64
104,23
93,38
83,72
72,89
58,44
47,93
42,87
0,00
183,31
280,95
287,06
296,21
304,60
315,28
325,20
335,11
336,64
345,03
355,71
364,10
383,93
382,41
390,80
400,72
403,77
408,35
411,40
414,45
415,97
418,26
424,36
0,889
0,732
0,718
0,700
0,679
0,656
0,630
0,605
0,569
0,541
0,508
0,473
0,441
0,386
0,342
0,301
0,258
0,229
0,204
0,176
0,140
0,115
0,101
69
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
0.19. Table. 44,00 Hz, power, losses, efficiency, power factor calculated data
0,00
255,53
268,22
279,80
279,84
266,70
262,95
257,11
249,53
241,71
231,30
219,56
200,34
188,36
173,81
157,85
140,60
121,04
101,27
85,82
77,10
65,56
54,29
43,29
32,38
16,30
5,33
0,00
0,00
10,95
12,81
16,33
20,88
26,46
27,28
28,47
29,68
30,92
32,05
33,34
32,70
33,86
34,79
35,72
36,81
38,05
38,61
40,59
41,02
41,16
41,45
41,74
42,18
42,18
42,92
43,80
29,48
295,96
310,51
325,56
330,16
322,60
319,66
315,05
308,64
302,11
292,83
282,39
262,57
251,72
238,10
223,09
206,96
188,65
169,48
156,02
147,73
136,34
125,39
114,68
104,24
88,19
77,97
73,54
29,48
29,48
29,48
29,43
29,43
29,43
29,43
29,48
29,43
29,48
29,48
29,49
29,53
29,50
29,50
29,52
29,55
29,57
29,60
29,61
29,61
29,62
29,65
29,65
29,69
29,71
29,73
29,73
0,00
86,34
86,38
85,94
84,76
82,67
82,26
81,61
80,85
80,01
78,99
77,75
76,30
74,83
73,00
70,76
67,94
64,16
59,75
55,00
52,19
48,08
43,30
37,75
31,06
18,49
6,83
0,00
0,00
266,48
281,04
296,13
300,73
293,16
290,22
285,57
279,21
272,63
263,35
252,90
233,04
222,22
208,60
193,57
177,41
159,08
139,87
126,41
118,12
106,72
95,74
85,03
74,56
58,48
48,24
43,80
0,00
326,65
353,32
398,86
451,09
507,74
515,53
526,64
537,75
548,86
558,85
569,96
564,42
574,41
582,19
589,96
598,85
608,86
613,30
628,86
632,18
633,30
635,52
637,75
641,07
641,07
646,63
653,30
0,816
0,795
0,742
0,667
0,577
0,563
0,542
0,519
0,497
0,471
0,444
0,413
0,387
0,358
0,328
0,296
0,261
0,228
0,201
0,187
0,169
0,151
0,133
0,116
0,091
0,075
0,067
70
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
0.20. Table. 56,40 Hz, power, losses, efficiency, power factor calculated data
0,00
363,21
367,57
368,48
366,37
356,40
340,59
312,86
305,70
294,70
284,56
271,74
258,35
243,94
231,40
221,61
206,49
187,71
168,85
148,01
127,76
105,52
88,35
80,28
68,20
56,04
45,05
29,85
17,23
0,00
0,00
15,46
17,78
19,80
21,72
24,67
28,03
31,49
32,44
33,41
34,90
36,03
37,05
38,09
39,00
37,18
37,96
38,74
39,80
40,60
41,42
42,10
42,24
43,06
43,34
43,62
44,04
44,18
44,18
44,94
62,27
440,94
447,65
450,57
450,41
443,39
430,94
406,73
400,52
390,46
381,81
370,07
357,80
344,44
332,82
321,28
306,92
288,98
271,24
251,24
231,80
210,34
193,30
186,09
174,32
162,47
151,90
136,83
124,21
107,74
62,27
62,27
62,30
62,29
62,32
62,32
62,32
62,38
62,38
62,35
62,35
62,30
62,40
62,41
62,41
62,49
62,47
62,53
62,59
62,63
62,63
62,72
62,72
62,75
62,78
62,81
62,81
62,81
62,81
62,81
0,00
82,37
82,11
81,78
81,34
80,38
79,03
76,92
76,32
75,47
74,53
73,43
72,21
70,82
69,53
68,98
67,28
64,96
62,25
58,91
55,12
50,17
45,70
43,14
39,12
34,49
29,66
21,81
13,87
0,00
0,00
378,66
385,35
388,28
388,09
381,07
368,62
344,35
338,14
328,11
319,46
307,77
295,40
282,02
270,41
258,79
244,45
226,45
208,65
188,62
169,17
147,62
130,58
123,34
111,54
99,66
89,09
74,03
61,41
44,94
0,00
496,64
532,76
562,08
588,88
627,60
668,98
709,28
719,97
730,52
746,55
758,37
769,45
780,21
789,55
771,19
779,14
787,44
798,41
806,58
814,60
821,73
823,06
831,24
834,06
836,89
840,91
842,24
842,24
849,41
0,762
0,723
0,691
0,659
0,607
0,551
0,485
0,470
0,449
0,428
0,406
0,384
0,361
0,342
0,336
0,314
0,288
0,261
0,234
0,208
0,180
0,159
0,148
0,134
0,119
0,106
0,088
0,073
0,053
71
TEI-09, O.Lyan, V.Monet
Research of PMG with compensated reactance winding
0.21. Table. 70,90 Hz, power, losses, efficiency, power factor calculated data
0,00
471,32
470,33
452,49
410,04
353,68
343,13
329,01
313,91
294,78
277,19
258,32
243,43
238,20
221,10
200,58
178,75
156,62
133,22
110,10
89,27
80,50
68,62
55,70
42,77
31,02
17,86
7,05
0,00
0,00
20,35
22,85
27,23
31,68
36,98
38,02
38,72
39,43
40,14
40,86
41,59
41,95
40,86
41,22
42,14
42,50
42,69
43,25
43,62
43,80
43,80
44,18
44,18
44,18
44,18
44,18
44,37
44,75
101,67
593,35
594,85
581,39
543,42
492,40
482,97
469,54
455,19
436,80
419,92
401,82
387,29
380,99
364,27
344,68
323,27
301,32
278,50
255,80
235,14
226,38
214,90
202,01
189,15
177,40
164,27
153,61
146,93
101,67
101,67
101,67
101,67
101,70
101,75
101,81
101,81
101,86
101,87
101,87
101,91
101,91
101,93
101,95
101,96
102,01
102,01
102,04
102,08
102,07
102,08
102,10
102,14
102,20
102,20
102,23
102,19
102,19
0,00
79,43
79,07
77,83
75,46
71,83
71,05
70,07
68,96
67,49
66,01
64,29
62,85
62,52
60,70
58,19
55,30
51,98
47,84
43,04
37,96
35,56
31,93
27,57
22,61
17,49
10,87
4,59
0,00
0,00
491,67
493,18
479,72
441,72
390,66
381,15
367,73
353,34
334,92
318,05
299,91
285,38
279,06
262,32
242,72
221,26
199,31
176,47
153,71
133,08
124,30
112,80
99,88
86,95
75,20
62,04
51,42
44,75
0,00
716,00
758,65
828,23
893,51
965,75
979,78
988,70
998,11
1007,24
1016,24
1025,59
1030,09
1016,74
1021,45
1032,77
1037,71
1039,96
1046,94
1051,88
1053,99
1054,13
1058,79
1059,16
1059,68
1059,75
1059,98
1061,86
1066,37
0,687
0,650
0,579
0,494
0,405
0,389
0,372
0,354
0,333
0,313
0,292
0,277
0,274
0,257
0,235
0,213
0,192
0,169
0,146
0,126
0,118
0,107
0,094
0,082
0,071
0,059
0,048
0,042
72