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KLAIPEDA UNIVERSITY
FACULTY OF MARINE ENGINEERING
DEPARTMENT OF ELECTRICAL ENGINEERING
I________________________HEREBY CONIFIRM
Head of department: prof. dr. Eleonora Guseinovienė
2013
BACHELOR STUDY PROGRAME OF ELECTRICAL ENGINEERING
(Code of studies 612H62003)
FINAL THESIS
RESEARCH OF PERMANENT MAGNET
GENERATOR WITH COMPENSATED
REACTANCE WINDINGS
Editor: ________________________
2013
Supervisors: Prof. dr. Eleonora Guseinovienė
Boris Rudnickij
2013
Authors: TEI-09 Oleg Lyan
HENALLUX Vincent Monet
2013
Klaipėda, 2013
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ABSTRACT
In this thesis, a patented “bifilar” coil (BC) type permanent magnet generator (PMG) is
constructed for scientific research and comparison with other technologies. The features, working
principle and elements of the BCPMG are analyzed.
The BCPMG is developed from the iron-cored “bifilar” coil topology based on (1) in an
attempt to overcome the problems with current rotary type generators, which have so far been
dominant on the market. One of the problems is armature reactance , which is usually bigger than
resistance . The circumstance creates difficulties for designers and operators of the generator.
That is why patented technology is offered to partially remove or absolutely neglect the reactance of
the machine. Drawings of the PMG parts and assembly are added. A finite element magnetic model
(FEMM) is presented and analyzed.
Also, this thesis contains an experimental analysis of the PMG characteristics, such as no-
load losses and EMF vs. speed, loaded voltage drop, power output and efficiency vs. load current at
different speeds.
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LIST OF TABLES
1.1. Table. “Alxion” constructors catalogue parameters ................................................................... 12
1.2. Table. “MOOG” constructors catalogue parameters .................................................................. 12
1.3. Table. Prototype generator specifications .................................................................................. 15
1.4. Table. Nominal characteristics of constructed TFPMDG .......................................................... 16
2.1. Existing magnet materials and parameters ................................................................................. 23
3.1. Table. Measurement device ........................................................................................................ 31
3.2. Table. Parameters of driving machines ...................................................................................... 31
3.3. Table. Motor current voltage data from A2. ............................................................................... 35
3.4. Table. Motor terminal voltage data from V2. ............................................................................. 35
3.5. Table. PMG terminal EMF frequency data from F. ................................................................... 36
3.6. Table. Power losses, calculated data. ......................................................................................... 37
3.7. Table. The parameters of calculated curves. .............................................................................. 38
5.1. Table. Practical parameters of the PMG topology ..................................................................... 46
5.2. Table. Consumed material quantity ............................................................................................ 46
0.1. Table. EMF and frequency data for phase A from V1, F ........................................................... 52
0.2. Table. EMF and frequency data for phase B from V1, F ........................................................... 53
0.3. Table. EMF and frequency data for phase C from V1, F ........................................................... 54
0.4. Table. 8,75 Hz, voltage and current data from F, V1, A1 .......................................................... 55
0.5. Table. 11,02 Hz, voltage and current data from F, V1, A1 ........................................................ 56
0.6. 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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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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2.9. Fig. Magnetic circuit flux lines of PMG topology with less magnets. ....................................... 24
2.10. Fig. Magnetic circuit flux lines of PMG while moving through steps. .................................... 25
2.11. Fig. 1/5 segment of patented PMG active material (3D model front view) ............................. 26
2.12. Fig. 1/5 segment of patented PMG active material (3D top view) ........................................... 26
2.13. Fig. Magnetic flux density vector plot (front view) ................................................................. 26
2.14. Fig. Magnetic flux density vector plot (top view) .................................................................... 27
2.15. Fig. Magnetic flux density continuous fringe plot on several sections: A – cross section of
magnet array, B – cross section of coils ............................................................................................ 27
2.16. Fig. Magnetic flux density continuous fringe plot on several sections: C – axial section of core
phase C, D – axial section of core phase A ....................................................................................... 27
2.17. Fig. 1/5 segment of patented PMG active material magnetic flux density with applied 3 phase
current 10A RMS .............................................................................................................................. 28
2.18. Fig. Magnetic flux density with applied 3 phase current 10A RMS axial section of first wound
rod (right side view) .......................................................................................................................... 28
2.19. Fig. Magnetic flux density with applied 3 phase current 10A RMS cross section of first array
of magnets (front view) ..................................................................................................................... 29
3.1. Fig. Arduino Nano V3.0 ............................................................................................................. 31
3.2. Fig. IGBT or MOSFET gate driver working principle ............................................................... 32
3.3. Fig. Gate driver “turning on” equivalent .................................................................................... 33
3.4. Fig. Gate driver “turned on” equivalent ..................................................................................... 33
3.5. Fig. Gate driver “turning off” equivalent ................................................................................... 34
3.6. Fig. Gate driver “turned off” equivalent ..................................................................................... 34
3.7. Fig. Mechanical and magnetic power losses versus frequency as TG signal ............................. 37
3.8. Fig. EMF vs. frequency as AC TG speed signal (OCC) ............................................................ 37
3.9. Fig. Linear relationship of reactance vs. frequency.................................................................... 38
3.10. Fig. Short circuit current vs. speed relationship ....................................................................... 39
3.11. Fig. Terminal voltage vs. load current performance characteristics at different speeds
(measured and calculated) ................................................................................................................. 40
3.12. Fig. Terminal voltage vs. load at different speeds (surface plot) ............................................. 40
3.13. Fig. Performance characteristics of independent synchronous generator: (a) equivalent circuit
diagram; (b) Terminal voltage vs. load current at constant rotating excitation field (2 p. 331) ........ 41
3.14. Fig. Power output vs. load current performance characteristics at different speeds (measured
and calculated) ................................................................................................................................... 41
3.15. Fig. Output power vs. load at different speeds (surface plot)................................................... 42
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3.16. Fig. Efficiency vs. load current performance characteristics at different speeds (measured and
calculated) .......................................................................................................................................... 42
3.17. Fig. Efficiency vs. load current at different speeds (surface plot) ............................................ 43
3.18. Fig. Efficiency vs. load current performance characteristics at different speeds (before
overload) ............................................................................................................................................ 43
3.19. Fig. Efficiency vs. load current performance characteristics at different speeds (after
overload) ............................................................................................................................................ 44
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LIST OF CONTENTS
INTRODUCTION…………………………………………………………………………… 9
1. OVERVIEW OF EXISTENT GENERATOR CONSTRUCTION TYPES……….. 10
1.1. The synchronous generator ...................................................................................... 10
1.2. Types of PM generator ............................................................................................ 11
2. DESIGN ASPECTS OF PMG………………………………………………………..17
2.1. Description of the prototype patent (1) .................................................................... 17
2.2. Materials .................................................................................................................. 23
2.3. Finite element magnetic model ................................................................................ 24
3. EXPERIMENTAL RESEARCH OF PMG………………………………………….. 29
3.1. Plan of the experiment ............................................................................................. 29
3.2. Measurement equipment and specifications ............................................................ 31
3.3. Electric schematic explanation ................................................................................ 32
3.4. Analysis of the results .............................................................................................. 35
3.4.1. No-load data analysis......................................................................................... 35
3.4.2. Load data analysis ............................................................................................. 38
4. GRATITUDE………………………………………………………………………... 45
5. CONCLUSIONS…………………………………………………………………….. 46
5.1. Parameters of the PMG and comparison ................................................................. 46
5.2. Material consumptions ............................................................................................. 46
5.3. Experiment characteristics ....................................................................................... 47
RECOMMENDATIONS…………………………………………………………………... 47
REFERENCE………………………………………………………………………………. 48
APPENDIX………………………………………………………………………………… 50
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INTRODUCTION
Relevance of the topic. Classic generators are based on electrical induction or electric
currents and magnetic fields. Each electric machine that uses permanent magnets, can act as a
generator or motor. One of existent problems of manufactured electric generators is that the coil
reactance , the most common, is greater than the active coil resistance . This fact creates
difficulties for designers and operators of generators. The proposed generator or motor should
partially or completely compensate reactance.
The object: Patented PMG prototype with reactance compensated winding.
The aim: Research the type of patented PMG, which is claimed to have significant internal
circuit reactance compensation by winding special coils and construction of before unseen machine.
Tasks:
1. Overview of present PMGs.
2. Review of patented PMG.
3. Prototype design.
4. Construction of prototype.
5. Finite element analysis of magnetic circuits.
6. Conduction of experiments.
7. Achieved data analysis.
Methods. Design aspects are evaluated with the help of literature, scientific articles and patent
analysis of existent PMG technologies. Prototype is designed and drawings are made with
SolidWorks. Magnetic analysis is conducted with FEMM (2D) and EMS add-on for SolidWorks
(3D). Electrical schematics are drawn with EAGLE CAD. Experiments are conducted in Klaipeda
university LAB facilities. Achieved data is analyzed and characteristics plotted with MS Excel.
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1. OVERVIEW OF EXISTENT GENERATOR CONSTRUCTION TYPES
1.1. The synchronous generator
The stator coils are positioned in slots, which are connected in series. The ends of the circuit
thus formed are the generator terminals.
For the rotor, there are 2 types:
salient pole rotor
non-salient pole rotor
Salient pole rotor usually has 4 or more poles.
Non-salient (smooth) pole rotor has 2 or 4 poles.
The coils are connected in series and placed on pole cores. There is an even number of
poles, successive around the wheel, North, South, North, South, etc... The windings of two
consecutive coils are reversed. The rotor is made laminated to reduce induced eddy current (2 p.
20).
1.1. Fig. View of a synchronous AC generator
In a PM generator, the rotor field windings are replaced by permanent magnets which do not
require additional excitation. As the permanent magnets are rotated, current is induced in the stator
windings.
PM generators offer several advantages: they have no rotor windings so they are less
complicated; they have high efficiencies; the gap field flux is not dependent on large pole pitches so
the machine requires less back iron and can have a greater number of smaller poles ; and they
usually require smaller and fewer support systems.
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1.2. Types of PM generator
Radial-flux permanent magnet generator with Internal Rotor (In-runner)
(a) (b)
1.2. Fig. In-runner PMG construction: (a) realistic view, (b) 3D CAD view
A typical radial-flux generator with permanent magnet poles rotating inside stationary
armature windings. The air-gap flux density is closely related to the remanence of the magnet and
the magnet working point (The Working Point is the point on the demagnetization curve where the
value of B & H corresponds to the actual working conditions of the magnet). So it is difficult to get
high air-gap flux densities with low remanence magnets in this configuration. The windings are
placed on the stator in slots, and the magnets are surface mounted on the rotor or buried in the rotor.
In general, the inner rotor machine possesses high torque/power capability, good heat
conduction and cooling properties making it ideal for high-speed, higher-power applications.
It has high efficiency and power/weight ratio (no rotor windings). The disadvantage is that
the magnets have to be implanted carefully so that the rotor does not fly apart (3) (4).
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As an example, a radial-flux permanent magnet generator with Internal Rotor from the
“Alxion” and “MOOG” constructors catalogues are respectively shown below:
1.1. Table. “Alxion” constructors catalogue parameters
The gravimetric power density of this PMG series is from to at a
rated speed of .
1.2. Table. “MOOG” constructors catalogue parameters
The gravimetric power density of this PMG series is from to at a
rated speed of .
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Radial-flux permanent magnet generator with External Rotor (Out-runner)
1.3. Fig. In-runner PMG construction 3D CAD view
As illustrated in figure above, the wound stator inside of external rotor configuration is
stationary, located in the center of the generator, while the magnets are mounted uniformly along
the internal circumference of the rotating drum supported by front and rear bearings.
The radial flux outer rotor machines are commonly used in hard disk drives, small computer
ventilation fans, and some blowers. This type of design is very efficient, low-cost, easy to
manufacture, and applicable for low-power applications such as wind generator. That type of
generator or motor can be driven with higher speeds rather than with internal rotor, because of
centrifugal forces (4) (5).
Axial flux permanent magnet generator
The axial flux machine is significantly different than the previous two because flux flows in
the axial direction vice radial direction and the windings are oriented radially vice axially.
A lot of different topologies exist, but here are some examples:
Double-Stator Slotted Axial-Flux Machine
The machine consists of two external stators and one inner rotor. The permanent magnets
are surface mounted or are embedded in the rotor disc. In all axial flux machines, the rotor rotates
relative to the stator with the flux crossing the air gap in the axial direction. The stator iron core is
laminated in the radial direction (6).
Double Rotor Slotted Axial-Flux Machine
This configuration is similar to that of the double-stator slotted axial-flux machine, except
that there is one stator and two rotors. The stator is located in the middle of the two rotors and
slotted on both sides (6). An example of non-slotted from (7) is shown below:
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1.4. Fig. Non-slotted axial field PMG
Axial-Flux Machine with Toroidal Winding
This kind of prototype generator has a simple construction and is often referred to as a Torus
machine. It is a slotless double-sided axial flux PM disc-typed machine. The two rotor discs are
made of mild steel and have surface-mounted PMs to produce an axially directed magnetic field in
the machine air gaps. The machine stator comprises a slotless toroidally wound strip-iron core that
carries a three-phase winding in a toroidal fashion by means of concentrated coils. The coils have a
rectangular shape according to the core cross section. The axially directed end-winding lengths are
relatively short, yielding low resistance and reduced power loss. The active conductor lengths are
the two radial portions facing the magnets, the polarities of which are arranged to induce additive
electromotive forces (EMFs) around a stator coil (6).
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Here is a prototype of an axial flux PMG (8):
1.5. Fig. Prototype axial flux PMG
By positioning the stator on both sides of the rotor, the magnetic flux on both sides of the
magnet can be utilized. In addition, by piling the rotor and the stator in the direction of the shaft, a
plurality of the air gap can be applied.
1.3. Table. Prototype generator specifications
Rated Power 1
Rated speed 840
No-load EMF 206
Number of rotors 7
Number of poles 12
Rotor size 140x6
Gap between rotors 6
Number of stators 6
Number of coils 9
Stator size 170x4
Number of loops per coil 53
Outside size 182x142
Weight 8,5
Cooling Natural
The gravimetric power density of this prototype at a rated speed of is
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In order to compare, here there is another prototype of an axial flux PMG (9):
1.6. Fig. The structure of the axial flux permanent magnet generators. (1) Stator core holder. (2)
Stator core. (3) Armature winding. (4) Rotor Disk. (5) Permanent Magnet
1.4. Table. Nominal characteristics of constructed TFPMDG
Load current 4
Output power of one module 400
Efficiency 90
Power factor 0,8985
Output power per active mass 0,298
Output power per volume 591
Active outer diameter of one module 166
Active inner diameter of one module, 96
Active thickness of one module, 47
Armature resistance 0,38
Direct synchronous reactance 6,824
Quadrature synchronous reactance 6,808
Output frequency 500
The disk-shaped profile of this prototype makes it very suitable for exploitation in wind
turbines. Also, the disk structure allows high rotational speed due to its ability to counteract
centrifugal forces acting on the permanent magnets.
In conclusion, the advantage of the axial flux model against the radial flux model is that they
can be designed to have a higher power/weight ratio resulting of the less core material and a higher
efficiency. Their disc shaped rotor and stator structure is also an advantage because suitable shape
and size to match the space limitation is crucial for some applications such as electric vehicle.
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Linear tubular permanent magnet generator
The mover of the tubular generator in study consists of iron core rings fixed on a shaft
alternated with permanent magnet rings magnetized in radial direction. They are used as linear
WEC (Wave Energy Converters) generator. An example from (10) is shown below
1.7. Fig. PM wave energy converter generator
2. DESIGN ASPECTS OF PMG
2.1. Description of the prototype patent (1)
In this section a “Hybrid Flux” permanent magnet generator topology with reactance
compensated windings is presented. The flux of this topology travels radially through the rotor and
axially through the stator.
The invention is in the field of generators and motors, and can be adapted to mechanical
rotational motion converting into electrical energy or electrical energy to translate mechanical
rotary motion.
Classic generators are based on electrical induction or electric currents and magnetic fields.
Each electric machine that uses permanent magnets, can act as a generator or motor. One of existent
problems of manufactured electric generators is that the coil reactance , the most common, is
greater than the active coil resistance. This fact creates difficulties for designers and operators of
generators. The proposed generator or motor should partially or completely compensate reactance.
The closest technical solution is the toroidal electric generator or motor, which is described
in the patent application EN 2011 036 (an application filed 2011-04-29). Toroidal generator or
motor proposed “bifilar” type of generator or motor, using “bifilar” (opposite) coil circuit mode.
Toroidal generator or motor magnetic flux passes through the coil windings, which set the air gap
between the magnets and the toroidal core. Air space has a large magnetic resistance; the fact
reduces the generator or motor power. The proposed “bifilar” type generator or motor does not have
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huge air gap between the magnetic core, cores have the ability to connect almost directly to the
magnets. This fact allows increasing the mentioned electrical machinery output.
(The proposed construction of the magnetic field direction changes from radial to axial and
vice versa. This circumstance prevents the coil-generated magnetic field to reach the point where
permanent magnets are demagnetized (coercive force).
Bifilar type generator or motor is constructed in order to reduce inductive coil reactance.
Due to the fact, the machine should give more power when working in the generator mode and
develop more power when working in the motor mode. This is achieved by applying “bifilar” coil
connection method. When the coils are physically separated, the mutual inductance determines the
total inductance of coils. While a current passes through a coil, the current having the same value
but opposite direction, these magnetic fields should partially or completely destroy each other and
hence destroy or decrease the total inductance. This type of generator or motor advantage when
compared to similar electric machines is the fact that each pair of inductive coils reactance is
reduced significantly.
Differences from other prototype are:
1. Type of “bifilar” generator or motor having permanent magnets wherein the coils are set out
at the air gap between the magnets and the core which has the ability to directly connect to
the magnets.
2. Type of “bifilar” generator or motor having permanent magnets, wherein the cores are not
toroidal and straight.
3. Type of “bifilar” generator or motor having permanent magnets is different in that it can
have an unlimited number of ferromagnetic cores.
2.1. Fig. Cross section view of PMG topology
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In figures 2.2–2.3, there is in reality not one but two series of magnets separated by a piece
of epoxy composed supporting slots for the cores [3] and mated to the shaft by a bearing. The Iron
or steel non-laminated core between the opposite pole magnet had been deleted because it was
useless, insignificant magnetic field passing through it, which is changed to radial direction,
differently from figure 2.3.
2.2. Fig. Axial section view of PMG topology
2.3. Fig. Magnetic circuit model of PMG topology
In figures 2.1–2.3 numberings are explained:
1) Magnets;
2) Windings;
3) Ferromagnetic cores;
4) Magnetic flux lines with direction arrow;
5) Iron or steel non-laminated core;
6) Rotor supporting part (non-magnetic);
7) Shaft.
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Stator
As shown in figure 2.4, each coil is wound on ferromagnetic cores [3]. The windings are
wound in one direction, then to the other [2] in order to have a same current with opposite
directions. These compensated windings should in theory limit the reactance. By turning the rotor,
the alternation of magnetic fields in ferromagnetic cores [3] and windings [2] creates an electrical
current. When the machine is operating in the generator mode, the current flowing in coil creates a
magnetic field that opposes the external magnetic field changes.
There are a total of 15 rods each wound with 2 coils. Each phase has 5 rods connected in
series.
2.4. Fig. Single wound rod of PMG topology stator
Rotor
As shown below, different topologies exist for rotor of PM generator or motor:
Surface-mounted magnets
As shown in figure 2.5 (a) the radially magnetized magnets are mounted on the steel-core
rotor structure. The relative permeability of the magnets material being near unity, it acts like a
large air gap. The effective air gap is therefore large, making (direct inductance) low. The
structure is magnetically non salient and thus . And, this topology, because of constant
magnetic gap between rotor and stator, can provide a square wave flux distribution (2 p. 356).
The inset (buried) magnets
For the inset (buried) topology, the magnets are embedded in the rotor steel as shown in
figure 2.5 (b) the construction provide a more secure magnet setting. The advantage is the
possibility to use straight magnets. Another advantage is the possibility to place the magnets to
acquire flux concentration in the air gap. Buried magnet machines can also have significant
structural issues in high-power applications.
The disadvantage is that some flux from the PM’s will ‘leak’ trough the rotor steel. This
means that this flux does not cross the air gap and contribute to the Eddy currents (2 p. 356).
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2.5. Fig. Permanent magnet rotor generator. (a) surface-mounted magnets. (b) Inset (buried)
magnets. (c) Buried magnet with radial magnetization. (d) Buried magnet with circumferential
magnetization (2 p. 355)
Inset (buried) magnet with radial magnetization.
As shown in figure 2.5 (c), the magnets are buried inside the rotor structure with radial
magnetization. For this configuration .
Inset (buried) magnets with circumferential magnetization.
As shown in figure 2.5 (d), the magnets are buried inside the rotor structure with
circumferential magnetization. Because of the flux-focusing effect, circumferential magnetization
yields a greater air gap flux rather than the radial magnetization. The structure is magnetically
salient, becomes large .
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Based on these topologies, it is chosen, that the magnets will be surface-mounted on the
rotor.
On the shaft [7] and the construction parts [5] and [6] are attached with magnets first It
consists of having the opportunity to rotate on its axis, rotor. The magnets [1] are mounted on the
magnetic construction [5].
Magnet poles of one magnet in each queue along the longitudinal axis are mounted in
opposite magnetic fields as shown in figures 2.6 and 2.2.
There are a total of 80 magnets. Each of the two parts of the two rotors is composed of 20 of
them.
2.6. Fig. Surface mounted magnets [1] on the ferromagnetic core [5]
2.7. Fig. 3D isometric view of PMG construction
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2.2. Materials
Magnets
The table below is an average of the magnets characteristics given the amount types of
permanent magnets existing.
2.1. Existing magnet materials and parameters
Magnets Typical
Typical
Typical
Curie
Temperature
Price extra
NdFeB
(sintered) 1,0-1,4 750-2000 200-440 310-400 +++
SmCo 0,8-1,1 600-2000 120-200 720 ++++
Low
temperature
coefficient
NdFeB
(bonded) 0,6-0,7 600-1200 60-100 310-400 ++
Low Eddy-
currents
Alnico 0,6-1,4 275 10-88 700-850 + Low Eddy-
currents
Ferrite 0,2-0,4 100-300 10-40 450 + High knee
point
The permanent magnet NdFeB has been chosen to develop the prototype because it has a
high remanence flux density which means a higher rotor excitation field. Therefore less copper is
needed to induce the same voltage in the windings. The Curie temperature of the NdFeB magnets is
enough for this application.
Between all types of NdFeB magnets, the N45 had been chosen because of a compromise
between prize and remanence (magnetic field). The N45 have a remanence between
tesla, a coercive force and a maximum operating temperature . The N48, 50
and 52 have a higher remanence but they are also much more expensive.
Wood Epoxy Fiber
The epoxy wooden fiber had been chose because it is a strong, cheap and easy to
manufacture material. There are also no eddy currents in those materials. This material is supporting
stator rods, as shown in drawings for Stator Slots and Stator Flanges (pp. 6–7).
Polyethylene
Material for the rotor had been chosen because it is light, so the rotor has less inertia. It is
also easy to manufacture, cheap and it is quite durable. More important, the rotor having no
windings it does not heat so the polyethylene won’t melt.
Wire
The copper wires used for the windings has 1 mm diameter. The choice of those wires had
been done because there were in stock so it was the cheapest way.
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2.3. Finite element magnetic model
A half of this PMG construction is unfolded into linear type and modeled in 2D
environment. Down below cores are shown as poles with wound coils around them and the magnets
from both sides surface mounted on iron plate. Another half of the generator is eliminated, because
it is impossible to have a full model in 2D environment.
2.8. Fig. Magnetic circuit flux lines of PMG topology with double magnets.
This topology has 4 magnets for 3 stator rods or 2 pole pairs for 3 phases. The original plan
was to put 10 permanents magnets on each of the four parts of the rotor. The reason is due to little
magnetic field interacting, if every second magnet from top and bottom is eliminated, there a half
area left for the other magnet pole, while the first one covers a full area flux, which causes high
cogging torques while spinning and only half of the flux from magnets is used. This problem has
been fixed by mounting 20 permanent magnets on each of the four parts of the rotor. With the
configuration, while the one coil faces one pole (north for example), the following two coils face 3
quarters of a south pole and a quarter of a north pole so the electromagnetic force of the coil A is
equal to the electromagnetic force of the coils BC.
2.9. Fig. Magnetic circuit flux lines of PMG topology with less magnets.
TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding
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A magnetic transition between rotor and stator is shown below in steps.
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Step 7
Step n
2.10. Fig. Magnetic circuit flux lines of PMG while moving through steps.
A 3D finite element analysis is made to show relationship between magnets and stator rods.
For that task a 1/5 segment of the generator is cut out and shown below. The numbering is the same
as in figures 2.1–2.3, 2.6.
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2.11. Fig. 1/5 segment of patented PMG active material (3D model front view)
2.12. Fig. 1/5 segment of patented PMG active material (3D top view)
2.13. Fig. Magnetic flux density vector plot (front view)
1 5
1
1 1
3
3
3
2
2
2
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2.14. Fig. Magnetic flux density vector plot (top view)
2.15. Fig. Magnetic flux density continuous fringe plot on several sections: A – cross section of
magnet array, B – cross section of coils
2.16. Fig. Magnetic flux density continuous fringe plot on several sections: C – axial section of core
phase C, D – axial section of core phase A
A
B
D
C
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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)
TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding
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2.19. Fig. Magnetic flux density with applied 3 phase current 10A RMS cross section of first array
of magnets (front view)
3. EXPERIMENTAL RESEARCH OF PMG
3.1. Plan of the experiment
In this part of thesis the plan of experiment is described. Several parameters are measured in
order to get full pictures of real characteristics. The conduction of experiment is described below.
Notice, every abbreviation corresponds to electronic schematic “BCPM Test & Control Circuit”.
Connection and mounting of the system:
1) PMG’s shaft is connected to the driving DC motor with mechanical coupler (G1-
M1);
2) A load block (resistors R, capacitors C, coils L) is connected to the terminals of the
PMG. The method of connection of PMG generating coils and load block is star with
0 wire (Y0-Y0);
3) Connection of measuring devices to circuit:
a. Voltmeter V1 is connected between A0 terminals, alternative AA’.
b. Voltmeter V2 is connected in parallel with armature M1.
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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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c. Each gear switch step, while the lathe is spinning the PM rotor, the stator is
loaded and the measured data is transferred to MS Excel Sheet.
3.2. Measurement equipment and specifications
3.1. Table. Measurement device
Measurement
device Model AC/DC Max scale
Tolerance
class Use
Ampermeter M1500T3
1984 DC 1,5
DC motor
armature
Voltmeter M1600
1979 DC 1,5
DC motor
armature
Multimeter Agilent
U1241A AC/DC 1000V
PMG voltage
and frequency
Multimeter Mastech
MS8222H AC/DC 10A PMG current
3.2. Table. Parameters of driving machines
Driving machine Model Power Gearbox Speed Year
DC motor П-42 7,2
kW No 2800 rpm 1976
Induction motor
– Lathe
Красный
Пролетарий
1K62
10 kW Yes
(Multiple)
1450 rpm
(50, 63, 80, 100, 125, 160, 200,
250, 315, 400) 500, 630
1971
DC motor controlling logic
Used “Arduino Nano V3.0” module, which is manufactured in USA “GRAVITECH”. This
board Bread-Board friendly. A Mini-B USB socket (12).
3.1. Fig. Arduino Nano V3.0
Specifications:
Microcontroller Atmel ATmega328 (8 bit)
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Logic level 5V
Voltage:
o Recommended 7–12V
o Maximum 6–20V
Digital outputs 14 (6 are PWM channels)
Analog inputs 8
Maximum current capabilities 40mA
Memory
o FLASH 32KB (2KB used for boot loader)
o SRAM 2KB
o EEPROM 1KB
Frequency 16MHz
Size
3.3. Electric schematic explanation
In section B2 of the electric schematic drawing, we can see thyristor rectifier. A rectifier is
an electrical device that converts alternating current (AC) to direct current (DC).
In section D5, D6, E5, E6, we can see Gate Driver. A gate driver is a power amplifier that
accepts a low-power input from a controller IC and produces a high-current drive input for the gate
of a high-power transistor such as an IGBT or power MOSFET.
In figure below, the arrows represent the path taking by the current when the transistor T0
(transistor from the opto-coupler 4N35) is open or not.
3.2. Fig. IGBT or MOSFET gate driver working principle
The equivalent circuit in figure 3.3 on the left symbolizes the behavior of the gate driver
when the transistor T0 is opening (red arrows). The transistor T1 is symbolized by a diode
(according to construction of NPN transistor). The transistor IGBT is symbolized by a capacitor and
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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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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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In section C4, there is a temperature sensor LM35. The output voltage is linearly
proportional to the Celsius (Centigrade) temperature.
3.4. Analysis of the results
3.4.1. No-load data analysis
The No Load results of the experiment provide the information of power losses in
mechanical and magnetic (eddy currents) parts, the size of EMF induced.
3.3. Table. Motor current voltage data from A2
( ) 0 0,90 0,93 0,98 1,01 1,04 1,08 1,13 1,16 1,19 1,22
( ) 0 0,90 0,94 0,99 1,02 1,05 1,09 1,13 1,17 1,20 1,23
0,000 0,130 0,165 0,215 0,245 0,275 0,315 0,360 0,395 0,425 0,455
1,26 1,31 1,35 1,39 1,42 1,44 1,48 1,53 1,57 1,60 1,64 1,68
1,27 1,32 1,35 1,39 1,42 1,45 1,49 1,53 1,58 1,61 1,65 1,69
0,495 0,545 0,580 0,620 0,650 0,675 0,715 0,760 0,805 0,835 0,875 0,915
Where: – Mean armature current of the motor;
min, max – Electronic unstable measurement range.
3.1. Equation. Arithmetic mean (14)
∑
Applied arithmetic mean value for the armature current:
( ( ) ( ))
3.4. Table. Motor terminal voltage data from V2
0,0 6,0 7,8 10,2 11,4 12,4 13,9 15,8 17,2 18,4
0,0 6,1 7,9 10,3 11,5 12,5 14,0 15,9 17,3 18,5
0,00 6,05 7,85 10,25 11,45 12,45 13,95 15,85 17,25 18,45
0,00 0,07 0,09 0,12 0,14 0,16 0,18 0,21 0,23 0,24
21,1 22,6 23,7 24,7 25,7 25,6 26,8 28,1 29,1 30,1 31,1
21,1 22,7 23,8 24,8 25,8 25,7 26,9 28,2 29,1 30,2 31,2
21,10 22,65 23,75 24,75 25,75 25,65 26,85 28,15 29,10 30,15 31,15
0,28 0,31 0,33 0,36 0,37 0,39 0,41 0,44 0,46 0,48 0,50
where
– Mean terminal voltage of the motor;
– Armature resistance.
Applied arithmetic mean value for the armature voltage:
TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding
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( ( ) ( ))
3.2. Equation. Ohm's law (15) (16 p. 54) (17)
where
– Resistance in ohms;
– Electric potential difference in volts;
– Electric current in amperes.
Applied Ohm’s law for the armature internal resistance voltage drop:
3.5. Table. PMG terminal EMF frequency data from Hz
0,00 7,52 11,45 15,10 17,18 19,32 22,17 25,58 28,18 29,97 31,99
0,00 7,77 11,52 15,15 17,22 19,27 22,23 25,65 28,22 30,04 32,03
0,000 7,645 11,485 15,125 17,200 19,295 22,200 25,615 28,200 30,005 32,010
33,76 36,15 38,47 40,40 39,48 41,11 42,94 44,53 46,73 33,76 36,15 38,47
33,92 36,24 38,50 40,45 39,42 41,14 42,95 44,77 46,75 33,92 36,24 38,50 33,840 36,195 38,485 40,425 39,450 41,125 42,945 44,650 46,74 33,840 36,195 38,485
Applied arithmetic mean value for the frequency:
( ( ) ( ))
In order to calculate the real mechanical and magnetic losses, we need to subtract Copper losses
from power fed to the motor.
3.3. Equation. Electrical power (18) (17)
where
– Electric charge in coulombs;
– Time in seconds;
Applied electric power equation for fed power:
3.4. Equation. Joule’s first law (heating) (19)
Applied Joule’s first law for copper losses in motor armature:
The mechanical and magnetic losses achieved from:
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Copper losses are insignificant compared to mechanical and magnetic losses.
3.6. Table. Power losses, calculated data
0,00 0,79 1,30 2,20 2,81 3,42 4,39 5,71 6,81 7,84 9,01
0,00 0,01 0,02 0,03 0,03 0,04 0,06 0,07 0,09 0,10 0,12
0,00 0,78 1,28 2,18 2,77 3,38 4,34 5,63 6,72 7,74 8,89
10,44 12,34 13,78 15,35 16,74 17,31 19,20 21,39 23,43 25,18 27,26 29,42
0,14 0,17 0,19 0,22 0,24 0,26 0,29 0,33 0,37 0,40 0,44 0,48
10,30 12,17 13,58 15,12 16,50 17,05 18,90 21,06 23,05 24,78 26,82 28,94
Notice: other shown values are calculated the same way as in the example before.
The curve in figure 3.7 is plotted to show the relationship of power loss and speed, the trend line
equation describes it:
3.7. Fig. Mechanical and magnetic power losses versus frequency as TG signal
The no-load data tables of EMF vs. speed ( ) are placed in appendix tables 0.1 – 0.3. The
plot of the curves is shown in figure 3.8. All the mean value calculations are done using equation
3.1 in MS Excel.
3 plotted curves are shown as a linear relationships and very low difference in figure 3.8. A
trend line is added and equation describing the curve is generated.
3.8. Fig. EMF vs. frequency as AC TG speed signal (OCC)
ΔP(f) = 0,0001f3 + 0,0046f2 + 0,0262f + 0,1773
0
5
10
15
20
25
30
35
0 10 20 30 40 50 60
Po
we
r lo
sse
s , W
Frequency, Hz
Measured
Predicted
E(f) = 6,3244f + 1,1674
0
100
200
300
400
0 10 20 30 40 50 60
EMF,
V
Frequency, Hz
EMF vs Frequency A
EMF vs Frequency B
EMF vs Frequency c
Predicted
TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding
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3.4.2. Load data analysis
Measured data from taken V1, Hz and A1 at different speeds and loads are placed in
appendix (0.4-0.12 tables). The same mean value equation is applied for voltage and current data.
The plot is constructed from raw data to show relationship of output characteristics ( ) at
different speeds. Armature active resistance is per phase.
Due to lack of accuracy in measurements, such as inductance in variable resistors, calculated
characteristics are added for comparison. The calculated parameters are presented in table below.
3.7. Table. The parameters of calculated curves
8,75 11,02 14,14 17,80 22,89 28,80 44,08 56,49 71,11
56,51 70,86 90,59 113,74 145,93 183,31 279,19 357,29 448,90
2,095 2,195 2,250 2,260 2,300 2,315 2,340 2,370 2,365
25,53 31,09 39,31 49,57 62,85 78,70 118,99 150,51 189,61
134,2 183,7 251,4 328,6 442,5 573,5 916,0 1204,6 1529,5
where
– Short circuit current in amperes;
– Synchronous reactance in ohms.
– Useful output power in watts;
Applied formula generated from trend line for EMF calculation:
3.5. Equation. Synchronous impedance using Ohm’s law for AC circuits
3.6. Equation. Reactance calculation from scalar vector formula
√
Relation between synchronous reactance and frequency is plotted in figure 3.9. A
linear trend line is added and equation describing the curve generated. That is stated to show, that
there is no non-linearity in PMG stator circuit.
3.9. Fig. Linear relationship of reactance vs. frequency
Xs (f) = 2,6141f + 3,6992 0
50
100
150
200
0 10 20 30 40 50 60 70 80
Re
acta
nce
, Ω
Frequency, Hz
Calculated
Predicted
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Predicting short circuit current ( ) using correlated values of and .
3.7. Equation. Short circuit current of SG with armature resistance (2 p. 330)
√
Substitute curve equations of EMF and reactance and get
( )
√( )
√
which describes the curve in figure 3.10.
3.10. Fig. Short circuit current vs. speed relationship
3.8. Equation. Vector and scalar representation of terminal voltage based on Kirchhoff’s II law
( ) √ ( )
3.9. Equation. Relation between terminal voltage and load current
( )
described by equation 6.36 from (2 p. 330) if
Substitute of above equations to terminal voltage ( ).
3.10. Equation. Terminal voltage of PMG performance
( ) √ ( ) ( ( ) )
which is used in MS Excel to get results plotted in figure 3.11.
0,0
0,5
1,0
1,5
2,0
2,5
0 10 20 30 40 50 60 70 80
Cu
rre
nt,
A
Frequency, Hz
Predicted
Measured
TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding
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3.11. Fig. Terminal voltage vs. load current performance characteristics at different speeds
(measured and calculated)
An interpolated surface plot is generated to have a better view.
3.12. Fig. Terminal voltage vs. load at different speeds (surface plot)
The curve of independent PMG displays armature voltage fall by quarter ellipse trajectory
because of synchronous reactance of the system as shown in figure 3.13. Measured curves seem
to be lower, because the load resistors have as explained in (2 p. 331), at small
load and short circuit, at .
0
50
100
150
200
250
300
350
400
450
500
0,0 0,5 1,0 1,5 2,0 2,5
Arm
atu
re V
olt
age
, V
Current, A
0,0 0,5 1,0 1,5 2,0 2,5
Current, A
70,80 Hz
56,50 Hz
44,08 Hz
28,80 Hz
22,89 Hz
17,80 Hz
14,14 Hz
11,08 Hz
8,75 Hz
TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding
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3.13. Fig. Performance characteristics of independent synchronous generator: (a) equivalent circuit
diagram; (b) Terminal voltage vs. load current at constant rotating excitation field (2 p. 331)
The power output curves ( ) are calculated from ( ) performance
characteristics.
3.11. Equation. 3 phase electric power of SG
Assuming that , therefore the function describing the curves is:
( ) ( )
This equation is used in MS Excel to get results plotted below:
3.14. Fig. Power output vs. load current performance characteristics at different speeds (measured
and calculated)
Notice that measured curves are slightly lower than the calculated one, which is due to the
load device . Evaluated measured ( ) , while calculated is
( ) (the difference in frequency is insignificant). Maximum
power output points are shown in figure 3.14 for the best performance at different speeds
( )
0
200
400
600
800
1000
1200
1400
1600
0,0 0,5 1,0 1,5 2,0 2,5
Po
we
r, W
Current, A
0,0 0,5 1,0 1,5 2,0 2,5
Current, A
max P
70,80 Hz
56,50 Hz
44,08 Hz
28,80 Hz
22,89 Hz
17,80 Hz
14,14 Hz
11,08 Hz
8,75 Hz
TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding
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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.
3.16. Fig. Efficiency vs. load current performance characteristics at different speeds (measured and
calculated)
All power losses consist of mechanical, magnetic and electric (20 p. 211):
Mechanical losses due to friction in bearings, ventilation.
0
20
40
60
80
100
0,0 0,5 1,0 1,5 2,0 2,5
Effi
cie
ncy
, %
Current, A
0,0 0,5 1,0 1,5 2,0 2,5
Current, A
70,80 Hz
56,50 Hz
44,08 Hz
28,80 Hz
22,89 Hz
17,80 Hz
14,14 Hz
11,08 Hz
8,75 Hz
TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding
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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 ( ).
3.18. Fig. Efficiency vs. load current performance characteristics at different speeds
(before overload)
0
10
20
30
40
50
60
70
80
90
100
0 200 400 600 800 1000 1200 1400 1600 1800
Effi
cie
ncy
, %
Power, W
70,80 Hz 56,50 Hz 44,08 Hz 28,80 Hz 22,89 Hz
17,80 Hz 14,14 Hz 11,08 Hz 8,75 Hz
TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding
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3.19. Fig. Efficiency vs. load current performance characteristics at different speeds
(after overload)
0
10
20
30
40
50
60
70
80
90
100
0 200 400 600 800 1000 1200 1400 1600 1800
Effi
cie
ncy
, %
Output Power, W
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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.
TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding
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5. CONCLUSIONS
5.1. Parameters of the PMG and comparison
In table below parameters of patented and 2 more of reviewed generator types are shown.
5.1. Table. Practical parameters of the PMG topology
Parameters Symbol
Generator types
Fig. 2.7 Fig. 1.5 Table. 1.1.
Table
Load current 1,65 3,2
Output power 1500 2100 1307
Rated speed 840 840 650
No-Load EMF 446 206 390
Voltage at rated power 309 243
Efficiency 92,4 81 76
Rated Power factor 0,69
Total mass 55 8,5 10,4
Output power per active mass 38,4 117,65 125,67
Output power per volume 138
Number of rotors 2 7
Number of poles (pair poles) 20 (10) 12 12(6)
Number of coils 30 9
Number of loops per coil 375 53
Active diameter 150
Rotor inertia 29,58 2,24
Phase armature resistance 8,7 8,6
Phase synchronous reactance 186,7
Phase inductance 442,5 60
Output frequency 70
Cooling Natural Natural Natural
5.2. Material consumptions
5.2. Table. Consumed material quantity
Material Mass, kg Number of pcs. or pkg.
Copper 13 30 coils
Laminated steel 20,7 15 rods 20x25x352
Non-laminated steel 4,4 4 rings, 1 shaft, fasteners
NdFeB N45 magnets 3,3 80
Wood Epoxy Fiber 10,3 5 parts
Polyethylene 1,8 2 cylindroids
Bearings 0,2 3
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5.3. Experiment characteristics
Power no-load losses vs. speed characteristic is a square function of speed (frequency),
which include friction, ventilation and iron losses (induction, eddy currents), at it
reaches of power loss.
No-load EMF vs. speed (frequency) characteristic has linear relationship.
As PMG is loaded, terminal voltage fall by quarter ellipse trajectory due to synchronous
reactance of the system as shown in figure 3.13.
Measured curves seem to be lower due to the load resistors with at small
load and short circuit, at .
Power Output vs. load current measured curves are slightly lower than the calculated one,
which are due to the load device . Measured ( ) ,
while calculated is ( ) . For applications a max power
output points are shown in figure 3.14 for the best performance at different
speeds ( ).
Efficiency covers a large area at different speeds and load currents, at efficiency
almost same ( ) . The bigger the speed, the bigger the load currents available
for higher efficiency, nominal thermal current is the limit, practically ,
, which is preferred to be rated, because magnet’s Curie temperature . The
machine can be driven to produce .
RECOMMENDATIONS
As for the thesis the research is incomplete. This is a bachelor final thesis, which leads to
continuity of scientific works and researches in future. These are the first tests of the
patented BC PMG, which has shown some abstract parameters of a single configuration. A
further development of the PMG and effect of coil configuration analysis is planned during
the summer and master studies.
Future plan for generator:
o Connect different types of loads for more accurate and rich analysis;
o Test different coil configurations;
o Test generator parts separately to discover the effect and describe the difference;
o Make a Simulink MATLAB model;
o Describe in equations and theory.
Preliminary all parameters can be modeled by a special simulation program EMS add-on for
SolidWorks.
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REFERENCE
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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.
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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 Permanent-
Magnet. Gent : s.n.
8. Hideki Kobayashi, Yuhito Doi, Koji Miyata, Takehisa Minowa. Design of the axial-
flux permanent magnet coreless generator for the multi-megawatts wind turbine. Kitago, Echizen-
shi, 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.
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74025 Heilbronn, Germany : Vishay Semiconductors, 6 11, 2012. TCRT1000, TCRT1010
Technical data. 83752.
14. Arithmetic Mean. Wikipedia The Free Encyclopedia. [Online] Wikimedia Foundation
Inc, May 3, 2013. [Cited: May 29, 2013.] https://en.wikipedia.org/wiki/Arithmetic_mean.
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15. Ohm's Law. Wikipedia The Free Encyclopedia. [Online] Wikimedia Foundation, May 3,
2013. [Cited: May 29, 2013.] http://en.wikipedia.org/wiki/Ohm's_law.
16. Millikan, Robert Andrews and Bishop, Edwin Sherwood. Elements of electricity.
Michigan : American Technical Society, 1917.
17. Pukys, Povilas, Stonys, Jonas and Virbalis, Arvydas. Teorinė elektrotechnika.
Elektros grandinių teorijos pagrindai. Kaunas : KTU leidykla Technologija, 2004. ISBN 9955-09-
561-X.
18. Electric Power. Wikipedia The Free Encyclopedia. [Online] Wikimedia Foundation Inc,
May 24, 2013. [Cited: May 29, 2013.] http://en.wikipedia.org/wiki/Electric_power.
19. Joule heating. Wikipedia The Free Encyclopedia. [Online] Wikimedia Foundation Inc,
April 22, 2013. [Cited: 05 29, 2013.] http://en.wikipedia.org/wiki/Joule%27s_first_law.
20. Gečys, Steponas, Kalvaitis, Artūras and Smolskas, Pranas. Elektros mašinos.
Sinchroninės mašinos. Nuolatinės srovės mašinos. [ed.] Rimantas Jonas Mukulys. Kaunas :
Technologija, 2010. Vol. II. ISBN 978-9955-25-774-5.
21. Mellis, David; Arduino. Arduino Nano. Arduino. [Online] Arduino, 8 15, 2009. [Cited:
01 13, 2013.] http://arduino.cc/en/Main/ArduinoBoardNano.
22. Kšanienė, Daiva; KLAIPĖDOS UNIVERSITETO SENATAS. NUTARIMAS DĖL
„KLAIPĖDOS UNIVERSITETO STUDENTŲ SAVARANKIŠKŲ RAŠTO IR MENO DARBŲ
BENDRŲJŲ REIKALAVIMŲ APRAŠO“ PATVIRTINIMO. 11 – 56, Klaipėda : KU Senatas, 4 9,
2010.
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APPENDIX
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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.
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0.1. Table. EMF and frequency data for phase A from V1, Hz
Phase A
Frequency EMF
min max average min max average
6,94 7,02 6,980 42 45 43,5
9,96 10,00 9,980 62 64 63
14,94 14,99 14,965 95 96 95,5
16,40 16,60 16,500 104 107 105,5
19,44 19,45 19,445 124 125 124,5
22,04 22,15 22,095 141 142 141,5
26,06 26,11 26,085 166 168 167
28,26 28,29 28,275 180 182 181
30,03 30,19 30,110 192 193 192,5
31,80 31,84 31,820 203 204 203,5
33,72 33,76 33,740 216 217 216,5
36,76 36,80 36,780 235 236 235,5
39,50 39,93 39,715 252 255 253,5
41,67 41,72 41,695 264 265 264,5
41,8 41,86 41,830 275 277 276,0
43,59 43,61 43,600 276 277 276,5
45,58 45,62 45,600 289 290 289,5
48,06 48,11 48,085 305 306 305,5
50,55 50,62 50,585 322 321 321,5
49,53 49,44 49,485 313 314 313,5
51,00 51,06 51,030 323 324 323,5
52,65 52,71 52,680 333 334 333,5
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0.2. Table. EMF and frequency data for phase B from V1, Hz
Phase B
Frequency EMF
min mat average min max average
7,44 7,58 7,51 46 50 48
11,44 11,48 11,46 72 74 73
15,48 15,53 15,505 98 100 99
17,73 17,79 17,76 113 114 113,5
19,81 19,86 19,835 126 127 126,5
22,45 22,46 22,455 143 144 143,5
25,93 25,96 25,945 165 167 166
28,55 28,58 28,565 182 183 182,5
30,45 30,5 30,475 195 195 195
31,15 31,24 31,195 199 199 199
34,36 34,39 34,375 219,7 220,3 220
36,87 36,93 36,9 226 227 226,5
39,03 39,08 39,055 249 249 249
40,4 40,43 40,415 258 258 258
42,09 42,12 42,105 268 270 269
43,85 43,87 43,86 280,6 280,6 280,6
45,9 45,95 45,925 294 294 294
48,41 48,47 48,44 309 319 314
50,83 50,88 50,855 325 326 325,5
52,95 52,98 52,965 338 338 338
54,7 54,75 54,725 349 349 349
54,14 54,35 54,245 345 346 345,5
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0.3. Table. EMF and frequency data for phase C from V1, Hz
Phase C
Frequency EMF
min max average min max average
8,34 8,38 8,36 53 55 54
11,95 12 11,975 75 77 76
16,58 16,63 16,605 105 107 106
18,12 18,88 18,5 119 120 119,5
20,86 20,92 20,89 132 133 132,5
23,84 23,87 23,855 151 153 152
27,16 27,2 27,18 172 173 172,5
29,61 29,7 29,655 187 190 188,5
31,18 31,21 31,195 198 199 198,5
32,79 32,82 32,805 208 209 208,5
35,1 35,14 35,12 223 224 223,5
37,58 37,62 37,6 240 240 240
40,16 40,37 40,265 256 258 257
41,67 41,7 41,685 265 266 265,5
43,41 43,44 43,425 276 277 276,5
45,2 45,25 45,225 287 288 287,5
43,35 43,41 43,38 275 276 275,5
46,22 46,24 46,23 293 294 293,5
48,42 48,45 48,435 307 307 307
50,32 50,35 50,335 319 319 319
52,12 52,17 52,145 330 330 330
53,89 53,93 53,91 341 342 341,5
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0.4. Table. 8,75 Hz, voltage and current data from Hz, V1, A1
8,75 56,5 56,5 56,51 0 0 0,000
8,75 45,6 46,1 45,85 0,76 0,82 0,790
8,75 44,8 45,3 45,05 0,79 0,84 0,815
8,75 44,2 45,3 44,75 0,82 0,89 0,855
8,75 43,7 44,5 44,10 0,88 0,96 0,920
8,75 42,9 43,2 43,05 0,91 0,99 0,950
8,75 41,8 42,7 42,25 0,99 1,07 1,030
8,75 41,3 42,2 41,75 1,05 1,11 1,080
8,75 39,2 40,2 39,70 1,08 1,16 1,120
8,75 38,1 38,7 38,40 1,13 1,24 1,185
8,75 36,5 37,4 36,95 1,2 1,32 1,260
8,75 35,5 36 35,75 1,28 1,39 1,335
8,75 33,7 34,5 34,10 1,38 1,46 1,420
8,75 31,9 32,5 32,20 1,46 1,58 1,520
8,75 29,9 30,7 30,30 1,54 1,66 1,600
8,75 25,7 26 25,85 1,58 1,71 1,645
8,75 22,4 23 22,70 1,67 1,8 1,735
8,75 19,8 20 19,90 1,76 1,9 1,830
8,75 15,9 16 15,95 1,89 2,01 1,950
8,75 10,3 10,5 10,40 1,85 2,02 1,935
8,75 6,1 6,3 6,20 1,99 2,11 2,050
8,75 0 0 0,00 2 2,19 2,095
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0.5. Table. 11,02 Hz, voltage and current data from Hz, V1, A1
11,02 70,9 70,9 70,86 0 0 0,000
11,02 53,8 54,2 54,00 0,95 0,99 0,970
11,02 53,5 53,5 53,50 0,97 1,01 0,990
11,02 52,28 53 52,64 1,03 1,07 1,050
11,02 51,9 52,2 52,05 1,08 1,1 1,090
11,02 50,8 51,2 51,00 1,1 1,15 1,125
11,02 49,9 50,1 50,00 1,16 1,21 1,185
11,02 48,8 49,1 48,95 1,24 1,27 1,255
11,02 47,6 47,7 47,65 1,27 1,31 1,290
11,02 46,1 46,5 46,30 1,27 1,32 1,295
11,02 44,8 45 44,90 1,34 1,38 1,360
11,02 43,3 43,4 43,35 1,43 1,45 1,440
11,02 41,3 41,4 41,35 1,49 1,53 1,510
11,02 39,4 39,5 39,45 1,55 1,6 1,575
11,02 37,4 37,5 37,45 1,63 1,69 1,660
11,02 34,9 35 34,95 1,7 1,74 1,720
11,02 27,9 28 27,95 1,76 1,77 1,765
11,02 24,4 24,5 24,45 1,82 1,87 1,845
11,02 20,7 20,8 20,75 1,88 1,94 1,910
11,02 16,7 16,8 16,75 1,98 2,04 2,010
11,02 11,3 11,3 11,30 2,04 2,11 2,075
11,02 6,2 6,3 6,25 2,11 2,15 2,130
11,02 2,09 2,09 2,09 2,17 2,22 2,195
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0.6. Table. 14,14 Hz, voltage and current data from Hz, V1, A1
14,14 90,6 90,6 90,59 0 0 0,000
14,14 74,4 74,5 74,45 0,82 0,85 0,835
14,14 73,6 74,2 73,90 0,85 0,88 0,865
14,14 72,8 73,3 73,05 0,9 0,92 0,910
14,14 71,4 72,2 71,80 0,94 0,99 0,965
14,14 71,9 72,3 72,10 1,01 1,04 1,025
14,14 68,7 69,4 69,05 1,07 1,12 1,095
14,14 67,1 67,6 67,35 1,16 1,2 1,180
14,14 63 63,4 63,20 1,2 1,24 1,220
14,14 61 61,1 61,05 1,25 1,31 1,280
14,14 57,8 57,9 57,85 1,33 1,4 1,365
14,14 54,2 54,3 54,25 1,45 1,51 1,480
14,14 53,3 53,4 53,35 1,53 1,58 1,555
14,14 45,5 45,6 45,55 1,66 1,71 1,685
14,14 40 40 40,00 1,8 1,85 1,825
14,14 34,7 34,8 34,75 1,88 1,95 1,915
14,14 30,9 31 30,95 1,79 1,84 1,815
14,14 28,1 28,4 28,25 1,84 1,9 1,870
14,14 24,5 24,5 24,50 1,88 1,95 1,915
14,14 20,4 20,5 20,45 1,95 2,02 1,985
14,14 15,7 15,8 15,75 2,01 2,07 2,040
14,14 11,4 11,5 11,45 2,06 2,11 2,085
14,14 6,7 6,7 6,70 2,09 2,16 2,125
14,14 2,23 2,23 2,23 2,12 2,2 2,160
14,14 0 0 0,00 2,25 2,25 2,250
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0.7. Table 17,80 Hz, voltage and current data from Hz, V1 and A1
17,8 113,7 113,7 113,74 0 0 0,000
17,8 89,9 90 89,95 1,08 1,1 1,090
17,8 88,6 88,7 88,65 1,116 1,125 1,121
17,8 86,6 86,7 86,65 1,17 1,179 1,175
17,8 84,8 84,9 84,85 1,215 1,224 1,220
17,8 81,2 81,3 81,25 1,26 1,26 1,260
17,8 79,9 80 79,95 1,341 1,35 1,346
17,8 76,6 76,7 76,65 1,404 1,413 1,409
17,8 74,3 74,4 74,35 1,476 1,485 1,481
17,8 70,1 70,2 70,15 1,512 1,521 1,517
17,8 66,1 66,2 66,15 1,557 1,566 1,562
17,8 60,9 61 60,95 1,665 1,674 1,670
17,8 55,2 55,3 55,25 1,737 1,746 1,742
17,8 48,9 49 48,95 1,818 1,827 1,823
17,8 42,3 42,4 42,35 1,917 1,944 1,931
17,8 36 36 36,00 1,998 2,007 2,003
17,8 27,9 28 27,95 2,007 2,088 2,048
17,8 19 19,1 19,05 2,142 2,151 2,147
17,8 13,2 13,4 13,30 2,16 2,169 2,165
17,8 4,4 4,6 4,50 2,178 2,196 2,187
17,8 3,3 3,5 3,40 2,196 2,205 2,201
17,8 0 0 0,00 2,25 2,27 2,260
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0.8. Table. 22,89 Hz, voltage and current data from Hz, V1, A1
22,89 145,9 145,9 145,93 0 0 0,000
22,89 132,8 132,8 132,80 0,66 0,66 0,660
22,89 120,9 121 120,95 0,971957 0,971957 0,972
22,89 106,7 106,7 106,70 1,292826 1,292826 1,293
22,89 104,8 104,8 104,80 1,337391 1,337391 1,337
22,89 101,7 101,8 101,75 1,399783 1,399783 1,400
22,89 98,9 99 98,95 1,453261 1,453261 1,453
22,89 95,4 95,4 95,40 1,515652 1,515652 1,516
22,89 91,8 91,8 91,80 1,578043 1,578043 1,578
22,89 87,8 87,9 87,85 1,649348 1,649348 1,649
22,89 84,1 84,2 84,15 1,711739 1,711739 1,712
22,89 78,9 78,9 78,90 1,720652 1,729565 1,725
22,89 73,1 73,2 73,15 1,809783 1,809783 1,810
22,89 66,8 66,9 66,85 1,863261 1,863261 1,863
22,89 59,7 59,7 59,70 1,961304 1,961304 1,961
22,89 51,8 51,8 51,80 2,014783 2,032609 2,024
22,89 43,6 43,7 43,65 2,095 2,103913 2,099
22,89 47,3 47,3 47,30 2,130652 2,139565 2,135
22,89 29,3 29,4 29,35 2,157391 2,166304 2,162
22,89 19,6 19,6 19,60 2,201957 2,21087 2,206
22,89 14,8 14,8 14,80 2,228696 2,237609 2,233
22,89 7,1 7,2 7,15 2,246522 2,255435 2,251
22,89 2,9 3 2,95 2,246522 2,264348 2,255
22,89 0 0 0,00 2,3 2,3 2,300
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0.9. Table. 28,80 Hz, voltage and current data from Hz, V1, A1
28,8 183,3 183,3 183,31 0 0 0,000
28,8 155,0 155,0 155,00 1 1 1,000
28,8 121,9 122 121,95 1,534013 1,531321 1,533
28,8 119,1 119,2 119,15 1,567389 1,564528 1,566
28,8 115,3 115,3 115,30 1,617452 1,61434 1,616
28,8 111,2 111,3 111,25 1,659172 1,664151 1,662
28,8 106,5 106,6 106,55 1,71758 1,722264 1,720
28,8 101,3 101,3 101,30 1,775987 1,772075 1,774
28,8 96,2 96,3 96,25 1,826051 1,830189 1,828
28,8 89,6 89,6 89,60 1,834395 1,838491 1,836
28,8 84,1 84,2 84,15 1,884459 1,88 1,882
28,8 77,6 77,7 77,65 1,942866 1,938113 1,940
28,8 70,9 70,9 70,90 1,984586 1,987925 1,986
28,8 64 64,1 64,05 2,093057 2,095849 2,094
28,8 54,1 54,1 54,10 2,084713 2,087547 2,086
28,8 45,5 45,6 45,55 2,134777 2,129057 2,132
28,8 37,7 37,7 37,70 2,184841 2,18717 2,186
28,8 29,7 29,7 29,70 2,201529 2,203774 2,203
28,8 24,1 24,1 24,10 2,226561 2,228679 2,228
28,8 19,3 19,4 19,35 2,243248 2,245283 2,244
28,8 14,1 14,2 14,15 2,259936 2,261887 2,261
28,8 7,6 7,6 7,60 2,26828 2,270189 2,269
28,8 2,7 2,8 2,75 2,284968 2,278491 2,282
28,8 0 0 0,00 2,31 2,32 2,315
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0.10. Table. 44,00 Hz, voltage and current data from Hz, V1, A1
43,96 279,2 279,2 279,19 0,00 0,00 0,000
43,96 218,4 218,4 218,40 1,16 1,18 1,170
43,96 211,9 212 211,95 1,26 1,27 1,266
43,94 195,8 195,9 195,85 1,42 1,44 1,429
43,94 173,2 173,2 173,20 1,61 1,62 1,616
43,94 146,6 146,7 146,65 1,81 1,83 1,819
43,94 142,4 142,4 142,40 1,84 1,85 1,847
43,96 136,3 136,3 136,30 1,88 1,89 1,886
43,94 129,5 129,6 129,55 1,92 1,93 1,926
43,96 122,9 123 122,95 1,96 1,97 1,966
43,96 115,5 115,6 115,55 1,99 2,01 2,002
43,965 107,5 107,6 107,55 2,03 2,05 2,041
43,985 99,1 99,1 99,10 2,02 2,02 2,022
43,97 91,5 91,6 91,55 2,05 2,06 2,057
43,97 83,3 83,4 83,35 2,08 2,09 2,085
43,98 74,7 74,7 74,70 2,11 2,12 2,113
43,995 65,5 65,6 65,55 2,14 2,15 2,145
44,005 55,5 55,5 55,50 2,18 2,18 2,181
44,02 46,1 46,1 46,10 2,20 2,20 2,197
44,025 38,1 38,1 38,10 2,25 2,25 2,252
44,025 34 34,1 34,05 2,26 2,27 2,264
44,03 28,9 28,9 28,90 2,27 2,27 2,268
44,04 23,8 23,9 23,85 2,28 2,28 2,276
44,04 18,9 19 18,95 2,28 2,28 2,284
44,06 14,1 14,1 14,10 2,29 2,30 2,296
44,07 7,1 7,1 7,10 2,29 2,30 2,296
44,08 2,3 2,3 2,30 2,32 2,32 2,316
44,08 0 0 0,00 2,34 2,34 2,340
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0.11. Table. 56,40 Hz, voltage and current data from Hz, V1, A1
56,31 357,3 357,3 357,29 0,00 0,00 0,000
56,31 261,3 261,3 261,30 1,39 1,39 1,390
56,32 246,5 246,6 246,55 1,49 1,49 1,491
56,315 234,2 234,3 234,25 1,58 1,57 1,573
56,325 222,3 222,4 222,35 1,65 1,65 1,648
56,325 202,9 203 202,95 1,75 1,76 1,756
56,325 181,9 182 181,95 1,87 1,87 1,872
56,345 157,7 157,7 157,70 1,99 1,98 1,984
56,345 151,8 151,8 151,80 2,02 2,01 2,014
56,335 144,2 144,2 144,20 2,04 2,04 2,044
56,335 136,2 136,3 136,25 2,09 2,09 2,089
56,32 128 128,1 128,05 2,12 2,13 2,122
56,35 120 120,1 120,05 2,15 2,16 2,152
56,355 111,8 111,8 111,80 2,18 2,19 2,182
56,355 104,8 104,8 104,80 2,21 2,21 2,208
56,38 102,8 102,8 102,80 2,16 2,16 2,156
56,375 94,8 94,8 94,80 2,18 2,18 2,178
56,395 85,3 85,3 85,30 2,20 2,20 2,201
56,415 75,7 75,7 75,70 2,23 2,23 2,230
56,425 65,7 65,7 65,70 2,25 2,25 2,253
56,425 56,1 56,2 56,15 2,28 2,28 2,275
56,455 46 46 46,00 2,29 2,30 2,294
56,455 38,4 38,5 38,45 2,30 2,30 2,298
56,465 34,6 34,6 34,60 2,32 2,32 2,320
56,475 29,3 29,3 29,30 2,33 2,33 2,328
56,485 24 24 24,00 2,34 2,34 2,335
56,485 19,2 19,2 19,20 2,34 2,35 2,346
56,485 12,7 12,7 12,70 2,35 2,35 2,350
56,485 7,33 7,33 7,33 2,35 2,35 2,350
56,485 0 0 0,00 2,37 2,37 2,370
TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding
63
0.12. Table. 71,90 Hz, voltage and current data from Hz, V1, A1
70,795 448,9 448,9 448,90 0,00 0,00 0,000
70,795 295,5 295,5 295,50 1,59 1,60 1,595
70,795 278,3 278,3 278,30 1,69 1,69 1,690
70,795 245,2 245,3 245,25 1,84 1,85 1,845
70,81 206 206,1 206,05 1,99 1,99 1,990
70,84 164,5 164,5 164,50 2,15 2,15 2,150
70,88 157,4 157,4 157,40 2,18 2,18 2,180
70,875 149,5 149,6 149,55 2,20 2,20 2,200
70,905 141,4 141,4 141,40 2,22 2,22 2,220
70,915 131,6 131,6 131,60 2,24 2,24 2,240
70,915 122,6 122,7 122,65 2,26 2,26 2,260
70,94 113,3 113,3 113,30 2,28 2,28 2,280
70,94 106,3 106,3 106,30 2,29 2,29 2,290
70,95 105,4 105,4 105,40 2,26 2,26 2,260
70,965 97,4 97,4 97,40 2,27 2,27 2,270
70,97 87,4 87,4 87,40 2,29 2,30 2,295
71 77,5 77,6 77,55 2,30 2,31 2,305
71 67,8 67,8 67,80 2,31 2,31 2,310
71,015 57,3 57,3 57,30 2,32 2,33 2,325
71,045 47,1 47,2 47,15 2,33 2,34 2,335
71,035 38,1 38,2 38,15 2,34 2,34 2,340
71,045 34,4 34,4 34,40 2,34 2,34 2,340
71,055 29,2 29,2 29,20 2,35 2,35 2,350
71,08 23,7 23,7 23,70 2,35 2,35 2,350
71,115 18,2 18,2 18,20 2,35 2,35 2,350
71,12 13,2 13,2 13,20 2,35 2,35 2,350
71,135 7,6 7,6 7,60 2,35 2,35 2,350
71,11 2,99 3 3,00 2,35 2,36 2,355
71,11 0 0 0,00 2,36 2,37 2,365
TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding
64
0.13. Table. 8,75 Hz, power, losses, efficiency, power factor calculated data
0,00 0,00 0,89 0,89 0,00 0,00 0,00
36,22 4,99 42,10 0,89 86,03 41,21 44,64 0,923
36,72 5,31 42,92 0,89 85,55 42,03 46,05 0,913
38,26 5,85 45,00 0,89 85,03 44,11 48,31 0,913
40,57 6,77 48,23 0,89 84,12 47,34 51,99 0,911
40,90 7,22 49,01 0,89 83,45 48,12 53,68 0,896
43,52 8,49 52,89 0,89 82,27 52,00 58,20 0,894
45,09 9,33 55,31 0,89 81,52 54,42 61,03 0,892
44,46 10,04 55,39 0,89 80,28 54,50 63,29 0,861
45,50 11,23 57,63 0,89 78,96 56,74 66,96 0,847
46,56 12,70 60,15 0,89 77,41 59,26 71,20 0,832
47,73 14,26 62,87 0,89 75,91 61,98 75,44 0,822
48,42 16,13 65,44 0,89 73,99 64,55 80,24 0,805
48,94 18,48 68,32 0,89 71,64 67,43 85,89 0,785
48,48 20,48 69,85 0,89 69,41 68,96 90,41 0,763
42,52 21,65 65,06 0,89 65,36 64,17 92,95 0,690
39,38 24,08 64,35 0,89 61,20 63,47 98,04 0,647
36,42 26,79 64,10 0,89 56,82 63,21 103,41 0,611
31,10 30,42 62,41 0,89 49,83 61,52 110,19 0,558
20,12 29,95 50,97 0,89 39,48 50,08 109,34 0,458
12,71 33,62 47,22 0,89 26,92 46,33 115,84 0,400
0,00 35,11 36,00 0,89 0,00 35,11 118,38 0,297
TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding
65
0.14. Table. 11,02 Hz, power, losses, efficiency, power factor calculated data
0,00 0,00 1,34 1,34 0,00 0,00 0,00 -
52,38 7,53 61,25 1,34 85,52 59,91 68,74 0,872
52,97 7,84 62,15 1,34 85,23 60,81 70,15 0,867
55,27 8,82 65,43 1,34 84,47 64,09 74,41 0,861
56,73 9,50 67,58 1,34 83,95 66,24 77,24 0,858
57,38 10,13 68,84 1,34 83,35 67,50 79,72 0,847
59,25 11,23 71,82 1,34 82,49 70,48 83,97 0,839
61,43 12,60 75,37 1,34 81,51 74,03 88,93 0,832
61,47 13,31 76,12 1,34 80,75 74,78 91,41 0,818
59,96 13,42 74,71 1,34 80,25 73,37 91,77 0,800
61,06 14,80 77,20 1,34 79,10 75,86 96,37 0,787
62,42 16,59 80,35 1,34 77,69 79,01 102,04 0,774
62,44 18,24 82,02 1,34 76,13 80,68 107,00 0,754
62,13 19,85 83,32 1,34 74,57 81,98 111,61 0,735
62,17 22,04 85,55 1,34 72,67 84,21 117,63 0,716
60,11 23,67 85,12 1,34 70,62 83,78 121,88 0,687
49,33 24,92 75,59 1,34 65,26 74,25 125,07 0,594
45,11 27,23 73,68 1,34 61,22 72,34 130,74 0,553
39,63 29,18 70,16 1,34 56,49 68,82 135,35 0,508
33,67 32,32 67,33 1,34 50,01 65,99 142,43 0,463
23,45 34,45 59,23 1,34 39,59 57,89 147,04 0,394
13,31 36,30 50,95 1,34 26,13 49,61 150,94 0,329
4,59 38,54 44,47 1,34 10,32 43,13 155,54 0,277
TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding
66
0.15. Table. 14,14 Hz, power, losses, efficiency, power factor calculated data
0,00 0,00 2,04 2,04 0,00 0,00 0,00 -
62,17 5,58 69,79 2,04 89,08 67,74 75,65 0,896
63,92 5,99 71,95 2,04 88,84 69,91 78,36 0,892
66,48 6,62 75,14 2,04 88,46 73,10 82,44 0,887
69,29 7,45 78,78 2,04 87,95 76,74 87,42 0,878
73,90 8,41 84,35 2,04 87,61 82,31 92,86 0,886
75,61 9,59 87,25 2,04 86,66 85,20 99,20 0,859
79,47 11,14 92,66 2,04 85,77 90,61 106,90 0,848
77,10 11,91 91,06 2,04 84,68 89,01 110,53 0,805
78,14 13,11 93,30 2,04 83,76 91,25 115,96 0,787
78,97 14,91 95,92 2,04 82,33 93,87 123,66 0,759
80,29 17,52 99,86 2,04 80,40 97,81 134,08 0,730
82,96 19,34 104,35 2,04 79,50 102,30 140,87 0,726
76,75 22,71 101,51 2,04 75,61 99,47 152,65 0,652
73,00 26,65 101,69 2,04 71,79 99,65 165,33 0,603
66,55 29,34 97,93 2,04 67,95 95,88 173,49 0,553
56,17 26,35 84,57 2,04 66,42 82,53 164,43 0,502
52,83 27,98 82,85 2,04 63,76 80,80 169,41 0,477
46,92 29,34 78,30 2,04 59,92 76,26 173,49 0,440
40,59 31,52 74,16 2,04 54,74 72,12 179,83 0,401
32,13 33,29 67,47 2,04 47,62 65,42 184,81 0,354
23,87 34,78 60,70 2,04 39,33 58,65 188,89 0,311
14,24 36,13 52,41 2,04 27,17 50,36 192,51 0,262
4,82 37,32 44,19 2,04 10,90 42,14 195,68 0,215
0,00 40,50 42,54 2,04 0,00 40,50 203,84 0,199
TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding
67
0.16. Table. 17,8 Hz, power, losses, efficiency, power factor calculated data
0,00 0,00 3,03 3,03 0,00 0,00 0,00 -
98,05 9,50 110,58 3,03 88,66 107,55 123,98 0,867
99,33 10,04 112,41 3,03 88,37 109,38 127,45 0,858
101,77 11,04 115,84 3,03 87,86 112,81 133,59 0,844
103,47 11,90 118,40 3,03 87,39 115,37 138,71 0,832
102,38 12,70 118,11 3,03 86,68 115,08 143,31 0,803
107,57 14,48 125,09 3,03 86,00 122,06 153,04 0,798
107,96 15,87 126,86 3,03 85,10 123,83 160,21 0,773
110,08 17,54 130,64 3,03 84,26 127,61 168,39 0,758
106,38 18,40 127,81 3,03 83,23 124,78 172,49 0,723
103,29 19,51 125,83 3,03 82,09 122,80 177,61 0,691
101,76 22,30 127,09 3,03 80,07 124,05 189,89 0,653
96,22 24,26 123,51 3,03 77,90 120,48 198,08 0,608
89,21 26,57 118,82 3,03 75,08 115,78 207,29 0,559
81,76 29,81 114,60 3,03 71,34 111,57 219,58 0,508
72,09 32,08 107,20 3,03 67,25 104,17 227,77 0,457
57,23 33,54 93,80 3,03 61,01 90,77 232,89 0,390
40,89 36,86 80,78 3,03 50,62 77,75 244,15 0,318
28,79 37,48 69,30 3,03 41,54 66,27 246,19 0,269
9,84 38,26 51,14 3,03 19,25 48,11 248,75 0,193
7,48 38,74 49,25 3,03 15,19 46,22 250,29 0,185
0,00 40,86 43,89 3,03 0,00 40,86 257,06 0,159
TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding
68
0.17. Table. 22,89 Hz, power, losses, efficiency, power factor calculated data
0,00 0,00 4,91 4,91 0,00 0,00 0,00 -
87,65 3,48 96,04 4,91 91,26 91,13 96,32 0,946
117,56 7,56 130,03 4,91 90,41 125,12 141,84 0,882
137,94 13,37 156,23 4,91 88,30 151,32 188,67 0,802
140,16 14,31 159,38 4,91 87,94 154,47 195,17 0,791
142,43 15,68 163,01 4,91 87,37 158,10 204,27 0,774
143,80 16,90 165,61 4,91 86,83 160,70 212,08 0,758
144,59 18,38 167,88 4,91 86,13 162,97 221,18 0,737
144,86 19,92 169,70 4,91 85,37 164,79 230,29 0,716
144,90 21,76 171,57 4,91 84,45 166,66 240,69 0,692
144,04 23,44 172,39 4,91 83,55 167,48 249,80 0,670
136,11 23,81 164,83 4,91 82,58 159,92 251,75 0,635
132,39 26,20 163,50 4,91 80,97 158,59 264,11 0,600
124,56 27,77 157,24 4,91 79,21 152,33 271,91 0,560
117,09 30,77 152,77 4,91 76,64 147,86 286,22 0,517
104,83 32,76 142,50 4,91 73,56 137,59 295,32 0,466
91,64 35,26 131,81 4,91 69,52 126,90 306,38 0,414
100,99 36,47 142,37 4,91 70,94 137,46 311,58 0,441
63,45 37,39 105,75 4,91 60,00 100,84 315,48 0,320
43,25 38,95 87,10 4,91 49,65 82,19 321,99 0,255
33,05 39,90 77,86 4,91 42,45 72,95 325,89 0,224
16,09 40,54 61,54 4,91 26,15 56,63 328,49 0,172
6,65 40,70 52,26 4,91 12,73 47,35 329,14 0,144
0,00 42,32 47,23 4,91 0,00 42,32 335,65 0,126
TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding
69
0.18. Table. 28,80 Hz, power, losses, efficiency, power factor calculated data
0,00 0,00 8,41 8,41 0,00 0,00 0,00 -
155,00 8,00 171,41 8,41 90,42 163,00 183,31 0,889
186,91 18,79 214,11 8,41 87,29 205,70 280,95 0,732
186,58 19,62 214,62 8,41 86,94 206,20 287,06 0,718
186,31 20,89 215,62 8,41 86,41 207,20 296,21 0,700
184,86 22,09 215,36 8,41 85,84 206,95 304,60 0,679
183,26 23,67 215,34 8,41 85,10 206,92 315,28 0,656
179,71 25,18 213,30 8,41 84,25 204,89 325,20 0,630
175,96 26,74 211,11 8,41 83,35 202,69 335,11 0,605
164,55 26,98 199,94 8,41 82,30 191,53 336,64 0,569
158,39 28,34 195,15 8,41 81,16 186,73 345,03 0,541
150,68 30,12 189,22 8,41 79,63 180,80 355,71 0,508
140,83 31,56 180,80 8,41 77,89 172,39 364,10 0,473
134,15 35,09 177,66 8,41 75,51 169,24 383,93 0,441
112,86 34,82 156,09 8,41 72,30 147,68 382,41 0,386
97,11 36,36 141,88 8,41 68,44 133,47 390,80 0,342
82,41 38,23 129,06 8,41 63,86 120,64 400,72 0,301
65,42 38,81 112,65 8,41 58,07 104,23 403,77 0,258
53,69 39,70 101,80 8,41 52,74 93,38 408,35 0,229
43,43 40,29 92,13 8,41 47,13 83,72 411,40 0,204
31,99 40,89 81,30 8,41 39,35 72,89 414,45 0,176
17,25 41,20 66,86 8,41 25,80 58,44 415,97 0,140
6,27 41,65 56,34 8,41 11,14 47,93 418,26 0,115
0,00 42,87 51,29 8,41 0,00 42,87 424,36 0,101
TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding
70
0.19. Table. 44,00 Hz, power, losses, efficiency, power factor calculated data
0,00 0,00 29,48 29,48 0,00 0,00 0,00 -
255,53 10,95 295,96 29,48 86,34 266,48 326,65 0,816
268,22 12,81 310,51 29,48 86,38 281,04 353,32 0,795
279,80 16,33 325,56 29,43 85,94 296,13 398,86 0,742
279,84 20,88 330,16 29,43 84,76 300,73 451,09 0,667
266,70 26,46 322,60 29,43 82,67 293,16 507,74 0,577
262,95 27,28 319,66 29,43 82,26 290,22 515,53 0,563
257,11 28,47 315,05 29,48 81,61 285,57 526,64 0,542
249,53 29,68 308,64 29,43 80,85 279,21 537,75 0,519
241,71 30,92 302,11 29,48 80,01 272,63 548,86 0,497
231,30 32,05 292,83 29,48 78,99 263,35 558,85 0,471
219,56 33,34 282,39 29,49 77,75 252,90 569,96 0,444
200,34 32,70 262,57 29,53 76,30 233,04 564,42 0,413
188,36 33,86 251,72 29,50 74,83 222,22 574,41 0,387
173,81 34,79 238,10 29,50 73,00 208,60 582,19 0,358
157,85 35,72 223,09 29,52 70,76 193,57 589,96 0,328
140,60 36,81 206,96 29,55 67,94 177,41 598,85 0,296
121,04 38,05 188,65 29,57 64,16 159,08 608,86 0,261
101,27 38,61 169,48 29,60 59,75 139,87 613,30 0,228
85,82 40,59 156,02 29,61 55,00 126,41 628,86 0,201
77,10 41,02 147,73 29,61 52,19 118,12 632,18 0,187
65,56 41,16 136,34 29,62 48,08 106,72 633,30 0,169
54,29 41,45 125,39 29,65 43,30 95,74 635,52 0,151
43,29 41,74 114,68 29,65 37,75 85,03 637,75 0,133
32,38 42,18 104,24 29,69 31,06 74,56 641,07 0,116
16,30 42,18 88,19 29,71 18,49 58,48 641,07 0,091
5,33 42,92 77,97 29,73 6,83 48,24 646,63 0,075
0,00 43,80 73,54 29,73 0,00 43,80 653,30 0,067
TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding
71
0.20. Table. 56,40 Hz, power, losses, efficiency, power factor calculated data
0,00 0,00 62,27 62,27 0,00 0,00 0,00 -
363,21 15,46 440,94 62,27 82,37 378,66 496,64 0,762
367,57 17,78 447,65 62,30 82,11 385,35 532,76 0,723
368,48 19,80 450,57 62,29 81,78 388,28 562,08 0,691
366,37 21,72 450,41 62,32 81,34 388,09 588,88 0,659
356,40 24,67 443,39 62,32 80,38 381,07 627,60 0,607
340,59 28,03 430,94 62,32 79,03 368,62 668,98 0,551
312,86 31,49 406,73 62,38 76,92 344,35 709,28 0,485
305,70 32,44 400,52 62,38 76,32 338,14 719,97 0,470
294,70 33,41 390,46 62,35 75,47 328,11 730,52 0,449
284,56 34,90 381,81 62,35 74,53 319,46 746,55 0,428
271,74 36,03 370,07 62,30 73,43 307,77 758,37 0,406
258,35 37,05 357,80 62,40 72,21 295,40 769,45 0,384
243,94 38,09 344,44 62,41 70,82 282,02 780,21 0,361
231,40 39,00 332,82 62,41 69,53 270,41 789,55 0,342
221,61 37,18 321,28 62,49 68,98 258,79 771,19 0,336
206,49 37,96 306,92 62,47 67,28 244,45 779,14 0,314
187,71 38,74 288,98 62,53 64,96 226,45 787,44 0,288
168,85 39,80 271,24 62,59 62,25 208,65 798,41 0,261
148,01 40,60 251,24 62,63 58,91 188,62 806,58 0,234
127,76 41,42 231,80 62,63 55,12 169,17 814,60 0,208
105,52 42,10 210,34 62,72 50,17 147,62 821,73 0,180
88,35 42,24 193,30 62,72 45,70 130,58 823,06 0,159
80,28 43,06 186,09 62,75 43,14 123,34 831,24 0,148
68,20 43,34 174,32 62,78 39,12 111,54 834,06 0,134
56,04 43,62 162,47 62,81 34,49 99,66 836,89 0,119
45,05 44,04 151,90 62,81 29,66 89,09 840,91 0,106
29,85 44,18 136,83 62,81 21,81 74,03 842,24 0,088
17,23 44,18 124,21 62,81 13,87 61,41 842,24 0,073
0,00 44,94 107,74 62,81 0,00 44,94 849,41 0,053
TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding
72
0.21. Table. 70,90 Hz, power, losses, efficiency, power factor calculated data
0,00 0,00 101,67 101,67 0,00 0,00 0,00 -
471,32 20,35 593,35 101,67 79,43 491,67 716,00 0,687
470,33 22,85 594,85 101,67 79,07 493,18 758,65 0,650
452,49 27,23 581,39 101,67 77,83 479,72 828,23 0,579
410,04 31,68 543,42 101,70 75,46 441,72 893,51 0,494
353,68 36,98 492,40 101,75 71,83 390,66 965,75 0,405
343,13 38,02 482,97 101,81 71,05 381,15 979,78 0,389
329,01 38,72 469,54 101,81 70,07 367,73 988,70 0,372
313,91 39,43 455,19 101,86 68,96 353,34 998,11 0,354
294,78 40,14 436,80 101,87 67,49 334,92 1007,24 0,333
277,19 40,86 419,92 101,87 66,01 318,05 1016,24 0,313
258,32 41,59 401,82 101,91 64,29 299,91 1025,59 0,292
243,43 41,95 387,29 101,91 62,85 285,38 1030,09 0,277
238,20 40,86 380,99 101,93 62,52 279,06 1016,74 0,274
221,10 41,22 364,27 101,95 60,70 262,32 1021,45 0,257
200,58 42,14 344,68 101,96 58,19 242,72 1032,77 0,235
178,75 42,50 323,27 102,01 55,30 221,26 1037,71 0,213
156,62 42,69 301,32 102,01 51,98 199,31 1039,96 0,192
133,22 43,25 278,50 102,04 47,84 176,47 1046,94 0,169
110,10 43,62 255,80 102,08 43,04 153,71 1051,88 0,146
89,27 43,80 235,14 102,07 37,96 133,08 1053,99 0,126
80,50 43,80 226,38 102,08 35,56 124,30 1054,13 0,118
68,62 44,18 214,90 102,10 31,93 112,80 1058,79 0,107
55,70 44,18 202,01 102,14 27,57 99,88 1059,16 0,094
42,77 44,18 189,15 102,20 22,61 86,95 1059,68 0,082
31,02 44,18 177,40 102,20 17,49 75,20 1059,75 0,071
17,86 44,18 164,27 102,23 10,87 62,04 1059,98 0,059
7,05 44,37 153,61 102,19 4,59 51,42 1061,86 0,048
0,00 44,75 146,93 102,19 0,00 44,75 1066,37 0,042