Bachelor's Thesis

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 2013 Boris Rudnickij 2013

Authors: TEI-09 Oleg Lyan HENALLUX Vincent Monet 2013

Klaipėda, 2013 TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding 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.

TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding 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 4

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 ...... 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

TEI-09, O.Lyan, V.Monet 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

TEI-09, O.Lyan, V.Monet 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

TEI-09, O.Lyan, V.Monet 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

TEI-09, O.Lyan, V.Monet 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.

TEI-09, O.Lyan, V.Monet 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.

TEI-09, O.Lyan, V.Monet 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).

TEI-09, O.Lyan, V.Monet 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 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 .

TEI-09, O.Lyan, V.Monet 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:

TEI-09, O.Lyan, V.Monet 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).

TEI-09, O.Lyan, V.Monet 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 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

TEI-09, O.Lyan, V.Monet 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 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.

TEI-09, O.Lyan, V.Monet 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

TEI-09, O.Lyan, V.Monet 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 18

TEI-09, O.Lyan, V.Monet 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.

TEI-09, O.Lyan, V.Monet 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 (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).

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

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 .

TEI-09, O.Lyan, V.Monet 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

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 Typical Typical Magnets Temperature Price extra

NdFeB 1,0-1,4 750-2000 200-440 310-400 +++ (sintered) Low SmCo 0,8-1,1 600-2000 120-200 720 ++++ temperature coefficient NdFeB Low Eddy- 0,6-0,7 600-1200 60-100 310-400 ++ (bonded) currents Low Eddy- Alnico 0,6-1,4 275 10-88 700-850 + currents High knee Ferrite 0,2-0,4 100-300 10-40 450 + 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.

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. 24

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.

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

2 3 3

1 1 2 3 1 5 1

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)

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)

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 (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. 29

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.

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 Tolerance Model AC/DC Max scale Use device class M1500T3 DC motor Ampermeter DC 1,5 1984 armature M1600 DC motor Voltmeter DC 1,5 1979 armature Agilent PMG voltage Multimeter AC/DC 1000V U1241A and frequency Mastech Multimeter AC/DC 10A PMG current MS8222H

3.2. Table. Parameters of driving machines

Driving machine Model Power Gearbox Speed Year 7,2 DC motor П-42 No 2800 rpm 1976 kW Красный 1450 rpm Induction motor Yes Пролетарий 10 kW (50, 63, 80, 100, 125, 160, 200, 1971 – Lathe (Multiple) 1K62 250, 315, 400) 500, 630

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)

TEI-09, O.Lyan, V.Monet Research of PMG with compensated reactance winding  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 32

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.

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. 34

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

( ) 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: 35

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 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: 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

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:

25 20 ΔP(f) = 0,0001f3 + 0,0046f2 + 0,0262f + 0,1773 15 Measured

10 Predicted Power losses , W 5 0 0 10 20 30 40 50 60 Frequency, Hz

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.

400

300

EMF vs Frequency A 200

EMF vs Frequency B EMF, EMF, V 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) 37

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 ( ) 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.

200

Ω 150 100 Calculated 50

Reactance, Xs (f) = 2,6141f + 3,6992 Predicted 0 0 10 20 30 40 50 60 70 80 Frequency, Hz

3.9. Fig. Linear relationship of reactance vs. frequency

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

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.

2,5

2,0

1,5

Predicted

Current,A 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.

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

500 450 70,80 Hz

400 56,50 Hz 350 300 44,08 Hz 250 28,80 Hz 200 22,89 Hz 150 17,80 Hz Armature Voltage, V 100 50 14,14 Hz 0 11,08 Hz 0,0 0,5 1,0 1,5 2,0 2,5 0,0 0,5 1,0 1,5 2,0 2,5 8,75 Hz Current, A 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 as explained in (2 p. 331), at small load and short circuit, at .

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 1200 56,50 Hz 1000 44,08 Hz 800 28,80 Hz

Power,W 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 0,5 1,0 1,5 2,0 2,5 11,08 Hz Current, A Current, A 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

80 56,50 Hz

44,08 Hz 60 28,80 Hz 40

22,89 Hz Efficiency, Efficiency, % 20 17,80 Hz 14,14 Hz 0 0,0 0,5 1,0 1,5 2,0 2,5 0,0 0,5 1,0 1,5 2,0 2,5 11,08 Hz Current, A Current, A 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.

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

60 50

40 Efficiency, Efficiency, % 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 22,89 Hz 17,80 Hz 14,14 Hz 11,08 Hz 8,75 Hz

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

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

100 90 80

60 50

40 Efficiency, Efficiency, % 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)

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.

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

Generator types Parameters Symbol Fig. 1.5 Table. 1.1. Fig. 2.7 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

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 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.

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 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. 12. Mellis, David; Arduino. Arduino Nano. Arduino. [Tinkle] Arduino, 2009 m. 8 15 d. [Cituota: 2013 m. 01 13 d.] http://arduino.cc/en/Main/ArduinoBoardNano. 13. Vishay Semiconductors. Reflective Optical Sensor with Transistor Output. 1.8, D- 74025 Heilbronn, Germany : Vishay Semiconductors, 6 11, 2012. TCRT1000, TCRT1010 Technical data. 83752. 14. Arithmetic Mean. Wikipedia The Free Encyclopedia. [Online] Wikimedia Foundation Inc, May 3, 2013. [Cited: May 29, 2013.] https://en.wikipedia.org/wiki/Arithmetic_mean.

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 9955-09- 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.

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

APPENDIX

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.

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 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

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 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

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 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

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 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

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 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

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 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

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

17,8 113,7 113,7 113,74 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

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

22,89 145,9 145,9 145,93 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

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

28,8 183,3 183,3 183,31 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

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

43,96 279,2 279,2 279,19 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

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

56,31 357,3 357,3 357,29 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 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 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 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 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 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 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 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 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 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 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