SLOTLESS, TOROIDAL WOUND, AXIALLY- MAGNETIZED PERMANENT MAGNET GENERATOR FOR SMALL WIND TURBINE SYSTEMS

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1 SLOTLESS, TOROIDAL WOUND, AXIALLY- MAGNETIZED PERMANENT MAGNET GENERATOR FOR SMALL WIND TURBINE SYSTEMS S.E. Skaar, O. Krovel, R. Nilssen and H. Erstad Department of Electrical Power Engineering Norwegian University of Science and Technology Abstract A toroidal wound three phase axially-magnetized, disc type, permanent magnet generator is presented in this paper. For a novel wind turbine application the generator must have a low reluctance torque and need to be direct-driven to reduce mechanical losses in the application. For this purpose the stator winding is wound around a slotless ring core. The rotor disc has 8 surface mounted magnet poles. A test of a proto type generator will be presented.. INTRODUCTION Along the long coastline of Norway lighthouses and smaller light signals used extensively. In the modern society automated lights are chosen to reduce cost. At the time the only good alternative for supplying power to the lighthouses are solar cells. This becomes a problem with the light conditions at the Norwegian coast. At the northern latitudes there is polar night with no sunlight for over two months at winter time, and limited sunlight for the rest of the winter. To overcome this obstacle the battery bank has to be fully charged during summer time, and be dimensioned to supply the lighthouse, without charging, throughout the polar night. An alternative to solar cells is wind power. Small conventional horizontal axial wind turbines along the coastline have proven to fail from the stress of high- and turbulent wind forces. Consequently, the need for a robust vertical axial wind turbine was stated. Such turbines are more expensive but may become very robust. These turbines are independent on wind direction and do not have to align up against the wind. A new generator to be used in this application is needed. The generator is direct-driven to reduce mechanical losses in transmission. The application concept and the generator are fully presented in []. A toroidal, axially-magnetized permanent generator concept was chosen. The generator must charge a 2 V battery bank and supply power to the light bulb. Figure. Generator concept 2. DESIGN OF GENERATOR When designing the generator, required rated power, voltage and wind speed for start of charging was chosen as main design parameters. In the following sections calculation of induced voltage, flux distribution and

2 harmonics from winding configuration will be presented. 2. Induced voltage The generator is designed as a disc type machine. Permanent magnets (NdFeB) on the rotor discs are placed with poles facing every other way giving a flux path shown in figure. The generator is designed to charge at rated power at a wind speed of 6 m/s. The generator has 8 poles on each of the rotor discs, and was designed for a rated speed of 230 rpm which results in an electrical frequency of approximately 34 Hz. Figure is only is a principal sketch of the machine. It does not show true magnet size nor the right number of coils pr. pole. In the actual machine the number of coils pr. pole are three. In the sketch the windings are shown as square and circulare conductors to indicate the changing winding direction needed to produce torque in the machine. In slotless machines, there should be no worries on slot harmonics in the design. A wound ring in centre of the machine may give a fixation problem towards the shaft. To solve this problem the machine was given 54 slots (teeth made of pressboard), whereas the term slot here would be the actual space where the coil is wound, and only 5 of these were wounded slots. This gives the machine 5 distributed coils to constitute the three phases. One coil covers a sector of 6 2/3º leaving three empty, unwound spaces to provide mechanical fix of the stator disc to the shaft. The three empty spaces can not be made with a somehow symmetric 20º angular displacement on the core, as this would lead to a cancellation of three coils in the same phase. The displacement was chosen to be at 0º, 26,67º and 233,33º, or slot number, 20 and 36. Each of the empty spaces cancels one coil in each of the three phases. From [2] induced fundamental phase voltage is calculated by: Emax 2π Ns Erms = = N f Φ max () N ph N is number of turn pr. coil, N s number of slots and N ph is number of phases. f is electric frequency and Φ max is peak value of the fundamental flux from the magnets, calculated from: Φ max = Amagn Bmax (2) where B max is maximum fundamental air gap flux density from the magnets. The magnet area is calculated by: π ( ro ri ) τ f ( ro ri) Nm Amagn = (3) Nm where r o is outer and r i is inner magnet radius, τ f is spacing between magnets and N m is number of magnets. Air gap flux density is calculated by: B lm max = B r (4) l δ m + B r is the remanent flux density of the magnet, l m is the magnet length and δ is the air gap length between one rotor disc and stator disc. This would give a rather optimistic value of the air gap flux density. To get a more realistic value an empirical correction factor of 0.75 is used. The air gap of the machine consists of the area needed for the copper winding and a small physical air gap to make clearing between rotor and stator. This air gap should be minimized to achieve maximum air gap flux density. The total air gap (including winding region) is 4 mm and the magnet thickness is 8 mm. This results a theoretical flux density in the air gap of 0.8 T. After correcting this value with the correction factor a maximum air gap flux density of 0.6 T is given. Using the inner and outer radius from table I the calculated magnet area becomes 7.7*0-4 m 2 and maximum flux from each magnet of 4.62*0-4 Wb. Using () the number of turns to provide the needed charging voltage can be calculated. For this machine 8 turns will induce high enough voltage. The voltage will be 9.5 V pr phase, with a line voltage of 6.5 V. Using a diode rectifier, the DC-voltage [3] becomes: Udc =.35Uac (5) This indicates a possible rectified voltage of 22.2 V Outer radius r o [mm] 92 Inner radius r i [mm] 59 Magnet spacing τ f [mm] 3 Number of magnets N m 8 Number of coils N s 5 Number of phases N ph 3 Magnet thickness l m [mm] 8 Air gap δ [mm] 4 Table I. Machine data 2.2 Flux distribution To verify the assumption of the air gap flux density, a 2D model of the machine was generated in FEMLAB TM. Three cross-section models were made with radiuses r o, r i and r m. Result of the middle cross-section is shown in figure 2. In this model saturation of iron is not taken into account. The parts of the machine being most

3 magnetically stressed are the yoke between the magnets. In figure 2 these areas has a reddish colour. Figure 2. Flux density in the middle section of the machine The most stressed areas will only lightly saturate. A graph of the flux density from one magnet in the middle of the air gap was obtained by using FEM calculations. The flux density is presented in figure 3. From the FEM calculation the assumption of an air gap flux density of 0.6 T seems to be reasonable. The models of the magnet at outer and inner radius both gave simular results. From this it would be fair to assume the model from the middle of the machine would describe the field satisfactorily. From an optimization point of view the end-effects should be taken into consideration. However this was not done in this case. 2.3 Harmonic components In [2] the fundamental flux value is used in the induced voltage calculation. Later in this paper measurement will show how small the contributions of sub-harmonics are compared to the fundamental component in the induced voltage. From [2] both distribution factor and coil-span factor must be taken into account when estimating the phase e.m.f. The distribution factor for the fundamental component from a phase spread of 60º is using: sin σ sin nσ k m = and kmn = (6) g 'sin ( σ / g') g'sin ( nσ / g') where g is the number of coils pr phase and σ the phase spread. From this the 5 th harmonic is 0.92 and the 7 th harmonic Figure 3. Flux density in the middle section of the machine The coil-span factor is given by: ke = cos ε and ken = cos nε (7) where ε is the chording angel obtained from shortpitching the winding. In this machine there is no shortpitch and the chording angel is 0º. Resulting winding factor is: Kwn = kmnken (8) where k en is for any n. The harmonic contribution of the e.m.f. can now be calculated by: Kwn Bn E = phn Eph Kw B (9) The values of B and B n are obtained from doing a harmonic analysis of the field. From [2] the analytical expression for this analysis is: B =.086 b+.67 b b b b5 +.67b6 (0) B5 =.323 b.67 b2.236 b b b5.67b6 In (0) the b-values are calculated by: l b = 00 g () l where l g is the gap length from where the flux lines leaves and enters iron and l is the length of the flux line. Using this analysis with approximated values for the b s gives the expression: Eph5 = 0.052Eph (2) (2) give an indication of the level of the 5 th harmonic e.m.f. The higher harmonics are not calculated since these would give even smaller contributions. The low value from (2) is the reason for using the fundamental flux value when calculating induced voltage.

3. PROTO TYPE BUILDING The generator stator consists of a ring core with thickness 0 mm. On each side of the core a 3 mm thick pressboard was glued.

A picture of the stator after casting is shown in figure 4. Figure 6. Assembled generator prototype A HMB Torque Transducer connected between the two machines measured the shaft torque.

The oscilloscope was connected to MatLab TM on a computer, providing an easy data processing of the measurements and curve forms.

4 3. PROTO TYPE BUILDING The generator stator consists of a ring core with thickness 0 mm. On each side of the core a 3 mm thick pressboard was glued. 6 mm straight slots for placing the winding were then milled out. After the stator was wound the ring core with windings and the shaft was cast in epoxy. A picture of the stator after casting is shown in figure 4. Figure 6. Assembled generator prototype A HMB Torque Transducer connected between the two machines measured the shaft torque. A Tektronix TDS204 oscilloscope was used to measure induced voltage and to record curve forms. The oscilloscope was connected to MatLab TM on a computer, providing an easy data processing of the measurements and curve forms. For the harmonic analysis a MatLab TM function using a true Fourier's analysis (TFA) was used. Figure 4. Stator disc and shaft cast in epoxy The rotor discs yoke are made of solid steel. A picture of one rotor disk with the magnets is shown in figure 5. A picture of the prototype machine is presented in figure 6. The proto type has an overall diameter of 200 mm and a length of 55 mm, -shafts not included. The generator was tested at no load, with a speed of 230 rpm giving an electrical frequency of 34 Hz. The phase voltage rms value was measured to 7.74 V. This indicates the correction factor of 0.75 used with the calculation is to large. From the measured voltage it should indicate an average flux density in the air gap of 0.5 T, giving a correction factor of Still, the induced voltage is satisfactory for the purpose of charging the battery bank. Figure 5. Rotor disc with magnets 4. GENERATOR TESTS The generator was tested in our laboratory. A 9.3kW DC-machine was connected to the shaft as a drive unit. Figure 7. Phase voltage compared to a sinusoidal signal at same frequency and amplitude

5 Figure 7 show curve form of measured induced phase voltage compared to a pure sinusoidal curve at the same frequency and with same amplitude. The curve of the phase voltage does not differ much from a pure sinusoidal signal, doing a TFA of the measured signal the result presented in figure 8 occur. From the measurement a total harmonic distortion (THD) of the voltage was calculated to 9.9%. At first view this is a high THD. Connecting the generator in a Y-connection would on the other hand eliminate the 3 rd harmonic and all its multiples. Taking this into account when calculating THD gives the much better value of.7% shown in figure 0, gives a THD of.8%. In figure 0 there is not a complete cancellation of the 3 rd harmonics. Not being able to get a complete cancellation with a Y- connection would imply unbalanced windings. There is also the possibility of numerical errors in the data processing. Figure 0. Fourier analysis of measured line voltage In figure the odd harmonics of the phase voltage are presented. In this figure the st and triple harmonic are left out, to give a better view of the odd harmonics. The measured 5 th harmonics has a peak value of 0.87V Figure 8. Fourier analysis of measured phase voltage The line voltage between two phases and a sinusoidal signal is presneted in figure 9. Figure. Harmonic contribution, without st and triple harmonics while using (2) would give a calculated value of 0.63V. Figure 9. Line voltage compared to a sinusoidal signal with same frequency and amplitude The almost matching curves of figure 9 show small subharmonic contribution. A TFA of the measured values, Compared to the fundamental peak value on 0.7V it is a good approximation to disregard the sub-harmonic contributions in the calculations for this machine.

6 5. LOAD TESTS The machine was tested with different load situations at constant speed. The test was run from no-load up to an output power of 08W. Figure 2 show a plot of current versus voltage. The load connected to the generator was a resistive load. The winding resistance was measured to 0.2 Ω. The reactance can be calculated by: Eph ( U + RI) X = (3) I E ph is the induced no load voltage, U and I is measured at the given load situation and R is the winding resistance. With an output power of 08W, measured voltage was 6.42V and measured current was 5.6A, resulting in a reactance of 0.3 Ω. the stator, which is the only manufacture challenge of the machine. The machine could be realized at a lowcost and would fit well into a package solution for coastline lighthouses. The behavior of the odd harmonic components in the voltage is at acceptable low values. Verification in the use of the fundamental flux when calculating induced voltage has been proven. The generator has a stiff voltage. During tests of the machine too coarse equipment for measuring torque ruined verification of the machine efficiency. 7. REFERENCES [] H. Erstad, "Vindbasert elektrisk kraftforsyning til Kystverkets lykter", (Wind based electric power supply for the Norwegian Coastal department s lighthouses), Master thesis NTNU 2002 [2] M.G. Say, "The performance and design of alternating current machines", 2 nd Ed, Pitman, London, 948, pp [3] Mohan, Undeland, Robbins, "Power electronics", 2 nd Ed, Wiley, New York, 995, pp 03-4 Figure 2. Current vs. voltage for different loads At a frequency this low it would be a good approximation to neglect core losses. The efficiency could then be expressed by: Pout η = (4) 2 Pout + PLosses + RI A load test with an output power of 08W, a current of 5.6A and a total loss of 6.2W, would have an estimated efficiency on It was however not possible to verify this estimation since the measure range of the shaft torque is too coarse to ensure correct measurement. If the measured no load losses, 33.5W, were used the total losses would become 39.8W and the efficiency would have dropped to CONCLUSION The generator meets its requirements. It should be possible to develop automatic winding techniques for

3. What is hysteresis loss? Also mention a method to minimize the loss. (N-11, N-12)

3. What is hysteresis loss? Also mention a method to minimize the loss. (N-11, N-12) DHANALAKSHMI COLLEGE OF ENGINEERING, CHENNAI DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING EE 6401 ELECTRICAL MACHINES I UNIT I : MAGNETIC CIRCUITS AND MAGNETIC MATERIALS Part A (2 Marks) 1. List