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Chapter 6—Asynchronous Generators 6–41 the rotor as it turns around the stator. This is called writing a pole. This pole then induces a voltage in the stator windings at the same frequency. The output frequency then has the same precision as the input frequency, independent of shaft speed over a range of perhaps two to one. If the excitation coil is driven by a crystal controlled oscillator with a precision of 0.01 Hz, the output will have the same precision. As rotor speed increases, the circumferential length of the poles increases, and fewer of them are written around the circumference of the rotor. As rotor speed decreases, the length of the poles shorten, so more of them are written around the periphery of the rotor. There will be an even pole synchronous speed where an even number of equal length poles are uniformly spaced around the rotor. At the other extreme, there will be an odd pole synchronous speed where an odd number of equal length poles are equally spaced around the rotor. Between these extremes there will be fractional poles in the vicinity of the excitor head as poles are being partially rewritten. At the even pole synchronous speed, the poles remain in the same position from one revolution to the next so no rewriting of poles actually takes place. There will be no rotor hysteresis loss in this case, since the rotor iron magnetization does not change with time. At the odd pole synchronous speed, however, every positive pole is being exactly replaced with a negative pole during each revolution, so rotor hysteresis losses will be a maximum at this speed. This loss can be made acceptably small with the proper choice of magnetic materials. There is an inherent limitation to the range of allowable speeds with any Roesel generator. The stator will have windings that span a given fraction of the circumferential length. Performance will be best when rotor speed is such that one pole has the same circumferential length on the rotor as the stator winding has on the stator. At half of this speed there has to be twice as many poles on the rotor to maintain the same output frequency. We now have two poles spanning one stator coil, which produces a zero net magnetic flux in the coil. The output voltage now becomes zero since there is no time changing flux in the coil. The output voltage will also become zero at twice the original speed. That is, a Roesel generator with a nominal speed of 1800 r/min will have its output go to zero at 900 and 3600 r/min. Practical speed limits would probably be 1200 and 2800 r/min in this case. Voltage regulation would be possible over this range by changing the amplitude of the excitation current to thereby change the flux seen by the stator windings. Such a range of speed is more than adequate for most applications, including variable speed wind turbine generators. The Roesel generator has several desirable features in its design. One is that there are no brushes or sliprings and no rotating windings. These features help to lower cost and improve reliability. Another feature is that the electronics only have to supply a single-frequency sinusoid of moderate voltage and current. No switching or filtering of the output power is required, with a resultant saving in cost as compared with the field modulated generator. Yet another advantage is that rotor speeds of perhaps 1200 to 1800 r/min represent good design values, as compared with the 6000 to 10,000 r/min of the field modulated generator. The lower speeds will simplify the gear box requirements and probably improve the overall efficiency. Early versions of the Roesel generator, built in sizes of 1 to 10 kVA by the Precise Power Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001
Chapter 6—Asynchronous Generators 6–42 Corporation, demonstrated the technical feasibility of this concept. Development is continuing on larger sizes. Questions of generator efficiency, reliability, and expected life have not been fully answered but there seem to be no insurmountable problems. 9 PROBLEMS 1. The Jacobs Model 60 is a dc shunt generator used for charging 32-V batteries. It is rated at I B =60AandV g = 40 V at 300 r/min. The circuit is that of Fig. 2. Assume V B =34V,R b =0.1Ω,R a =0.5Ω,andR f = 40 Ω. Assume the diode is ideal and the load switch is open. The rotor diameter is 4.4 m and rated windspeed is 12 m/s. (a) Find E at 300 r/min when I B =60A. (b) Find the generated power at 300 r/min (c) Find the electrical power delivered to the battery at 300 r/min. (d) Find the ratio of generated power P e to the power in the wind P w at rated load and rated windspeed. Assume standard conditions. (Note: The formula for P w is given in Chapter 4.) (e) Find the rotor speed at which the batteries will just start to charge, ignoring armature reaction. Assume the generator is operating well into saturation so the flux is constant for small changes in I f ,whichmakesE vary only with rotational speed. 2. A three-phase PM generator connected into a resistive (unity power factor) load is rated at 5 kW, 225 V line to line, 60 Hz, at 1800 r/min. The no load voltage is 250 V line to line at 1800 r/min. The circuit is given in Fig. 5. (a) Find the rated current. (b) Find k e of Eq. 15. (c) Assume R s = 0 and find X s . (d) What is the percentage change in P e (given by Eq. 17) for a 10 percent decrease in speed, if the total three-phase power is 5 kW at 1800 r/min? 3. What is the rated power of the PM generator in the previous problem at 5400 r/min, assuming the rated current does not change with speed? 4. Zephyr Wind Dynamo Company sells a 15-kW, three-phase, 108-pole, 240-V, permanentmagnet ac generator for home heating applications where frequency is not critical. Rated power is reached at 300 r/min. (a) What is the frequency of the generated voltage at rated speed? (b) What rotor speed would yield an output frequency of 60 Hz? Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001
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