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Transcript

Joan Peuteman KHBO (translation) August 2011 The asynchronous generator 1: Introduction 1.1: Generators in wind turbines The wings of a wind turbine convert the kinetic energy of the wind into a rotation of the axis. This axis is connected, with or without gearbox, with the rotor of a generator. This generator converts the mechanical energy of the rotating axis into electrical energy. In wind turbines, several types of electrical generators are used. More precisely, we consider: 1) the squirrel-cage induction generator 2) the induction generator with wound rotor allowing a larger slip 3) the doubly fed induction generator 4) the synchronous generator 5) the permanent magnet synchronous generator Also a linear induction generator, a switched reluctance motor or a brushless doubly fed induction generator can be used. 1.2: Manufacturers Several manufacturers are selling their products. Depending on the manufacturer and the size of the wind turbine, a specific generator is used. An overview of the most important manufacturers can be found in Table 1 (Soens). An overview of the used abbreviations: - SCIG = squirrel-cage induction generator DFIG = doubly-fed induction generator SG = synchronous generator Some wind turbines have a gearbox between the wings and the generator. In case a wind turbine does not have a gearbox, one has a “direct drive” wind turbine. The manufacturer Jeumont sells large wind turbines where large permanent magnet synchronous generators are used. 1 Joan Peuteman Manufacturer KHBO Market share (%) 2002 Vestas Enercon MEG-Micon (Vestas) Gamesa (Vestas) GE Wind Bonus (Siemens) Nordex 22.2 18.5 14.3 (translation) August 2011 SCIG Rated power (MW) DFIG SG (direct drive) 0.85 – 4.5 0.3 – 4.5 0.75 – 1.65 2.75 – 4.2 11.8 0.66 – 2 8.8 7 1.5 – 3.6 0.6 – 2.3 7 0.6 – 1.3 1.5 – 2.5 Table 1: The use of different types of generators generatortypes Notice asynchronous generators are not only used in wind turbines. They are also used in small and medium sized hydraulic power stations. 2: Induction machines In the present document, the working principle of the three phase induction machine is not explained, more information can be found in (Belmans – Hameyer; Geysen – Vandenput; op ’t Roodt). The torque speed characteristic is visualised in Figure 1. Figure 1: Torque speed characteristic of an induction machine 2 Joan Peuteman KHBO (translation) August 2011 An induction machine, with p pole pairs, fed by a voltage with a frequency f has a synchronous speed nS 60 f . p At that synchronous speed, no torque will be developed. In case the induction machine behaves as a motor, the speed of rotation is smaller than the synchronous speed and the motor develops a torque T. This implies the motor does not have a synchronous speed explaining its name “asynchronous machine”. Due to the magnetisation current in the stator windings, a sinusoidal rotating magnetic field is available. This magnetic field rotates at the synchronous speed. When the induction machine behaves as a motor, its speed n < nS. The speed of rotation of the rotor is smaller than the speed of the rotating magnetic field implying there is a speed difference. Due to this speed difference, voltages are induced in the rotor conductors. In case these rotor conductors are an electrically closed circuit, rotor currents are flowing (a current flowing in a conductor in a magnetic field). Due to the Lorentz forces, a driving torque is available. In the region where (0 ≤ n ≤ nS), motor working occurs as indicated in Figure 1. The slip s nS n nS has values between 0 and 1. When the rotor has another direction of rotation than the rotating magnetic field, the slip s > 1 and the machine behaves as a brake. The developed torque has the same direction as the rotating magnetic field implying the torque is opposed to the direction of rotation of the rotor. Indeed, a braking effect occurs. In the present document, expecially the region where generator working occurs is important. The rotor rotates in the same direction of the rotating magnetic field but the rotor has a supersynchronous speed. More precisely, n > nS implying the slip s < 0. 2.1: The working principle of an asynchronous generator The rotor has a supersynchronous speed implying there is a speed difference between the rotor and the rotating magnetic field. This implies voltages are induced into the rotor windings (the polarities of these voltages are opposed to the polarities of the induced voltages in case of motor working). In case these rotor conductors are an electrically closed circuit, rotor currents are flowing (a current flowing in a conductor in a magnetic field). Due to the Lorentz forces, a torque is available. This torque is not a driving torque, the torque opposes the direction of rotation of the rotating magnetic field and the rotor. 3 Joan Peuteman KHBO (translation) August 2011 Due to the mechanical driving torque of the turbine and the electrical braking torque of the generator, the steady state speed is constant. Both torques have, in a steady state situation, the same magnitude. But they have a different polarity implying the speed of rotation remains constant. In order to maintain the speed of rotation, mechanical energy must be supplied. The machine injects electrical energy into the grid meaning the machine really functions as a generator. There are two important situations. The generator can be connected with a strong electrical grid or the generator can work in island mode. In both situations, the generator generates active power but the generator consumes reactive power. When the generator is connected with a strong grid, the grid supplies the magnetization current. The grid supplies the reactive power consumed by the generator. Moreover, the grid is able to consume all the active power supplied by the generator. When working in island mode, capacitors are needed in parallel with the stator. The capacitors generate the reactive power consumed by the generator. The present text mainly focuses on the use of an asynchronous generator in island mode. 3: Asynchronous generator fed by capacitors 3.1: Working principle The rotor of an asynchronous generator is mechanically driven at a speed n (with a corresponding pulsation ωm). As visualised in Figure 2, the three phase switch S is open implying the capacitors (connected as a triangle) are not (yet) connected in parallel with the stator windings of the induction machine. Figure 2: Asynchronous generator in island mode 4 Joan Peuteman KHBO (translation) August 2011 The rotor consists of ferromagnetic material having remanent magnetism. Due to this rotating rotor, a small rotating magnetic field is obtained inducing voltages into the stator windings. These induced voltages have: - a frequency proportional with the speed of rotation of the rotor, an amplitude proportional with the speed of rotation of the rotor. The machine operates as a synchronous generator, the generated frequency f1 = p n. Here, p equals the number of pole pairs of the machine and n is the speed of rotation of the rotor (expressed in revolutions per second). Since the switch S is open, the generator provides no current and no power at all. The driving torque is only required to overcome the friction losses. When the switch S closes, the generator will be connected with the capacitors and the generator will provide a capacitive current. The generator provides a capacitive current or equivalently the generator consumes a inductive current. As illustrated by Figure 3, this inductive current lags an angle of 90° with respect to the generated voltage. Figure 3: Generator provides a capacitive current of consumes an inductive current The voltage u and the current i in Figure 3 are both visualized as single phase signals. Also the flux Ф is visualized as a single phase signal. However, when considering a three phase induction machine (and we consider a three phase induction machine here) the generated voltage u is a three phase voltage. Three voltages are generated and have the same magnitudes with phase differences equal to 120°. The capacitors are a three phase symmetric load implying a symmetric three phase current is flowing. These three currents have the same magnitudes and have phase differences equal to 120°. These three phase currents are flowing in the stator windings. Each stator winding generates a stationary pulsating magnetic field. The currents are displaced in time by 5 Joan Peuteman KHBO (translation) August 2011 an angle of 120°. Since the coils are displaced in space by an angle of 120°, three stationary pulsating magnetic fields displaced in time and space by an angle of 120° are obtained. The sum of these three stationary pulsating magnetic fields equals a rotating magnetic field. Actually, there are two rotating magnetic fields. First, there is a rotating field due to the remanence of the ferromagnetic material in the rotor. Secondly, there is a rotating field due to the stator currents. These two rotating fields have the same phase and they must be added. The rotating magnetic field of the rotor induces a voltage u lagging with an angle of 90°. The generator provides a capacitive current leading with an angle of 90° with respect to the voltage. The magnetic field generated by the stator has the same phase as the stator current. This implies the rotating magnetic fields of the stator and the rotor have the same phase and amplify each other. The originally small remanent magnetic field will be amplified. A larger rotating magnetic field induces a larger voltage u in the stator windings implying also the current i becomes larger. This implies a further increase of the total rotating magnetic field implying - an even increased voltage u will be induced, an increased current i will flow, a rotating magnetic field with a larger amplitude will be obtained, an even increased voltage u will be induced, an increased current i will flow, … The amplitude of the rotating magnetic field will increase until saturation of the ferromagnetic material limits this increase of the amplitude. Also the amplitude of the generated voltage u will be limited or bounded. 3.2: The resulting steady state voltage In the previous paragraph, we studied how the magnetic field in the machine is obtained and how an increasing voltage will be generated in the stator windings. The maximum amplitude of the voltage will be determined by: - the magnetization characteristic of the machine, the values of the capacitors in parallel with the machine. The generated voltage determines, by the magnetization characteristic, the reactive magnetization current Im = IREACTIEF in the stator windings. Curve 1 in Figure 4 gives the relationship U = f(Im). Due to the generated voltage U over the capacitors with a value C, the current equals 6 Joan Peuteman KHBO (translation) August 2011 I C 2 f1 CU . Curve 2 in Figure 4 gives the relationship between the capacitor current IC and the voltage U. The point P is the steady state working point P where the current in the capacitors equals the magnetization current. Figure 4: Working point of the generator The working point P is determined by the shape of the magnetization characteristic (curve 1) and the slope of the capacitor characteristic (curve 2). What is the effect of a larger (and also of a smaller) speed of rotation on the magnetization characteristic? What is the effect of the capacitor value C on the capacitor characteristic? Explain that a higher speed of rotation of the generator implies a steady state voltage with a larger amplitude (and also a higher frequency). Explain that the use of larger capacitor values implies the generated steady state voltage is larger. At present, the generator is only loaded with capacitors. The generator generates no active power, the rotor of the generator has a synchronous speed (the same speed as the rotating magnetic field). 7 Joan Peuteman KHBO (translation) August 2011 3.3: Reaching the steady state working point There are two ways to reach the steady state working point: - the speed ωm is kept constant and the capacitor values is gradually increased, the capacitor values are not changed, but the speed ωm is gradually increased. The first approach is illustrated in Figure 5. Initially, the capacitor value C is small and equals C1. There is no intersection point between the magnetization characteristic and the capacitor characteristic. It is impossible to start up the generator i.e. the generated voltage is limited to the small voltage generated by the remanent magnetism in the rotor. Figure 5: Changing the capacitor characteristic When C = CCR (the critical capacitor value), the slope of the capacitor characteristic equals the slope of the linear part of the magnetization characteristic. When C > CCR, as C increases the generated voltage will be larger. The phenomenon appears until the final C2 value is obtained and the steady state working point P has been reached. This means the rotor accelerates until the desired speed has been reached while the switch S is still open. Then, the switch S will be closed with initially a small C (C1 < CCR). The capacitor value will be increased gradually until C = C2. 8 Joan Peuteman KHBO (translation) August 2011 The second approach is illustrated in Figure 6. While the rotor stand still, the switch S in Figure 2 will be closed with immediately the final C-value. At present, the speed of rotation will be increased gradually. In the beginning, for small speeds of rotation ωm1, the magnetization curve and the capacitor characteristic do not intersect each other. The magnetization characteristic lies below the capacitor characteristic having a steep slope. Figure 6: Changing the capacitor characteristic and the magnetization characteristic As ωm increases and becomes larger than the critical value ωmCR, the working point moves towards the steady state working point P at ωm2. 4: Loading the asynchronous generator Up until now, we did not load the asynchronous generator. Only the capacitors, which are needed to supply the magnetization current, are connected in parallel with the stator. In the present paragraph, we will study the behaviour of the generator when the generator is additionally loaded with: - a pure inductive load, a pure ohmic load, an ohmic-inductive load. 9 Joan Peuteman KHBO (translation) August 2011 We leave it as an exercise for the interested student to study the situation in case of an ohmic-capacitive load. 4.1: The equivalent scheme of an induction machine The analysis will be a steady state analysis with sinusoidal voltages and currents. This analysis can be done based on the equivalent scheme of Figure 7 giving a single phase representation of a three phase induction machine. R1 R*2 X1σ g X*2σ XD1 R*2(1-s)/s Figure 7: Equivalent scheme When considering Figure 7, we find: - R1: ohmic resistance of the stator windings, X1σ: leakage reactance of the stator windings, g: resistance whose losses correspond to the iron losses, XD1: magnetizing reactance, R*2: ohmic resistance of the rotor windings refered to the stator, X*2σ: leakage reactance of the rotor windings refered to the stator, R*2 (1-s)/s: slip dependent load resistance representing the slip dependent active power. Figure 8: Equivalent scheme asynchronous generator in island mode Very often, the equivalent scheme of Figure 7 is simplified by: 10 Joan Peuteman - KHBO (translation) August 2011 omitting R1 and g, moving XD1 = ω1 LD1. Such a simplified equivalent scheme is visualised in Figure 8 where Z1 R j1 L models the load (“belasting”). Figure 8 also shows the capacitors which generate the magnetization current. Notice the currents I1 (load current), IC (capacitor current), Im (magnetization current) and I’2 (load current consumed by the stator of the machine). A vector diagram visualizing these currents with respect to the voltage U1 is shown in Figure 9. Figure 9: The currents of Figure 8 Notice that in Figure 8 the slip s < 0 since the generator has a supersynchronous speed. Based on the current law of Kirchoff one obtains that (vectors) I m I '2 I C I1 0. Based on the active current components, one obtains that I1 cos I '2 cos and based on the reactive current components, one obtains that I C I m I1 sin I '2 sin . 11 Joan Peuteman KHBO (translation) August 2011 Based on these expressions, it is possible to study the behaviour of the asynchronous generator with different types of loads. 4.2: The asynchronous generator at no-load When there is no load, I1 = 0 and the slip s = 0 implying also I’2 = 0. The vector diagram of Figure 9 reduces to the diagram on the left in Figure 10. Figure 10: Vector diagram of an asynchronous generator with no load and with a purely inductive load At no load, Im = IC implying the steady state working point P is visualised in Figure 4 (this is the situation described in Paragraph 3.2). 4.3: The asynchronous generator with a purely inductive load When the load of the asynchronous generator is a purely inductive load, no active power will be generated. The rotor has a synchronous speed implying s = 0 and I’2 = 0. The load current is purely inductive implying Im + I1 = IC. This means the capacitors generate the magnetization current and the load current. This is the situation at the right in Figure 10. The working point at no load (loaded with an inductance L which equals infinity) is visualised on the left in Figure 11 with P4 and a voltage U’1. But when the inductance has a finite value, this inductance consumes a part of the reactive current generated by the capacitors. Having the same capacitors, the magnetization current flowing to the generator will be smaller implying the generated voltage decreases from the value U’1 to the value U”1. Here, the working points P2 and P3 are relevant. The difference between the currents in P2 and P3 is the inductive load current. As L decreases, also the voltage U1 decreases. Initially, the current in L increases as L decreases. But below a certain L-value, the generated voltage U1 decreases considerably implying the current in L also decreases. 12 Joan Peuteman KHBO (translation) August 2011 This means the inductance L short circuits the asynchronous generator. This implies it is allowed to short circuit an asynchronous generator. When the stator is short circuited, Im and IC are zero implying there is no voltage generated and in principle there is no short circuit current. This situation is different with the situation of a synchronous generator. When short circuiting a synchronous generator, large short circuit currents are flowing. Figure 11: Current flowing in a purely inductive load Notice that when considering Figure 11, the speed of rotation is constant. This implies also the frequency of the generated voltage is constant since the slip is always zero. The magnetization characteristic and the capacitor characteristic are independent of the inductive load. 4.4: The asynchronous generator with a purely ohmic load At the bottom of Figure 12, the vector diagrams of the currents are visualized in case the asynchronous generator feeds a purely ohmic load. Since the generator generates active power, the slip is not zero. A vector diagram is visualised with a negative slip s1. When the load resistance has a smaller value, the slip s2 becomes more negative; also this situation is visualised in a vector diagram. When considering the active current, I1 I '2 cos and when considering the reactive currents, 13 Joan Peuteman KHBO (translation) August 2011 I C I m I '2 sin . Suppose the generator (and the rotor) has a constant speed n (the pulsation ωm is constant). As the generated active power increases, the generator (the slip is more negative) generates a lower frequency f1 = p ns where nS n . 1 s The capacitor characteristic has a different slope (a smaller current with a voltage having the same amplitude). This decrease of the frequency f1 influences the magnetization current in the stator windings (a higher current if the amplitude of the voltage remains the same). The change from slip s1 to slip s2, is visualised in figure a and figure b of Figure 12. Figure 12: Asynchronous generator with an ohmic load Show in figures a and b the curents Im, IC and I’2sinψ? 14 Joan Peuteman KHBO (translation) August 2011 At no laod (loaded with an R which equals infinity), the load current I1 = 0. When the resistance R first equals infinity and then decreases: - the slip becomes more negative, the frequency f1 of the generated voltage decreases, the magnetization characteristic and the capacitor characteristic are moving implying I’2 sinψ decreases. When the resistance R decreases, then also I1 = I’2cosψ increases. If the current I’2 sinψ decreases, while I’2cosψ increases, this means that ψ decreases. The decrease of ψ is visualised in Figure 12. With a more negative slip s2, ψ is smaller than with a slip s1. Due to a smaller load resistance R, the magnitude of the voltage U1 decreases as visualised in Figure 12. First, a smaller R value will, although U1 decreases, imply a larger I1. But when the resistance decreases significantly, U1 will decrease implying also I1 decreases. When the resistor R equals zero and the generator is short circuited, U1 equals zero implying the short circuit current is very small. Indeed, with U1 = 0 the currents IC and Im are both zero. Figure 14 visualises the magnitude of the load current I1 with an ohmic load (curve 2). The evolution of the current is comparable with the evolution of the current in case the load is purely inductive (figure b of Figure 11). As Figure 14 illustrates, the asynchronous generator with a purely ohmic load (curve 2) generates a larger current than with a purely inductive load (curve 1). Indeed, an inductive load consumes the reactive current generated by the capacitors implying the magnetization current of the generator decreases. The generated voltage will decrease more rapidly implying only a smaller current can be sent to the load. When considering an ohmic load, the reactive current generated by the capacitors will entirely flow to the generator. The generated voltage is larger implying a larger current can be provided to the load. 4.5: The asynchronous generator with ohmic-inductive load The behaviour of an ohmic-inductive loaded asynchronous generator is a mixture of the behaviours in case the load is purely inductive and the case the load is purely ohmic. Figure 13 visualises the vector diagrams. It is clear that I1 cos I '2 cos and that I C I m I1 sin I '2 sin . Since the generator generates active power, the slip is not equal to zero. A vector diagram with a negative slip s3 is visualised in Figure 13. When the generator has to 15 Joan Peuteman KHBO (translation) August 2011 generate a larger active power, the slip s4 becomes more negative. This situation is visualised on the right in Figure 13 with a vector diagram. In case the generator has a constant speed n, the generated frequency f1 will decrease if the generator has to generate more power (the slip will become more negative). The slope of the capacitor characteristic changes (a smaller current with the same amplitude of the voltage). This decrease of the frequency f1 has also an impact on the magnetization current in the stator windings (a higher current with the same amplitude of the voltage). The change from slip s3 to slip s4, is visualised in figure a and figure b of Figure 13. Figure 13: Ohmic-inductive loaded asynchronous generator Show in figure a and b the currents Im, IC and I1sinφ + I’2sinψ? Suppose the generator has to generate a larger power while φ is constant (this means R and L are smaller with a constant R/L-ratio). Then I1cosφ and I1sinφ will increase implying also I’2cosψ increases. Figuur 13 visualises that I1sinφ + I’2sinψ decreases 16 Joan Peuteman KHBO (translation) August 2011 although I1sinφ increases. This implies I’2sinψ decreases while I’2cosψ increases. This means that when the generator generates a larger power, the angle ψ decreases. Due to a smaller load impedance, U1 decreases as visualised in Figure 13. Initially, a smaller impedance, although U1 decreases, will imply a larger I1. But with a significant decrease of the impedance, U1 will decrease implying also I1 decreases. The currents and the accompanying voltages are visualised in Figure 14. Curve 1 shows the generator with a purely inductive load, curve 2 shows the generator with a purely ohmic load and curve 3 shows the generator with an ohmic-inductive load. Figure 14: Comparison ohmic, inductive and ohmic-inductive loaded generator 4.6: Conclusions An asynchronous generator is well suited to generate active power. An asynchronous generator is not suited to provide reactive power (contrary to an overexcited synchronous generator). When inductive loads must be fed, it is certainly useful to have capacitors to improve the power factor. It is allowed to short circuit an asynchronous generator (contrary to a synchronous generator which has large short circuit currents). When an asynchronous generator operates in island mode, when the speed is constant and when the required active power increases then 17 Joan Peuteman - KHBO (translation) August 2011 the generated frequency decreases, the amplitude of the generated voltage decreases. In order to keep the amplitude of the generated voltage constant, as the required power increases, it is possible to - increase the speed of rotation, increase the capacitor values. 5: References Belmans R. and Hameyer K., Elektrische energie: fundamenten en toepassingen, Garant, Leuven, 1999. Geysen W. and Vandenput A., Elektrische machines – deel 3: asynchrone machines, Acco, Leuven, 1986. Op ’t Roodt, Elektriciteit 3: elektrische machines, Van In, Lier, 1992. Peuteman J., De synchrone generator, KHBO, written as a part of a course on wind turbines, februari 2007. Soens J., Impact of wind energy in a future power grid, PhD thesis, KULeuven, december 2005. 18