[雙語(yǔ)翻譯]--外文文獻(xiàn)翻譯--風(fēng)電系統(tǒng)中最大功率點(diǎn)跟蹤法的穩(wěn)定分析（原文）

1、IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 49, NO. 3, MAY/JUNE 2013 1129Stability Analysis of Maximum Power Point Tracking (MPPT) Method in Wind Power SystemsYu Zou, Malik E. Elbuluk, Senior Member, IEEE, and Yilma

2、z Sozer, Member, IEEEAbstract—The maximum power point tracking (MPPT) method is the key to notably improve efficiency and energy extraction in wind turbine systems. The MPPT method through the charac- teristic power curv

3、e is one of the popular MPPT methods. The reference current can be obtained using the relationship between power and current without requiring real-time wind speed infor- mation. This paper presents the steady-state and

4、dynamic analyses of this MPPT method and proposes a single-pole transfer function to describe the effect of variation of wind speed on the generator speed. This is conducted by applying the small-signal analysis on a non

5、linear turbine-rotor mechanical system. To verify the performance of the wind turbine system, both simulation and experimental systems are implemented based on MPPT power control. By the variation of wind speed, the beha

6、vior of the gener- ator speed presents good consistency among the proposed theory, simulation, and experiments.Index Terms—Doubly fed induction generator (DFIG), maxi- mum power point tracking (MPPT) method, small-signal

7、 model, wind emulator, wind power system.I. INTRODUCTION A S ONE OF the most commonly used renewable energy sources, wind is the most promising one for replacing the fossil fuel in the near future. To achieve high effici

8、ency in a wind power conversion system, the maximum power point tracking (MPPT) in variable-speed operation systems, like doubly fed induction generator (DFIG) and permanent- magnet synchronous generator systems, attract

9、s a lot of atten- tion [1]–[3]. The studied MPPT methods in the history include three strategies, namely: 1) methods relying on wind speed; 2) methods relying on output power measurement and calcu- lation; and 3) methods

10、 relying on characteristic power curve. Most wind energy control systems are based on the wind speed measurement [4], [5]. In these systems, anemometers are typically required to measure the wind speed. Such systems suf-

11、 fer from additional cost of sensors and complexity. To solve this problem, wind speed estimation methods have been reportedManuscript received June 30, 2011; revised December 19, 2011; accepted May 8, 2012. Date of publ

12、ication March 13, 2013; date of current version May 15, 2013. Paper 2011-IACC-163.R1, presented at the 2011 IEEE Industry Applications Society Annual Meeting, Orlando, FL, USA, October 9–13, and approved for publication

13、in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Industrial Automation and Control Committee of the IEEE Industry Applications Society. Y. Zou was with the Department of Electrical and Computer Engineering, The U

14、niversity of Akron, Akron, OH 44325-3904 USA. He is now with the Department of Electrical and Computer Engineering, Saginaw Valley State University, Saginaw, MI 48710 USA (e-mail: yzoul123@svsu.edu). M. E. Elbuluk and Y.

15、 Sozer are with the Department of Electrical and Computer Engineering, The University of Akron, Akron, OH 44325-3904 USA (e-mail: melbuluk@uakron.edu; ys@uakron.edu). Color versions of one or more of the figures in this

16、paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIA.2013.2251854Fig. 1. Characteristic power curve-based MPPT.[6]–[9]. Relying on complex software algorithms, the wind speed ca

17、n be captured for controlling the optimal tip-speed ratio so that the MPPT can be implemented. In addition, tracking the maximum power could also be implemented through measuring the output power directly [10]–[13]. The

18、idea of this method is the online measurement of the output power and checking the rate of change of power with respect to speed, i.e., dP/dω, to extract maximum power from the wind turbine system. MPPT can be achieved w

19、hen dP/dω = 0, through adjusting either the rotor speed or duty cycle of the converter. This method relies on a large amount of online computation, and thus, it would be difficult to achieve MPPT for fast-varying wind sp

20、eeds. Although the varying tracking step could be used to improve computation speed, this disadvantage cannot be eliminated. Recently, a proposed method of employing the power versus rotor speed characteristic curve is f

21、requently used due to its simplicity in hardware and software [14]–[17]. The optimal reference power curve is constructed according to experimental tests and programmed in a microcontroller memory, working as a lookup ta

22、ble. The system configuration is illustrated in Fig. 1. One could either measure the rotor speed and obtain the power reference to regulate the power or measure the wind speed and obtain the rotor speed reference to regu

23、late the rotor speed. The former produces more accurate output power while the latter will have faster control response [18]. Aside from an accurate reference power curve, analysis is necessary to verify the stability of

24、 the method in terms of varying wind speed and output power. Few publications just address the stability issue of such method [19], but more detailed quantitative analysis should be conducted. This paper studies the perf

25、ormance of wind turbine under reference power curve MPPT power control. In particular, it presents a small-signal analysis on generator speed dynamics induced by variable wind speed. Also, an experimental setup to emulat

26、e the wind turbine operation in torque control mode is presented. Both steady-state and dynamic responses are implemented to verify the proposed analysis and conclusions. Section II will present how to obtain the optimal

27、 reference power curve and analyze the stability of this method by con- ducting the small-signal analysis. Section III will present the0093-9994/$31.00 © 2013 IEEEZOU et al.: STABILITY ANALYSIS OF MPPT METHOD IN WIN

28、D POWER SYSTEMS 1131Fig. 3. Convergence of system operation to the reference power curve.Fig. 4. SISO model of wind mechanical system.where J denotes the inertia of the combined system, B is the damping coefficient, ωm i

29、s the generator rotor speed, and Tm and Te represent the turbine and generator torques, respectively. Combining the relationship between torque and power, (2) can be rewritten in terms of power asJ dωmdt = Pwωm ? Peωm ?

30、Bωm (3)where Pw and Pe are the turbine and generator powers, respec- tively. Pw is determined by wind speed Vw, generator speed ωm, air density ρ, and blade swept area A = πR2 asPw = 0. 5ρAV 3 wCp(ωm,Vw) (4)where Cp(ωm,V

31、w) is the turbine performance coefficient and is expressed as follows [4]:Cp(ωm,Vw) = c1? c2λp ? c3β ? c4?e? c5λi + c6λ (5)where 1/λp = (1/(λ + 0. 08β)) ? (0. 035/(β2 + 1)),λ = (ωmR/Vw), β is the pitch angle, and c1 ～ c6

32、 are the coef- ficients determined by individual turbine characteristics. Combining (1)–(5), we can write˙ ωm = f(ωm,Vw). (6)Therefore, the mechanical system can be modeled as a nonlin- ear single-input single-output (SI

33、SO) system as shown in Fig. 4. Linearizing (6) at optimal operating points leads toΔ ˙ ωm = a1Δωm + a2ΔVw (7)where, for given wind speed index i,a1(i) = ?f?ωm? ? ? ? ωm=ωmopt(i), Vw=Vw(i) (8)a2(i) = ?f?Vw? ? ? ? ωm=ωmopt

34、(i), Vw=Vw(i). (9)TABLE I SIMULATION SYSTEM PARAMETERSIn other words, (7) explores the stability of system transitioning from one optimal point to another, due to the variation in Vw. Applying the Laplace transform on (7

35、) yieldssΔωm(s) = a1Δωm(s) + a2ΔVw(s). (10)The transfer function between Δωm(s) and ΔVw(s) is derived asΔωm(s)ΔVw(s) = a2(i)s ? a1(i). (11)From (11), it is clear that the transition from one optimal point (ωmopt(i),Vw(i)

36、) to another (ωmopt(i + 1),Vw(i + 1)) is stable, as long as a1(i) < 0.III. SIMULATION AND EXPERIMENTAL RESULTSSince the analysis is conducted on general turbine-rotor system, the conclusion drawn earlier will be appro

37、priate to different wind power systems employing the discussed MPPT method. To verify the stability analysis, the characteristic power curve MPPT method is employed on a simulation of a 1.5-MW DFIG wind power system. The

38、 system parameters are listed in Table I. The control schemes are shown in Fig. 5, where h(Ψs,Pref,ωm) is the relationship between stator flux and rotor d-axis current and is discussed in detail in [20]. By applying the

39、stator voltage field orientation, the rotor- and stator-side con- verters are controlled to regulate the output active and reactive powers and the dc bus voltage, respectively, where Ploss and Ψs are the power loss and s

40、tator flux while the subscripts d, q, r, s, rc, and sc represent the d-axis, q-axis, rotor, stator, rotor-side converter, and stator-side converter quantities [20]. On the other hand, a scaled down experimental system is

41、 built to emulate the turbine operations. Therefore, both steady-state and dynamic system behaviors can be implemented and investigated.A. System SimulationTo conduct the MPPT, the optimal operating power curve Pe(ωm) mu

42、st be determined by finding the optimal operating points (ωmopt, Popt). The method of determining the ωmopt and Popt for the wind speed of 9 m/s is executed first through simulations. A continuous step in the generator s

43、peed command is applied with fixed step magnitude | Δωm|= 0. 005 rad/s and period Ts_var = 2 s. The power and generator speed data are ob- tained from DFIG system simulations and are shown in Fig. 6. Although the oscilla