[2010] Optimal power point tracking for stand-alone PV system using particle swarm optimization
噪声估计算法
太原理工大学毕业设计（论文）任务书噪声估计算法的研究及MATLAB仿真摘要日常的通信过程中,语音会常常受到环境噪声的干扰而使通话质量下降,严重时使得语音处理系统不能正常工作。
因此,必须采用信号处理方法通过语音增强来抑制背景噪声从而提高语音通信质量,而噪声估计的准确性又直接影响语音的增强效果。
可见,噪声估计是语音增强的一个非常重要的部分,所以研究噪声估计算法有很好的实用价值。
本文主要研究两种噪声估计算法:基于最小统计和最优平滑的噪声估计算法和最小值控制递归平均法的噪声估计算法,通过实验仿真比较最终研究了一种改进的最小值统计量控制递归平均噪声估计算法。
本文的主要工作总结归纳为以下几方面：首先,本文对几种经典的噪声估计算法进行研究,了解它们的各自优缺点,在此基础上选定两种较好的算法进行具体分析。
其次,了解最小统计和最优平滑和噪声功率谱统计跟踪的噪声估计算法的原理,它的基本思路是先用最优平滑滤波器对带噪语音的功率谱滤波,得到一个噪声的粗略估计，然后找出粗略估计噪声中的在一定时间窗内的最小值，对这个最小值进行一些偏差修正，即得到所要估计的噪声的方差。
通过MATLAB仿真看其特征。
再次,研究了基于非平稳噪声的估计算法,最后通过比较研究了一种改进的最小值控制递归平均算法。
算法采用递归平均进行噪声估计，其递归平均的平滑量控制递归平均噪声估计算因子受语音存在概率控制，而语音存在概率的计算采用了两次平滑和最小统计量跟踪。
与I．Cohen提出的IMCRA算法相比，本文研究采用了一种快速有效的最小统计量跟踪算法。
仿真结果表明：在非平稳噪声条件下，该算法具有较好的噪声跟踪能力和较小的噪声估计误差，可以有效地提高语音增强系统的性能。
最后,对整体论文总结,通过研究发现改进的最小统计量控制递归平均噪声算法在IMCRA算法的基础上,采用了一种简单有效地最小统计量估计算法,在保证噪声估计准确性的同时,减小了算法的复杂度。
同时,基于这种噪声估计的语音增强系统能有效地提高增强语音的信噪比,并且能有效地消除增强语音中的音乐噪声。
毕业设计风力发电外文文献
Abstract--The purpose of this paper is to find an innovative, high efficiency, practical and low cost control system structure with an optimized control strategy for small-scale grid-connected wind turbine with direct-driven permanent magnet synchronous generator (PMSG). This research adopts the sensorless vector control strategy based on phase-locked loop (PLL) for PMSG control, and the grid-side inverter control strategy is based on the single-phase PLL. The simulation demonstrates that the sensorless control strategy and single-phase grid-side inverter control strategy are practical solutions for grid-connected PMSG wind turbines, and they can provide both generator speed control for optimized wind power tracking and good power quality control for electricity delivered to the grid. The designed system offers many unique advantages, including simple topology, optimized control strategy, cost-effective and fast respond to grid failures.Index Terms--Maximum power point tracking (MPPT), PMSG, pulse-width modulation (PWM) converter, speed control, variable-speed wind turbine.I. I NTRODUCTIONn recent years, great attention has been paid on renewable energy sources, such as wind and solar energy. Wind energy is the most popular renewable energy source due to its relatively low cost. The overall system cost can be further reduced by optimal control of high efficiency power electronic converters to extract maximum power in accordance with atmospheric conditions [11].The wind energy conversion system based on permanent magnet synchronous generator (PMSG) is one of the most favorable and reliable methods of power generation. Reliability of variable-speed direct-driven PMSG wind turbines can be improved significantly comparing to doubly-fed induction generator (DFIG) wind turbines with gearboxes. Noise, power loss, additional cost, and potential mechanical failure are typical problems for a DFIG wind turbine because of the existence of a gearbox. The use of direct-driven PMSG could solve these problems. Moreover, low voltage ride through (LVRT) is also a big issue for DFIG because the This work was supported in part by the special funds from Beijing Municipal Education Commission.Chunxue Wen, Guojie Lu, Peng Wang and Zhengxi Li are with the Power Electronics and Motor Drivers Engineering Research Centre, North China University of Technology,Beijing,China(e-mail: wenchx1980@, lugod307@, catdapeng2008@, lzx@).Xiongwei Liu and Zaiming Fan are with the School of Computing, Engineering and Physical Sciences, University of Central Lancashire, Preston, PR1 2HE, UK (e-mail: xliu9@, zmfan@) electromagnetic relationship between the stator and the rotor is more complex than PMSG. Therefore, it’s more difficult for DFIG to solve LVRT problem safely and reliably.In a variable-speed PMSG system, vector control approach is often used to achieve nearly decoupled active and reactive power control on the grid-side inverter which is a current regulated voltage source inverter. In this way, the power converter maintains the DC-link voltage and improves the power factor of the system [1], [7], [10]. Different control methods for maximum power point tracking (MPPT) in variable-speed wind turbine generators have been discussed in [2], [4], [7].This research adopts the sensorless vector control strategy based on phase-locked loop (PLL) for PMSG control [2]. The method requires only one active switching device, i.e. insulated-gate bipolar transistor (IGBT), which is used to control the generator torque and speed so as to extract maximum wind power. It is a simple topology and low cost solution for a small-scale wind turbine because of the sensorless vector control strategy. The grid-side inverter control strategy is based on the single-phase PLL, which applies a control method in Direct-Quadrature (DQ) rotating frame to single-phase inverter and achieves superior steady state and dynamic performance [6].For small-scale wind turbine, single-phase power supply to consumers is popular. There are many control methods for single-phase inverter, such as PI controller, quasi-PR controller, etc. [5]. However, these methods can’t decouple the active power and reactive power so as to have good power control performance. Single-phase PLL method based on DQ rotating frame can well solve this problem. On the other hand, encoders are vulnerable components for wind turbines, particularly for small wind turbines, because small wind turbines experience severer vibrations than their large counterparts. The sensorless vector control opts out the encoders, and therefore the reliability of wind turbines is much improved. For these reasons, the sensorless vector control and single-phase PLL method have their unique advantages for small-scale wind turbines.This paper is structured further in following three sections. In section II, the principle of the full power back-to-back PWM converter is introduced. Then the vector control of small-scale grid-connected wind power system including sensorless control, vector control of PMSG, single-phase PLL, vector control of grid-side inverter are described in section III. Finally, in section IV, the simulation results and conclusion are given.Vector control strategy for small-scale grid-connected PMSG wind turbine converter Chunxue Wen, Guojie Lu, Peng Wang, Zhengxi Li Member IEEE, Xiongwei Liu Member IEEE,Zaiming Fan Student Member IEEEIII. T HE PRINCIPLE OF FULL POWER BACK-TO-BACK PWMCONVERTERTypical topology model of direct-driven PMSG wind turbine is shown in Fig. 1. Converters of the system adopt back-to-back pairs of pulse-width modulation (PWM) architecture. The generator-side converter controls the generator speed in order to achieve maximum capture of wind power, and the grid-side inverter controls the stability of DC-bus voltage and the power factor of the system. This topology can be a good way to improve performance, and the control method is flexible. Converters have four-quadrant operation function, which can fulfill the generator speed control anddeliver the fine quality of electricity to the grid [7], [8].Fig. 1. Topology of permanent magnet direct-driven wind power systemIII. T HE VECTOR CONTROL OF SMALL-SCALE GRID-CONNECTEDDIRECT-DRIVEN WIND POWER SYSTEM CONVERTERFig. 2 shows the back-to-back PWM voltage convertervector control block diagram. The machine-side PWMconverter controls the electromagnetic torque and statorreactive power (reactive power is often be set to 0) byadjusting the current of the d-axis and q-axis of the machine-side converter. This control mechanism helps the PMSG tooperate in variable speed, so that the wind turbine can workwith maximum power point tracking (MPPT) under the ratedwind speed. The grid-side PWM inverter stabilizes the DC-busvoltage and accomplishes active and reactive decouplingcontrol by adjusting the current of the d-axis and q-axis of thegrid-side. The grid-side PWM inverter also controls thereactive power flow to the grid, usually at unity power factorcondition.A. Sensorless control based on PLLThe speed and position control is achieved throughsensorless vector control of the machine-side converter basedon all-digital phase-locked loop. The phase-locked loop isdesigned to control the frequency of the D-Q axis voltagethrough minimizing the difference of the output voltage phaseangle and the given voltage phase angle, until the outputvoltage phase angle tracks the given voltage phase angle. Asthe phase-locked loop has frequency closed-loop trackingmechanism, the generator voltage frequency and the anglebetween d-axis voltage and rotor flux can be measured withthis characteristic, then the generator speed and rotor positionangle can be derived [2]. The control accuracy is generallygood using this method, however some problems may occurwhen the generator operates at very low speed. The windpower system often works above the cut-in wind speed, so thismethod can be applied to wind power generation system.Fig. 2.The back-to-back PWM voltage converter vector control block diagramThe actual rotor position of PMSG is indicated in the D-Q coordinate system. The estimated location for ∧θ is the d q ∧∧− coordinate system, αβ is the stationary coordinate system, as shown in Fig. 3. As the rotor position of PMSG is estimated rather than measured in the sensorless vector control system, there exists an error θΔ between the actual rotor position θ and the estimated location ∧θ. At the same time, the back-EMF (electromotive force) generated by the rotor permanent magnets generates two d-axis and q-axis components in the estimated rotor position orientation coordinates, which are expressed as sd e ∧and sq e ∧respectively. Conventional PI controller can achieve zero error control, i.e. sd e ∧or θΔ can be adjusted to zero value. The PLL sensorless vector control schematic diagram is shown in Fig. 4, and the value of sd e ∧and sq e ∧can be obtained from (1).sd sd s sd dq sq sd sq sq s sq q d sd sq di u R i L L i e dt di u R i L L i e dt ωω∧∧∧∧∧∧⎧=+−−⎪⎪⎨⎪=+++⎪⎩(1)Fig. 3. Presumed rotating coordinate systemFig. 4. Principle of PLL based sensorless vector controlIf we ignore the current differential items in (1), then wehavesd s sd q sq sd sq sq s sq d sd ˆˆˆˆˆarctan(arctan(ˆˆˆˆˆu R i L i ee uR i L i ωθω−+Δ=−=−−− (2)where sd u , sq u , sd i and sq i are the d, q-axis components of the output voltage and current of the generator stator; d L q L and s R are the inductance and resistance of the stator; ω is thegenerator electrical angular velocity of the generator; "∧" indicates estimated value.Block diagram of sensorless vector control based on digital PLL is shown in Fig. 5. The back-EMF (electromotive force) value of the estimated rotating coordinates can be obtained by calculating the three-phase voltages and currents of the PMSGstator. The calculated angle difference θΔcan be used to estimate the angular velocity through the PI controller. Then the value of the estimated angle can be obtained by integral element. Generally, the speed has considerable fluctuations using this method. Therefore it will achieve a better estimation by adding a low-pass filter (LPF), as shown in Fig. 5.∧Fig. 5. Block diagram of sensorless vector control based on digital PLLB. Vector control of PMSGIn order to study the torque control of PMSG, it is necessary to establish a mathematical model. Because q-axis leads d-axis 90° in the D-Q coordinate system, the generator voltage equation can be expressed as [8]: sd sd s sd d sq sq sq sq sq q d sd di u R i L L i dt di u Ri L L i dt ωωωψ⎧=+−⎪⎪⎨⎪=+++⎪⎩(3) The significance of various physical quantities in (3) is the same as in (1).The generator electromagnetic torque equation can be expressed as:33()22e sq d q sd sq T p i p L L i i ψ=+− (4) where p is the number of generator pole pairs, and ψ is the magnetic flux.Based on the above mathematical model, the sensorless vector control program of PMSG is established, and its controlblock diagram is shown in Fig. 6.sa i sbi Fig. 6. Sensorless vector control block diagram of PMSGGenerator rotor position and speed which are estimated by sensorless algorithm can be used in vector control. Thereference value of motor torque can be obtained by the speedcontroller. The voltage reference of generator can also be gotby current controller, and then the control signals of rectifier switching device can be obtained by a set of PWM modulation algorithms. The position and speed of generator rotor which is necessary to vector control is obtained by sensorless algorithm.C. Single-phase grid-connected PLLFig. 7 shows the block diagram of the single-phase gird-connected PLL. In order to ensure that the converter outputvoltage is in the same phase with the output current, the PLLis used to achieve unity power factor control. At the sametime, the converter also provides the angle of the referencecurrent transformation [5].Fig. 7. The block diagram of the single-phase PLLThe transformation between orthogonal a-b and D-Q reference frames can be described by trigonometric relations, which are given in (5) and (6), and the rotating reference frame is shown in Fig. 8.Fig. 8. Definition of rotating reference frame⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡−=⎥⎦⎤⎢⎣⎡b a q d f f f f θθθθcos sin sin cos (5) ⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡−=⎥⎦⎤⎢⎣⎡q d b a f f f f θθθθcos sin sin cos (6)Active power and reactive power equations can beexpressed as:⎩⎨⎧−=+=d q q d qq d d i v i v Q i v i v P (7) If the phase voltage and q-axis coincide, then 0=d v andv v q =, active power and reactive power equations can besimplified as:||||q dP v i Q v i =⎧⎪⎨=−⎪⎩ (8) D. The vector control strategy of the grid-side inverterFor a three phase converter, simple PI compensators designed in a D-Q synchronous frame can achieve zero steady state error at the fundamental frequency, but this method is not applicable to single-phase power converter because there is only one phase variable available in a single-phase power converter, while the D-Q transformation needs at least two orthogonal variables.In order to construct the additional orthogonal phaseinformation from the original single-phase power converter,the imaginary orthogonal circuit is developed, as shown inFig. 9. The imaginary orthogonal circuit has exactly the samecircuit components and parameters, but the current b i and the voltage b e , maintain 90D phase shift with respect to their counterparts in the real circuit- a i and a e [6].Fig. 9. Real circuit and its imaginary orthogonal circuitFrom Fig. 9, the voltage equation can be expressed as:⎥⎦⎤⎢⎣⎡−−+⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡−=⎥⎦⎤⎢⎣⎡b b a a b a b a v e v e L i i L R i i p 11001 (9) Transforming the voltage equations into the synchronousreference frame using (5) and (6), and considering 0=d v and v v q =, we have: ⎥⎦⎤⎢⎣⎡−+⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡−−−=⎥⎦⎤⎢⎣⎡||1//v e e L i i L R L R i i p qd q d q d ωω (10) To achieve decoupled control of active power and reactive power, the output voltage of the inverter in the synchronousreference frame can be expressed as:||)(1v i x L e d q +−=ω (11))(2q d i x L e ω+= (12)Substituting (11) and (12) into (10), system equations canbe rewritten as follows:⎥⎦⎤⎢⎣⎡+⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡−=⎥⎦⎤⎢⎣⎡211001x x i i L R i i p q d q d (13) The active power and reactive power could be controlled by d i and q i respectively. Therefore, system control can be completed by current feedback loops as follows:))((211q q i i s k k x −+=∗(14)))((212d d i i sk k x −+=∗(15) Fig. 10 shows the control block diagram of the grid-sideinverter. It should be noted that the given active and reactive power should be set at two times of the desired values, because the imaginary circuit will not deliver any active andreactive power to the grid.θωFig. 10. The vector control block diagram of the grid-side inverterIV. S IMULATION RESULTSA simulation model in Matlab/Simulink is developed based on above theoretical analysis, and the system simulation block diagram is shown in Fig. 11.Fig. 11. The system simulation block diagramA. The simulation results of the machine-side converterIn the simulation model, the Reference speed represents the wind speed. At the beginning of the simulation (i.e. 0s), the generator speed is 4rpm and its input torque is -50Nm. At the time of 0.5s, the generator speed is 17 rpm and the input torque maintains at the value of -50Nm. At 1s, the generator speed maintains at 17 rpm and the input torque is -80Nm. The simulated waveforms are shown in Fig. 12, Fig. 13, Fig. 14, Fig. 15, respectively.It can be seen from Fig. 12 and Fig. 13, the error between the estimated rotor position angle and the actual measurement of the rotor position angle is very small in the steady state, there are some fluctuations in the dynamic response, but the rotor position angle is stabilized quickly.It can be seen from Fig. 14 and Fig. 15, there is a small error between the estimated and measured generator rotor speed at low speed. At high speed, however, the error is very small and can be ignored, and the transient response is very short. At the time 1s, the input torque increase affects thegenerator rotor speed slightly, and soon the transientdisappears.ˆ,(d e g )θθ()t sFig. 12. The estimated and measured rotor position angle(rad/s)θθ∧−(s)tFig. 13. The error of estimated and measured rotor position anglet(s)()nrpmFig. 14. The measured generator rotor speedt(s)t()esirpmnFig. 15. The estimated generator rotor speedThe simulation waveforms of the machine-side converterdemonstrate that the sensorless vector control algorithm canestimate the rotor angular position accurately, and the vectorcontrol strategy of the machine-side converter can realizegenerator speed control for the wind turbine to follow theoptimized power curve, i.e. MPPT when the wind speed isbelow rated wind speed.B. The simulation results of the grid-side inverterThe simulation results of the grid-side inverter is shown inFig. 16, Fig. 17 and Fig. 18 respectively.It can be seen from Fig. 16, when the generator outputtorque increases, the DC bus voltage is maintained constant.Fig. 17 shows that θu followsavvery well, and Fig. 18shows thatai followsavvery well.Fig. 16. The simulated DC voltageavuθuθFig. 17. The generator output A phase voltage and the grid voltage vectorangleFig. 18. The output voltage and current of the grid-side inverterFrom the simulation results of the grid-side inverter, it canbe seen that the single-phase PLL algorithm can accuratelytrack the grid-side voltage, and the vector control strategy ofthe grid-side inverter can stabilize the DC bus voltage, andcontrol the grid power factor.V. C ONCLUSIONThis research developed a power electronic converter for asmall direct-driven PMSG wind turbine using the back-to-back pulse-width modulation (PWM) topology. Thesimulation results demonstrate that1) The machine-side converter can control the generatorspeed and torque for the wind turbine to follow the optimizedpower curve, i.e. maximum power point tracking (MPPT)when the wind speed is below rated wind speed.2) The sensorless phase-locked loop (PLL) controlalgorithm can realize the vector control of the generator.3) The grid-side inverter control algorithm based on single-phase PLL can stabilize the DC bus voltage of the converter and control the grid power factor.VI. R EFERENCESPeriodicals:[1]De Tian, “The wind power technology status and development trend inthe world,” New Energy Industry, in press.[2]Ruzhen Dou, Lingyun Gu, Baotao Ning, “Sensorless control of thePMSM based on the PLL,” Electric Machines & Control Application, vol. 32, pp. 53-57, 2005.Books:[3]Qingding Guo, Yibiao Sun, Limei Wang, Modern permanent magnet ACservo motor system. China Electric Power Press, Beijing. In press.Papers from Conference Proceedings (Published):[4]S. Song, S. Kang, and N. Hahm, “Implementation and control of gridconnected AC-DC-AC power converter for variable speed wind energy conversion system,” in Proc. 2003 IEEE Applied Power Electronics Conference and Exposition, vol.1, pp.154 – 158.[5]M. Ciobotaru, R. Teodorescu and F. Blaabjerg, “A new single-phasePLL structure based on second order generalized integrator,” Record of IEEE PESC 2006, Korea, pp.1511-1516.[6]R. Zhang, M. Cardinal, P. Szczesny, M. Dame, “A grid simulator withcontrol of single-phase power converters in D-Q rotating frame,” Power Electronics Specialists Conference, vol.3, pp.1431 – 1436, 23-27 June 2002.[7]R. Esmail, L. Xu, D.K. Nichols, “A new control method of permanentmagnet generator for maximum power tracking in wind turbine application,” IEEE Power Engineering Society Meeting, vol.3, pp. 2090-2095, August 2005.[8]Yang Zhenkun, Liang Hui, “A DSP control system for the gridconnected inverter in wind energy conversion system,” IEEE ICEMS 2005 Electrical Machines and Systems, vol. 2, 2005, pp. 1050-1053, June 2005.[9]N V Suresh Kumar Srighakollapu, Partha Sarathi Sensarma, “Sensorlessmaximum power point tracking control in wind energy generation using permanent magnet synchronous generator,” Industrial Electronics 2008, 34th Annual Conference Of IEEE, Iecon , pp.2225-2230.Dissertations:[10]Cheng Lu, “The coordination control of dual PWM converter for VSCFwind power generation system,” MSc thesis, Graduate School of Chinese Academy of Sciences, Beijing, 2004.[11]Shenbing Wu, “Research on CSC-based small-scale grid-connectedwind power generation system”, MSc thesis, Hefei University of Technology, Hefei, 2009.VII. B IOGRAPHIESChunxue Wen received his BSc degree from Inner Mongolia University of Technology in 2001, MSc degree from Wuhan University in 2006, and PhD degree from the Institute of Electrical Engineering, Chinese Academy of Sciences in 2009. In 2010 he joined the Wind Energy Engineering Research Group at the University of Central Lancashire as a visiting researcher. He is currently working as a Lecturer at the Power Electronics and Motor Drivers Engineering Research Center, North China University of Technology, Beijing, China. His research interests include power electronics, wind turbine control system, converters for wind turbines.Guojie Lu received his BSc degree from North China Electric Power University in 2006. He worked in Beijing Xinhuadu Special Transformer Company from 2007 to 2009, and was responsible for the technical service transformer. At present, he is registered as a postgraduate research student at the Power Electronics and Motor Drivers Engineering Research Center, North China University of Technology, Beijing, China. His research area is wind turbine control system.The project aims to develop maximum power point tracking control algorithm for grid-connected small wind turbines.Peng Wang received his BSc degree from Taiyuan University of Technology in 2003, MSc degree from North China University of Technology in 2011. Since 2008, he has been working as a research assistant in Electrical Engineering at the Power Electronics and Motor Drivers Engineering Research Center, North China University of Technology, Beijing, China. In 2010 he joined the Wind Energy Engineering Research Group at the University of Central Lancashire as a visiting student. His research areas are permanent-magnet synchronous generator control and wind energy engineering.Zhengxi Li received his PhD degree from the University of Science and Technology, Beijing. He is the Chair Professor in Power Electronics and Motor Drivers and Head of the Power Electronics and Motor Drivers Engineering Research Center, North China University of Technology, Beijing, China. He is also Vice President of North China University of Technology. His research interests include power electronics, high voltage power transmission and distribution, intelligent transportation and renewable energy. Xiongwei Liu was born in Xiangtan, China, in 1965. He received his BEng (Hons) degree from National University of Defense Technology, Changsha, in 1985, and his MSc (Distinction) and PhD degrees from Harbin Institute of Technology in 1988 and 1991 respectively.His employment experience included Northwestern Polytechnical University, Huaqiao University, Leeds Met University, University of Hertforshire and University of Central Lancashire. His research interests include wind energy engineering, renewable energy technologies, smart grid and microgrid, and intelligent energy management system.He received a research fellowship from Alexander-von-Humboldt Foundation of Germany, which allowed him to visit Ruhr University Bochum, as a research fellow for 18 months from 1993. In 1999 he was awarded a Bronze Medal by Huo Yingdong Education Funding Council and a Model Worker Medal by the Mayor of Quanzhou, China, due to his excellent contributions in higher education when he served as a professor at Huaqiao University. He received a research fellowship from Chinese Scholarship Council, which allowed him to visit Technical University Berlin as a senior research fellow for 6 months in 2000.Xiongwei Liu is currently working as Chair Professor of Energy and Power Management and Head of Wind Energy Engineering Research Group at the University of Central Lancashire.。
基于模糊控制的光伏系统最大功率点跟踪
基于模糊控制的光伏系统最大功率点跟踪xxx摘要：针对光伏发电系统的最大功率点跟踪（MPPT ）原理进行了详细的分析和阐述，介绍了传统的扰动观测法的优缺点，在此基础上提出了基于模糊控制的变步长扰动观察法来实现最大功率点跟踪。
通过Matlab/simulink 进行系统仿真，给出了光照突变时最大功率点跟踪曲线。
实验结果表明，该模糊控制算法具有更好的系统响应特性和稳态特性。
关键词：光伏；最大功率点；模糊控制Maximum power point tracking by using fuzzy control forphotovoltaic power systemAbstract ：Based on analying the principle of maximum power point tracking in photovolatic energy generation system ，this paper introduces the merit and shortcoming of the disturbance observation.Then it brings up the fuzzy control theory based on the maximum power tracking algorithm.Through simulation by Matlab&simulink ，it gives the maximum power point tracking curve when the illumination are changing.The experimental results show that the fuzzy control method has the better system and steady-state response characteristics.Key words ：photovolatic ；MPPT ；fuzzy control太阳能资源丰富，分布广泛，开发利用前景广阔。
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性 别
专业
综合排 专业 综合考查 综合 学分绩 名占百 学分绩 人数 学分绩 排名 排名 分比%
学分绩 占百分 比%
各类竞赛、科研成果、创新实践等情况 实用新型：一种洗漱间节能系统， 第一专利人 软件著作：大学洗漱间节能管理嵌入式软件V1.0，第一专利 人 实用新型：一种自动控温保暖衣，第三专利人
分项获 总获奖 奖分值 分值 47 5
基于模拟退火粒子群算法的波浪发电系统最大功率跟踪控制
喏名L乃农别名阄2017,44 (10)控制与应用技术I EMCA基于模拟退火粒子群算法的波浪发电系统最大功率跟踪控制邹子君\杨俊华\杨金明2(!广东工业大学自动化学院，广东广州510006;2.华南理工大学电力学院，广东广州 510641)摘要：波浪发电系统最大功率点跟踪控制中，传统粒子群算法存在早熟收敛和局部搜索能力不足问题，为此提出基 算法的粒子群 方案。
该算法 粒子的速度和位置时，通过比较当前粒子的 与随机数的大小，粒子中 局最 的，粒子群算法在发生早熟收敛时能 局部最 局最。
，与传统粒子群 算法相比，粒子群算法 波浪发电系统 局部最大功率点，局最大功率跟踪，波浪能捕获率。
关键词：波浪发电;最大功率点跟踪;模拟退火粒子群算法中图分类号：TM 301.2 文献标志码：A 文章编号：1673-6540(2017)10-0013-06Maximum Power Point Tracking Algorithm Based on Simulated AnnealingParticle Swarm Optimization for Wave Power SystemsZOUZijun1，YANG Junhua1，YANG Jinming2(1. School of Automation，Guangdong University of Technology，Guangzhou 510006，China;2.School of Electric Power，South China University of Technology，Guangzliou 510641，China)Abstract：The particle swarrm optimization (PSO) algorithm has low probability in searching global optimization and premature convergence i n the maximum power point tracking ( MPPT) control of the wave energy generationsystem. A novel simulated annealing particle swarm optimization ( SA-PSO) algorithm was proposed to solve t problem of the traditional PSO. When t he speed and position of each particle were updated with SA-PSO，thereplacement value of the global maximum from all particles was confirmed by comparing the fitness of each particle ofthe current temperature and the random number value. As a result，the new algorithm could escape local m the premature convergence and quickly discover global optimum solution. The simulation results showed that tliis novelalgorithm could make the wave energy generation systemeffectively avoid the local optimization and fast achieve globalMPPT control. The capture rate of wave energy was improved.Key words：wave energy generation；maximum power point tracking(MPPT); simulated annealing particle swarm optimization(SA-PSO))*都议定书）压力及日益増加的能源需求，清洁可生能源的开发和 获得广 。
基于模糊PI调节Boost电路的光伏系统最大功率点跟踪控制_尤鋆
光伏电池的输出电压、电流分别为 Upv 和 Ipv，其
I-U 特性等效为光生电流 Iph 减去二极管电流 Id，即：
Ipv = Iph - Id
（1）
# ! " $ Id = I0
exp
q（Upv + Ipv Rs） akT
-1
（2）
根据式（1）和式（2）可推出：
Upv =
akT q
ln Iph + I0 - Ipv I0
≥
≥
- U ≥
DC
+≥ ≥
L
≥
0 ≥≥
≥
≥ ≥
d赞≥
≥ ≥ ≥ ≥≥ ≥
≥
≥
（9）
电力自动化设备
第 32 卷
根 据 式 （9） 可 求 得 光 伏 阵 列 电 压 的 小 信 号 增 量
u赞 pva 对占空比 d 的小信号增量 d赞 的传递函数：
Gvd（s） =
u赞 pva（s） d赞 （s）
=
s2
Boost 电路开关频率 10 kHz，根据表 1 参数估算并取
裕量，取 C1= 200 μF。 稳态条件下，电感电流连续的临界条件为：每个
开关周期的开始或结束的时刻，电感电流正好为零，
即 IDC ≥ IVD2，可得：
L ≥ UDCTs d（1- d）2
（6）
2IDC
其中，Ts 为 Boost 电路的开关工作周期，一般取 100 μs；d 为 Boost 电路的可变占空比；根据估算可取 Boost 电
高效的光伏系统 MPPT 控制是实现高效的光伏 逆变器的前级组成部分，其电路 拓 扑 主 要 有 Boost Buck［5 ］ 、Buck-Boost ［6-7］、Buck 、Boost 等 。 Meza C 等 人 设计了 Boost-Buck 变结构控制电路，其 MPPT 控制 仍然是由 Boost 电路来实现，而由传统意义上的全桥 电路逆变电路来实现 Buck 变换器输出单位功率因 数的目的。 因为在光伏应用中，Boost 电路的效率比 Buck 高［8］，而根据文献［6 - 7］，Buck-Boost 可工作于 等效的 Boost 状态或 Buck 状态。 为了降低系统所需
光伏控制英语
IntroductionPhotovoltaic (PV) systems, harnessing the power of sunlight to generate electricity, have emerged as a pivotal component of global renewable energy strategies. The efficient and reliable operation of these systems is largely dependent on sophisticated control mechanisms that optimize their performance, ensure safety, and facilitate seamless integration with electrical grids. This comprehensive analysis delves into various aspects of PV control, exploring the technologies, methodologies, and standards that underpin high-quality, high-standard PV systems.I. Fundamental Principles of Photovoltaic ControlThe core objective of PV control is to maximize energy yield while maintaining system stability and compatibility with the grid. Key principles guiding this endeavor include:1. Maximum Power Point Tracking (MPPT): MPPT algorithms dynamically adjust the operating point of the PV array to extract the maximum available power under varying environmental conditions such as solar irradiance and temperature. Advanced MPPT techniques, such as perturb-and-observe, incremental conductance, and fuzzy logic, offer improved tracking accuracy and response time.2. Power Quality Management: PV inverters, responsible for converting DC power from the PV array to AC power compatible with the grid, must adhere to stringent power quality standards. Harmonic distortion, voltage flicker, and reactive power compensation are critical parameters that need to be controlled to prevent grid instability and equipment damage.3. Grid Interfacing and Compliance: PV systems must comply with grid codes and regulations, which vary across jurisdictions. Key requirements include low-voltage ride-through capability, frequency and voltage regulation support, and provision of ancillary services like reactive power control and active power curtailment.II. Advanced Control Strategies for Enhanced Performance1. Distributed MPPT: In large-scale PV installations, employing multiple MPPT units per inverter or using module-level power electronics can significantly enhance overall system efficiency by mitigating the effects of partial shading, module mismatch, and soiling.2. Forecasting and Predictive Control: Integrating weather forecasting and historical data analysis enables proactive control strategies that anticipate changes in solar irradiance and temperature, thereby optimizing power output and reducing energy losses. Machine learning algorithms can further enhance predictive capabilities by learning patterns and adapting to site-specific conditions.3. Hybrid Energy Systems Control: In scenarios where PV is combined with other renewable sources or energy storage, advanced control strategies are necessary to coordinate the operation of these components, ensuring optimal energy utilization, stability, and cost-effectiveness.III. Cybersecurity and Communication ProtocolsAs PV systems increasingly rely on digital communication and remote monitoring, cybersecurity becomes a paramount concern. Ensuring secure data transmission, protecting against cyber threats, and maintaining system integrity are vital for high-quality, high-standard PV control. Key aspects include:1. Secure Communication Protocols: Implementing industry-standard communication protocols like Modbus TCP/IP, DNP3, or IEC 61850, with robust encryption and authentication mechanisms, safeguards against data breaches and unauthorized access.2. Intrusion Detection and Prevention Systems: Deploying advanced cybersecurity measures, such as firewalls, intrusion detection/prevention systems (IDS/IPS), and regular firmware updates, fortifies PV systems against potential cyberattacks.3. Cybersecurity Standards Compliance: Adhering to international standards like IEC 62443 for industrial control systems security and NIST Cybersecurity Framework ensures a systematic approach to addressing cybersecurity risks in PV systems.IV. Quality Assurance and StandardizationTo guarantee high-quality, high-standard PV control, adherence to rigorous testing, certification, and standardization processes is essential. Key aspects include:1. International Standards: Compliance with international standards like IEC 61727 for MPPT performance evaluation, IEC 61000 for electromagnetic compatibility, and UL 1741 for inverter safety and performance ensures consistency and interoperability across different PV systems and markets.2. Certification and Testing: Third-party certification by recognized bodies like TÜV Rheinland, UL, or Intertek provides independent validation of PV control systems' compliance with relevant standards, enhancing reliability and consumer confidence.3. Continuous Monitoring and Maintenance: Regular system monitoring, performance assessment, and maintenance according to guidelines like O&M Best Practices Guidelines for Photovoltaic Systems ensure sustained high performance and early detection of potential issues.V. Future Perspectives and Technological AdvancesThe ongoing evolution of PV control is driven by advancements in areas such as:1. Digital Twins and Virtual Commissioning: Digital replicas of PV systems enable virtual testing and optimization of control strategies before deployment, reducing commissioning time and costs while enhancing overall system performance.2. Edge Computing and AI: Integrating edge computing devices and artificial intelligence algorithms can enable real-time, autonomous decision-making at the component level, further improving MPPT efficiency, fault detection, and predictive maintenance.3. Grid 2.0 Integration: As power grids transition towards more decentralized, flexible, and intelligent architectures (Grid 2.0), PV control systems will need to adapt to support bi-directional power flows, enhanced grid stability services, and participation in local energy markets.ConclusionHigh-quality, high-standard photovoltaic control is a multifaceted endeavor that encompasses advanced control strategies, robust cybersecurity measures, rigorous quality assurance, and continuous adaptation to technological advancements. By diligently addressing these aspects, the global PV sector can accelerate its contribution to a sustainable, resilient, and low-carbon energy future.。
风力发电机组优化控制器的设计
风力发电机组优化控制器的设计作者：杨德亮李泰邹博刘海舰王琪祥高斌来源：《科技创新导报》 2015年第9期杨德亮李泰邹博刘海舰王琪祥高斌（江苏科技大学电子信息学院江苏镇江 212003）摘要：风力发电机组是一种复杂时变非线性系统，当风在额定值以上时，机械载荷能力和功率波动的范围是影响风电机组稳定性的重要因素。
在风轮、传动系统、风力电机基础上建立风速双频环模型；并且通过低频环PI控制变浆距系统来实现额定功率控制；高频环设神经网络控制器以减少系统的机械振荡和保持系统运行的稳定性。
仿真结果表明该双频环优化控制器能够实现的功率稳定输出，有效减少负载的扰动，同时为神经网络控制器在风能转换系统中的应用提供了一种新的思路。
关键词：风能转换系统双频环优化控制节距角中图分类号：TP273 文献标识码：A 文章编号：1674-098X（2015）03（c）-0062-0320世纪90年代以来，全球风能产业迅速发展[1]，风能逐步被广泛应用到很多领域。
在风速低于额定值时，提高风能转换效率是最受到人们关注的问题之一，国内外相关学者就捕获最大风能方面的研究已经取得了很多的成果，常用方法是MPPT和LPV [2-3]。
当风速在额定值以上时，常用到的控制方法有PI、LQG等[4-5]。
但是会出现PI控制超调值过大、LQG控制参数过多等问题。
近年来，神经网络技术因其在处理非线性和不确定性方面的优势以及自身的并行性和不依赖数学模型的独立性，以及每个神经元具有的非线性激活函数，为解决风电变桨距问题提供了一种有效的方案[6-7]。
神经网络自身的并行性和硬件实现在变桨距中的应用有着十分重要的理论研究和工程应用价值[8-10]。
文中建立风轮，风机的数学模型，针对额定风速以上的情况，设计了神经网络控制器，建立了仿真模型，结果表明该方法可以有效保持功率稳定输出及维持风能转换系统稳定。
为神经网络在风电控制系统中的应用提供了较好的思路。
1 风能转换系统的建模1.1 风轮数学模型风经过风轮时产生的功率和气动转矩为：2.2 神经网络BP控制器设计高频环稳态优化的目的为使功率保持在其额定值，采用结构为2-4-1的BP网络，网络输入分别为高频参考风速与实际高频风速误差和电机高频转速，网络输出为高频节距角，BP网络结构如图3所示：3 仿真分析仿真参数如表1。
Time-optimal path tracking for robots -- a convex optimization approach
15
Existing solution methods:
Indirect methods
Numerical searches and forward and backward integration to determine “switching points” tedious implementation. exhaustive searches for candidate switching points. not very flexible.
subject to τ (s) = m(s)a(s) + c(s)b(s) + g(s), b(0) = and b(1) = sT , ˙2 b (s) = 2a(s), b(s) ≥ 0, τ (s) ≤ τ (s) ≤ τ (s), for s ∈ [0, 1]. Convex objective function, linear constraints and time is eliminated.
Time-Optimal Path Tracking for Robots 13
Convex reformulation
objective function can be rewritten as
T s(T )
T =
0
1dt =
s(0)
1 ds = s ˙
1 0
1 ds. s ˙
(12)
introduce optimization variables a(s) = ¨, s b(s) = s ˙ and additional linear constraint b (s) = 2a(s). (15)
基于横磁通发电机的永磁直驱风力发电系统
基于横磁通发电机的永磁直驱风力发电系统包广清;郑文鹏;毛开富【摘要】The transverse flux permanent magnet generator (TFPG) has ideal characteristics in terms of modular configuration, high torque density, low velocity and brushless, which makes it applicable to direct-driven wind energy conversion systems (WECS). Combined with the advantages of structural decoupling of the space requirement of flux carrying core iron path and the armature winding as well as the e-lectromagnetic decoupling of the armature windings in different phases, the use of TFPG working in variable speed wind turbine system was discussed. A novel maximum power point tracking ( MPPT) control scheme based on optimal electromagnetic torque reference was proposed. The generator-converter arrangement was described, the inverter switching effects were analyzed and the switching strategy was derived which is verified by the lOkVA laboratory experiment. It is proved that THD and power factor of grid side converter are 2. 8% and 0. 98 respectively, which meets the technical requirements for connecting WECS to power network.%为满足直驱式风力发电机组的低速、大转矩要求,对新型横磁通永磁多相发电机的转矩密度、模块化结构及其系统建模进行深入分析,针对此类电机电枢绕纽和主磁路在空间结构上的相对独立性和各相绕组间的电磁解耦特点,进行变速恒频风力发电控制系统设计,根据风力机输出特性,提出基于最优电磁转矩特性曲线的发电机最大功率跟踪方案.并搭建了10kVA样机系统,通过全功率逆变器完成电能转换与并网控制,实验测试结果表明发电系统馈入电网的电流THD为2.8％,功率因数为0.98,电能质量达到了风电入网标准.【期刊名称】《电机与控制学报》【年(卷),期】2012(016)011【总页数】6页(P39-44)【关键词】风力发电系统;同步发电机;永磁电机;功率变换器;并网;电能测量【作者】包广清;郑文鹏;毛开富【作者单位】兰州理工大学电信学院,甘肃兰州730050;中国电子科技集团公司第21研究所,上海200233;兰州理工大学电信学院,甘肃兰州730050【正文语种】中文【中图分类】TM3410 引言随着化石能源的日益枯竭与生态环境的不断恶化，风力发电以其无污染和可再生性，受到世界各国的重视。
Design of a Maximum Power Tracking System for Wind-Energy-Conversion Applications
Design of a Maximum Power Tracking System for Wind-Energy-Conversion ApplicationsEftichios Koutroulis and Kostas KalaitzakisAbstract—A wind-generator(WG)maximum-power-point-tracking(MPPT)system is presented,consisting of a high-efficiency buck-type dc/dc converter and a microcontroller-based control unit running the MPPT function.The advantages of the proposed MPPT method are that no knowledge of the WG optimal power characteristic or measurement of the wind speed is required and the WG operates at a variable speed.Thus,the system features higher reliability,lower complexity and cost,and less mechanical stress of the WG.Experimental results of the proposed system indicate near-optimal WG output power,increased by11%–50%compared to a WG directly connected via a rectifier to the battery bank. Thus,better exploitation of the available wind energy is achieved, especially under low wind speeds.Index Terms—Buck converter,maximum power point tracking (MPPT),microcontroller,variable speed,wind generator(WG).I.I NTRODUCTIONW IND GENERATORS(WGs)have been widely used both in autonomous systems for power supplying re-mote loads and in grid-connected applications.Although WGs have a lower installation cost compared to photovoltaics,the overall system cost can be further reduced using high-efficiency power converters,controlled such that the optimal power is acquired according to the current atmospheric conditions.The WG power production can be mechanically controlled by changing the blade pitch angle[1].However,WGs of special construction are required,which is not the usual case,especially in small-size stand-alone WG systems.A commonly used WG control system[2]–[4]is shown in Fig.1(a).This topology is based on the WG optimal power ver-sus the rotating-speed characteristic,which is usually stored in a microcontroller memory.The WG rotating speed is measured; then,the optimal output power is calculated and compared to the actual WG output power.The resulting error is used to control a power interface.In a similar version found in[5], the WG output power is measured and the target rotor speed for optimal power generation is derived from the WG optimal power versus rotor-speed characteristic.The target rotor speed is compared to the actual speed,and the error is used to control a dc/dc power converter.The control algorithm has been implemented in LabVIEW running on a PC.Manuscript received February26,2003;revised May30,2004.Abstract published on the Internet January25,2006.The authors are with the Department of Electronic and Computer Engineer-ing,Technical University of Crete,Chania GR-73100,Greece(e-mail:koskal@ electronics.tuc.gr).Digital Object Identifier10.1109/TIE.2006.870658In permanent-magnet(PM)WG systems,the output current and voltage are proportional to the electromagnetic torque and rotor speed,respectively.In[6]and[7],the rotor speed is calculated according to the measured WG output voltage, while the optimal output current is calculated using an ap-proximation of the current versus the rotational-speed optimal characteristic.The error resulting from the comparison of the calculated and the actual current is used to control a dc/dc converter.The disadvantage of all above methods is that they are based on the knowledge of the WG optimal power charac-teristic,which is usually not available with a high degree of accuracy and also changes with rotor aging.Another ap-proach using a two-layer neural network[8]updates online the preprogrammed WG power characteristic by perturbation of the control signals around the values provided by the power characteristic.However,under real operating conditions where the wind speed changes rapidly,the continuous neural-network training required results in accuracy and control-speed reduction.A control system based on wind-speed measurements[2] is shown in Fig.1(b).The wind speed is measured,and the required rotor speed for maximum power generation is com-puted.The rotor speed is also measured and compared to the calculated optimal rotor speed,while the resulting error is used to control a power interface.Implementations of fuzzy-logic-based control systems trans-ferring the maximum power from a wind-energy-conversion system to the utility grid or to a stand-alone system have been presented in[9]and[10],respectively.The controllers are based on a polynomial approximation of the optimal power versus the wind-speed characteristic of the WG.Apart from the accuracy reduction due to the approximation of the WG characteristics,an accurate anemometer is required for the implementation of the aforementioned methods,which increases the system cost.Furthermore,due to wind gusts of low-energy profile,extra processing of wind-speed measure-ment must be incorporated in the control system for a reliable computation of the available wind energy,which increases the control system complexity.In this paper,an alternative approach for WG maximum-power-point-tracking(MPPT)control is described.The block diagram of the proposed system is illustrated in Fig.2.The MPPT process is based on monitoring the WG output power using measurements of the WG output voltage and current and directly adjusting the dc/dc converter duty cycle according to the result of comparison between successive WG-output-power values.Thus,neither knowledge of the WG power0278-0046/$20.00©2006IEEE2πρC p(λ,β)R2V3(1)whereρis the air density(typically1.25kg/m3),βis the pitch angle(in degrees),C p(λ,β)is the wind-turbine power coefficient,R is the blade radius(in meters),and V is the wind speed(in m/s).The termλis the tip-speed ratio,defined asλ=ΩRV(2)whereΩis the WG rotor speed of rotation(rad/s).R(4)whereΩn is the optimal WG speed of rotation at a wind velocity V n.Besides the optimal energy production capability,another advantage of variable-speed operation is the reduction of stress on the WG shafts and gears,since the blades absorb the wind torque peaks during the changes of the WG speed of rotation. The disadvantage of variable-speed operation is that a power conditioner must be employed to play the role of the WG ap-parent load.However,the evolution of power electronics helps reduce the power-converter cost and increase its reliability, while the higher cost is balanced by the energy production gain. The torque curves of the WG,consisting of the intercon-nected wind-turbine/generator system,for various generator output voltage levels under various wind speeds,are shown in Fig.4.The generator is designed such that it operates in the approximately linear region corresponding to the straight portion of the generator torque curves in Fig.4,under any wind-speed condition.The intersection of the generator torque curve with the wind-turbine torque curve determines the WG operating point.During the MPPT process,a change of the WGapparent load results in variable generator output voltage level;thus,the generator torque is adjusted such that the generator∆D k−1(5)dΩ=0(6)whereΩis the WG rotor speed.Applying the chain rule,the above equation can be written asdP dΩ=dPdD·dDdV WG·dV WGdΩe·dΩedΩ=0(7)where V WG is the rectifier output voltage level andΩe is the generator-phase-voltage angular speed.In case of a buck-type dc/dc converter,its input voltage is related to the output(battery)voltage and the duty cycle as follows:D=V o V WGdD dV WG =−1V2WGV o=0(8)where V o is the battery voltage level.The wind-turbine rotor speed is related to the generator speed as follows:Ωe=p·ΩdΩedΩ=p>0(9) where p is the generator number of pole pairs.The rectifier output voltage V WG is proportional to the gener-ator phase voltage V ph;considering Fig.4,it is concluded thatdV phdΩe>0(10) anddV WGdΩe>0.(11)Considering(7)–(11),it holds thatdPdΩ=0⇔dPdD=0.(12)Thus,the function P(D)has a single extreme point,coinciding with the WG MPP,and the dc/dc converter duty-cycle adjust-ment according to the control law of(5)ensures convergence to the WG MPP under any wind-speed condition.The power maximization process is shown in Fig.5.Since the duty-cycle adjustment follows the direction of dP/dD,the duty-cycle value is increased in the high-speed side of the WG characteristic,resulting in a WG-rotor-speed reduction and power increase,until the MPP is reached.Similarly when the starting point is in the low-speed side,following the direction of dP/dD results in duty-cycle reduction and the subsequent convergence at the MPP,since the WG rotor speed is progres-sively increased.The proposed method can also be applied to maximize the output power of the WG in case of alternative dc/dc converter configurations.1)Boost converter:V WG=(1−D)V o,dV WG/dD=−V o=0.2)Buck–boost converter:V WG=V o(1−D)/D,dV WG/dD=−(1/D2)V o=0.3)Cuk converter:V WG=V o(1−D)/D,dV WG/dD=−(1/D2)V o=0.4)Flyback converter:V WG=V o(1−D)/D,dV WG/dD=−(1/D2)V o=0.In order to reduce the impact of the sensor accuracy on the generated power,the control law of(5)has been implementedFig.6.Detailed diagram of the proposed system.based on incremental WG power measurements,rather than absolute measurements,as follows:D k=D k−1+∆D k−1∆D k−1=C2·sign(∆D k−2)·sign(P in,k−1−P in,k−2)(13) where∆D k−1is the duty-cycle change at step k−1;P in,k−1 and P in,k−2are the converter input-power levels at steps k−1 and k−2,respectively;C2is a constant determining the speed and accuracy of the convergence to the MPP;and the function sign(x)is defined assign(x)=1,if x≥0sign(x)=−1,if x<0.(14)B.Power-Electronic InterfaceThe detailed diagram of the proposed system is depicted in Fig.6.The WG ac output voltage isfirst converted to dc form using a three-phase full-wave bridge rectifier.The rectifier output capacitor value C r is calculated as follows:C r≥112fR L1+1√2RF(15)where R L is the WG load resistance,f is the WG output voltage frequency,and RF is the rectifier output voltage ripple factor.A buck-type dc/dc converter is used to convert the high dc input voltage to the24-V battery voltage level.Theflyback diode D is of fast-switching type,while four power MOSFETs are connected in parallel,to comply with the converter powercapability requirements.A power MOSFET is used to switchon and off a 10-Ωresistive dummy load,thus limiting the WG speed of rotation under severe conditions.The power inductor L and the input and output capacitor values,C in and C ,respectively,are calculated as follows [11]:L ≥V om (1−D cm )f s |∆I Lm |(16)C ≥18(1−D cm )L f 2s RF o (17)C in ≥(1−D cm )I om D cm RF in V WGm f s(18)where f s is the dc/dc converter switching frequency,D cm is the duty cycle at maximum output power of the converter,∆I Lm is the peak-to-peak ripple of the inductor current,V om is the maximum of the dc component of the output voltage,I om is the dc component of the output current at maximum output power,RF o is the output voltage ripple factor (typically RF o ≤2%),RF in is the input voltage ripple factor (typically RF in ≤2%),and V WGm is the converter input voltage at maxi-mum power.The control unit is supplied by the battery and consists of an Intel 80C196KC microcontroller unit with an external erasable programmable ROM (EPROM)and a static RAM (SRAM),the interface circuits comprising of sensors and am-plifiers connected to the on-chip A/D converter,as well as the power MOSFET IC drivers.A 39.2-kHz 8-bit-resolution on-chip pulsewidth modulation (PWM)output is used to control the power MOSFETs of the buck converter through the IR2104driver IC,while an I/O port pin controls the power MOSFET that switches the dummy load through the IR2121driver IC.Another I/O port is used to drive a liquid crystal display (LCD)showing various parameters of the system operation.The WG and battery voltages are measured by means of voltage dividers interfaced to operational-amplifier (op-amp)-based voltage-follower circuits.The dc/dc converter input cur-rent is equal to the average value of the power MOSFET current,which has a pulse-type waveform and is measured with a unidirectional current transformer.The flowchart of the control algorithm is shown in Fig.7.The battery voltage is monitored and when it reaches a predefined set point,the MPPT operation is suspended in order to protect the battery stack from overcharging.The PWM duty-cycle value is stored in an 8-bit register of the microcontroller,taking values that correspond to duty-cycle values 0%–99.6%.The WG output power is calculated and compared to the WG output power at the previous iteration of the algorithm.According to the result of the comparison,the sign of the duty-cycle change ∆D is either complemented or remains unchanged.Subsequently,the PWM output duty cycle is changed appropriately,thus implementing the control law described by (13).After the duty-cycle regulation,the WG voltage is checked;if it is higher than the maximum preset limit,the dummy load is connected to the dc/dc converter input in order to protect theP in=P o P o +P d(19)where P in and P o are the dc/dc converter input and output power,respectively,and P d is the power loss consisting of the MOSFET and diode conduction and switching losses,the inductor core and copper losses,and the control system power consumption.The theoretical and measured efficiency for various output-power levels is shown in Fig.9.The theoretical values were calculated using data given by the manufacturers of the circuit elements.It is observed that the efficiency is quite high and rela-tively constant for a wide output power range.This is important in WG systems since the generated power depends strongly on the atmospheric conditions and varies over a wide range.The wind speed,the WG output power,and the corresponding rotor speed of rotation,measured during a 22-min time period and sampled with a 0.1-Hz rate,are depicted in Fig.10.It is observed that the WG power production follows the changes of the windspeed.n in ij =1P ij (20)Ωi =1n i n i j =1Ωij(21)where Ωij is the j th rotational-speed measurement in the i th interval,P ij is the j th power measurement in the i th interval,and n i is the number of data sets in the i th interval.The resulting ensemble averages (P i ,Ωi )were used to build the diagram shown in Fig.11.It can be concluded that,usingn kn kp=1P kp(22)V k=1n kn kp=1V kp(23)where V kp is the p th wind-speed point in the k th interval,P kp is the p th power point in the k th interval,and n k is the number of data sets in the k th interval.The resulting ensemble averages(P k,V k)are used to build the diagram shown in Fig.12.It is noticed that the WG output power follows the optimal WG power versus wind-speed char-acteristic with a maximum deviation of approximately6.5%, while the rectifier power loss is responsible for30%of this deviation.The power production of a WG directly connected to a battery-rectifier load is also indicated in the samefigure.The WG-output-power benefit using the proposed MPPT method, compared to the battery-rectifier configuration,is11%–50%in the power range of100–600W.It is clearly concluded that the proposed method results in a better exploitation of the available wind energy,especially in the low wind-speed range of2.5–4.5m/s.The power transferred to the battery bank is derived consider-ing the dc/dc converter efficiency,the WG output power,andthe[3]V .Valtchev,A.Bossche,J.Ghijselen,and J.Melkebeek,“Autonomousrenewable energy conversion system,”Renew.Energy ,vol.19,no.1,pp.259–275,Jan.2000.[4]E.Muljadi and C.P.Butterfield,“Pitch-controlled variable-speed windturbine generation,”IEEE Trans.Ind.Appl.,vol.37,no.1,pp.240–246,Jan.2001.[5]A.M.De Broe,S.Drouilhet,and V .Gevorgian,“A peak power tracker forsmall wind turbines in battery charging applications,”IEEE Trans.Energy Convers.,vol.14,no.4,pp.1630–1635,Dec.1999.[6]O.Honorati,G.Lo Bianco, F.Mezzetti,and L.Solero,“Powerelectronic interface for combined wind/PV isolated generating systems,”in Proc.Eur.Union Wind Energy Conf.,Göteborg,Sweden,1996,pp.321–324.[7]G.Lo Bianco,O.Honorati,and F.Mezzetti,“Small-size stand alone windenergy conversion system for battery-charging,”in Proc.31st Universities Power Engineering Conf.,Iráklion,Greece,1996,pp.62–65.[8]R.Spee,S.Bhowmik,and J.Enslin,“Novel control strategies for variable-speed doubly fed wind power generation systems,”Renew.Energy ,vol.6,no.8,pp.907–915,Nov.1995.[9]A.Z.Mohamed,M.N.Eskander,and F.A.Ghali,“Fuzzy logic con-trol based maximum power tracking of a wind energy system,”Renew.Energy ,vol.23,no.2,pp.235–245,Jun.2001.[10]R.M.Hilloowala and A.M.Sharaf,“A rule-based fuzzy logic controllerfor a PWM inverter in a stand alone wind energy conversion scheme,”IEEE Trans.Ind.Appl.,vol.32,no.1,pp.57–65,Jan./Feb.1996.[11]N.Mohan,T.Undeland,and W.Robbins,Power Electronics:Converters,Applications and Design ,2nd ed.New York:Wiley,1995,pp.164–172.Eftichios Koutroulis was born in Chania,Crete,Greece,in 1973.He received the B.S.,M.S.and the Ph.D.degrees in the area of power electronics and renewable energy sources (RES),in 1996,1999,and 2002,respectively,from the Department of Elec-tronic and Computer Engineering,Technical Univer-sity of Crete,Chania,Greece.He is currently a Research Associate in the De-partment of Electronic and Computer Engineering,Technical University of Crete.His research interests include photovoltaic and wind-energy-conversionsystems,energy management systems with RES,power electronics (dc/ac inverters and dc/dc converters),data-acquisition systems,sensors and transduc-ers,and microcontroller-basedsystems.Kostas Kalaitzakis was born in Chania,Crete,Greece,in 1954.He received the B.S.degree in elec-trical and mechanical engineering from the National Technical University of Athens,Zographou,Greece,and the Ph.D.degree in renewable energy sources (RES)from the School of Electrical Engineering,Democritus University of Thrace,Xanthi,Greece,in 1977and 1983,respectively.He is currently a Professor at the Technical Uni-versity of Crete,Chania,Greece.He served as an Adjunct Assistant Professor at the Georgia Instituteof Technology,Atlanta.His current research interest include renewable energy sources,energy saving in buildings,power electronics,sensors and measure-ment systems,smart cards applications,fuzzy,neural,and genetic decision support and control systems,bioengineering,and local operating networks.。
纯方位角定位的单步最优观测轨迹算法
纯方位角定位的单步最优观测轨迹算法权宏伟;彭冬亮;薛安克【摘要】纯方位角无源定位时,观测平台的运动轨迹对目标最终的定位精度有重要影响.针对之前在求取观测平台最优轨迹时限制条件多、算法可能只是局部最优的问题,提出了一种观测平台的单步最优轨迹算法.计算机仿真算例表明:与通常的最优观测平台轨迹算法相比,该算法在求解最优轨迹时只需已知观测平台的初始状态,同时算法不受观测次数和终止条件的限制,具有较强的工程实用性.【期刊名称】《探测与控制学报》【年(卷),期】2010(032)003【总页数】4页(P18-21)【关键词】纯方位角定位;最优轨迹设计;Fisher信息矩阵;Cramer-Rao下限【作者】权宏伟;彭冬亮;薛安克【作者单位】华东理工大学信息科学与工程学院,上海,200237;杭州电子科技大学信息与控制研究所,浙江,杭州,310037;杭州电子科技大学信息与控制研究所,浙江,杭州,310037【正文语种】中文【中图分类】TP2710 引言纯方位角定位与跟踪是信号检测及滤波理论领域内一类较难解决的问题[1-5]。
实际观测过程中,目标定位精度不仅受随机观测噪声的影响,而且也与观测平台的运动轨迹有关[6]。
为提高目标的定位精度,通常要求观测平台沿某条最优轨迹运动,以保证最后得到的关于目标状态的估计量具有最小的估计误差。
观测平台最优轨迹设计是指选取适当的系统优化性能指标,使得在该观测轨迹下得到目标定位精度最高。
本文研究的即是如何设计最优观测平台轨迹的问题。
目前,国内外大多数学者都使用Fisher信息矩阵(FIM)作为轨迹优化的性能指标,但在具体算法上对FIM的处理不同。
Andrew提出了信息论方法,通过最大化观测量序列的互信息来求取最优观测路径。
这种方法实质上等同于最大化FIM的行列式[7]。
Passerieux引入信息率的概念,给出了目标在匀速直线运动时的最优观测平台轨迹[8]。
上述方法在求取最优观测轨迹时,都加入了一定的限制性条件,如限定观测次数及观测平台终止状态等。
基于LS-SVM的太阳能最大功率点跟踪的研究
基于LS-SVM的太阳能最大功率点跟踪的研究摘要：针对光伏组件中最大功率跟踪方法存在的不足，提出了应用最小二乘法支持向量机进行最大功率点的跟踪，并利用粒子群算法对支持向量机参数进行寻优。
通过对实测数据进行的仿真分析表明，lssvm具有较高的泛华能力，更高的预测精度和稳定性。
关键词：太阳能；最小二乘法支持向量机（ls-svm）；最大功率点跟踪（mppt）；最优化中图分类号：tk511文献标识码：a文章编号：随着社会的不断发展，对能源的需求日益增加，能源危机亦逐步加深，太阳能作为一种清洁的、可持续的能源备受青睐。
为了获得太阳能最大的利用效率和经济利益，太阳能最大功率点跟踪（mppt）技术被广泛引用到太阳能发电中。
本文针对常规算法在快速跟踪效率低等诸多缺点，尝试应用一种新的机器学习方法-最小二乘法支持向量机（ls-svm）来实现mppt技术。
ls-svm简介ls-svm算法在svm算法的基础上，将最小二乘法引入其中构成了最小二乘法支持向量机（ls-svm），将标准支持向量计算法中的不等式约束化成等式约束而得到。
最小二乘法支持向量机的模型为：（1）取径向基核函数（2）则最小二乘法支持向量机的预测模型可以写为：（3）上式中取值过大将使模型过早收敛，达不到预测的目的，取值较大可以使训练样本数据和测试数据拟合的更好，即提高泛化能力。
两个参数选取合适才能保证模型的预测精度，利用粒子群算法来进行两个参数的寻优：假设一个有m个粒子组成的群体在n维搜索空间中以一定的速度飞行。
粒子i在t时刻的状态可以表达如下：位置：速度：个体搜索到的最优位置：全局最优位置：则粒子在t+1时刻的位置按照以下公式更新：（4）其中：为惯性因子；是常数，他们分别称为自身因子和全局因子；是[0,1]之间的随机数。
为了能够提高参数优化的效果，采用了能够反映svm回归性能的均方差函数为粒子群算法的适应度函数：（5）光伏mppt系统利用svm算法实现太阳能mppt技术的结构图如下所示：svm实现mppt系统结构图利用svm对样本数据进行拟合，得到最大功率点电压vmp与开路电压voc、温度t、时间t的函数关系。
文献综述【模板】
柔性直流输电系统逆变侧控制方法改进1 引言近年来，中国风电产业规模延续暴发式增长态势。
2008年就已达到10000兆瓦的发展目标，2010年更是实现了30000兆瓦的风电装机目标。
中国风电2010年新增装机容量达到18,928兆瓦，占全球新增装机容量48%，成为世界第一大风力发电市场[1]。
尽管如此，各地可被利用的风能却很分散，要想将其转化为电能，大规模利用，无疑，需要建立众多中小规模的分散风电场，这无疑增大了输电，并网的经济成本，技术困难等[2]。
然而，基于电压压源型换流器（VSC）的高压直流输电（HVDC）系统可独立调节有功和无功功率并且实现四象限运行、可以向无源网络供电，并且具有联网非同步运行的独立电网、方便构成多端直流系统、不需要交流侧提供无功功率并能够起到STATCOM的作用、不会增加系统的短路容量、可以便捷高效地连接风能、太阳能等距离偏远、地理分散的可再生能源或―绿色‖能源等优势。
因此，柔性直流输电技术（VSC-HVDC）被更多的应用[3]。
传统VSC-HVDC换流站控制回路中，往往使用PI调节器来实现对反馈律设计[4]。
但是随着现代科技的发展对控制精度和响应速度极大地提高，逐渐凸显出PI应用的局限性，因此我们有必要对换流站PI控制器进行改换优化，从而使控制精度，输电效率都得到提高[5]。
2 VSC-HVDC系统的基本控制原理柔性直流输电(VSC-HVDC)的基本任务是实现两端系统之间的功率交换，同时保证直流线路有功功率的平衡，且每个换流站能够独立控制其无功潮流，为系统提供无功支持。
为实现有功功率的平衡，必须有一个换流站采用直流控制器来控制直流电压，另一个换流站采用功率控制器使有功功率维持在定值。
由于VSC 换流站采用PWM控制技术，可以实现有功功率和无功功率独立解耦控制，无功功率可以通过控制站端交流电压来实现，而无需改变直流电压。
典型的柔性直流输电系统控制方式主要有：定直流电压控制，定有功功率控制，定交流电压控制，定无功功率控制，不同的应用场合采用的控制器也不同。
最大功率点追踪算法matlab代码
最大功率点追踪算法matlab代码摘要：一、引言二、最大功率点追踪算法概述1.最大功率点概念2.最大功率点追踪算法分类三、MATLAB 代码实现1.代码结构2.代码详解a.初始化参数b.获取太阳能电池的输出特性c.计算最大功率点d.最大功率点跟踪四、结论正文：一、引言最大功率点追踪（Maximum Power Point Tracking，简称MPPT）算法是光伏发电系统中关键技术之一，其作用是在光伏发电过程中实时追踪太阳能电池的最大功率点，以保证光伏发电系统始终工作在最佳状态，从而提高系统的能源利用率。
本文旨在介绍一种简单的最大功率点追踪算法，并提供相应的MATLAB 代码实现。
二、最大功率点追踪算法概述最大功率点（Maximum Power Point，简称MPP）是指太阳能电池在工作时，输出功率最大的工作点。
太阳能电池的输出功率与电压、电流之间存在一定的关系，通过调整电压和电流，可以使太阳能电池的工作点接近最大功率点。
根据这一原理，可以设计最大功率点追踪算法。
最大功率点追踪算法主要分为以下几类：1.基于电压调制的最大功率点追踪算法：通过调整太阳能电池的电压，使其工作在最大功率点附近。
2.基于电流调制的最大功率点追踪算法：通过调整太阳能电池的电流，使其工作在最大功率点附近。
3.基于电压- 电流双调制的最大功率点追踪算法：同时调整太阳能电池的电压和电流，使其工作在最大功率点附近。
三、MATLAB 代码实现本文提供的MATLAB 代码实现是一种基于电压- 电流双调制的最大功率点追踪算法。
代码主要包括以下几个部分：1.初始化参数：设置一些必要的参数，如太阳能电池的额定电压、额定电流、温度等。
2.获取太阳能电池的输出特性：根据太阳能电池的参数，计算其输出特性曲线，以便后续计算最大功率点。
3.计算最大功率点：根据输出特性曲线，计算最大功率点对应的电压和电流。
4.最大功率点跟踪：实时调整太阳能电池的电压和电流，使其工作在最大功率点附近。
最大功率点追踪算法matlab代码
最大功率点追踪算法matlab代码最大功率点追踪（Maximum Power Point Tracking，MPPT）是在太阳能电池系统中用于提取最大功率的一种技术。
其中，一种常见的MPPT 算法是Perturb and Observe（P&O）算法。
以下是P&O 算法的MATLAB 代码示例：```matlab% P&O MPPT Algorithmfunction [Vmp, Pmp] = perturb_observe(V, I, Vmin, Vmax, stepSize)% 初始化Vmp = (Vmax + Vmin) / 2;Pmp = Vmp * interp1(V, I, Vmp, 'linear', 'extrap');% 迭代调整while trueVmp_new = Vmp + stepSize;Pmp_new = Vmp_new * interp1(V, I, Vmp_new, 'linear', 'extrap');% 检查功率变化的方向if Pmp_new > PmpVmp = Vmp_new;Pmp = Pmp_new;elsebreak; % 如果功率下降，则停止迭代endendend```这个简单的P&O MPPT 算法的工作原理是通过微小的扰动（`stepSize`）改变电压，观察功率的变化方向，从而找到最大功率点。
在代码中，输入参数包括电压（V）和电流（I）的数组，以及电压的最小值（Vmin）、最大值（Vmax）和扰动步长（stepSize）。
你可以使用这个函数来调用P&O 算法并获取最大功率点的电压（Vmp）和功率（Pmp）。
例如：```matlab% 示例用法V = linspace(0, 50, 100); % 电压数组I = 5 - 0.1 * V; % 对应的电流数组（简化模型）Vmin = 0;Vmax = 50;stepSize = 0.1;[Vmp, Pmp] = perturb_observe(V, I, Vmin, Vmax, stepSize);% 显示结果disp(['最大功率点电压：', num2str(Vmp), 'V']);disp(['最大功率点功率：', num2str(Pmp), 'W']);```请注意，这只是一个简化的示例，实际应用中需要根据具体的太阳能电池模型和系统特性进行调整。
基于电导增益的光伏最大功率点的跟踪算法及仿真
基于电导增益的光伏最大功率点的跟踪算法及仿真陈艳;张科智【摘要】根据光伏电池的工程数学模型,利用Matlab/simulink软件对光伏电池的输出特性进行了仿真,模拟了光伏电池的输出特性,讨论了温度和光照强度对光伏电池输出特性的影响.此外,还研究了基于电导增益法的最大功率点跟踪算法,分析了最大功率点附近的振荡现象.结果表明,采用变步长的电导增益法,可以有效地抑制最大功率点附近的振荡现象.【期刊名称】《西北师范大学学报（自然科学版）》【年(卷),期】2018(054)004【总页数】7页(P52-57,98)【关键词】光伏电池;最大功率点跟踪;电导增益【作者】陈艳;张科智【作者单位】河西学院物理与机电工程学院,甘肃张掖734000;河西学院新能源研究所,甘肃张掖734000;河西学院物理与机电工程学院,甘肃张掖734000;河西学院新能源研究所,甘肃张掖734000【正文语种】中文【中图分类】TM914.4目前，人类对能源的需求量越来越大.然而，由于科学技术与制造工艺的滞后，迄今为止光伏电池的转换效率仍然很低.光伏电池是一种输出不稳定的非线性电源，其输出功率容易受光照强度、温度和负载变化的影响，不能始终保持最大功率输出.因此，最大功率跟踪控制研究，一直是光伏发电领域研究的重要内容[1-3].在光伏发电系统引入最大功率点跟踪(Maximum power point tracking，简称MPPT)控制技术，可以使系统时刻工作在最大功率点，从而提高系统整体的发电效率.国内外学者对光伏发电MPPT控制技术做了大量研究，各种MPPT控制算法层出不穷.变步长增量电导法是其中一种非常高效的MPPT 控制方法，在跟踪速度和稳态精度上能够达到很高的性能.因此文中在Matlab/simulink环境下建立了光伏电池的仿真模型，研究了光照强度和温度对光伏电池最大输出功率的影响，并且利用变步长增量电导法对系统进行了仿真，呈现了其跟踪效果，并分析了优缺点，提出了改进的跟踪算法，并分析了其跟踪效果.1 光伏电池的数学模型光伏电池是利用半导体材料的光电效应原理制成的，实际光伏电池的等效电路如图1所示.图1 实际光电池的伏等效电路Fig 1 The equivalent circuit of practical photoraltaic cells图1中Iph=Isc为光子在光伏电池中激发的电流;R为光伏电池的外接负载;U为输出电压;I为输出电流;Rs为等效串联电阻;Rp为等效并联电阻;Id为等效二极管电流，其方向与光生电流相反.假设在参考条件下，Isc为光伏电池短路电流;Uoc为光伏电池开路电压;Um,Im分别为光伏电池MPPT对应的电压和电流.考虑太阳辐射强度S(W·m-2)和环境温度T(℃)有极大关系,根据电子学理论，当负载为纯电阻时，得到太阳能电池的数学模型为其中，I0为光伏电池里的等效二极管P-N结的反向饱和电流，一般为常数，反映的是光伏电池复合光生载流子的最大能力，仅与电池材料的性能有关，而与光照强度无关;Ud为光伏电池内部等效二级管两端的电压;q为电子电荷;k为玻尔兹曼常量;T为绝对温度;A为P-N结曲线常数.但在实际问题中，光伏电池的电流-电压曲线会受到外界因素的影响，为了便于工程应用，对上述方程进行修正和简化处理，得到了比较实用的光伏电池工程数学模型[4-7]:(5)其中，Voc与Isc分别是光伏电池等效电路的开路电压和短路电流;Vm 与Im分别是光伏电池的最大输出电压和电流;C1与C2是修正系数;在任意外界环境下，Voc,Isc,Vm和Im会按照一定的规律进行变化.通过引入相应的补偿系数，可以近似推算出任意光照强度S和温度T下的个技术参数.(6)其中,ΔS=S/Sref-1,ΔT=T-Tref.根据以上分析和公式在Matlab/simulink环境下建立光伏电池的仿真模型.图2 光伏电池仿真模型封装Fig 2 Simulation madel package of photovoltaic cells如图2所示，模型的仿真参数设置如下，标准状态下光照强度和温度的参考值为Sref=1 000 W·m-2和Tref=25 ℃;短路电参考流Isc-ref=10 A;开路参考电压Voc-ref=105 V;最大功率点的电压和电流的参考值为Vm-ref=80 V和Im-ref=8.5 A;修正因子a=0.002 5 ℃-1，b=0.5,c=0.002 28 ℃-1.利用这些参数，可以仿真出光伏电池在不同的温度和光照强度下的I-V曲线和P-V曲线.2 光伏电池输出特性的仿真模拟2.1 温度对光伏电池输出特性的影响在研究温度对光伏电池输出功率的影响时，采用控制变量的方法，控制光照强度为S=1 000 W·m-2不变,取不同的温度值10 ℃,25 ℃,40 ℃在仿真系统中进行仿真，其结果如图3所示.图3 S=1 000 W·m-2时不同温度的U-P曲线和U-I曲线Fig 3 The U-P and U-I curves for different temperature图3分别为光照强度S=1 000 W·m-2时不同温度下P-U和U-I的变化曲线.从P-U图中可以看到随着温度的增大，输出功率略有减小.表明温度的大小可以影响太阳能电池的输出效率，温度越大光伏电池的输出功率就越小反之输出功率就越大.从不同温度下的U-I输出曲线可看出曲线走势一样，且随着温度的上升，短路电流减小，开路电压增大，但影响不大.仿真的数据表明温度的高低能够影响光伏电池的输出特性曲线，从而影响光伏电池的效率，并且温度每升高1 ℃，光伏电池输出功率降低4%.2.2 光照强度对光伏电池输出特性的影响在研究光照强度对光伏电池输出功率的影响时，同样采用控制变量的方法，保持光伏电池的温度T=25 ℃不变，取不同的光照强度1 000 W·m-2,900 W·m-2,700 W·m-2在仿真系统中仿真.其结果如图4所示.从图中可以看出，光照强度在很大的程度上影响着光伏电池的输出特性，光照强度越大,光伏电池的输出功率也就越大反之输出功率越小.通过以上对温度和光照强度的模拟，可以得出光伏电池的工作效率受温度和光照强度的影响，且输出曲线具有明显的非线性特征.利用Matlab/simulink数学模型的仿真得到的P-U曲线和I-U曲线与光伏电池理论上分析的曲线比较吻合，证明了Matlab/simulink数学模型的可行性.该仿真模型在温度和光照强度下发生变化的情况下，其输出特性可以迅速的做出相应的响应，从而表现出良好的动态性，达到了预期的效果.图4 T=25 ℃时不同光照强度U-P曲线和U-I曲线Fig 4 The U-P and U-I curves for different light intensity3 基于电导增益法的光伏电池最大功率点跟踪分析根据光伏电池的特性，其输出功率会随着温度和光照强度的变化而变化；在一定的温度和光照强度下其输出功率会随着工作点的变化而变化且存在最大功率点.要充分利用光能发电，光伏系统需采用最大功率跟踪(MPPT)控制.3.1 电导增益法的基本原理电导增益法是实现MPPT最常用的自寻优类方法之一.电导增益法来源于光伏系统电导系数的导数(变化率)，通过光伏电池输出特性曲线的斜率与输出电压、电流之间的关系来判断系统是否在最大功率点处运行.通过以上对光伏电池输出特性曲线的模拟，可以看出，正常温度和光照强度下光伏电池的P-U输出特性曲线是一个以最大功率点为极值的单峰函数，在最大功率点处有dP/dU=0，那么最大功率点的跟踪实质上就是搜索满足dP/dU=0的工作.由于数字控制有精度上的限制，dP/dU以ΔP/ΔU近似代替,从而影响了精确性.为了提高跟踪的精确度，用功率的全微分来近似代替dP的算法，从dP=UdI+IdU出发，推导出以电导和电导变化率之间的关系为搜索判据的算法，这种方法就是电导增益法.在实际过程中，用ΔI/ΔU近似代替dI/dU,用电导增益法进行最大功率点跟踪的判据如下[8-9]:(5)本质上说电导增益法就是求出工作电压变化前后的功率，找出满足Δp/ΔU=0的工作点.3.2 电导增益法仿真模型电导增益法按每次系统调整工作点时固定改变的电压量ΔU*，分为定步长电导增益法和变步长电导增益法，定步长电导增益法的流程如图5所示.其中，ΔU*为每次系统调整工作点时固定改变的电压量，即步长，Uref为下一工作点的电压.先对ΔU计算后进行其是否为0的判定，使流程图出现两条分支，其左边的分支与上述分析相互吻合，右边的分支是为了防止外部辐射发生突变时导致误判而设置的.建立的定步长电导增益法的仿真模型如图6所示.图5 电导增益法流程图Fig 5 The flow chart of conductance increment method3.3 仿真结果与分析设置环境温度T为25 ℃;日照强度S为1 000 W·m-2;运行时间为300 s;仿真中设置基于固定步长扰动算法的步长分别为0.1,1和5 3种情况，仿真结果如图7-8所示.图6 定步长电导增益法的仿真模型Fig 6 The simucation model for fixed step conductance increment method图7 定步长电导增益法的仿真结果Fig 7 The simulation result for fixed step conductance in crement method图8 放大后的仿真结果Fig 8 The amplified simulation result由图7中看到，跟踪曲线功率在600～800有重叠部分，将重叠部分分别放大，图8可知采用固定步长5.0时，跟踪速度最快，动态性能最好，但达到稳态后，可以看出输出电压、输出功率的振荡幅度最大，而采用固定步长1.0时，跟踪速度次之，动态性能次之，达到稳态后，可以看出输出电压、输出功率的振荡幅度较5.0时要小.采用固定步长0.1时，跟踪速度最慢，动态性能最差，但达到稳态后，输出电压、输出功率的振荡幅度最小.通过上述讨论，在定步长模拟过程中产生了跟踪速度和跟踪精度不能同时满足的现象，为了解决这一矛盾，对模型进行了改进.3 变步长电导增益对最大功率点的仿真与分析在电导增益法跟踪最大功率值时，一般采用差分ΔP/ΔU近似代替微分dP/dU,这就使传统的电导增益法存在一定的截断误差，也就是说，传统电导增益法很难精确满足dP/dU=0.然而，无论怎样提高精度都无法解决最大功率点附近振荡的问题.电导增益法通过一些很小变化的阀值，判断目前工作点在最大功率点的那一侧.如果ΔI/ΔU>I/U，则系统判定当前工作点在最大功率点左侧，这时会增加ΔU*后再进行判断，工作点会逐渐靠近最大功率点.当足够靠近最大功率点时，由于ΔU*为常数(定步长)，在下一次增加后，如果ΔI/ΔU<-I/U，则系统判定当前工作点在最大功率点右侧，这时会减去ΔU*，工作点又会回到最大功率点左侧，然后会发生重复加减ΔU*的现象，就会使得在最大功率点附近来回跳动，这是产生振荡的原因[10-13].图9 变步长的电导增益法的仿真模型Fig 9 The simulation model for variable step conoluctance increment method为了解决变步长的电导增益法在最大功率点附近的振荡现象，对其模型进行了改进，如图9所示.图9中运用Memory模块和Gain模块来替代定步长C(常数)，Gain为增益模块，这里设定值为0.9，使得每一次判断后增加或减去的ΔU*为上一次的0.9倍.图10为变步长的跟踪模拟曲线.由图10可见，采用变步长的电导增益法，在远离MPP的区域内，采用了较大的步长提高了跟踪速度，减少了光伏电池在低功率输出区的时间；在MPP附近区域内，采用了较小的电压扰动步长保证了跟踪精度，最后，准确有效地跟踪了光伏电池的最大功率点，显然，变步长电导增益法很好地解决了MPPT精度与快速性之间的矛盾.图10 变步长电导增益法的仿真结果Fig 10 The simulation result for variablestep comductance increment method4 结束语光伏电池的输出特性受到外界因素的影响有很多，其曲线具有明显的非线性，从仿真实验的结果中得到了温度和光照强度对光伏电池输出特性的影响.光照强度相同时，随着温度的升高,光伏电池的输出功率略有减小，当温度相同时，随着光照强度的增大，光伏电池的输出功率增大.从模拟曲线中可以知道，无论在任何温度、光照强度下，光伏电池的最大功率点只有一个，当温度或光照强度发生改变时，最大功率点的位置也将发生改变.此外文中利用电导增益法可以很好的对最大功率点进行跟踪，对不同步长下的跟踪曲线进行了分析和研究，当步长ΔU*为常数时，随着步长的增加，对最大功率点的跟踪速度会增大，其跟踪精度会减小，即振荡越明显.对产生震荡现象的原因进行了分析，发现、采用变步长电导增益法对跟踪模型做出了改进，消除了振荡现象.文中很好的解决了传统(定步长)电导增益法对最大功率点的跟踪仿真中，跟踪速度和跟踪精度之间的矛盾，为提高光伏电池工作效率方面的研究提供了一种很好的方法.参考文献:【相关文献】[1] 冯垛生.太阳能发电原理与应用[M].北京：人民邮电出版社，2007.[2] KOVACIK P,HAZELE A,ANDREW A R,et al.Morphology control in coevaporated bulk heterojunctionsolar cells[J].Solar Energy Materials & Solar 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solar cellarray[J].ActaOpticaSinica,2013,33(5):0508001.[9] ZHANG Li,CHEN Zhi-ming,DONG Qian-min,et al.Design and analysis of ring-shaped-focus Fresnel concentrator[J].Laster & Optoelectronic Progress,2012,49(9):092201.[10] 何艳荣.世界太阳能行业发展趋势[J].太阳能信息光伏专刊，2006(8):5.[11] 杨金焕，邹乾林，谈蓓月,等.各国光伏路线图与光伏发电的进展[J].阳光能源，2006(8):51.[12] 郑建邦.太阳能内部电阻对其输出特性影响的仿真[J].太阳能学报，2006,27(2):121.[13] 赵争鸣，刘建政，孙晓英,等.太阳能光伏发电及其应用[M].北京：科学出版社，2005.。
四旋翼无人机轨迹跟踪控制研究
四旋翼无人机轨迹跟踪控制研究秦澍祺;王国胜;梁冰【摘要】本文通过使用黎卡提( Riccati ) 矩阵方程来求解微型四旋翼无人机的线性二次型跟踪( Linear Quadratic Tracking LQT )控制器.首先,根据四旋翼的悬停条件,线性化四旋翼的非线性模型,用以解决最优控制问题.然后,通过定义成本函数来更好的权衡跟踪性能和能量消耗.最后,通过使用黎卡提方程来求解时变的最优控制增益.通过仿真表明,与传统的 PID 或者是固定增益的 LQR 控制相比, LQT 控制器具有良好的跟踪控制性能.【期刊名称】《科技视界》【年(卷),期】2018(000)029【总页数】2页(P101-102)【关键词】四旋翼无人机;最优控制;线性二次型跟踪控制器【作者】秦澍祺;王国胜;梁冰【作者单位】陆军装甲兵学院兵器与控制系,中国北京 100072 ;陆军装甲兵学院兵器与控制系,中国北京 100072 ;江西理工大学信息工程学院,江西赣州 341000【正文语种】中文【中图分类】V2490 引言四旋翼是一个具有高机动的、非线性的、耦合的和欠驱动的系统。
所以许多研究人员设计了各种的线性、非线性或者混合控制技术来控制四旋翼飞行器。
比如传统的PID 控制器[1]、反步法控制器[2]、滑膜控制器[3]、模型预测控制器[4]和的线性二次型[5]控制器等。
这些控制器一般使用恒定的控制增益作为状态反馈控制，专注于对四旋翼无人机的稳态控制而不是轨迹或者目标跟踪的精度。
本文则提出使用线性二次型跟踪器（LQT），通过轨迹来调节控制增益从而更好追踪期望轨迹。
同时与线性PID 和LQR 控制器作为对比，三者都在状态估计上加入了相同的白噪声干扰模拟实际环境。
1 模型建立与线性化四旋翼飞行器模型考虑为线性定常系统，状态矩阵A、B、C 和D 都为静态的不随时间改变。
定义如下：x 为状态向量，y 为输出向量，u 为输入向量，根据文献[6]建立的四旋翼模型，线性化后状态空间矩阵A、B 为：其中，12 维状态量[x y z u v w φ θ ψ p q r]T 包括位置、速度、角度、角速度。
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Optimal Power Point Tracking For Stand-Alone PV System Using Particle Swarm OptimizationMohamed AzabElectrical and Electronic Engineering DepartmentYanbu Industrial College-Saudi Arabiamazab@.sa , pe_bhit@Abstract- A particle swarm optimization (PSO) technique is used to identify the optimal power point of a photovoltaic module used in a stand-alone PV system as a battery charger. The PSO algorithm searches the maximum power point of the PV module by determining the array voltage at maximum point (V MPP ). The tracked variable is used as a reference value (set point) to an ON/OFF controller with a tolerance band which controls the operation of a dc boost chopper such that the PV module is forced to operate at the optimal power point. According to the obtained results of the proposed system, the tracking efficiency is not less than 98 % with a convergence time of 14 ms. Compared with the well known Perturb and Observe tracking method, the proposed system is accurate and reliable.I. I NTRODUCTIONRecently, the massive consumption and exhaustion of fossil fuel resulted in enormous interest to utilize renewable sources of energy such as solar energy. Photovoltaic power is an established technology and has recently experienced rapid growth over the last ten years [1].A solar cell basically is a p-n semiconductor junction. When exposed to light, a dc current is generated. The light-generated current varies linearly with the solar irradiance. PVs offer several advantages such as: high reliability, low maintenance cost, no environmental pollution, and absence of noise. However, a major drawback of the PV source is its ineffectiveness during low insolation periods or during partially shaded conditions [2]. The equivalent circuit of the PV cell is shown in Fig.1.The PV module exhibits nonlinear characteristics as shown in Fig. 2. The PV curves vary with solar insolation and module temperature. Equation (1) and (2) are used to describe the characteristics of PV array.shs PV PV AkT)R I q(V o L PV R R I V - 1)(eI I I S PV PV +−−=+ (1)P PV = V PV . I PV(2)Where: I PV is the PV module current (A) , I L is the light generated current (A) , I o is the diode saturation current , q is the charge of electron (coulomb) , K is the Boltzmann's constant (j/K) , A is the diode factor , T is the module temperature (K) , R s is module series resistance (ohm) , R sh is module parallel resistance (ohm) , V PV is the module output voltage (V), and P PV is the extracted PV power (W). In order to extract the maximum possible power from the PV system, the PV module must operate at the optimal power point. Thus, instantaneous maximum power point of PV module is tracked with the aid of a power electronics converter driven by a suitable MPPT algorithm.Several MPPT methods are developed. They are generally categorized into the following groups: 1. Perturb and observe method [3].2. Incremental conductance method [4].3. Fractional open circuit voltage [5].4. Fractional short circuit current [6].In reference [7] general overviews and comparisons between different MPPT schemes are presented.This paper proposes a reliable MPPT scheme based on PSO algorithm. The PSO algorithm tracks the optimal power point by searching the PV array voltage at maximum power point (V MPP ). Once the V MPP is identified, the actual PV array voltage is controlled to such optimal value computed by the PSO algorithm. The PV module is forced to operate at such optimal operating point with the aid of a power conditioner(dc boost chopper) driven by On/Off voltage controller with suitable tolerance band.The investigated system consists of a PV solar module that feeds the power to the dc load (a set of batteries) through a step-up (boost) chopper. The chopper is driven by an On/Off voltage controller to adjust the operating point of the PV module. The core of tracking system is the on-line PSO algorithm that identifies the instantaneous value of V MPP of the PV module. According to the obtained results, the minimum tracking efficiency is found to be 98 % , with a convergence time of 14 ms.II. O VERVIEW OF P ARTICLE S WARM O PTIMIZATION PSO technique introduced by Kennedy and Eberhart [8] is a method for optimizing nonlinear functions based on metaphor of social behavior of flock of birds searching for corn through social cooperation with other birds around it (not by each individual).In PSO, each particle in swarm represents a solution to the problem and it is defined with its position and velocity [9]. The particles are placed in the search space of a certain problem or function. All particles have fitness values based on their position, and have velocities which direct the flight of the particles. At current location of each particle an objective function is evaluated.generations. In every iteration, each particle is updated by two best values [10]. The first one is the best solution the particle has achieved so far. This value is called local best (L i ). The second best value tracked by the particle swarm optimizer is the best value obtained so far by any particle within the neighborhood, which is considered as the best particle among the entire population, and is called global best (G ). After finding the two best values, the particle updates its velocity and position with following equations:[][])( )( )( )( )( )(22111k k k k k k i i i i i x G r c x L r c v w v −+−+=+ (3))( )( )(11+++=k k k i i i v x x(4)So, all particles fly through the problem space using simplerules of equations (3) and (4).Where: w is the inertia weight factor; v i (k ) is the particle velocity at iteration k ; x i (k ) is the particle position in the search space at iteration k ; r 1 and r 2 are random numbers between (0,1); c 1 and c 2 are called acceleration constants are also between (0,1). Generally, the next iteration takes place after all particles have been moved. Eventually the swarm as a whole, like a flock of birds moves close to an optimum of the fitness function. The factor w affects the overall performance of the PSO.A large value of w can favor higher ability for global search, while lower value of w implies a higher ability for local search. III. D ESCRIPTION OF I NVESTIGATED PV S YSTEM The block diagram and circuit diagram of stand-alone PV system under investigation are shown in Fig. 3 and Fig. 4 respectively, where a single PV module is used to charge 3 series batteries of 12 V through a dc boost chopper. The boost converter is chosen because both the input current and output current are continuous; however, it could be replaced with any other power circuit, such as buck-boost converter. At any instant, the output power from the PV is a function of light insolation, PV module temperature, and the PV current/voltage. A maximum power can be obtained only at a certain array current/voltage. Due to randomly changing weather conditions, the duty ratio needs to be adjusted continuously so that maximum power can be transferred to the load. The design goal of the proposed MPP tracking system is to find the optimal value of PV array voltage (V MPP ) such that the controller regulates the actual PV voltage to such instantaneous optimal value. Hence, the maximum power point is identified and tracked continuously with unforeseen weather and load changes.A. Operation of DC Boost ChopperThe dc boost chopper is connected between the PV moduleand the dc load as shown in Fig. 3 and Fig. 4. It can be regarded as a variable active resistor that can be adjusted by duty ratio in order to control the input resistance seen by the PV module. Consequently, either the current drawn from the PV or the voltage across the PV are controlled. Actually, the PV module can be forced to operate at the instantaneous maximum power point of the (I-V) curve provided that the tracking algorithm determines correctly the optimal operating point.The average output voltage is determined by (5): in o V DV −=11 (5) Fig. 3 Investigated Maximum Power Point Tracking SystemFig. 4 Circuit diagram of the investigated PV systemWhere V out and V in are the output and input voltages of the boost chopper respectively, and D is the chopper duty ratio. In the case of ideal converter, the input power of the converter equals to the output power, yielding the following equations:DI I outin −=11 (6)()21D I V I V R outoutin in in −==(7)()21D R R out in −= (8)From Equation (8), the operating point of PV module can be controlled by the duty cycle of the boost chopper. Since different operating voltages of the PV module produce different output powers. Thus, the ripple voltage of PV module will degrade the performance of the PV system. So, it is desired to reduce the PV ripple voltage by connecting a DC capacitor parallel to the PV.The dc boost converter is modeled in state-space form inMatlab ®based on the following equations:Bu(t)Ax(t)(t)x+=& (9)Let x 1 = i L , and x 2 = V C2.()()u(t) 01/L V i RC 1-C S -1L 1S 0 V i C2L 22C2L ⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡+⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡−=⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡′′ (10)Where S is the switching state of the boost chopper (0 or 1), and u(t) is the input voltage of the boost chopper which isthe PV voltage (V PV ) .B. PSO AlgorithmThe procedure of the developed PSO algorithm is presented in the flowchart shown in Fig. 5, where the algorithm is divided into major six steps:1. Initialization of swarm positions with random guess for the searched solution V MPP .2. Evaluation of the objective function of the corresponding initialized V MPP . The objective function is chosen to be the inverse of PV power (obj_fun = 1/Power).3. Updating swarm position and velocity according to equations (3) and (4).4. Evaluation of the updated population.5. Check if all iterations are carried out.6. Output the global best result of V MPP that satisfied the objective function.Actually, the V MPP computed from the PSO is applied to the PV system shown in Fig. 3 as a set point to the control system. The measured PV voltage and current are fed to thealgorithm to compute the objective function and to update both swarm velocities and positions.The proposed tracking system is simulated and studied usingMatlab/Simulink and Sim Power Systems. Several simulation activities are carried out and linked together between Matlab m-files, Simulink environment, and Sim Power Systems. The simulation activities include the following tasks: 1. Modeling and simulation of PV module under different levels of solar insolation. 2. Modeling and simulation of boost chopper supplied fromPV array and regulates the PV voltage to the V MPP .3. Matlab file to implement PSO algorithm.4. Matlab link file, which synchronizes the operation andhandles the data between previous files.Simulation parameters related to the system under investigation are summarized in Table I.Fig. 5 Flowchart of PSO algorithmTABLE I S IMULATION P ARAMETERS Solver ODE 15s L 2 mH C 1 = C 2 1000 μF Load : Battery3x12 V Tolerance band of on/off controller+ 0.02 V Swarm Size 25 birds Bird Steps25 stepsPV CharacteristicsV OC 21.8 VI SC3.17 AOptimum current I MPP 2.89 A Optimum voltage V MPP 17.3 V Maximum Power50 WIV. S IMULATION R ESULTSThe selected simulation results are divided into three major groups: (a) Results of the PV module, (b) Results of the overall PSO-based MPP tracker system, and (c) Evaluation of the PSO-based MPP tracking algorithm.A. Simulation Results of PV ModuleThe I-V family curves and P-V family curves of PV module are plotted under different levels of solar irradiance. The simulation results are shown in Figure 6.B. Simulation Results of PSO-Based MPP TrackerIn this section, selected simulation results of online MPP tracking of the optimal operating point of the PV module are presented. The presented results are divided into two groups: (1) Transient performance of the tracking system, and (2) Steady state behavior of the stand-alone PV system.1. Online Tracking of Optimal Power PointFig. 7 illustrates the evolution of on-line tracked optimal PV voltage V MPP using the PSO algorithm. According to the obtained results, the algorithm requires only six iterations (steps) in order to identify the optimal operating point and satisfy the objective function, which is selected to be theThe evolution of objective function is presented in Fig. 8. After six iterations, the objective function reached to the minimum value. The online tracking process is observed and shown in Fig. 9, where V MPP obtained from the PSO algorithm is used to disturb the boost chopper.By studying the results of Figures 7, 8, and 9 together, the PSO algorithm succeeded to satisfy the objective function after six iterations in 14 ms. So that, the tracking time of the algorithm is 14 ms. The PSO program is designed to disturb the system each 2.5 ms, which allowed enough time to compute the objective function to evaluate the system performance. According to the results of Fig. 9, the waveform of actual PV voltage is repeated several cycles during every iteration time, which can permit (theoretically) extra reduction in the actual disturbing time to reduce the overall convergence time of the algorithm.2. Steady State PerformanceFig. 10 , 11, and 12 illustrate the steady state response of thestand-alone PV system used to charge the set of batteries (3x12V). In Fig. 10, the steady state PV voltage is plotted. According to the result, the voltage is well controlled to the reference value V MPP (17.2 V) identified by the PSO algorithm (see Fig. 7).In Fig. 11, the steady state waveform of the current drawn from the PV is illustrated. According to the result, the PV current I PV is controlled to 2.75 A, which is PV current for V MPP = 17.2 V. The corresponding instantaneous value of the extracted power from the PV is presented in Fig. 12. As shown in Fig. 12, the PV power oscillates around 45 Watt, which is (very close to) the maximum power point.0.030.040.050.060.070.080.090.1101214161820The simulation results prove that the PSO-based MPPT algorithm incorporated with the dc boost chopper is efficient to identify the optimal power point of the PV array after a few number of iterations.Fig. 10. Steady state response of PV voltage (V PV )V P V (V )01234253035404550C. Evaluation of PSO-Based MPP TrackerTable II presents actual and tracked values of PV voltage and the corresponding maximum power for different possible operating points when the PV is exposed to different values of solar irradiance. In each case, the percentage of absolute error of PV voltage estimation and the corresponding tracking efficiency are computed and presented. According to the obtained results, the minimum observed tracking efficiency of the proposed PSO-based tracking system is 97.9 %. The tracking efficiency is computed according to the following equation:(ACTUAL)MAX (PSO) MAX P P =η x 100 % (11)V. C OMPARISON WITH O THER MPPT M ETHOD The proposed MPP tracking method is compared with thewell known tracking method: perturb & observe. The results of comparison are summarized in Table III. It has been observed that the proposed method works successfully under partial shading conditions, which leads to existence ofmultiple local maxima with a unique global point that can not be tracked easily with perturb & observe.C ONCLUSIONIn this paper a reliable and accurate on-line maximum power point tracker for stand-alone PV system based on particle swarm optimization technique is proposed and studied.The obtained results demonstrate that the tracking efficiency of the online PSO-based tracker is not less than 97 %, with a convergence time of 14 ms. The proposed scheme is characterized by a high tracking efficiency and a relatively high convergence speed, which can enhance the performance of PV solar systems. Moreover, the proposed PSO-based tracking system does not require any derivatives calculation, so that it is robust and noise-resistive.R EFERENCES[1] W. Xiao, N. Ozog, W.G. Dunford, “Topology Study of PhotovoltaicInterface for Maximum Power Point Tracking,” IEEE Trans. Industrial Electronics, vol. 54, no. 3, pp. 1696–1704, June 2007.[2] H. Patel, et. al., “Maximum Power Point Tracking Scheme for PVSystems Operating Under Partially Shaded Conditions,” IEEETransactions on Industrial Electronics, Vol. 55, No. 4, pp. 1689-1698.[3] E. Koutroulis, et. al., “Development of a microcontroller-based,photovoltaic maximum power point tracking control system,” IEEE Trans. Power Electronics, vol. 16, pp. 46–54, 2001. [4] K. Hussein, et. al. , “ Maximum photovoltaic power tracking: an algorithm for rapidly changing atmospheric conditions,” Proc. Indst. Elect. Eng., vol. 142, no. 1, pp. 59–64, Jan. 1995.[5] D.-Y. Lee, et. al. , “An improved MPPT converter using currentcompensation method for small scaled PV applications,” in Proc.Applied Power Electronics Conf. ’03, vol. 1, Feb. 2003, pp. 540–546.[6] T. Noguchi, et. al., “Short-current pulse-based maximum-power-point tracking method for multiple photovoltaic- and-converter modulesystem,” IEEE Trans. Ind. Electron., vol. 49, pp. 217–223, Feb. 2002.[7] T. Esram, P. L. Chapman, “Comparison of Photovoltaic ArrayMaximum Power Point Tracking Techniques,” IEEE Trans. EnergyConversion, vol. 22, pp. 439-449, June 2007. [8] J. Kennedy , R. Eberhart, “Particle Swarm Optimization,” in Proc.IEEE Inter. Conf. on Neural Networks '95, Vol. IV, pp.1942-1948, 1995.[9] Y. B Wang , et. al., “A New Particle Swarm Optimization Based AutoTuning of PID Controller,” in Proceedings of IEEE Inter. Conf. on Machine Learning and Cybernetics, pp.1818-1823, July 2008.[10] Mohamed Azab, “Global maximum power point tracking for partially shaded PV arrays using particle swarm optimisation,” Int. Journal ofRenewable Energy Technology, Vol. 1, No. 2, pp. 211-234, 2009. Fig. 11 Steady state response of PV current (I PV )I P V (A )Fig. 12 Steady state response of PV power (P PV )P P V (W )。