毕业论文（设计）基于DSP 控制的60° 坐标系下三电平逆变器SVPWM 的研究31311.doc

基于DSP控制的60°坐标系下三电平逆变器SVPWM的研究SVPWM Algorithm Using 60° Coordinate Frame for Three-level Inverter Based on DSP Controler 王畅 王聪 刘健东 中国矿业大学（北京）Wang Chang, Wang Cong, Liu Jiandong, China University of Mining & Technology, Beijing 摘要:针对传统的SVPWM算法计算复杂的缺点，提出了基于60°坐标系的三电平逆变器的SVPWM算法，该算法仅需进行简单的逻辑判断就可以得到参考矢量的具体位置, 并且用简单的加减运算就可以得到基本矢量作用时间，能够极大简化SVPWM的运算。DSP的实验结果表明了这种基于60°坐标系的三电平逆变器SVPWM算法的正确性。关键词:三电平逆变器SVPWM60°坐标系Abstract: Aim at the complex computation of the classical SVPWM, a fast space-vector pulse width modulation algorithm using 60°coordinate frame applied to three-level inverter was introduced. This SVPWM algorithm needs not to compute trigonometric function, so the computer is extremely simple. The position of reference vector and the time of every vector are easily confirmed base on 60°coordinate frame, Experiment results based on DSP show that the space-vector pulse width modulation algorithm is correct.Keywords: Three-level inverter, SVPWM, 60° Coordinate frame中图分类号TN86 文献标识码 A 文章编号：1561-0349（2011）05-1 引言 近年来，多电平技术越来越多的应用到逆变设备上，特别是大功率设备。虽然多电平技术具有很多优越性，但是因为其控制的原因，高于三电平的多电平逆变器还没有被大规模的采用1。而三电平技术由于其承受高电压、电压电流上升率低、谐波含量少的优势受到越来越多的关注。 PWM控制策略是三电平NPC逆变器研究中的关键技术之一，国内外专家学者已经提出了许多的PWM方法2-4，基本上可以分为载波调制法和空间矢量调制法两类。其中SVPWM具有易于数字实现、电压利用率高、输出电压形式丰富和易于控制中点电压等优点，被大部分逆变器采用。但经典的三电平SVPWM理论基于 坐标系，计算十分复杂。 本文采用60°坐标系，避免了三角函数等复杂的运算，将SVPWM算法极大简化，实验结果验证了该算法的正确性和有效性。2 传统三电平逆变器SVPWM算法的弊端 三电平SVPWM算法是根据参考电压矢量合成的原则，分成区域判断、时间计算、时间状态分配三个步骤，实现三电平逆变器SVPWM控制。 经过一系列的判断确定参考电压所在区域之后，可以得出合成参考电压矢量的基本矢量。假设参考矢量落在第一大扇区内，计算可以得出每个特定电压矢量的合成时间，从表1中可以看出，合成时间的关系式中含有三角函数，计算较复杂，计算量也比较大。同时传统的矢量分区算法中也含有大量的三角运算（见表1），这也给三电平逆变器SVPWM的实时控制带来一定的困难。表1 小扇区t1t2t3第一小扇区2msin(-)1-2msin(+)2msin第二小扇区2-2msin(+)2msin2msin(-)-1第三小扇区1-2msin2msin(+)-11-2msin(-)第四小扇区2-2msin(+)2msin(-)2msin-13 60°坐标系下三电平逆变器SVPWM算法3.1 三电平逆变器的空间电压矢量的转化 在 正交坐标系中，考虑到三电平基本空间矢量图为正六边形，电压矢量再做一次坐标变换，将 坐标系变换成gh非正交新的坐标系，让g轴与轴重合，h轴由g轴逆时针旋转60，并且只采用它的第一象限5。参考电压如果落入第一象限之外，可以通过参考电压矢量逆时针旋转左n60(n=1，2，3，4，5)，得到对应矢量图的第（2-6）扇区，应用几何理论，可知坐标系和gh坐标系下的坐标变化为 （1）当参考矢量为uf用a b c坐标表示时,设三相电压为u(u a, u b, u c)6，由Clark变换可以得到a b c坐标系到g h坐标系的坐标变换公式为 （2） 这样在新的坐标系统中，原来的空间电压矢量用坐标刻度来表示，对应的开关矢量坐标都变成整数点，新的坐标系统中原来的空间电压矢量可以用整数点坐标来表示，坐标变换矢量图如图1所示7。图1假设，我们需要得到的电压为uf，先将uf归一化，使得uf的归一值落在六边形之内。六边形的最大值为ud，即最大输出电压为直流侧电压的0.66倍，而此时对应的长度为2。所以，用目标电压矢量除以，即将电压矢量归一到六边形之内。将得到的电压矢量投影到ABC三相轴上，就可以得到ua，ub，uc。，坐标公式为： = （3） 根据公式（1），（2），（3）就将给定的uf值转化为ug和uh，这样给定的uf只通过三个余弦变换就得到了60°坐标系的数值。 3.2 区域判断和3个临近基本电压矢量的确定 将g h坐标系划分为六个大扇区，如表2所示。设参考电压矢量在g h坐标系中的坐标为（g，h），参考矢量所处的大扇区位置可以通过该表简单的逻辑判断得到。表 2ug + uh >0ug + uh<0ug>0ug <0ug <0ug >0uh >0uh <0第二扇区uh >0uh <0第五扇区第一扇区第六扇区第三扇区第四扇区在六个大扇区中,每个大区又分为4个小扇区，如图1所示。以第一扇区为例(其它区算法类似), 通过表3简单的算术运算，可以得到参考矢量所处的小扇区。完成矢量分区以后,就可以按照相邻三矢量原则来确定每个矢量的作用时间。表3判断条件区域判断最近基本矢量ug<1， uh<1， ug + uh <1第一小扇区(0，0)，(0，1)，(1，0)ug<1， uh<1， ug + uh >1第二小扇区(1，0)，(2，0)，(1，0)ug>1， uh <1， ug + uh >1第三小扇区(0，1)，(1，0)，(1，1)ug<1， uh >1， ug + uh >1第四小扇区(0，1)，(0，2)，(1，1).3.3 计算各个基本矢量的作用时间 根据上述方法得到最近三矢量后，对于一个给定的参考矢量uf，由伏秒平衡原理，可以计算出在g h坐标系SVPWM算法中各个电压矢量的作用时间。假设，某一扇区选择好的3个临近的基本矢量为(x1，y1)，(x2，y2)，(x3，y3)，它们对应的作用时间分别为t1，t2，t3 。将选择好的基本矢量用于伏秒平衡方程组，列出下列矩阵方程式：t1+t2+t3=T （4）其中：T为开关周期。计算矩阵方程可以计算出3个基本矢量的作用时间： t3= （5） t2= （6） t1=T- t2- t3 （7）其中：a=x1×y2-x2×y1；b=y3×x1-x3×y1；c=uh×x1-ug×y1； A=a×(y1-uh)-c×(y1-y2)；B=a×(y1-y3)-b×(y1-y2)。以第一大扇区为例，根据表4得出3个基本矢量对应的作用时间。表4 单位：T时间t1t2t3第一大扇区第一小扇区ug1-ug-uhuh第二小扇区1-uhug+uh-11-ug第三小扇区2-ug-uhuhug-1第四小扇区2-ug-uhuh-1ug 从上面分析可以看出，大区间和小区间的判断只需要将得到的ug，uh和ug+ug与0和1相比较就可以得出具体的区间值，这样使得区间判断的方法大大简化，并且使得判断的运算时间大大减少，很利于SVPWM算法的计算机实现。在时间计算中，不仅仅利用了区间运算得到的结果，并且计算的时间也只是ug和uh的简单运算，使得传统三电平SVPWM中的最复杂的三角运算转化为简单的加减运算，这样将运算的时间大大减少，有利于算法的计算机实现。因为在区间判断和时间计算大大简化，这就使DSP的计算时间减少，可以使开关频率大大增加。同时，60°坐标系的DSP程序实现也较为简单，避免了复杂的判断，使得在整个过程中都大大简化。60°坐标系下的SVPWM比传统模式下的算法更具有可实现性和可行性。4 60°坐标系下三电平逆变器SVPWM 算法的DSP实现根据上述理论和计算的结果，进行DSP编程，并且烧进DSP中，对其中的管脚进行观察波形。我们设定逆变频率为50HZ和25HZ，逆变电压为500V和250V。其中图2为250V，25HZ情况下，DSP的管脚发出的触发脉冲，图中为其中的三个触发脉冲的对比图。图3为250V，50HZ情况下，DSP的管脚发出的触发信号图。图4和图5分别为500V逆变电压，25HZ和50HZ的逆变频率下，DSP的管脚发出的触发信号图。图2图3图4图55 结论 讨论了在传统的三电平逆变器SVPWM控制算法的基础上，提出了一种基于非正交60°坐标变换的SVPWM简便算法。该算法在参考电压矢量区间判断和基本矢量作用时间计算上，都避免了三角函数运算，大大降低了计算量，更易于数字化的实现，并且能大大增加控制回路的开关频率。通过在DSP上的实验，验证了所提出的SVPWM简便算法的正确性和有效性。参考文献：【1】Nikola Celanovic and Dushan Boroyevich，A Fast Space-Vector Modulation Algorithm for Multilevel Three-Phase Converters，IEEE TRANSACTIONS ON INDUSTRY 【2】Chhborty C，Hori Y，Fast Efficiency Optimization Techniques for the Indirect Vector Controlled Induction Motor Drive，IEEE Trans. on Industry Applications, 2003,39【3】Famouri P, Cathey J J，Loss Minimization Control of an Induction Motor Drive，IEEE Transactions on Industry Applications, 1991,27(1):32-37【4】Kouns H，Analysis of Performance Characteristics of Electric Vehicle Traction Drive in Low Speed/LowTorque Range，M.S. Thesis, Virginia Polytechnic Institute and State University, 2001【5】梁英，三电平逆变器空间电压矢量调制算法研究，西南交通大学研究生学位论文， 【6】李国丽，夏秋实，胡存刚，三电平NPC逆变器SVPWM方法研究，电气传动，2007 年，第37卷，第12期 【7】谢鸣静，一种新型的三电平SVPWM控制策略，西安理工大学硕士学位论文 【8】李启明，三电平SVPWM算法研究及仿真，合肥工业大学硕士论文 Editor's note: Judson Jones is a meteorologist, journalist and photographer. He has freelanced with CNN for four years, covering severe weather from tornadoes to typhoons. Follow him on Twitter: jnjonesjr (CNN) - I will always wonder what it was like to huddle around a shortwave radio and through the crackling static from space hear the faint beeps of the world's first satellite - Sputnik. I also missed watching Neil Armstrong step foot on the moon and the first space shuttle take off for the stars. Those events were way before my time.As a kid, I was fascinated with what goes on in the sky, and when NASA pulled the plug on the shuttle program I was heartbroken. Yet the privatized space race has renewed my childhood dreams to reach for the stars.As a meteorologist, I've still seen many important weather and space events, but right now, if you were sitting next to me, you'd hear my foot tapping rapidly under my desk. I'm anxious for the next one: a space capsule hanging from a crane in the New Mexico desert.It's like the set for a George Lucas movie floating to the edge of space.You and I will have the chance to watch a man take a leap into an unimaginable free fall from the edge of space - live.The (lack of) air up there Watch man jump from 96,000 feet Tuesday, I sat at work glued to the live stream of the Red Bull Stratos Mission. I watched the balloons positioned at different altitudes in the sky to test the winds, knowing that if they would just line up in a vertical straight line "we" would be go for launch.I feel this mission was created for me because I am also a journalist and a photographer, but above all I live for taking a leap of faith - the feeling of pushing the envelope into uncharted territory.The guy who is going to do this, Felix Baumgartner, must have that same feeling, at a level I will never reach. However, it did not stop me from feeling his pain when a gust of swirling wind kicked up and twisted the partially filled balloon that would take him to the upper end of our atmosphere. As soon as the 40-acre balloon, with skin no thicker than a dry cleaning bag, scraped the ground I knew it was over.How claustrophobia almost grounded supersonic skydiverWith each twist, you could see the wrinkles of disappointment on the face of the current record holder and "capcom" (capsule communications), Col. Joe Kittinger. He hung his head low in mission control as he told Baumgartner the disappointing news: Mission aborted.The supersonic descent could happen as early as Sunday.The weather plays an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. The balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary layer (called the tropopause), he can expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet (22.7 miles/36.53 kilometers). Here, "Fearless Felix" will unclip. He will roll back the door.Then, I would assume, he will slowly step out onto something resembling an Olympic diving platform.Below, the Earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. Still, he'll be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. It will be like he is diving into the shallow end.Skydiver preps for the big jumpWhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. Like hitting the top of the water, he will begin to slow as he approaches the more dense air closer to Earth. But this will not be enough to stop him completely.If he goes too fast or spins out of control, he has a stabilization parachute that can be deployed to slow him down. His team hopes it's not needed. Instead, he plans to deploy his 270-square-foot (25-square-meter) main chute at an altitude of around 5,000 feet (1,524 meters).In order to deploy this chute successfully, he will have to slow to 172 mph (277 kph). He will have a reserve parachute that will open automatically if he loses consciousness at mach speeds.Even if everything goes as planned, it won't. Baumgartner still will free fall at a speed that would cause you and me to pass out, and no parachute is guaranteed to work higher than 25,000 feet (7,620 meters).It might not be the moon, but Kittinger free fell from 102,800 feet in 1960 - at the dawn of an infamous space race that captured the hearts of many. Baumgartner will attempt to break that record, a feat that boggles the mind. This is one of those monumental moments I will always remember, because there is no way I'd miss this.