毕业论文（设计）基于Matlab 改进遗传算法的有功负荷分配研究.doc

基于Matlab改进遗传算法的有功负荷分配研究梁思聪 王维庆 张新燕（新疆大学电气工程学院，新疆乌鲁木齐， 830008）摘要：遗传算法在优化多约束、多目标问题时有明显的优势。Matlab为该算法实现提供了简单的方法。用爬山算法和遗传算法相结合，可以在一定程度上克服遗传算法在局部搜索能力方面的不足和爬山算法在全局搜索能力方面的不足。机组负荷优化分配是一种可提高电厂经济性的手段, 但目前还没有得到一种绝对严格的算法。为了解决这个问题，引入模糊理论建立了电站机组负荷分配模型，并运用爬山算法与遗传算法相结合求解。该算法不同于常规优化算法特点在于：优化过程简单，容易得到全局最优解，适合大规模的复杂系统求解。方法的有效性通过算例分析得到了验证。关键词：有功负荷分配；隶属函数；遗传算法（GA）；优化 Study of Active power dispatch based on improved genetic algorithm optimization in Matlab Liang Si-cong, Zhang Xin-yan,Wang Wei-qing(College of Electrical Engineering, Xinjiang University, Urumqi Xinjiang, 830008) Abstract Genetic algrithm has remarkable superiority as optimizing multi-objective,many restriction problem.Matlab provided a simple and convenient method for the algrithm's realization. The hybrid genetic algorithm witch is the combination of genetic algorithm and hill-climbing algorithm, can overcom the weakness of genetic algorithm in local search and hilling-climbing in global search. The optimization of active power dispatch among power generating sets is a measure for improving economy of power plants, but now there is no absolutely strict algorithm. In this paper,a model of optimization of load allocation among power generating sets is established with fuzzy theory; and applied the hybrid genetic algorithm to solve the model. The algorithm is different from normal optimization algorithms as follows : simple language; easier getting best solutions in full place; and being suitable for solving the complicated systems with large scale. Finally, an example is given to illustrate the validity of the approach.Keywords ：active power dispatch; membership function; genetic algorithm; optimization0 引言随着电力系统规模的日益扩大，电力系统的经济运行越来越重要，机组负荷分配就是其中一个非常重要的问题。机组负荷分配是在预先规定的调度周期内，在确保机组安全运行，并满足各种约束条件下，合理确定所有可用机组的启、教育部博士点专项基金项目 (20060755001) ;自治区高校高技术研究重点项目(XJEDU2004I04 ); 国家自然基金课题（50767003）停机状态和电站各机组间的负荷分配，使系统总运行费用最小。机组负荷分配是一个包含整型和连续变量的高维、离散、非凸的混合非线性优化问题,当系统的规模较大时,要从理论上求得精确的最优解相当困难。随着计算机运行速度的提高,现代智能优化算法在机组优化负荷分配中体现出优势,主要包括模拟退火、遗传算法、进化策略、人工神经网络、蚁群优化、混沌优化等方法。其中，遗传算法( GA)由于其对求解问题的限制较少，不要求目标函数连续且可微而备受关注1；另外，GA在求解非线性问题时表现出较强的鲁棒性、全局优化性和可并行处理性，这些优点使其在电力系统的经济运行中得到广泛的应用。采用遗传算法解决机组组合问题，是未来的发展方向之一 2。Matlab 的遗传算法工具箱（GAOT）在求解负荷分配问题的可行解或满意解时，总体上解的质量不是很高。许多学者为此对GA做出了很多改进，但无论是通过改变计算参数，算法结构还是运算规模，总的效果依旧不是很理想。针对这一不足，本文将局部搜索能力很强的爬山算法与Matlab 的遗传算法工具箱（GAOT）相结合，提出了一种性能良好，且操作简单的计算策略来对电站机组负荷经济分配进行优化求解。同时，在考虑机组组合负荷优化分配不确定的基础上，将模糊理论引入所研究的问题中，采用梯形模糊数来表示每台机组的运行负荷，建立了电站机组负荷分配的模糊模型，并通过一个例子对上述模糊建模和计算策略进行了验证。1 电厂机组负荷分配模糊建模1.1 数学模型电厂机组负荷分配即各台机组在安全可靠运行的前提下，经济合理地承担负荷获得最小煤耗量的多约束最优化问题。电厂机组的煤耗可用二次曲线方程表示，() (1)式中, ,为第台机组的煤耗特性系数;为第台机组的煤耗;为第台机组的负荷。设全厂有台机组可以投入运行，总负荷为，经济运行的目的就是根据煤耗特性，在满足负荷需求和约束条件下，将此负荷合理的分配在台机组上，使总的煤耗量为最小。其模型描述如下。(1) 目标函数考虑机组启停,目标函数为 （2）式中，表示机组的运行状态(0表示停机，1表示运行)。(2) 功率平衡约束 (3)(3) 功率上下限约束 (4) (5) (6)式中, 为调度下达到电厂系统总负荷；, 为第台机组的负荷上、下限。从目标函数可以看到，状态参数的加入把优化问题提升为的规模，为使下面设计的算法加快计算速度，根据机组负荷分配的特点，文献3将机组状态隐含在负荷中，其具体操作是：设为功率判断参数，将机组功率下限置零，这样在0,之间遍历。如果，则中间变量 ,否则，将中间变量代入目标函数中进行计算，其效果等同于式(2)中的。通过该处理方法，将机组状态判断隐含在负荷 的取值区间，优化问题减少为 规模。目标函数转化为 （7）1.2 隶属函数 考虑的不确定性因素是每台机组的负荷，即把每台机组的负荷看作模糊数。 模糊建模的关键在于确定模糊变量的隶属函数，隶属函数的确定目前还没有一套成熟的方法，基本上是根据试验或者经验来确定。梯形隶属函数与人们研究不确定性问题的思考方式相近，所以很多文献都采用该类型的函数来考虑机组负荷的随机性。故模糊变量也采用梯形函数来表示4。(8) 式中, 为电厂机组负荷的隶属函数。相应的函数图形如图1所示。10P 图 1 机组有功隶属函数 Fig.1 Membership of generating power令，经过推导， (9) （10）这样，原问题就等价成了一个以电厂机组负荷分配的隶属度为变量的非线性规划模型。2 改进的计算策略设计2.1 改进策略的设计思想先采用Matlab 的遗传算法工具箱（GAOT）对问题进行优化求解，当GA群体进化到预定代数或当前最佳个体的适应值改善低于预定的阈值时，选择当前最佳个体作为初始个体，采用爬山算法继续完成局部搜索过程，以提高后期的计算效率。 2.2 Matlab 的遗传算法工具箱（GAOT）及其参数设置简介5、6Matlab 的遗传算法工具箱（GAOT）核心函数主程序ga. m 和初始种群的生成函数initializega.m提供了遗传算法工具箱与外部的接口。在Matlab 环境下，运行这两函数并设定相应的参数, 就可以完成优化。根据优化问题的特点，在设置GAOT参数时选用浮点数编码。限制各决策变量机组负荷的隶属度 在其取值范围内取值，在进化过程中，按所设计的交叉和变异算子产生的子代均被限制在其取值范围内,故发电机组功率上下限约束自动满足。对其他约束条件，采用动态惩罚函数法进行处理。处理后得到如下新的目标函数： （13）式中动态惩罚函数 这里为进化代数，C通常取0.5,。因GAOT优化时只能计算函数的最大值，故在计算时需将式（13）取负。即 2.3 爬山算法的设计7爬山算法的程序流程如图2所示。该程序以遗传计算的结果作为初值，由两个循环完成主体计算；其终止条件为：a 适应值最大值大于某一个值且连续若干代所获得的最优解没有变化，则认为已成熟收敛。b 迭代次数超过某一规定的限值。遗传计算终止，得到当前最佳个体 计算个体适应度值：；置初值体:生成随机序列: 体:顺序取体:对位基因进行变异，即计算新个体的适应度：体:If> then =, =体:k = k + 1体:k n体:是判断:满足终止条件吗？体:否终 止体: 图2 爬山算法流程图 Fig.2 flow chart of hill-climbing algorithm3 电站机组负荷分配优化计算实例及分析 某火电厂有一台150MW和两台300MW发电机组，其机组发电煤耗特性系数和负荷上下限约束如表1 所示。 表1 机组发电煤耗特性系数和负荷上下限约束 Tab.1 Cofficients of coal consumption and power limits机组 ，1 0.0007 0.30 4 80， 150 2 0.0004 0.32 4.5 100， 300 3 0.00045 0 .30 3.5 100， 300 根据本文2.2节的结论和表1的数据，用Matlab语言编制本例的适应度函数文件，并以fs.m为文件名存放在Matlabk中的work工作组中。根据优化问题的特点，编码方式选用浮点式，种群规模设为pop _ size = 30,交叉率Pc=0.4, 变异率Pm=0.08。下面为基于GAOT对该实例进行求解的调用程序：bounds=ones(3,1)*0 1;initPop=initializega(30,bounds,'fs');X endPop bPop trace = ga(bounds,'fs', , initPop , 1e-6 1 1 , 'maxGenTerm', 50,'normGeomSelect',0.1,'arithXov', 2 , 'nonUnifMutation', 2 80 3 );plot(trace(: , 1),trace(: , 3), 'r - ') ;hold onplot(trace(: , 1),trace (: , 2) , 'b*') ;xlabel('Generation');ylabel( 'Fittness') ;运行以上程序后，得到的适应度值进化曲线如图3所示。 图3 适应度变化曲线 Fig.3 Evaluating curve of value图2中由*组成的曲线表示平均适应值的变化；另一条曲线表示每代最优适应值的变化。由图可知，随迭代数的增加，种群的平均值呈现了稳定上升的趋势；相应地每代解也向最优解方向靠拢。最后种群平均值和代最优解都趋于平稳。在通过以上计算得出初步优化结果后，应用本文2.4节的爬山算法程序得出最后的优化解，对上面两结果分别比较如表2和表3所示。 表2 机组组合方案结果比较(1)Tab.2 Comparison of units commitment according to different methods（1）方法 GAOT 0 0.10296 0.14704 307.5147 混合法 0 0.10296 0.14705 307.5136 表3 机组组合方案结果比较（2）Tab.2 Comparison of units commitment according to different methods（2）方法 GAOT 150 279.4080 270.5920 307.5147 混合法 150 279.4080 270.590 307.5136由以上两表可以看出，本文提出的计算策略对单纯的遗传算法在局部搜索能力方面的不足有很好的补偿作用。在对以上两种方法各进行100次运算后统计发现，单纯的遗传算法有62次可以收敛到质量较高的优化值，而用本文的混合法后，有87次可以收敛到最优解。另外，由于在相同迭代代数下，爬山算法比遗传算法用时要少得多，所以在适当情况下可以减少遗传算法的代数，这样就为一些需要进行在线大规模运算场合的应用提供了可能。下面仍以上例各发电机组为例，假设1、2、3号机组所用燃料的价格分别为100、110、90元/t，在考虑价格因素下用本文的计算策略重新分配各机组负荷。对于这一计算，只需对上例中的适应度函数文件做一简单修改，然后按照上例计算步骤进行完全相同的操作，其计算结果如表4所示。表4 考虑燃煤价格后的机组组合方案结果Tab.4 units commitment considering different price of coal M/(元) 150 215.09 334.91 30472 由上表可看出，在考虑各机组燃煤价格因素后，2号机组比上例少发了64.318MW，3号机组比上例多发了64.32MW，这是因为3号机组所用燃煤价格比2号便宜所致。由些可看出，用本文的计算策略，不仅可以得到质量很高的最优解，计算效率高，而且编程很简单，使用者几乎可以用现成的程序就可以完成运算。3 结论 本文采用模糊理论建立了电站机组负荷分配的模糊模型，提出了一种基于Matlab 的遗传算法工具箱（GAOT）和爬山算法相结合的计算策略，用实例验证了它的有效性和优越性。通过实例可以明显地发现，这一策略不仅具有编程语言简单，容易得到全局最优解的显著特点，而且因为其计算效率高，为大规模的复杂系统的在线求解提供了一种可行的办法。参考文献：1 Haupt R L , Haupt S E. Practical Genetic AlgorithmsM . New York : John Wiley & Sons ,1998.2 Maifeld T T. Sheble Genetic - Based Unit Commitment Algorithm J . IEEE Trans on Power Systems，1996 ，11 (3) ：135921370.3 廖艳芬,马晓茜. 改进的混沌优化方法在电站机组负荷分配中的应用J . 动力工程,2006 ,26 (1) :93296.4 陈海焱,陈金富,段献忠. 含风电场电力系统经济调度的模糊建模及优化算法 J . 电力系统自动化, 2006 , 30(2) :22226.5 雷英杰, 张善文等. Matlab 遗传算法工具箱及应用M. 西安: 西安电子科技大学出版社,20056 陈秋莲等. 基于Matlab 遗传算法工具箱的优化计算实现J . 现代电子技术, 2007,第2 期7 刑维建,张国力. 基于改进遗传算法的有功经济负荷分配J . 华北电力大学报,2005,32(1)8 赵晶,董红斌. 基于遗传算法的目标优化研究J. 应用科技,2007,34(8)9 康积涛,苏琳,杨武. 改进自适应遗传算法用于电力系统无功优化J. 电气应用,2006,5(10)10 Yokota T , Gen M. Optimal Design of System Reliabilityby an Approved Genetic Algorithm J . Transactions ofInstitute of Elect ronics Information and CommunicationEngineers , 1995 ,78 (6) : 7022709.11 苏玲. 基于混沌搜索的遗传算法在电力系统无功优化中的研究D. 河北：华北电力大学，200412 陈怡等. 电力系统分析M. 北京：中国电力出版社,2005作者简介：梁思聪（1980），男，汉，新疆人，新疆大学在读硕士，研究方向为高压线路继电保护。王维庆（1959，男，教授，博士生导师，研究方向为集散控制系统与风能、太阳能控制技术，2004-2005 年在德国作高级访问学者。张新燕(1964)，女，新疆人，教授，硕士生导师，西安交通大学在读博士，研究方向为风力机控制，电气系统优化设计，2006-2007年在德国作访问学者。作者姓名：梁思聪 工作单位：新疆大学通讯地址:新疆乌鲁木齐市友好北21号新疆大学电气工程学院电力系统及其自动化研究生 邮政编码：830008 手机号：13999921078电子邮箱：lscmxmEditor'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.