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1、基于改进遗传算法的配电网网架规划徐赫（东北电力大学电气工程学院，吉林 吉林 132012）摘要：配电网规划属于多目标、受约束、离散非线性的混合整数规划问题，应用传统的遗传算法在求解过程中会出现收敛速度慢、早熟现象等问题，针对这些不足，引入了单亲遗传算法，以网架线路年综合费用最小为优化目标建立配电网网架规划的数学模型，并运用改进的单亲遗传算法求得模型优化解。仿真算例验证了该方法的可行性和有效性。关键词：配电网规划； 单亲遗传算法；电力系统Distribution network planning based on improved GAXU He(College of Electrical En
2、gineering, Northeast Dianli University, Jilin 130012, China)Abstract: Distribution network planning is a multi-objective, constrained and non-linear mixed integer programming problem which usually appeared convergence slowly and convergence prematurely by the traditional genetic algorithm solving th
3、e process. For these shortcomings, this paper introduces Partheno-genetic algorithm and establishes a mathematical model of distribution network structure planning, of which objective function is to get the minimum annual comprehensive cost, then obtain the optimal solution of the model in the impro
4、ved PGA . The simulation results verify the feasibility and validity of this method.Key words: distribution network planning; Partheno-genetic algorithm(PGA); power system0 引言配电网规划是一个非常复杂的大规模组合优化问题，涉及变电站、馈线段的建设和容量大小的最优选择，以满足负荷增长的要求，同时服从变电站容量、馈线段容量、电压降落、辐射状网络结构等约束，具有时变性、离散性、非线性及随机性，求解相当复杂1。近年来，遗传算法2（
5、GA）在解决此类问题中得到了广泛的应用，它能以较大概率求得问题的全局最优解，适用于解决组合优化问题以及目标函数或某些约束条件不可微的非线性优化问题，这使得电网规划的非线性、多约束、多目标的求解难度降低。但在实际应用中GA仍存在未成熟收敛、收敛于局部最优解、收敛速度慢等问题。单亲遗传算法（Partheno-genetic Algorithm，以下简称PGA）的基本思想是取消遗传算法的交叉算子，所有的遗传操作只在一个个体上进行，从而简化遗传操作。本文将PGA引入配电网规划，消除了GA中双亲杂交算子对方案可行性的影响；由于采用整数编码策略，可直接对导线截面进行选择，避免了在确定网架结构和选择导线截面
6、时带来的局部最优问题；并对PGA的遗传算子进行改进，有效解决了GA存在的“早熟现象”和局部收敛等问题。仿真结果表明了本文所提方法的有效性。1 配电网网架规划的数学模型1.1 目标函数本文中网架规划模型以线路年综合费用最小为目标函数，包括线路投资费用、折旧维修费用和运行中的电能损耗费用。规划模型为： （1）式中：为线路年综合费用，为架设线路总数；=，为投资回收率，为设备折旧维修费用率；为新建支路的费用；为维决策矢量，代表规划问题中可选的条线路。当线路新建时取，否则取；为单位电价；为最大负荷利用小时数；为支路有功损耗。等式右边的前一部分为网架投资费用，后一部分为网损费用。1.2 约束条件1）连通性
7、约束。要求对所有负荷点供电。2）辐射网结构。3）潮流约束。 式中，为节点关联矩阵，为网络潮流，为负荷需求。4）容量约束。 式中，为支路潮流，为支路最大允许容量。5）电压降落约束。 。2 改进的单亲遗传算法单亲遗传算法最初是为解决常规遗传算法在求解组合优化问题时的不足提出来的，它在遗传操作中是通过单个父代个体来产生子代个体的。其基本原理是：通过遗传算子作用于当前种群，从而产生出适应性更强的后代种群；反复上述过程，进而达到种群进化的目的3。本文对单亲遗传算法进行了改进，主要体现在选择算子、基因重组算子及基因突变算子的改进。对选择算子采用最优保存策略和两两竞争相结合的选择方法。基本思想为：从经过基因
8、重组、突变的子代以及父代组成的群体里，选择适应度最好的个个体直接放入下一代；然后通过两两竞争的方法，每次从种群中随机选取两个串，将适应值的串加入匹配集，反复执行这一操作，直到选择（）个个体为止，与已选择的个个体组成下一代的父代。其中，为种群规模。对于重组算子和突变算子的改进，采用最优个体保持的最小代数作为终止判据，设为最优个体已经保留的代数，当较小时，说明还未收敛，需要减小基因重组率，促使算法收敛，而当较大时，说明算法已经收敛，则需要加大基因重组率以帮助个体脱离局部最优，让基因突变率随着最优个体已经保留代数的变化而发生变化。由于采用改进的基因重组算子和基因突变算子，可以在收敛末期加大个体变化，
9、这样能够有效地避免把局部最优解判断为全局最优解，保证了算法的可靠性。因此，将最优个体的最少保留代数作为收敛准则。这种收敛充分利用了PGA在进化过程中的积累，比常规最大单亲遗传代数判据更为合理。3 改进的单亲遗传算法在配电网网架规划中的应用3.1 染色体编码将任意两个节点之间的连线作为一个基因元素，并采用整数编码策略，将导线截面选择和馈线支路选择统一起来架设备选导线型号有5种：LGJ-25、LGJ-50、LGJ-70、LGJ-95、LGJ-120，则染色体基因的取值范围为0，1，2，3，4，5，依次代表线路不架设及架设上述5种之一导线。对于拥有m条馈线支路、r条原有线路的情况，编码如下：12.r
10、r+1r+2m前面1 r位代表r条原有线路，其元素取非零值。后面r+1 m位代表m r条备选线路，其元素取值可为零。3.2 初始群体的产生初始群体的产生方法采用跟节点融合法4。这样可以确保初始方案的可行性（辐射及连通）且操作简单。其步骤为：（1）初始化。标记电源节点为“true”，其他的节点和线路均不做标记。所有被标记为“true”的节点称为根节点，它们构成根节点群。（2）从与根节点群相连且未做任何标记的支路中随机选择一条，并标记为“true”，同时其另一端节点也标记为“true”，即把该端点加入根节点群。（3）扫描所有支路，将那些两端节点均为根节点且未做任何标记的支路标记为“false”。（
11、4）检查所有节点是否全部被标记为“true”，如果是，则结束，否则转步骤（2）。3.3 个体优劣评价文中采用上述介绍的配电网网架规划模型进行网架优化，同时采用惩罚函数处理线路输送的功率和节点电压约束，把惩罚系数引入到目标函数中，进而得到增广目标函数，表示如下： （2）式中，分别为线路输送功率和节点电压约束条件的惩罚系数。通常要求性能越好的个体其适应度值越大，因此适应度值可表示为： （3）其中，为与染色体对应的适应度值；为很大的常数。3.4 单亲遗传操作改进单亲遗传算法运行的流程图如图1所示：4 算例本文使用C+ +语言编写了配电网络规划的计算程序，应用该程序对实验配电网网架进行优化规划，引用文
12、献5中的算例来验证。已知10个节点的位置和其负荷容量、变电站位置，以及馈线支路情况。初始网架如图2所示，图中实线表示已架线路，即原有线路，虚线表示备选线路。算法的参数选择分别为：导线的型号有五种，其截面为LGJ-25mm2、LGJ-50mm2、LGJ-70mm2、LGJ-90mm2、LGJ-120mm2；年运行系数0.155，电价0.05元/kw.h，最小负荷损耗小时数3000h。对遗传算法、单亲遗传算法的最大迭代次数和改进单亲遗传算法的最优个体最小保留代数，在其他参数恒定的情况下，进行多次取值计算。结果表明，当=2400，=1800时，运算结果达到最优，规划年计算费用为最小值。三种算法的运算
13、结果分别为：45.356万元、42.725万元、41.298万元。=1800时，改进PGA的优化结果如表1所示：优化规划后的网架结构如图3所示：实验表明，使用改进的PGA比用PGA、GA所得到的结果更优，达到最优规划时的迭代次数（1800次）也远小于前面两种算法（2400次），时间复杂度明显降低；同时在局部收敛和全局收敛性能方面，改进的PGA要强于PGA和GA，得到了全局最优解（41.298万元）5 结论本文将单亲遗传算法引入到配电网网架规划的计算中，消除了常规遗传算法中对网络可行性破坏严重的双亲交叉算子；同时针对单亲遗传算法在染色体选择、基因操作、收敛准则等方面的不足，提出具体的改进措施，采
14、用最优保留策略和两两竞争相结合的染色体选择方法，以及最优个体的最少保留代数为收敛准则，从而提高了算法的局部搜索效率和全局优化能力。算例表明，基于改进单亲遗传算法的配电网网架规划方法是可行和有效的。参考文献：1 王锡凡. 电力系统优化规划M. 北京: 水利电力出版社, 1990.2 Miranda V, Ranito J V, Procenca L M. Genetic Algorithm in Optimal Multistage Distribution Network PlanningJ. IEEE Trans on Power Systems, 1994,9(4): 1927-1933.
15、3 李茂军, 童调生. 单亲遗传算法及其全局收敛性分析J. 自动化学报, 1999, 25 (1): 68-71.4 迟忠先, 左恺, 李宪廷. 常用组合算法程序汇编M. 大连: 大连工学院出版社, 1987.5 陈俊红, 黄丽华. 基于配电网络规划的优化算法的研究J. 微计算机信息, 2006, 22 (4-3): 293-295.作者简介： 徐 赫：（1985- ），男，硕士研究生，研究方向电力系统规划及可靠性。Editors note: Judson Jones is a meteorologist, journalist and photographer. He has freelan
16、ced 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 worlds first satellite - Sputnik.
17、 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 sp
18、ace race has renewed my childhood dreams to reach for the stars.As a meteorologist, Ive still seen many important weather and space events, but right now, if you were sitting next to me, youd hear my foot tapping rapidly under my desk. Im anxious for the next one: a space capsule hanging from a cran
19、e in the New Mexico desert.Its 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
20、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 jo
21、urnalist 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 pai
22、n 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
23、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
24、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 atmo
25、sphere (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
26、 (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 Olympi
27、c diving platform.Below, the Earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. Still, hell 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 pre
28、ps 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 to
29、o fast or spins out of control, he has a stabilization parachute that can be deployed to slow him down. His team hopes its 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 success
30、fully, 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 wont. Baumgartner still will free fall at a speed that would cause you and me to pass out, and no parachute
31、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 Id miss this.