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1、基于搜索-回溯和广度优先搜索的配电网重构孙 涛，黄唯一，曾远立(广东工业大学自动化学院，广州 510090)摘要：电力系统的配电网重构作为优化网络、降低损耗的一项有效手段, 受到人们广泛的重视。本文将搜索-回溯法和广度优先搜索算法用于配网重构问题的研究。搜索-回溯法是穷举法的改进，通过对寻优过程的有效控制, 避免了在寻优过程中大量不可行解的产生, 提高了计算效率;广度优先搜索算法通过逐层推进可以快速得到电网的结构。关键词：配电网重构 降损 搜索-回溯法 广度优先算法Abstract: As an effective approach for network optimization and l
2、oss reduction ，distribution network reconfiguration of power system receives extensive attention. In this paper, the Search-backtracking and the breadth-first search algorithms are used to solve the reconfiguration problem. The search-backtracking algorithm improves the efficiency of the enumeration
3、 algorithm by keeping the process optimization under effective control without bringing a lot of unworkable solutions, and the breadth-first search algorithm can be used for getting the power system framework quickly by advancing lay by lay.KEY WORDS: Distribution network, Reconfiguration, Loss-redu
4、ction, Breadth-first search, Search-backtracking1引言电网的线损就是在给定时段内、电网中所有支路所产生的电能损耗。线损电量占供电量的百分数称为线损率。线损率反映了电网结构和运行方式的合理性，以及一个电网的规划设计、生产技术和运营管理水平。1995 年全国城网110 kV 以下配电网线损占总线损的60% , 可见降低配电网线损是降损工作的关键问题之一。配电网具有环网结构,而通常以开环方式运行。重构是降低配电网线损的有效途径,通过网络重构还可以均衡负荷、消除过载、提高供电电压质量。12在配电网重构的研究中最优网络结构搜索算法一直是研究的焦点，最优配电
5、网络重构技术最早是由Merlin 和Back于1975 年提出来的,之后不断有研究成果发表,提出了多种方法,如：(1) 启发式算法3，主要包括最优流模式算法和支路交换法。(2）近全局寻优算法4，主要包括模拟退火法(SA),遗传算法（GA）和禁忌搜索算法（TS）。(3) 人工智能算法4，主要包括人工神经网络法（ANN）和专家系统（ES）。经过研究几种算法在网络的优化组合搜索问题中的应用，总结发现主要矛盾集中在计算速度和能否保证对解空间搜索的完整性（得到全局最优解），二者难以同时得到满足。本文利用搜索-回溯法(search-backtracking)进行结构的优化组合搜索，结合电网运行的一些约束条
6、件（包括所有节点的电压不越限，所有线路的电流不越限，还有不可能的网络结构等），在搜索过程中剔除不可能出现的配电网结构，加强了寻优过程的控制。在保证完整搜索到解空间得到全局最优解的基础上，一定程度的提高了算法速度。2数学模型本文中，配电网重构的目标是重构后的网损最小。其数学公式是： (1)其中：I=I1，I2,，In为各支路电流幅值， （2）5Pi、Qi，为节点的有功功率和无功功率；Ui为节点电压；ri为支路电阻；n为配电网的支路数目。由于在配电网重构过程中的馈线潮流计算结果是用于比较有功损耗大小，故不需要计算出精确的损耗值。以同一支路的末节点功率占首节点功率的比率求得该支路电流的平方。（3）馈
7、线首端的电压已经给定，由式（2）和式（3）得：(4)同理(5)支路各末节点的注入功率已经知道，但是节点的功率还要累计与其连接的下一段支路末节点的功率，并且为提高准确性，还必须计及馈线中连接在该节点以下部分的损耗累积。为了在重构的同时保证新的电网结构不会出现过载和电压质量过低的问题，并且减少程序对不适合的结构进行无效的计算，需要在重构过程中考虑电网约束条件。支路负载约束：(6)式中：Imax为支路稳定电流限制节点电压约束：(7)式中：Umin和Umax分别为电压上限和下限辐射状网络运行约束：（8）组合搜索损耗计算判断程序结束组合搜索还未结束图1 主体流程图式中：gk为当前的网络结构；Gk为全部允
8、许的辐射状网络结构的集合。3程序算法重构的基本过程如图1：在本文中，由于对一段支路进行分/合与对该开关进行分/合的作用等同，所以根据论述需要不同以支路或者开关进行说明；联络开关的邻域定义为联络开关所在的环里（除了直接连接电源的）所有的开关；环的定义为由一电源开始通过不重复的若干支路连接到另外一个电源，之间通过的支路的集合组成一个环。重构需要解决的问题主要有：（1）环的搜索；（2）组合搜索；（3）辐射状网络结构的搜索。 (1)环的搜索组合搜索的范围是配电网里所有联络开关的邻域。邻域的范围由联络开关所在的环里所有开关组成的。由于联络开关和其所在的环一一对应，故借助深度优先搜索算法以联络开关为中心往
9、两边分别搜索 到电源点，中间经过的开关的集合构成环。(2)组合搜索重构必须是在每个联络开关所在的环(联络开关的邻域) 里选取合适的分段开关进行组合，然后交换二者的开关状态得到一种新的结构，这样才能保证在新结构里不会出现有的节点无法连接到电源（孤岛）或连接了多个电源（闭环）等情况。假设一个有3个环的网络，每个环内有4个开关，进行组合搜索需要从每个环里取一个开关。以矩阵的形式表示： 图 2 图 3如图2所示，在矩阵a34里1，2，12是开关号，每个环占用一行，如1，2，3,4组成一个环。组合的过程就是从每行取一个元素，因此只要能求得不同行元素的所有组合就可以完整的搜索到所有可能出现的配电网结构。借
10、助对矩阵元素下标进行操作可以计算得到不同行元素的所有组合。得到的组合数目有43=4*4*4=64种。实际的配电网中，联络开关所在的环包含的开关数目是不一样的。为此，上述数组amn的列数取一个环里包含的最大开关数，有的环包含的开关比较少，其所在行的元素就不够满，缺少的部分以-1标记，如图3。在程序搜索出一种组合后，对该组合里的开关号进行判断，如果出现-1就应该丢弃，所以图2里数组的组合总数为：4*3*4=54种。(3)辐射状网络结构搜索的方法图4 IEEE 三馈线测试系统利用广度优先搜索算法来搜索重构后配电网的网络拓扑，广度优先搜索算法的过程就是从某个顶点出发，利用一个在访问过程中逐渐建立起来的
11、链表，依次访问各顶点所有未曾访问过的顶点，再从这些顶点出发，继续广度优先的遍历下一层的顶点，直至网络中所有已被访问的顶点的邻接点均被访问过。如上图4所示网络里，在输入数据时已经包含了支路的首节点、末节点。为搜索出一条馈线的结构，需要从电源点开始，建立源点队列，把支路首节点存入队列，寻找与其连接的所有末节点，再清空源点队列，把找到的所有末节点存入源点队列,所有在本轮搜索得到的与首末节点对应的支路作为同一层的支路存入生成树链表，继续搜索，直到源点队列里的所有节点搜索不到与其末节点，则完成一条馈线的结构搜索。调整重构后的节点关系，如图5、图6所示。图5 IEEE 三馈线测试系统-重构前 图6 IEE
12、E 三馈线测试系统-重构后重构后应该对原来初始数据中给出的支路首、末节点进行修改，在改变断开的开关后同时对调旧联络开关到新联络开关之间的所有开关的首、末节点号，旧联络开关的首、末节点也要做相应修改。4算例IEEE标准16节点多电源配电系统6的网络结构如图3所示对初始状态的系统结构进行计算的结果是有功损耗0.534954 (MW)；运行程序得到重构后的最优解为打开开关S19、S21和S25，最优结构的有功网损为0.478300(MW),和初始结构相比损耗降低了10.59%。重构结果见表4-3。图3IEEE三馈线测试系统表4-3网络重构的计算结果重构前重构后联络开关位置S15、S21、S26S19
13、、S21、S25有功损耗534.954（KW）478.300(KW)网损降低率010.59%图433节点系统图4中系统出现环嵌套，环互相影响的类型将多样化，程序将无法区分环与环之间的影响，也就无法判断要断开哪些开关，从而无法继续进行重构。待添加的隐藏文字内容35结论本文对配电网重构的实用化进行了一些研究工作。1.提出了结合配电网实际运行情况的配电网重构的解决方案。2.实现了配电网重构程序。3.对IEEE标准16节点多电源多环网系统进行了试算，计算的结果表明：程序能够得到损耗最小并且符合电网各约束条件的配电网结构，但由于局限性而无法应用于网络中存在环嵌套的结构中。参考文献1 沈晓东,刘俊勇,孙毅
14、 配电网重构的研究和发展 四川电力技术,2003,1-52 张大海,江世芳,赵建国 配电网重构研究的现状与展望 电力自动化设备2002,22(2)3 刘健，毕鹏翔，董海鹏 复杂配电网简化分析与优化 中国电力出版社。2002年4 王凌 智能优化算法及其应用 清华大学出版社 2001年5 何仰赞，温增银 电力系统分析 华中科技大学出版社 2002年6 S K Goswami, S k Basu. A new algorithm for the reconfiguration of distribution feeders or loss minimization J . IEEE Trans. o
15、n Power Delivery, 1992, 7 (3) :1484- 14917 谭浩强 C程序设计（第二版） 清华大学出版社 1999年8 赵建周 杨庆祥 C和C+程序设计教程 航空工业出版社 2000年第一作者简介：孙涛（1983.02），男，河南固始人，本科专业电气工程及其自动化（电力方向），现为广东工业大学自动化学院控制理论与控制工程研究生。Editors note: Judson Jones is a meteorologist, journalist and photographer. He has freelanced with CNN for four years, cov
16、ering 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. I also missed watching Neil Arm
17、strong 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 childhoo
18、d 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 crane in the New Mexico desert.Its l
19、ike 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
20、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
21、 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 k
22、icked 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 cou
23、ld 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 we
24、ather 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 o
25、ur 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
26、 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 Ear
27、th 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 preps for the big jumpWhen he jumps
28、, 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,
29、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 successfully, he will have to slow to 1
30、72 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 is guaranteed to work higher tha
31、n 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.
