遗传算法在配电网无功优化的运用

遗传算法在配电网无功优化的运用摘 要：配电网无功优化问题是指给定配电网网络结构和参数、注入有功和无功功率以及负荷有功和无功功率的情况下，如何通过投入最佳无功补偿设备使得配电网供电可靠性和经济性达到最优，无功优化问题在本质上是一个非线性优化问题。传统算法求解非线性问题会面临计算难收敛以及效率低等问题。本文采用遗传算法(Genetic Algorithm)作为无功优化问题的算法并根据实际要求编写了应用程序，结合内蒙古某工业区的具体例子，展现了遗传算法在无功优化中的价值，在实际工程应用中具有较大的开发利用潜力。关键词：无功优化 ；配电网； 遗传算法Genetic Algorithm Used for reactive power optimization in power distribution networkAbstract: The optimization of the distribution network refers to how to make the distribution network reliability and how to make the economy achieve the peak level. Putting the best optimal reactive power compensation equipment when given the distribution networks structure parameters、injected active and reactive power as well as injected active power and reactive power of the load. Reactive power optimization is essentially a nonlinear optimization problem. Traditional algorithm for solving nonlinear problems will confront with difficult calculation convergence and low efficiency. This paper uses genetic algorithms as reactive power optimization and carries out the application in accordance with the real requirements, with the example of the industrial zone of the Inner Mongolia. This paper shows the value of genetic algorithm in optimizing the reactive power. In practical engineering applications, it has great potential for practical uses.Keywords: reactive power optimization; power distribution network; Genetic Algorithm1 引言无功优化是电力系统安全经济运行的重要组成部分，无功补偿是无功优化的重点，它通过调节电容器的安装位置和投入容量，使各种条件下的网络损耗达到最低限度，以满足电力系统安全经济运行的要求1。随着电网的安全经济运行以及无功补偿重要作用的体现，通过无功优化规划，可以给电网的运行带来以下利益：(1)使电网各点电压运行在允许的范围内，从而保证电网供电的电压质量；(2)改善电网的安全性；(3)降低运行功率的损耗，节约能源，提高网络运行的经济效益;(4)减少并合理分配无功，减少线路和变压器的负荷;(5)全面考虑所有网络变压器分接头位置的合理性，达到最优程度;(6)合理安排无功补偿地点及容量，使无功电源建设的投资与电网的运行成本最小2。2遗传算法的简介和计算流程遗传算法(Genetic Algorithm)是由一种生物进化基准法（优胜劣汰，适者生存的遗传机制）和随机搜索方法发展而来的。它由美国的J.Holland教授1975年首先提出，其主要特点是直接作用于物体的结构，没有导数和函数的限制，具有内在的隐并行性和更好的全局寻优能力；采用概率化的寻优方法，能自动获取和指导优化的搜索空间，自适应地调整搜索方向，不需要确定的规则。遗传算法的这些性质，已被人们广泛地应用于组合优化、机器学习、信号处理、自适应控制和人工生命等领域。它是现代有关智能计算中的关键技术3。遗传算法GA把问题的解表示为“染色体”，在算法中即以二进制为编码的串。在执行遗传算法之前，给出一群“染色体”，也即是假设解，把这些假设解置于问题的“环境”中，并按适者生存的原则，从中选择出较适应环境的“染色体”进行复制，再通过交叉、变异过程产生新一代更适应环境的“染色体”群。这样一代一代地进化下去，不断淘汰不适应环境的“染色体”，最终结果就会收敛于最适应环境的“染色体”上，它就是问题所求的最优解4。遗传算法的计算步骤总结如下：(1)产生初始种群；(2)对群体迭代执行下面的步和步，直到满足终止条件。计算群体中每个个体的适应值；应用选择、交叉和变异产生下一代；(3)把任意一代种群中出现的最好个体串指定为遗传算法的执行结果，它表示为问题的一个解（近似解）5。遗传算法的基本流程如图1所示。是否输出最优解是否满足终止条件开始遗传代数：t=0群体初始化个体适应度评估保存最优个体进行选择、交叉、变异t=t+1图1. 遗传算法流程图3 无功优化及其计算过程 本小节将阐述如何将遗传算法与无功优化计算问题相结合。 在编码方面，本文采用的是浮点数编码方式。采用该方式编码的解的数字串将比用二进制表示的数字串简短得多，遗传算子的相应的计算量会降低，因此计算时间缩短。该参数需要进行编码和解码的优化，因此，在解的精度上也不存在问题。对于无功优化计算的数学模型，以可行空间的一组电容器补偿方案作为一个种群，表示为：(n为种群规模，本文取 30) (1) 其中，任一电容器补偿方案作为一个个体，表示为：(SC为补偿节点i的电容器补偿容量) (2)在种群初始化方面，初始种群中各电容器补偿方案是随机产生的。本文具体实现方法是令作为基因的第i（i（1,l）个电容器补偿容量的初始取值在该补偿容量的定义域（即可投切电容器容量上下限）内随机产生。由于MATLAB中rand ( )函数产生的随机数范围为 01，因此需要在随机函数 rand ( )与补偿容量的定义域之间进行转换，使得随机产生的值总在其定义域范围内6。转换公式如下： (3)在适应度函数的建立方面，可以将适应度函数表示为： (4)其中，为一足够大的数，使转化以后的适应度函数值为正数即可。在本文研究的遗传算法中，寻优是严格按照式(4)来进行的，式(4)的最优解即是 (5)式(5)的最优解。式中： (6) (7) (8) 其中，是总惩罚因子；是电压越界惩罚因子；是补偿容量越界惩罚因子。为了将不符合运行条件的解排除，系数，可取为无穷大或一个很大的正数。这样，不满足不等式约束的解将会使得目标函数值 F 非常大，从而被排除可行解之外。从遗传算法角度看，该惩罚方法使不满足条件的个体的适应度急剧下降，大大降低其繁衍的概率，达到淘汰较差个体的目的。在选择操作方面，本文采用的是赌盘选择法。比例算子为： (9)其中，为该种群中每一电容器补偿方案代入无功优化目标函数后得到的目标函数值。该补偿方案的目标函数值越大，其适应度越高，被随机选中的概率也越大。本文根据将轮盘分为相应的对应扇区，产生一个随机数(i=1,2,3n)，判断属于哪一个扇区，则选中该扇区对应的个体到配对库中。随机选择n次，能得到n个新的无功补偿方案。由于本文采用浮点数编码，其基因是实数形式，而交叉和变异操作需要通过二进制形式完成7，因此，将这n个新方案内的补偿容量分别转换成二进制编码形式，再分别根据预先设定的交叉概率和变异概率对这n个新个体进行两两配对交叉操作和变异操作后，将其转换回十进制编码形式，这样就能得到一个经过一次进化后的新种群8。4 内蒙古某工业园区配电网无功优化计算 为验证本文给出的无功优化算法的有效性，经过现场实测，本文利用提出的无功优化算法对内蒙古某工业园区一个典型配电网进行无功优化计算。4.1 配电网实际原始数据图 2 给出内蒙古某工业园区其中一个地区配电网接线。图2. 某地区典型地区电网接线图该电网基本情况如下：(1)电网有三个电压等级，其基准值分别为：220kV、110kV 和 10kV，基准功率为100MVA。(2)包含22个节点，21条支路。其中，220kV节点1个、110节点7个、13个10kV节点、1 个三绕组变压器的虚拟等效节点（节点 2），其电压等级设为 1kV。节点电压范围设定为 0.9-1.07。(3)虚拟发电机一台，装设在 220kV 母线端，作为平衡节点，其功率下限设为 0，防止无功倒送。(4)220kV 母线上共有六条进线，将其并联等效为一条 220kV 输电线。110kV 输电线 6 条。10kV 出线 13 条。(5)变压器支路 14 条，其中包括两条三绕组变压器等效支路。(6)无功补偿点 13 个。(7)表1到表 5 给出该电网 2014 年 4 月 23 日的相关参数。表1负荷有功数据，24h(MW)时段节点号67891112140:005.5721.2921.6912.796.690.4511.651:005.9920.7623.3212.035.370.459.852:005.7120.9122.4612.075.230.458.533:006.1421.4222.5311.215.040.378.024:005.6921.3022.5511.634.750.457.725:005.4120.6022.811.564.710.457.626:005.7522.7122.9512.215.120.298.097:004.9221.7823.638.376.030.4510.368:004.7225.2926.7510.637.370.811.459:004.9525.0431.1914.18.710.814.6710:004.9225.6333.2114.739.140.815.8411:005.3624.7333.6915.4110.230.8717.3212:005.7123.5129.314.149.460.5818.5113:005.6122.4227.9713.078.710.5816.1714:005.7623.4530.5813.319.130.5714.6715:006.0924.4033.0614.079.430.7316.6916:006.0425.8732.8914.439.790.7717.4317:005.7626.0632.114.439.980.818.6118:005.9425.6730.5315.969.730.5120.4519:004.5724.9931.6216.79.820.7320.7320:005.2324.7133.4415.679.760.5120.7821:004.9723.2231.3715.719.350.6619.7322:004.7522.7828.5413.038.920.6618.2723:004.9222.1527.9513.128.030.5715.3时段节点号1517182021220:0011.648.269.478.374.991.71:009.416.918.598.194.901.52:008.126.228.378.134.741.43:007.285.897.937.794.811.34:007.115.747.977.954.511.45:007.275.598.047.764.511.46:008.336.077.937.974.451.27:0010.839.708.668.164.631.48:0012.3212.8010.208.834.963.49:0014.0515.9412.5810.716.73510:0016.9616.6313.3111.367.585.511:0019.6417.5113.8211.397.555.5612:0022.1715.9413.6711.146.643.513:0019.1913.4911.4410.326.273.714:0017.5415.5411.4110.636.734.6415:0018.6118.0213.2011.277.255.116:0019.3317.1513.6011.397.255.317:0020.7717.7714.0411.367.195.318:0023.0715.3213.7111.146.064.3219:0023.6216.4514.4410.905.974.4420:0023.2917.7414.0810.756.004.1421:0022.417.5913.029.965.78422:0020.0716.6012.329.375.393.523:0015.2214.9911.008.805.022.86表2负荷无功数据，24h(Mvar)时段节点号67891112140:002.228.919.774.781.020.022.81:002.368.928.894.390.790.022.352:002.468.978.624.510.830.011.923:002.499.068.343.930.710.011.894:002.289.178.464.30.690.011.845:002.258.558.34.441.270.021.786:002.239.738.54.170.59-0.021.627:001.79.128.234.50.820.091.988:001.6611.2410.44.823.060.332.839:001.7310.8912.786.722.550.274.5910:001.6211.1913.546.942.780.385.2611:001.8110.2813.616.453.060.264.9912:002.248.8011.774.822.090.074.5513:002.199.2811.475.012.080.063.914:002.099.8912.315.752.470.243.7715:002.5710.5713.786.52.860.275.0516:002.5411.4913.56.82.840.165.1817:002.5111.7613.065.962.890.25.3718:002.2210.3512.416.022.040.134.519:001.559.8412.676.72.020.054.7720:001.8110.0314.175.951.990.085.4621:001.619.0412.745.821.680.124.6622:001.748.9511.445.121.470.074.4323:001.799.0712.084.771.380.023.45时段节点号1517182021220:003.392.243.152.771.600.231:002.871.922.942.771.600.122:002.61.863.022.631.6503:002.231.792.712.591.62-0.014:002.261.732.862.601.52-0.095:002.231.662.852.541.49-0.086:002.111.502.632.611.53-0.217:002.572.432.752.581.470.198:003.464.343.602.992.191.279:004.56.575.284.422.953.310:005.716.955.884.393.313.2611:006.156.655.774.432.963.4212:006.264.464.773.572.361.1213:005.313.783.793.552.400.9714:005.365.534.314.122.672.4715:006.347.035.544.502.973.2116:006.516.375.514.512.783.3417:006.586.605.594.442.812.8518:005.94.384.283.862.061.5219:006.634.314.673.732.071.720:007.215.664.923.662.261.6321:006.745.314.413.181.921.3422:005.594.883.933.051.921.123:004.464.653.542.861.730.93表3 线路参数标么电阻标么电抗标么半容纳110kV 1线0.009820.025750.00415110kV 2线0.005070.016940.00765110kV 4线0.000960.005030.00765110kV 3线0.00490.015960.00765110kV 5线0.003850.068360.00765110kV 6线0.001150.00340.00765220kV等效输电线0.0.0.00415表4. 可投切电容器组配置情况额定无功（MVar）额定电压（kV）单组造价（元）使用年限220kV 1站#1变低47.80110.5.7212110kV 3站#1变低24.00910.5.6412110kV 3站#2变低24.00910.5.6412110kV 6站#1变低24.20110.5.312110kV 6站#2变低24.20110.5.312110kV 4站#1变低24.00910.5.6312110kV 4站#2变低24.00910.5.6312110kV 1站#1变低25.00110.5.412110kV 1站#2变低25.00110.5.412110kV 5站#1变低24.00110.5.6512110kV 5站#2变低23.00110.5.6512110kV 2站#1变低24.20110.5.612110kV 2站#2变低24.20110.5.612表5. 变压器参数标幺电阻标幺电抗主变档位范围220kV 1站#1高-中0.00330.09471.0380.015220kV 1站#1高-低0.00260.1627220kV 1站#1中-低0.00200.0513110kV 1站#10.00350.1695180.015110kV 1站#20.00370.2080110kV 5站#10.00530.3283110kV 5站#20.00370.2700110kV 2站#10.00390.2625110kV 2站#20.00360.2713110kV 2站#10.00250.1667110kV 2站#20.00340.4933110kV 6站#10.00390.2620110kV 6站#20.00380.2655110kV 4站#10.00390.2688110kV4站#20.00360.26254.2 计算结果与分析本文对 2014 年 4 月 23 日全天负荷数据进行无功优化。假设每个整点时刻的负荷数据在未来一个小时内不再变化。假设系统电价为0.7元/kWh，各电容器造价和使用年限如表4所示，电容器组的年折旧费用约为8.16元/kVar。本文以电容器投切组数作为优化对象，电容器组在系统原补偿方案和经本文方法优化后的补偿方案投入情况如表6所示。表7 给出本文所研究电网在 11:00 时段补偿前、系统原补偿方案和优化后补偿方案的节点电压值，其他时段的计算结果相似，这里不全部列出。电压对比图如图3所示。表6.电容器组投入情况方案时段节点号6789111214151718202122原补偿方案00:00220200001001001:00220100001001002:00220100001001003:00220100001001004:00220100001001005:00220100001001006:00220100001001007:00220000001001008:00220100001001109:00221200102101210:00221200112101211:00221200112101212:00221100112101013:00221100111001014:00221100111001115:00221200111101116:00221200111101117:00221210111101118:00221210111001019:00221210111001120:00221210111001021:00221200111001022:00221100201001123:002211002010011动作次数0017202224008总动作次数28优化方案00:00021200000000001:00121100000000002:00121100000000003:00121000000000004:00211000000000005:00211000000000006:00211000000000007:00211000000000008:00211100001000009:00222100001100010:00222100002100011:00212100002100012:00211100001100013:00211100000100014:00212100001100015:00212200011100016:00222100011100017:00212200011100018:00212100001100019:00212100001100020:00212100101100021:00212100001100022:00212000011000023:002120000100000动作次数2538002362000总动作次数31表7. 节点电压对比节点号补偿前电压系统补偿方案电压优化后电压11.051.051.0521.04541.04871.047431.04531.04871.047441.02971.04041.039151.02031.04041.03960.99051.01031.00970.93570.95430.953180.97120.98130.980290.99961.01021.0087101.04451.04781.0465111.0141.01721.016121.0141.01731.016131.03911.04561.043141.02361.03011.0275151.00851.01511.0124161.03831.04531.0427171.02281.02991.0273180.99351.00020.9978191.04481.04841.0469201.01431.01771.0163211.02931.03291.0313221.04531.04871.0474图3. 优化前后节点电压对比图 由对比可知，在经过无功补偿后，各节点电压得到一定程度的提升。系统原补偿方案和优化后的补偿方案相比，两者电容器动作次数相当，分别为 28和31次。另外，两者节点电压相差不大，电压合格率均为 100%。优化前后网络有功损耗和运行费用指标对比如表8所示。三种方案全天各时段的总费用对比如图 4所示。表8. 优化前后指标对比Table8. Index comparison before and after optimization指标时段01234567补偿前有功损耗654.95617.01585.23572.01568.84552.19614.73595.88总补偿容量00000000网损费458.48431.81409.68400.41410.81386.53430.41417.12电容折旧费00000000总费用458.49431.81409.68400.41398.21386.53430.31417.12原补偿方案有功损耗577.73550.11519.04509.26504.83491.80548.50540.67总补偿容量3220827208272082720827208272082720822208网损费404.42385.08363.33356.48353.38344.26383.85378.47电容折旧费30.0025.3425.3425.3425.3425.3425.3420.68总费用434.42410.42388.67381.82378.72369.6408.29398.16优化后有功损耗584.79552.66521.28517.50511.61497.86555.32541.14总补偿容量21000200002000015000160001600016001600网损费408.42386.86364.80362.25358.13348.5388.72378.80电容折旧费19.5618.6318.6313.8714.8014.8014.9014.70总费用428.98405.47383.53376.22373.03363.40403.62393.7指标时段89101112131415补偿前有功损耗819.721086.71218.01275.21114.2952.561037.61234.8总补偿容量00000000网损费573.97760.83852.6892.64779.74666.77727.72864.35电容折旧费00000000总费用573.97760.83852.6892.64779.74666.77727.72864.35原补偿方案有功损耗726.41932.981044.01109.6999.77847.18913.301062.3总补偿容量3500865216692246922448624402244802457224网损费508.49653.09730.8776.72699.84593.03639.31743.61电容折旧费32.6160.7564.4864.4845.2937.4744.7353.5总费用541.10713.84795.28841.2745.13630.5684.04797.11优化后有功损耗726.71944.221054.91124.01011.6859.31917.651068.8总补偿容量2520037400416003860029400252003440043408网损费508.70660.95738.43786.8708.12601.52642.36748.16电容折旧费23.4734.8438.7535.9627.3923.4732.0440.43总费用532.17695.79777.18822.76735.51624.99674.4788.59指标时段1617181920212223补偿前有功损耗1285.01300.71256.71276.41321.81185.81010.5888.71总补偿容量00000000网损费880.6910.48879.76893.55925.33830.13707.28622.09电容折旧费00000000总费用880.6910.49879.76893.55925.33830.13707.28622.09原补偿方案有功损耗1105.61125.71119.01138.61170.31061.2905.40788.35总补偿容量5722461425494245722449424452244802448024网损费773.92787.99783.3797.02819.21742.84633.78551.85电容折旧费53.557.2246.0453.3046.0442.1344.7344.73总费用827.42845.21829.33850.32865.25784.97678.51596.58优化后有功损耗1114.21133.51127.51148.21175.81067.8913.95799.79总补偿容量4140843408344003440038408344002