对牵引负荷实测数据的分类改

摘要：随着电气化铁路在铁路运输中的迅猛发展以及电压等级的不断提高，电气化铁路牵引负荷对电网的负序和谐波影响也随之增大。为了建立准确有效的电气化铁路牵引负荷模型以评估其对电网的影响程度，本文根据全国部分牵引变电所实测数据，利用matlab仿真软件对实测数据进行分析处理，得到其概率密度函数图以及对应累积分布函数图。根据累积分布函数图，对牵引负荷实测数据进行分类整理。关键词：电气化铁路牵引负荷；实测数据；概率密度函数；累积分布函数；分类1引言由于列车在运行过程中受到加速、恒速、惰行、制动等牵引工况的变化,以及受到坡道、弯道、站场、道岔、气候、司机操作等其它因素的综合影响,使得电气化铁道牵引负荷呈现出随机波动的统计特性。因此对单个牵引变电所的牵引负荷实测数据进行统计分析并没有太大的实际意义。为此我们选择将大量实测的牵引负荷实测数据按照概率密度函数图和累积分布函数图进行统计分析,找到这些负荷之间的大致规律并进行分类。2牵引负荷主要特征参数的定义牵引负荷平均值avI牵引负荷平均值在统计学上表征了一个周期时间内的数学期望。其数学定义1njjaviIn牵引负荷方均根值rmsI牵引负荷方均根值,也就是通常所说的负荷平均有效值,表征了一个周期时间内的二阶原点矩。其数学定义21jnijrmsIn牵引负荷最大值maxI牵引负荷最大值表征了一个周期时间内的最大负荷值,数学定义maxmaxjIi牵引负荷空载电流0I牵引负荷空载电流表征了该供电臂无列车运行时的最大电流，其确定方法可参见文献基于带电有效系数的空载电流选取方法研究，这里不再赘述。牵引负荷主要数字特征空载概率0P其数学定义为空载电流占全日电流的百分比，其计算公式为00100%kPn其中，0k为ji中小于等于空载电流0I的电流个数。带电有效系数gk01rmsgavIPkI3牵引负荷实测数据的统计分析采用的实测数据是西南交通大学电气工程学院在全国各铁路线上的数十个牵引变电所测试的数据。测试仪器每3s采样和记录一次数据,一个完整的测试周期(24h)共采样28800个点的数据。对已有的实测数据，采用matlab软件对其进行分析处理，得到各个牵引变电所负荷概率密度函数图和累积分布函数图以及牵引负荷主要特征参数和数字特征。根据统计发现，具有相似累积分布函数图的变电所负荷主要特征参数和数字特征基本相似，现将具有代表的累积分布函数图进行分类整理，统计结果如下所示：第一类01234502468I1/IeP/%01234500.51I1/IeF(x)EmpiricalCDF安定a3556.3096139.8076114.56795114.567904.85571.22031.45.40.572301234502468I1/IeP/%01234500.51I1/IeF(x)EmpiricalCDF安定a2590.3514145.7305122.21555122.215504.83041.19241.76.50.423601234502468I1/IeP/%01234500.51I1/IeF(x)EmpiricalCDF安定b3803.8539164.9059130.66685130.671106.15191.2621.36.51.1705012345602468I1/IeP/%012345600.51I1/IeF(x)EmpiricalCDF安定b2安定b2943.3326169.2805134.96795134.967906.98931.25421.48.30.8226012345602468I1/IeP/%012345600.51I1/IeF(x)EmpiricalCDF石板滩a1022176136.65136.607.51.31.17.31.24170123402468I1/IeP/%0123400.51I1/IeF(x)EmpiricalCDF漕河b756.4152194.4355171.18835107.946304.41861.13582.816.90.653501234502468I1/IeP/%01234500.51I1/IeF(x)EmpiricalCDF广武b997.563204.2749167.63895167.644405.95071.21851.57.70.468601234502468I1/IeP/%01234500.51I1/IeF(x)EmpiricalCDF洛阳东b洛阳东b1207.5269.2227.15227.105.31.21.77.20.213501234502468I1/IeP/%01234500.51I1/IeF(x)EmpiricalCDF新乡b1090.5269.4236.923704.61.13.512.60.67010123402468I1/IeP/%0123400.51I1/IeF(x)EmpiricalCDF江油a963.4429273.9773220.29555220.295504.37341.24371.240.957101234502468I1/IeP/%01234500.51I1/IeF(x)EmpiricalCDF东城乡b854.4554361.4654318.16575318.165702.68561.13611.72.90.039901234502468I1/IeP/%01234500.51I1/IeF(x)EmpiricalCDF洛阳东a1476.8470.6403.55403.503.71.21.43.70.137第二类0123456702468I1/IeP/%0123456700.51I1/IeF(x)EmpiricalCDF双桥a488.821676.429254.56951766.286222.34728.95781.23421.529.673.5707012345602468I1/IeP/%012345600.51I1/IeF(x)EmpiricalCDF石板滩b453.238688.56372.168572.16806.28031.22721.57.97.0176012345602468I1/IeP/%012345600.51I1/IeF(x)EmpiricalCDF西固b588.0094100.804873.144573.146208.04241.37820.864.57740123456702468I1/IeP/%0123456700.51I1/IeF(x)EmpiricalCDF双桥b641.2805103.906281.3161581.32150.00697.88631.27781.38.64.02750123456702468I1/IeP/%0123456700.51I1/IeF(x)EmpiricalCDF白石渡a801.1253125.809399.5286108.26468.23968.04921.21091.7211.0110.3474012345602468I1/IeP/%012345600.51I1/IeF(x)EmpiricalCDF江油b789.6483134.9578111.40785111.407807.08791.21141.710.37.2778012345602468I1/IeP/%012345600.51I1/IeF(x)EmpiricalCDF马角坝a920.7399169.0585130.78945130.793607.03991.29261.16.96.22910123402468I1/IeP/%0123400.51I1/IeF(x)EmpiricalCDF马角坝b1108325.9252.75252.704.41.30.932.64190123402468I1/IeP/%0123400.51I1/IeF(x)EmpiricalCDF沙城东a1402.2450.1355.95355.903.91.30.82.42.25120123402468I1/IeP/%0123400.51I1/IeF(x)EmpiricalCDF沙城东b1582.2499391.15391.2041.30.82.62.0291第三类012345602468I1/IeP/%012345600.51I1/IeF(x)EmpiricalCDF下庄b459.231989.521966.7999572.66868.11086.87471.28511.160.5217012345602468I1/IeP/%012345600.51I1/IeF(x)EmpiricalCDF木林b木林b519.932891.530669.5003679.817713.1287.4811.22751.528.360.7401234502468I1/IeP/%01234500.51I1/IeF(x)EmpiricalCDF东城乡a486.7074101.380876.5381792.057917.43066.3591.20361.626.941.6043012345602468I1/IeP/%012345600.51I1/IeF(x)EmpiricalCDF木林a787.3057142.794190.660619127.361830.29068.68411.3150.995.121.261801234502468I1/IeP/%01234500.51I1/IeF(x)EmpiricalCDF安定a1712.7892155.0589122.44935130.80286.57975.82111.22651.46.30.5083012345602468I1/IeP/%012345600.51I1/IeF(x)EmpiricalCDF安定b1安定b1943.0616176.0394134.78439156.628314.59196.99681.2161.587.910.7943012345602468I1/IeP/%01234500.51I1/IeF(x)EmpiricalCDF白石渡b765.5776223.1794178.85175107.94633.95494.28051.22381.69.91.27260123402468I1/IeP/%012345600.51I1/IeF(x)EmpiricalCDF金州a11003.7304.4233.55233.70.14.31.30.92.91.71840123402468I1/IeP/%0123400.51I1/IeF(x)EmpiricalCDF荥阳b1149.4349.3270.45286.65.64.31.30.82.50.4873第四类0123456702468I1/IeP/%0123456700.51I1/IeF(x)EmpiricalCDF江山b2300.333145.699214.5807562.647880.579320.5981.38120.662.5273.598201234502468I1/IeP/%01234500.51I1/IeF(x)EmpiricalCDF江山a2267.958861.956828.22246100.933973.55139.49451.1291.893.1345.4850123456702468I1/IeP/%0123456700.51I1/IeF(x)EmpiricalCDF江山a1429.264164.344126.21186122.531579.998316.37681.09793.197.9961.3958012345678902468I1/IeP/%012345678900.51I1/IeF(x)EmpiricalCDF西固a558.218668.683838.7972976.84451.954914.38811.28841.177.3210.7949012345602468I1/IeP/%012345600.51I1/IeF(x)EmpiricalCDF江山b1612.189972.552229