欧姆法计算书
计算依据
《工厂与民用配电设计手册》第四章p90,p91,p99,p114,p116,p120页的公式
已知条件
元件1--高压系统:
高压侧系统短路容量Ss=200.000MVA
电阻R1 =0.0995*160/S\"=0.0995*160/200.000MVA=0.079mΩ
电抗X1 =0.995*160/S\"=0.995*160/200.000MVA=0.792mΩ
相保电阻Rφp 1 =2R1 /3=2*0.079mΩ/3=0.053mΩ
相保电抗Xφp 1 =2X1 /3=2*0.792mΩ/3=0.528mΩ
元件2--高压线路:
线路长度L=1.000km
平均额定电压Un=10.500kV
线路每公里电阻R0 =0.236Ω/km
线路每公里电抗X0 =0.225Ω/km
电阻R2 =1000*R0 L*0.42 /Un2 =1000*0.236Ω/km*1.000km*0.42 /10.500kV2 =0.342mΩ
电抗X2 =1000*R0 L*0.42 /Un2 =1000*0.225Ω/km*1.000km*0.42 /10.500kV2 =0.327mΩ
相保电阻Rφp 2 =2R2 /3=2*0.342mΩ/3=0.228mΩ
相保电抗Xφp 2 =2X2 /3=2*0.327mΩ/3=0.218mΩ
元件3--变压器:
额定电压Ur=10.5kV
额定容量Sr=2000KVA
短路电压Ud%=6
变压器短路损耗ΔP=14
零序电阻R0 =0.560
零序电抗X0 =4.767
电阻R3 =106 *ΔP(Ur/Sr)2 *(0.42 /Ur2 )=14kW*(10.5kV/2000kVA)2 *(0.42 /Ur2 )*106 =0.560mΩ
阻抗Z3 =104 *Ud%Ur2 /(100Sr)*(0.42 /Ur2 )=6*10.5kV2 /(100*2000kVA)*(0.42 /Ur2 )*104 =4.80000
电抗X3 =(Z3 2 -R3 2 )0.5 =(4.800002 -0.5602 )0.5 =4.767
相保电阻Rφp 3 =R3 =0.560mΩ
相保电抗Xφp 3 =X3 =4.767mΩ
元件4--低压母线:
母线长度L=10.000m
母线单位长度电阻值R0 =0.014mΩ/m
母线单位长度电抗值X0 =0.147mΩ/m
母线单位长度相保电阻Rφp0 =0.054mΩ/m
母线单位长度相保电抗Xφp0 =0.340mΩ/m
电阻R4 =R0 L=0.014mΩ/m*10.000m=0.140mΩ
电抗X4 =X0 L=0.147mΩ/m*10.000m=1.470mΩ
相保电阻Rφp 4 =Rφp0 L=0.054mΩ/m*10.000m=0.540mΩ
相保电抗Xφp 4 =Xφp0 L=0.340mΩ/m*10.000m=3.400mΩ
元件5--低压线路:
线路长度L=0.100m
线路单位长度电阻值R0 =0.146mΩ/m
线路单位长度电抗值X0 =0.076mΩ/m
线路单位长度相保电阻Rφp0 =0.596mΩ/m
线路单位长度相保电抗Xφp0 =0.152mΩ/m
电阻R5 =R0 L=0.146mΩ*0.100m=0.015mΩ
电抗X5 =X0 L=0.076mΩ*0.100m=0.008mΩ
相保电阻Rφp 5 =Rφp0L=0.596mΩ*0.100m=0.060mΩ
相保电抗Xφp 5 =Xφp0L=0.152mΩ*0.100m=0.015mΩ
计算公式和过程
短路点1
冲击系数Kc=1.8
电阻Rs=R1 =0.07900mΩ
电抗Xs=X1 =0.79200mΩ
相保电阻Rφp =Rφp1 =0.05300mΩ
相保电抗Xφp =Xφp1 =0.52800mΩ
短路电流总阻抗Zk=(Rs2 +Xs2 )0.5 =(0.079002 +0.792002 )0.5 =0.79593mΩ
相保阻抗Zφp =(Rφp 2 +Xφp 2 )0.5 =(0.053002 +0.528002 )0.5 =0.53065mΩ
三相短路电流I\"=230/Zk=230/0.79593=289.42580kA
单相接地故障电流Id=220/Zkφp =220/0.53065=413.43957kA
短路冲击电流ich=1.414KcId=1.414*1.8*289.42580=736.75780kA
短路全电流最大有效值Ich=[1+2(Kch-1)2 ]0.5 Id=[1+2(1.8-1)2 ]0.5
*289.42580=437.02337kA
短路点2
冲击系数Kc=1.8
电阻Rs=R1 +R2 =0.079+0.342=0.42100mΩ
电抗Xs=X1 +X2 =0.792+0.327=1.11900mΩ
相保电阻Rφp =Rφp1 +Rφp2 =0.053+0.228=0.28100mΩ
相保电抗Xφp =Xφp1 +Xφp2 =0.528+0.218=0.74600mΩ
短路电流总阻抗Zk=(Rs2 +Xs2 )0.5 =(0.421002 +1.119002 )0.5 =1.19558mΩ
相保阻抗Zφp =(Rφp 2 +Xφp 2 )0.5 =(0.281002 +0.746002 )0.5 =0.79717mΩ
三相短路电流I\"=230/Zk=230/1.19558=192.67931kA
单相接地故障电流Id=220/Zkφp =220/0.79717=275.21560kA
短路冲击电流ich=1.414KcId=1.414*1.8*192.67931=490.48145kA
短路全电流最大有效值Ich=[1+2(Kch-1)2 ]0.5 Id=[1+2(1.8-1)2]0.5
*192.67931=290.93938kA
短路点3
冲击系数Kc=1.8
电阻Rs=R1 +R2 +R3 =0.079+0.342+0.560=0.98100mΩ
电抗Xs=X1 +X2 +X3 =0.792+0.327+4.767=5.88600mΩ
相保电阻Rφp =Rφp1 +Rφp2 +Rφp3 =0.053+0.228+0.560=0.84100mΩ
相保电抗Xφp =Xφp1 +Xφp2 +Xφp3 =0.528+0.218+4.767=5.51300mΩ
短路电流总阻抗Zk=(Rs2 +Xs2 )0.5 =(0.981002 +5.886002 )0.5 =5.96719mΩ
相保阻抗Zφp =(Rφp 2 +Xφp 2 )0.5 =(0.841002 +5.513002 )0.5 =5.57678mΩ
三相短路电流I\"=230/Zk=230/5.96719=38.60490kA
单相接地故障电流Id=220/Zkφp =220/5.57678=39.34048kA
短路冲击电流ich=1.414KcId=1.414*1.8*38.60490=98.27203kA
短路全电流最大有效值Ich=[1+2(Kch-1)2 ]0.5 Id=[1+2(1.8-1)2*38.60490=58.29212kA
]0.5
短路点4
冲击系数Kc=1.8
电阻Rs
=R1 +R2 +R3 +R4
=0.079+0.342+0.560+0.140
=1.12100mΩ
电抗Xs
=X1 +X2 +X3 +X4
=0.792+0.327+4.767+1.470
=7.35600mΩ
相保电阻Rφp
=Rφp1 +Rφp2 +Rφp3 +Rφp4
=0.053+0.228+0.560+0.540
=1.38100mΩ
相保电抗Xφp
=Xφp1 +Xφp2 +Xφp3 +Xφp4
=0.528+0.218+4.767+3.400
=8.91300mΩ
短路电流总阻抗Zk=(Rs2 +Xs2 )0.5 =(1.121002 +7.356002 )0.5 =7.44093mΩ
相保阻抗Zφp =(Rφp 2 +Xφp 2 )0.5 =(1.381002 +8.913002 )0.5 =9.01935mΩ
三相短路电流I\"=230/Zk=230/7.44093=30.95888kA
单相接地故障电流Id=220/Zkφp =220/9.01935=24.32470kA
短路冲击电流ich=1.414KcId=1.414*1.8*30.95888=78.80844kA
短路全电流最大有效值Ich=[1+2(Kch-1)2 ]0.5 Id=[1+2(1.8-1)2*30.95888=46.74688kA
短路点5
冲击系数Kc=1.8
]0.5
电阻Rs
=R1 +R2 +R3 +R4 +R5
=0.079+0.342+0.560+0.140+0.015
=1.13600mΩ
电抗Xs
=X1 +X2 +X3 +X4 +X5
=0.792+0.327+4.767+1.470+0.008
=7.36400mΩ
相保电阻Rφp
=Rφp1 +Rφp2 +Rφp3 +Rφp4 +Rφp5
=0.053+0.228+0.560+0.540+0.060
=1.44100mΩ
相保电抗Xφp
=Xφp1 +Xφp2 +Xφp3 +Xφp4 +Xφp5
=0.528+0.218+4.767+3.400+0.015
=8.92800mΩ
短路电流总阻抗Zk=(Rs2 +Xs2 )0.5 =(1.136002 +7.364002 )0.5 =7.45111mΩ
相保阻抗Zφp =(Rφp 2 +Xφp 2 )0.5 =(1.441002 +8.928002 )0.5 =9.04354mΩ
三相短路电流I\"=230/Zk=230/7.45111=30.91658kA
单相接地故障电流Id=220/Zkφp =220/9.04354=24.25964kA
短路冲击电流ich=1.414KcId=1.414*1.8*30.91658=78.70076kA
短路全电流最大有效值Ich=[1+2(Kch-1)2 ]0.5 Id=[1+2(1.8-1)2*30.91658=46.68301kA
计算结果
短路点1
短路电流总阻抗Zk=0.79593mΩ
相保阻抗Zφp =0.53065mΩ
]0.5
三相短路电流I\"=289.42580kA
单相接地故障电流Id=413.43957kA
短路冲击电流ich=736.75780kA
短路全电流最大有效值Ich=437.02337kA
短路点2
短路电流总阻抗Zk=1.19558mΩ
相保阻抗Zφp =0.79717mΩ
三相短路电流I\"=192.67931kA
单相接地故障电流Id=275.21560kA
短路冲击电流ich=490.48145kA
短路全电流最大有效值Ich=290.93938kA
短路点3
短路电流总阻抗Zk=5.96719mΩ
相保阻抗Zφp =5.57678mΩ
三相短路电流I\"=38.60490kA
单相接地故障电流Id=39.34048kA
短路冲击电流ich=98.27203kA
短路全电流最大有效值Ich=58.29212kA
短路点4
短路电流总阻抗Zk=7.44093mΩ
相保阻抗Zφp =9.01935mΩ
三相短路电流I\"=30.95888kA
单相接地故障电流Id=24.32470kA
短路冲击电流ich=78.80844kA
短路全电流最大有效值Ich=46.74688kA
短路点5
短路电流总阻抗Zk=7.45111mΩ
相保阻抗Zφp =9.04354mΩ
三相短路电流I\"=30.91658kA
单相接地故障电流Id=24.25964kA
短路冲击电流ich=78.70076kA
短路全电流最大有效值Ich=46.68301kA
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